TMDPresentation- Tatical Ballistic Missile

Professional Development Short Course on

Tactical Missile Design

Eugene L. Fleeman Tactical Missile Design E-mail: [email protected] Web Site: http://genefleeman.home.mindspring.com

2/24/2008

ELF

1

Outline Introduction / Key Drivers in the Design Process Aerodynamic Considerations in Tactical Missile Design Propulsion Considerations in Tactical Missile Design Weight Considerations in Tactical Missile Design Flight Performance Considerations in Tactical Missile Design Measures of Merit and Launch Platform Integration Sizing Examples Development Process Summary and Lessons Learned References and Communication Appendices ( Homework Problems / Classroom Exercises, Example of Request for Proposal, Nomenclature, Acronyms, Conversion Factors, Syllabus ) 2/24/2008

ELF

2

Emphasis Is on Physics-Based, Analytical Sizing of Aerodynamic Configuration Area

Emphasis

Aero Configuration Sizing Aero Stability & Control Aero Flight Performance Propulsion Structure Weight Warhead Miss Distance Cost Additional Measures of Merit Launch Platform Integration

Primary Emphasis

Seeker, Sensors, and Electronics

Secondary Emphasis

Power Supply

Tertiary Emphasis

-

Safe, Arm, and Fuzing 2/24/2008

ELF

Not Addressed

3

Tactical Missiles Are Different from Fighter Aircraft Tactical Missile Characteristics

Example of State-of-the-Art

Axial Acceleration Maneuverability Speed / altitude Dynamic pressure Size Weight Production cost Observables Range Kills per use Target acquisition Superior 2/24/2008

Comparison With Fighter Aircraft

AGM-88 AA-11 SM-3 PAC-3 Javelin FIM-92 GBU-31 AGM-129 AGM-86 Storm Shadow LOCAAS Better

Comparable ELF

– – –

– Inferior 4

Aero Configuration Sizing Parameters Emphasized in This Course

Nose Fineness

Propulsion Sizing / Propellant or Fuel

Diameter

Stabilizer Geometry / Size

Wing Geometry / Size

Thrust Profile

Flight Conditions ( α, M, h ) Flight Control Geometry / Size

2/24/2008

ELF

Length

5

Conceptual Design Process Requires Evaluation of Alternatives and Iteration • Mission / Scenario Definition

Update Initial

• Weapon Requirements, Trade Studies and Sensitivity Analysis • Launch Platform Integration

Revised Trades / Eval

Initial Reqs

Alt Concepts

Initial Carriage / Launch

Effectiveness / Eval

Baseline Selected Iteration

Refine Weapons Req

• Weapon Concept Design Synthesis

Alternate Concepts ⇒ Select Preferred Design ⇒Eval / Refine

• Technology Assessment and Dev Roadmap

Initial Tech Tech Trades

Initial Revised Roadmap Roadmap

Note: Typical conceptual design cycle is 3 to 9 months. House of Quality may be used to translate customer requirements to engineering characteristics. DOE may be used to efficiently evaluate the broad range of design solutions.

2/24/2008

ELF

6

Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics Propulsion Weight

Resize / Alt Config / Subsystems / Tech

Trajectory Meet Performance?

No

Yes Measures of Merit and Constraints

No

Yes 2/24/2008

ELF

7

Examples of Air-Launched Missile Missions / Types Air-to-air

Example SOTA

• Short range ATA. AA-11.

Maneuverability

• Medium range ATA. AIM-120.

Performance / weight

• Long range ATA. Meteor.

Range

10 feet

Air-to-surface • Short range ATS. AGM-114.

Versatility

• Medium range ATS. AGM-88.

Speed

• Long range ATS. Storm Shadow. Modularity

Permission of Missile Index. Copyright 1997©Missile.Index All Rights Reserved 2/24/2008

ELF

8

Examples of Surface-Launched Missile Missions / Types Surface-to-surface

Example SOTA

• Short range STS. Javelin.

Size

• Medium range STS. MGM-140.

Modularity

• Long range STS. BGM-109.

Range

10 feet

Surface-to-air

2/24/2008

• Short range STA. FIM-92.

Weight

• Medium range STA. PAC-3.

Accuracy

• Long range STA. SM-3.

High altitude

Permission of Missile.Index. Copyright 1997©Missile.Index All Rights Reserved ELF

9

Aero Configuration Sizing Has High Impact on Mission Requirements Impact on Weapon Requirement Aero Measures of Merit Aero Configuration Sizing Parameter

Other Measures of Merit

Range / Time to RobustMiss ObservWeight Maneuver Target ness Lethality Distance ables Survivability Cost

Constraint Launch Platform

Nose Fineness Diameter Length Wing Geometry / Size Stabilizer Geometry / Size Flight Control Geometry / Size Propellant / Fuel Thrust Profile Flight Conditions ( α, M, h ) Very Strong 2/24/2008

Strong

Moderate ELF

–

Relatively Low 10

Example of Assessment of Alternatives to Establish Future Mission Requirements Measures of Merit Alternatives for Precision Strike

Cost per Shot

Number of Launch Platforms TCT Required Effectiveness

Future Systems Standoff platforms / hypersonic missiles Overhead loitering UCAVs / hypersonic missiles Overhead loitering UCAVs / light weight PGMs Current Systems Penetrating aircraft / subsonic PGMs

–

Standoff platforms / subsonic missiles Note:

Superior

– –

Good

Average

– Poor

Note: C4ISR targeting state-of-the-art for year 2010 projected to provide sensor-to-shooter / weapon connectivity time of less than 2 m and target location error ( TLE ) of less than 1 m for motion suspended target. 2/24/2008

ELF

11

C4ISR Tactical Satellites and UAVs Have High Impact on Mission Capability

LaunchPlatforms Platforms Launch

Off-boardSensors Sensors Off-board

•FighterAircraft Aircraft •Fighter •Bomber •Bomber

•TacticalSatellite Satellite •Tactical •UAV •UAV

•Ship/ Submarine / Submarine •Ship •UCAV •UCAV

PrecisionStrike StrikeWeapons Weapons Precision •HypersonicSOW SOW •Hypersonic •SubsonicPGM PGM •Subsonic •SubsonicCM CM •Subsonic

TimeCritical CriticalTargets Targets Time •TBM/ TEL / TEL •TBM •SAM •SAM

•C3 •C3 •OtherStrategic Strategic •Other

Note: C4ISR targeting state-of-the-art for year 2010 projected to provide sensor-to-shooter / weapon connectivity time of less than 2 m and target location error ( TLE ) of less than 1 m for motion suspended target. 2/24/2008

ELF

12

Example of System-of-Systems Analysis to Develop Future Mission Requirements t1

TBM Launch Launch Pt Rcvd

t2

100

t3

Hypersonic Missile Launch

HM Intercept at XXX nm

Altitude – 1000 ft

t0

3. Alt / Speed / RCS Required For Survivability

60 40 20 0

4. Lethality W/H W3 > W2 W/H W2 > W1 Warhead W1

Lethality / Concrete Penetration ( ft )

Time, Min

Range 3 > R2 Range 2 > R1 Range 1

3-4

1-2

120 100 80 60 40 20 0

4000 6000 2000 Average Speed to Survive, fps

0

2- 3

Cruise Missile Launch

2. Time To Target

RCS1

80

5. Campaign Model Weapons Mix ( CM, Hypersonic Missile ) Results RCS2 > RCS1 ( eg., Korean Scenario )

4-5

1. Compare Targeting of Subsonic Cruise Missile Versus Hypersonic Missile

50 40 30 20 10

0

2/24/2008

1000

2000 3000 4000 Average Speed, fps

5000

0

0

ELF

1000 2000 3000 Impact Velocity, fps

4000

Selected For All: • Value of Speed / Range • Time Urgent Targets • High Threat Environments • Buried Targets • Launch Platform Alternatives • Operating and Attrition Cost in Campaign • Weapon Cost in Campaign • Mix of Weapons in Campaign • Cost Per Target Kill • C4ISR Interface

13

Example of Technological Surprise Driving Immediate Mission Requirements

Sidewinder AIM-9L ( IOC 1977 ) Performance •+/- 25 deg off boresight

Archer AA-11 / R-73 ( IOC 1987 )

•6.5 nm range

Performance •> +/- 60 deg off boresight •20 nm range

New Technologies •TVC •Split canard •Near-neutral static margin •+/- 90 deg gimbal seeker •Helmet mounted sight

2/24/2008

ELF

Note: AIM-9L maneuverability shortfall compared to Archer drove sudden development of AIM-9X. 14

Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics Propulsion Weight

Resize / Alt Config / Subsystems / Tech

Trajectory Meet Performance?

No

Yes Measures of Merit and Constraints

No

Yes 2/24/2008

ELF

15

Baseline Design Benefits and Guidelines Benefits of Baseline Design Allows simple, conceptual design methods to be used with good accuracy Well documented benchmark / configuration control / traceability between cause and effect Balanced subsystems Gives fast startup / default values for design effort Provides sensitivity trends for changing design Baselines can cover reasonable range of starting points Baselines can normally be extrapolated to ±50% with good accuracy

Guidelines Don’t get locked-in by baseline Be creative Project state-of-the-art ( SOTA ) if baseline has obsolete subsystems Sensors and electronics almost always need to be updated

2/24/2008

ELF

16

Example of Missile Baseline Data Configuration Drawing

Weight / Geometry

11.6

37°

11.5

Body 16.5

Transport Air Duct Payload Bay

Fore-body

Aftbody Engine

Tail ( Exposed )

126.0

76.5 Mid-body

Aft-body

Area ( 2 panels ), ft2 Wetted area ( 4 panels ), ft2 Aspect ratio ( exposed ) Taper ratio Root chord, in Span, in. ( exposed ) L.E. sweep, deg M.A.C., in Thickness ratio X MAC, in Y MAC, in ( from root chord )

Tail Cone 159.0

171.0

Note: Dimensions are in inches

Reference values:

Source: Bithell, R.A. and Stoner, R.C. “Rapid Approach for Missile Synthesis”, Vol. II, Air-breathing Synthesis Handbook, AFWAL TR 81-3022, Vol. II, March 1982.

Reference area, ft2 Reference length, ft

Aerodynamics

C 0 0

1

3 2 M, Mach Number

4

C D

0

4.0

.40

-.4

.1

0

-.8

-1.2

Mach

.30

1.5

0 .20

1

2

3

4 2.0

M, Mach Number

3.0 4.0

4.0 3.0 2.0

0

4

8

12

1.5

16

α, Angle of Attack ~ deg

0

Mach

.10

0

-1.6

1.2

4 8 12 α, Angle of Attack ~ deg

1.2

Mach 1.2 1.5 2.0

3.0

3.0 4.0

2.0

Isp, Specific Impulse, sec

.05

SRef = 2.264 ft2 LRef = Dref = 1.698 ft Xcg @ Sta 82.5 in.

.2

Axial Force Coefficient, CA

Pitching Moment Coefficient, Cm

C N ~ per deg δ

.10

•

1,000

15,000 • •

500

Note: φ =1

••

142.5 142.5

31.6 31.0 37.0 70.0 1,262.6 476.0 1,738.6 31.0 11.5 1,781.1 449.0 2,230.1

165.0 165.0 164.0 157.2 81.8 87.0 83.2 164.0 126.0 84.9 142.5 96.5

Ramjet Engine Station Identification

0

1.0

0 0

4

8

12

16

4

3

5

6

Rocket Propulsion

•

h = SL

•

Note: φ =1

••

1

10

2

3

4

M, Mach Number

α, Angle of Attack ~ deg

0 0

1

• •

h = 40K ft • • •

• •

2

1.0

2.0

Note: Constant altitude flyout

•

• 0

( ISP )Booster = 250 sec

20

0

h = 20K ft • •

3

h = 60K ft • • h = 80K ft

2.0

ML = 0.80 constant altitude flyout

1.0

0 0

20 40 h, Altitude 1,000 ft

4

60

3.0 Time ~ sec

4.0

5.0

6.0

3.0

2.5

2.0

0

20 40 60 h, Altitude 1,000 ft

80

M, Mach Number

House of Quality

60,000 ft 300

200 40,000 ft 20,000 ft h = SL

Note: • ML = 0.8, Constant Altitude Flyout 0 0 1 2 3 Example: • Breguet Range for Mach 3 / 60 Kft flyout: M, Mach Number Rmax = V ISP ( L / D )Max ln [ WBC / ( WBC - Wf )] = 2901 ( 950 ) ( 3.15 ) ln ( 1739 / ( 1739 - 476 )) = 2,777,192 ft or 457 nm

•

•

5,000 0

2

1

Free Stream Inlet Throat Subscripts 0 Free stream conditions ( Ramjet Baseline A0 = 75.4 in2 at Mach 4, α = 0 deg, Note: AC = 114 in2 ) 1 Inlet throat ( Ramjet Baseline A1 = AIT = 41.9 in2 ) 2 Diffuser exit ( Ramjet Baseline A2 = 77.3 in2 ) 3 Flame holder plane ( Ramjet Baseline A3 = 287.1 in2 ) 4 Combustor exit ( Ramjet Baseline A4 = 287.1 in2 ) 20.375 in diameter 5 Nozzle throat ( Ramjet Baseline A5 = 103.1 in2 ) 6 Nozzle exit ( A6 = 233.6 in2 ) Ref Reference Area ( Ramjet Baseline Body Cross-sectional Area, SRef = 326 in2 )

0

400 Range ~ nm

44.5 33.5

10,000

500

2/24/2008

101.2 80.0 112.0 121.0 121.0

30

16

Flight Performance

100

95.2 103.0 30.0 20.0 5.0

20,000

SRef = 2.264 ft2 LRef = DRef = 1.698 ft Xcg @ Sta 82.5 in.

.3

0

33.5 33.5 60.0 60.0

1,500

.4

-.2

Normal Force Coefficient, CN

m ~ per deg δ

SRef = 2.264 ft2 LRef = DRef = 1.698 ft Xcg @ Sta 82.5 in.

0

2.264 1.698

15.7

64.5 510.0

Inlet capture area Ac = 114 in2 Inlet throat area Reference area 120° Nozzle throat area Specific impulse Equivalence ratio – operating fuel / air ratio divided by fuel / air ratio for stochiometric combustion

Ramjet Propulsion

-.4

+ .4

Tailcone2.24 Exit Duct 8.96 Controls 1.64 Fins ( 4 )0.70 End of 16.5 Cruise 23.0 Ramjet Fuel ( 6.9 ft3 ) 37.0 Start of Cruise 14.2Nozzle ( Ejected ) Boost 0.04 Port Frangible 150.5 End of Boost 5.4 Boost Propellant Booster Ignition

15.9 42.4 129.0

Ac AIT SRef A5 Isp φ

Boost Thrust ~ 1000 lbs

43.5

28.33 Midbody Inlet68.81 0.58 Electrical N/A Hydraulic Fuel15.0 Distribution

CG Sta, In.

Boost Range ~ nm

23.5 Nose

Boost Propellant Booster, and Ramjet Engine

20.375 Payload Bay 8.39 Warhead

Weight, lb

Paredo Sensitivity for DOE Nondimensional Range Sensitivity to Parameter

Sta 0.

Ramjet Fuel

Warhead

Forebody 171.0 Guidance

T, Net Thrust, lb

Guidance

( CD0 )Nose Corrected = ( CD0 )Nose Uncorrected x ( 1 - Ac / SREF )

17.7 8.36 Component 0.52 Nose 0.29

Length, in Diameter, in Fineness ratio Volume, ft3 Wetted area, ft2 Base area, ft2 ( cruise ) Boattail fineness ratio Nose half angle, deg

Boost Nozzle

Chin Inlet

Conical forebody angle, deg Ramp wedge angle, deg Capture area, ft2 Throat area, ft2

Burnout Mach Number

Sta 150.3

20.375 dia

Flow Path Geometry

Inlet

1.5 1 0.5 0 ISP

-0.5

Fuel Weight

Thrust

-1

CD0, Zero- CLA, LiftCurveLift Drag Slope Coefficient Coefficient

Inert Weight

Parameter 4

Sea Level Flyout at Mach 2.3 40 Kft Flyout at Mach 2.8

ELF

20 Kft Flyout at Mach 2.5 60 Kft Flyout at Mach 3.0

17

Baseline Design Data Allows Correction of Computed Parameters in Conceptual Design PCD, C = ( PB, C / PB, U ) PCD, U PCD, C PB, C PB, U PCD, U Example

Parameter of conceptual design, corrected Parameter of baseline, corrected ( actual data ) Parameter of baseline, uncorrected ( computed ) Parameter of conceptual design, uncorrected (computed )

• Ramjet Baseline with RJ-5 fuel ( heating value = 11,300,000 ft-lbf / lbm ) • Advanced Concept with slurry fuel ( 40% JP-10 / 60% boron carbide = 18,500,000 ft-lbf / lbm ) • Flight conditions: Mach 3.5 cruise, 60k ft altitude, combustion temperature 4,000 R • Calculate specific impulse ( ISP )CD,C for conceptual design, based on corrected baseline data ( ISP )B, C = 1,120 s – ( ISP )B, U = 1387 s – ( ISP )CD, U = 2,271 s – ( ISP )CD, C = [( ISP )B, C / ( ISP )B, U ] ( ISP )CD, U = [( 1120 ) / ( 1387 )] ( 2271 ) = 0.807 ( 2271 ) = 1,834 s –

2/24/2008

ELF

18

Summary of This Chapter Overview of Missile Design Process Examples Tactical missile characteristics Conceptual design process SOTA of tactical missiles Aerodynamic configuration sizing parameters Processes that establish mission requirements Process for correcting design predictions

Discussion / Questions? Classroom Exercise

2/24/2008

ELF

19

Introduction Problems 1.

2. 3. 4. 5. 6. 7. 8. 9. 2/24/2008

The missile design team should address the areas of mission / scenario definition, weapon requirements, launch platform integration, design, and t_______ a_________. The steps to evaluate missile flight performance require computing aerodynamics, propulsion, weight, and flight t_________. Air-to-air missile characteristics include light weight, high speed, and high m______________. Air-to-surface missiles are often versatile and m______. Four aeromechanics measures of merit are weight, range, maneuverability, and t___ to target. The launch platform often constrains the missile span, length, and w_____. An enabling capability for hypersonic strike missiles is fast and accurate C____. An enabling capability for large off boresight air-to-air missiles is a h_____ m______ sight. A baseline design improves the accuracy and s____ of the design process. ELF

20

Outline Introduction / Key Drivers in the Design Process Aerodynamic Considerations in Tactical Missile Design Propulsion Considerations in Tactical Missile Design Weight Considerations in Tactical Missile Design Flight Performance Considerations in Tactical Missile Design Measures of Merit and Launch Platform Integration Sizing Examples Development Process Summary and Lessons Learned References and Communication Appendices ( Homework Problems / Classroom Exercises, Example of Request for Proposal, Nomenclature, Acronyms, Conversion Factors, Syllabus ) 2/24/2008

ELF

21

Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics Propulsion Weight

Resize / Alt Config / Subsystems / Tech

Trajectory Meet Performance?

No

Yes Measures of Merit and Constraints

No

Yes 2/24/2008

ELF

22

Missile Diameter Tradeoff Drivers toward Small Diameter • Decrease drag • Launch platform diameter constraint

Drivers toward Large Diameter • Increase seeker range and signal-to-noise, better resolution and tracking • Increase blast frag and shaped charge warhead effectiveness ( larger diameter ⇒ higher velocity fragments or higher velocity jet ) • Increase body bending frequency • Subsystem diameter packaging • Launch platform length constraint

Typical Range in Body Fineness Ratio 5 < l / d < 25 • Man-portable anti-armor missiles are low l / d ( Javelin l / d = 8.5 ) • Surface-to-air and air-to-air missiles are high l / d ( AIM-120 l / d = 20.5 ) 2/24/2008

ELF

23

Small Diameter Missiles Have Low Drag D = CD q SRef = 0.785 CD q d2

D / CD, Drag / Drag Coefficient, lb

100000

Note: D = drag in lb, CD = drag coefficient, q = dynamic pressure in psf, d = diameter ( reference length ) in ft

10000

Dynamic Pressure = 1,000 psf Dynamic Pressure = 5,000 psf Dynamic Pressure = 10,000 psf

1000

100

Example for Rocket Baseline: d = 8 in = 0.667 ft

10

Mach 2, h = 20k ft, ( CD )Powered = 0.95

4

8

12

16

20

q = 1/2 ρ

0

V2

= 1/2 ρ ( M a )2

= 1/2 ( 0.001267 ) [( 2 ) ( 1037 )]2 = 2,725 psf

d, Diameter, in

D0 / CD = 0.785 ( 2725 ) ( 0.667 )2 = 952 0

D0 = 0.95 ( 952 ) = 900 lb 2/24/2008

ELF

24

Large Diameter Radar Seeker Provides Longer Detection Range and Better Resolution RD = { π σ n3/4 / [ 64 λ2 K T B F L ( S / N ) ]}1/4 Pt 1/4 d 100

θ3dB = 1.02 λ / d, θ3dB in rad

Assumptions: Negligible clutter, interference, and atmospheric attenuation; non-coherent radar ( only signal amplitude integrated ); uniformly illuminated circular aperture; receiver sensitivity limited by thermal noise Symbols:

σ = Target radar cross section, m2 n = Number of pulses integrated λ = Wavelength, m K = Boltzman’s constant = 1.38 x 10-23 J / K T = Receiver temperature, K B = Receiver bandwidth, Hz 1 F = Receiver noise factor 0 5 10 15 20 L = Transmitter loss factor S / N = Signal-to-noise ratio for target detection d, Diameter, Inches Pt = Transmitted power, W d = Antenna diameter Example Seeker Range for Transmitted Power Pt = 100 W, nm Example: Rocket Baseline Example Seeker Range for Transmitted Power Pt = 1,000 W, nm d = 8 in = 0.20 m, Pt = 1000 W, λ = 0.03 m ( f = 10 GHz ) Example Seeker Range for Transmitted Power Pt = 10,000 W, nm RD = Target detection range = { π ( 10 ) ( 100 )3/4 / [ 64 ( Example Seeker Beam Width, deg 0.03 )2 ( 1.38 x 10-23 ) ( 290 ) ( 106 ) ( 5 ) ( 5 )( 10 )]}1/4 ( Note for figure: σ = 10 m2, n = 100, λ = 0.03 m ( f = Transmitter 1000 )1/4 ( 0.203 ) = 13,073 m or 7.1 nm frequency = 10 x 109 Hz ), T = 290 K, B = 106 Hz ( 10-6 s pulse ), F θ3dB = 3-dB beam width = 1.02 ( 0.03 ) / 0.203 = 0.1507 = 5, L = 5, S / N = 10 rad or 8.6 deg 10

2/24/2008

ELF

25

Large Diameter IR Seeker Provides Longer Detection Range and Better Resolution RD = Target detection range, m ( IT )Δλ = Target radiant intensity between λ1 and λ2= ε IFOV = dp / [ ( f-number ) do ] Lλ ( λ2 - λ1 ) AT, W / sr ηa = Atmospheric transmission Ao = Optics aperture area, m2 10 D* = Specific detectivity, cm Hz1/2 / W Δfp = Pixel bandwidth, Hz Ad = Detectors total area, cm2 ( S / N )D = Signal-to-noise ratio required for detection 1 ε = Emissivity coefficient 0 2 4 6 8 10 L = Spectral radiance ( Planck’s Law ) = 3.74 x 104 / { λ 4 do, Optics Diameter, Inches λ5 { e[ 1.44 x 10 / ( λ TT )] – 1 }}, W cm-2 sr-2 μm-1 λ2 = Upper cutoff wavelength for detection, μm Example Seeker Range for Exo-atmospheric, km λ1 = Lower cutoff wavelength for detection, μm Example Seeker Range for Humidity at 7.5 g / m3, km AT = Target planform area, cm2 Example Seeker Range for Rain at 4 mm / hr, km λ = Average wavelength, μm Example Seeker IFOV, 10-5 rad TT = Target temperature, K IFOV = Instantaneous field-of-view of pixel, rad Example: do = 5 in = 0.127 m, exo-atmospheric 4 f-number = dspot / ( 2.44 λ ) Lλ = 3.74 x 104 / { 45 { e{ 1.44 x 10 / [ 4 ( 300 ) ]} – 1 }} = 0.000224 W cm-2 sr-2 dp = Pixel diameter, either μm μm-1, ( IT )Δλ = 0.5 ( 0.000224 ) ( 4.2 – 3.8 ) 2896 = 0.1297 W / sr, Ad = 256 x 256 x ( 20 μm )2 = 0.262 cm2, f-number = 20 / [ 2.44 ( 4 ) ] = 2.05 dspot = Spot resolution if diffraction limited = dp, μm RD = { 0.1297 ( 1 ) ( 0.01267 ) { 8 x 1011 / [( 250 )1/2 ( 0.262 )1/2 ]} ( 1 )-1 Figure: dT = 2 ft ( 60.96 cm ), TT = 300 K, λ1 = 3.8 μm, }1/2 = 12, 740 m λ2 = 4.2 μm, ε = 0.5, λ = 4 μm, FPA ( 256 x 256, 20 μm IFOV = 0.000020 / [ 2.05 ( 0.127 )] = 0.0000769 rad ), D* = 8 x 1011 cm Hz1/2 / W, ( S / N ) = 1, Δf = 250 Hz. 100

RD = { ( IT )Δλ ηa Ao { D* / [( Δfp )1/2 ( Ad )1/2 ]} ( S / N )D-1 }1/2

D

2/24/2008

ELF

p

26

First Mode Body Bending Frequency, rad / s

Missile Fineness Ratio May Be Limited by Impact of Body Bending on Flight Control ωBB = 18.75 { E t / [ W ( l / d

10000

Assumes body cylinder structure, thin skin, high fineness ratio, uniform weight distribution, free-free motion. Neglects bulkhead, wing / tail stiffness. ωBB = First mode body bending frequency, rad / s E = Modulus of elasticity in psi t = Thickness in inches W = Weight in lb l / d = Fineness ratio

) ]}1/2

E t / W = 1,000 per in E t / W = 10,0000 per in E t / W = 100,000 per in

1000

Example for Rocket Baseline:

100 0

10

20

30

l / d, length / diameter

l / d = 18 EAVG = 19.5 x 106 psi tAVG = 0.12 in W = 500 lb E t / W = 19.5 x 106 ( 0.12 ) / 500 = 4680 per in ωBB = 18.75 ( 4680 / 18 )1/2 = 302 rad / sec = 48 Hz ωActuator = 100 rad / sec = 16 Hz ωBB / ωActuator = 302 / 100 = 3.02 > 2

Derived from: AIAA Aerospace Design Engineers Guide, American Institute of Aeronautics and Astronautics, 1993. 2/24/2008

ELF

27

Nose Fineness Tradeoff High Nose Fineness Superior Aerodynamically, Low Observables Example: lN / d = 5 tangent ogive

d

Low Nose Fineness Ideal Electromagnetically, High Propellant Length / Volume Example: lN / d = 0.5 ( hemisphere )

d

Moderate Nose Fineness Compromise Dome Examples: lN / d = 2 tangent ogive

lN / d = 2 faceted

lN / d = 2 window

lN / d = 2 multi-lens

d ow Wind 2/24/2008

ELF

28

Faceted and Flat Window Domes Can Have Low Dome Error Slope, Low Drag, and Low RCS Firestreak

Mistral

SLAM-ER Faceted Dome ( Mistral ) Video

JASSM

THAAD 2/24/2008

ELF

29

Supersonic Body Drag Driven by Nose Fineness while Subsonic Drag Driven by Wetted Area ( CD0 )Body = (CD0 )Body,Friction + ( CD0 )Base + ( CD0 )Body, Wave (CD0 )Body,Friction = 0.053 ( l / d ) [ M / ( q l )]0.2. Based on Jerger reference, turbulent boundary layer, q in psf, l in ft. ( CD0 )Base,Coast = 0.25 / M, if M > 1 and (CD0 )Base,Coast = ( 0.12 + 0.13 M2 ), if M < 1 ( CD0 )Base,Powered = ( 1 – Ae / SRef ) ( 0.25 / M ), if M > 1 and ( CD0 )Base,Powered = ( 1 – Ae / SRef ) ( 0.12 + 0.13 M2 ), if M < 1 ( CD0 )Body, Wave = ( 1.59 + 1.83 / M2 ) { tan-1 [ 0.5 / ( lN / d )]}1.69, for M > 1. Based on Bonney reference, tan-1 in rad.

Note: ( CD )Body,Wave = body zero-lift wave drag coefficient, ( CD )Base = body base drag coefficient, ( CD )Body, Friction = body skin 0 0 0 friction drag coefficient, ( CD )Body = body zero-lift drag coefficient, lN = nose length, d = missile diameter, l = missile body 0 length, Ae = nozzle exit area, SRef = reference area, q = dynamic pressure, tan-1 [ 0.5 / ( lN / d )] in rad. Example for Rocket Baseline:

10

1

0.1

0.01 0

1

2

3

4

5

(CD0)Body,Wave; lN / d = 0.5 (CD0)Body,Wave; lN / d = 1 (CD0)Body,Wave; lN / d = 2 (CD0)Body,Wave; lN / d = 5 (CD)Base,Coast

( CD )Body, Wave ( CD )Body, Friction 0

0

( CD )Base

lN / d = 2.4, Ae = 11.22 in2, SRef = 50.26 in2, M = 2, h = 20k ft, q = 2725 psf, l / d = 18, l = 12 ft ( CD )Body, Friction = 0.053 ( 18 ) { ( 2 ) / [( 2725 ) 0 ( 12 ) ]}0.2 = 0.14 ( CD )Base Coast = 0.25 / 2 = 0.13 ( CD )Base Powered = ( 1 - 0.223 ) ( 0.25 / 2 ) = 0.10 ( CD )Body, Wave = 0.14 0

( CD )Body, Coast = 0.14 + 0.13 + 0.14 = 0.41

M, Mach Number

0

( CD )Body, Powered = 0.14 + 0.10 + 0.14 = 0.38 0

2/24/2008

ELF

30

Moderate Nose Tip Bluntness Causes a Negligible Change in Supersonic Drag Steps to Calculate Wave Drag of a Blunted Nose 1.

Relate blunted nose tip geometry to pointed nose tip geometry lN dNoseTip

2.

dRef

Compute (CD0 )Wave,SharpNose for sharp nose, based on the body reference area ( CD )Wave,SharpNose = ( 1.59 + 1.83 / M2 ) { tan-1 [ 0.5 / ( lN / d )]}1.69 0

3.

Compute ( CD0 )Wave,Hemi of the hemispherical nose tip ( lNoseTip / dNoseTip = 0.5 ), based on the nose tip area ( CD0 )Wave,Hemi = ( 1.59 + 1.83 / M2 ) {[ tan-1 ( 0.5 / ( 0.5 )]}1.69 = 0.665 ( 1.59 + 1.83 / M2 )

4.

Finally, compute ( CD0 )Wave,BluntNose of the blunt nose, based on the body reference area ( CD0 )Wave,BluntNose = ( CD0 )Wave,SharpNose ( SRef - SNoseTip ) / SRef + ( CD0 )Wave,Hemi SNoseTipi / SRef

Example Rocket Baseline ( dRef = 8 in ) with 10% Nose Tip Bluntness at Mach 2

2/24/2008

• • •

( CD0 )Wave,SharpNose = [ 1.59 + 1.83 / ( 2 )2 ] [ tan-1 ( 0.5 / 2.4)]1.69 = 0.14 dNoseTip = 0.10 ( 8 ) = 0.8 in SNoseTip = π dNoseTip2 / 4 = 3.1416 ( 0.8 )2 / 4 = 0.503 in2 = 0.00349 ft2

•

( CD0 )Wave,Hemi = 0.665 [ 1.59 + 1.83 / ( 2 )2 ] = 1.36

•

( CD0 )Wave,BluntNose = 0.14 ( 0.349 - 0.003 ) / 0.349 + ( 1.36 ) ( 0.003 ) / ( 0.349 ) = 0.14 + 0.01 = 0.15 ELF

31

Boattail Decreases Base Pressure Drag Area

Base Pressure Drag Area Without Boattail

dRef

θBT With Boattail

During Motor Burn After Motor Burnout dBT

Note: Boattail angle θBT and boattail diameter dBT limited by propulsion nozzle packaging, tail flight control packaging, and flow separation Reference: Chin, S. S., Missile Configuration Design, McGraw-Hill Book Company, New York, 1961 2/24/2008

ELF

32

Boattailing Reduces Drag for Subsonic Missiles CDO, Example Zero-Lift Drag Coefficient

0.45 Nose

0.40 3.00

0.35

Center body

Boattail

6.00 10.50

1.50

0.30 0.25 0.20

dBT / dRef = 1.0 dBT / dRef = 0.9 dBT / dRef = 0.8 Note: dBT / dRef = 0.6 dBT = Boattail Diameter dBT / dRef = 0.4 dRef = Body Reference Diameter

0.15 0.10 0.05 0.0

0.5

1.0

1.5

2.0

2.5

M∞

3.0

3.5

4.0

4.5

5.0

5.5

Note: Boatail half angle should be less than 10 deg, to avoid flow separattion. Source: Mason, L.A., Devan, L. and Moore, F.G., “Aerodynamic Design Manual for Tactical Weapons,” NSWC TR 81-156, July 1981 2/24/2008 ELF 33

Lifting Body Has Higher Normal Force ⏐ CN ⏐ = [⏐( a / b ) cos2 φ + ( b / a ) sin2 φ ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin2 α ] Note: If α negative, CN negative Based on slender body theory ( Pitts, et al ) and cross flow theory ( Jorgensen ) references Valid for l / d > 5 Example l / d = length / diameter = 20 a/b=3 1/2 d=2 (ab) φ = 0°

150

CN, 100 Example Normal Force Coefficient for l / d = 20 50

0

CN

2b

a/b=2

φ 2a

0

20

a/b=1

40

60

80

100

α, Angle of Attack, Deg 2/24/2008

ELF

34

L / D Is Impacted by CD0, Body Fineness, and Lifting Body Cross Section Geometry L / D = CL / CD = ( CN cos α – CD0 sin α ) / ( CN sin α + CD0 cos α ) For a lifting body, ⏐ CN ⏐ = [⏐( a / b ) cos2 ( φ ) + ( b / a ) sin2 ( φ ) ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin2 α ]

4

L / D, Lift / Drag

3

High drag, low fineness body ( a / b = 1, l / d = 10, CDO = 0.5 ) Low drag nose ( a / b = 1, l / d = 10, CDO = 0.2 ) High fineness, low drag ( a / b = 1, l / d = 20, CDO = 0.2 ) Lifting body, high fineness, low drag ( a / b = 2 @ φ = 0°, l / d = 20, CDO = 0.2 )

2

CN

1 0

0

20

40

60

80

100

φ

2b

2a

α, Angle of Attack, Deg Note: • If α negative, L / D negative •d = 2 ( a b )1/2 •Launch platform span constraints ( e.g., VLS launcher ) and length constraints ( e.g., aircraft compatibility ) may limit missile aero configuration enhancements 2/24/2008

ELF

35

Lifting Body Requires Flight at Low Dynamic Pressure to Achieve High Aero Efficiency L / D = CL / CD = ( CN cos α – CDO sin α ) / ( CN sin α + CDO cos α ) ⏐ CN ⏐ = [⏐( a / b ) cos2 ( φ ) + ( b / a ) sin2 ( φ ) ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin2 α ] Example L / D, Lift / Drag

4

Example: q = 500 psf

3

•a / b = 1 ⇒ L / D = 2.40 •a / b = 2 ⇒ L / D = 3.37

2

q = 5,000 psf •a / b = 1 ⇒ L / D = 0.91

1

•a / b = 2 ⇒ L / D = 0.96

0 100

1000

10000

100000

q, Dynamic Pressure, lb / ft2 Circular Cross Section ( a / b = 1 )

2/24/2008

Lifting Body ( a / b = 2 )

Note. Example figure based on following assumptions: Body lift only ( no surfaces ), cruise flight ( lift = weight ), W = L = 2,000 lb, d = 2 ( a b )1/2, S = 2 ft2, l / d = 10, CD0 = 0.2 ELF

36

Trade-off of Low Observables and ( L / D )Max Versus Volumetric Efficiency

( L / D )Max, ( Lift / Drag )Max

6

Tailored Weapons

5 Conventional Weapons ( circular cross section )

Advantages: • ( L / D )Max • Low RCS

Lower

Advantages: • Payload • Launch Platform Integration

4 Radar Cross Section 3 2

Circular 4 Cross Section

6 Body Planform Area

8

10

( Body Volume )2/3 2/24/2008

ELF

37

Δ Cm / Δ α and Static Margin Define Static Stability xAC

Statically Stable: ΔCm / Δα < 0, with xac behind xcg

Statically Unstable: ΔCm / Δα > 0, with xac in front of xcg

xCG

Cm

δ2 α

α

α

δ2

Non-oscillatory Divergent

Non-oscillatory Convergent

Oscillatory Convergent

xCG

δ1

Cm

δ1

xAC

α t

t

Oscillatory Divergent

Note: Statically unstable missile requires high bandwidth autopilot. Autopilot negative rate feedback provides stability augmentation.

2/24/2008

ELF

38

Body Aerodynamic Center Is a Function of Angle of Attack, Nose Fineness, and Body Length Distance to Body Aerodynamic Center / Length of Nose

( xAC )B / lN = 0.63 ( 1 - sin2 α ) + 0.5 ( lB / lN ) sin2 α

5 4

total length of body / length of nose = 1 total length of body / length of nose = 2 total length of body / length of nose = 5 total length of body / length of nose = 10

3 2 1

Example:

0

19.2

143.9

Rocket Baseline Body

0

20

40

60

80

Angle of Attack, Deg

100

lB / lN = 143.9 / 19.2 = 7.49 α = 13 deg ( xAC )B / lN = 0.81

Note: Based on slender body theory ( Pitts, et al ) and cross flow theory ( Jorgensen ) references. No flare. ( xAC )B = Location of body aerodynamic center, lN = length of nose, α = angle of attack, lB = total length of body.

2/24/2008

ELF

39

Flare Increases Static Stability CNα = ( CNα )B + ( CNα )F

( C N )B α

+M

( CNα )F d dF

9

+α x=0

( xac )B

lN

xAC xCG

Based on Slender Body Theory:

xF l B ( xac )F

( CNα )F = 2 [( dF / d )2 – 1 ] ( xac )F = xF + 0.33 lF [ 2 ( dF / d ) + 1 ] / [ ( dF / d ) + 1 ] ( CNα )B = 2 per rad ( xac )B = 0.63 lN

ΣM = 0 at Aerodynamic Center. For a Body-Flare: ( CNα )B {[ xCG – ( xAC )B ] / d } + ( CNα )F [ xCG – ( xAC )F ] / d = - [( CNα )B + ( CNα )F ] [( xAC – xCG ) / d ]

Static Margin for a Body-Flare ( xAC – xCG ) / d = - {( CNα )B {[ xCG – ( xAC )B ] / d } + ( CNα )F {[ xCG – ( xAC )F ] / d }} / [( CNα )B + ( CNα )F ] 2/24/2008

ELF

40

Flare Increases Static Stability ( cont ) Example of Static Margin for THAAD ( Statically Unstable Missile ) CNα = ( CNα )B + ( CNα )F (C ) Nα B

( CNα )F 14.6 18.7 in

9

( xac )B = 57.7

91.5 146.9 xAC = 140.9

230.9 242.9 ( xac )F = 237.1

( CNα )F = 2 [( 18.7 / 14.6 )2 – 1 ] = 2 [(1.28)2 – 1 ] = 1.28 per rad ( xac )F = 230.9 + 0.33 ( 12.0 )[ 2 ( 18.7 / 14.6 ) + 1 ] / [ ( 18.7 / 14.6 ) + 1 ] = 237.1 in ( xac )B = 0.63 ( 91.5 ) = 57.7 in xCGLaunch = 146.9 in ( xAC – xCG )Launch / d = - { 2 {[ 146.9 – 57.7 ] / 14.6 } + 1.28 {[ 146.9 – 237.1 ] / 14.6 }} / [ 2 + 1.28 ] = - 0.41

2/24/2008

ELF

41

Tail Stabilizers Have Lower Drag While Flares Have Lower Aero Heating and Stability Changes

Type Stabilizer

Drag

Span

Heating

ΔCNα Tail Control

Flare ( e.g., THAAD ) –

–

Tails ( e.g., Standard Missile ) –

Note: 2/24/2008

Superior

Good ELF

–

Average

– Poor 42

Wing Sizing Trades Advantages of Small Wing / Strake / No Wing • • • • •

Range in high supersonic flight / high dynamic pressure Max angle of attack Launch platform compatibility Lower radar cross section Volume and weight for propellant / fuel

Advantages of Larger Wing • • • • • • • •

Range in subsonic flight / low dynamic pressure Lower guidance time constant* Normal acceleration* High altitude intercept* Less body bending aeroelasticity ( wing stiffens body ) Less seeker error due to dome error slope ( lower angle of attack ) Less wipe velocity for warhead ( lower angle of attack ) Lower gimbal requirement for seeker

*Based on assumption of aerodynamic control and angle of attack below wing stall 2/24/2008

ELF

43

Most Supersonic Missiles Are Wingless

2/24/2008

Stinger FIM-92

Grouse SA-18

Grison SA-19 ( two stage )

Gopher SA-13

Starburst

Mistral

Kegler AS-12

Archer AA-11

Gauntlet SA-15

Magic R550

Python 4

U-Darter

Python 5

Derby / R-Darter

Aphid AA-8

Sidewinder AIM-9X

ASRAAM AIM-132

Grumble SA-10 / N-8

Patriot MIM-104

Starstreak

Gladiator SA-12

PAC-3

Roland ( two stage )

Crotale

Hellfire AGM-114

ATACM MGM-140

Standard Missile 3 ( three stage )

THAAD

Permission of Missile Index. Copyright 1997©Missile.Index All Rights Reserved ELF

44

Wings, Tails, and Canards with Large Area and at High Angle of Attack Have High Normal Force ⏐( CN )Surface ⏐ = [ 4⏐sin α’ cos α’⏐ / ( M2 – 1 )1/2 + 2 sin2α’ ] ( SSurface / SRef ), if M > { 1 + [ 8 / ( π A )]2 }1/2 ⏐( CN )Surface ⏐ = [ ( π A / 2) ⏐sin α’ cos α’⏐ + 2 sin2α’ ] ( SSurface / SRef ), if M < { 1 + [ 8 / ( π A )]2 }1/2

( CN )Wing SREF / SW, Wing Normal Force Coefficient for Rocket Baseline

Note: Linear wing theory applicable if M > { 1 + [ 8 / ( π A )]2 }1/2, slender wing theory applicable if M < { 1 + [ 8 / ( π A )]2 }1/2, A = Aspect Ratio < 3, SSurface = Surface Planform Area, SRef = Reference Area M < 1.35, based on slender wing theory + Newtonian impact theory M = 2, based on linear wing theory + Newtonian impact theory M = 5, based on linear wing theory + Newtonian impact theory 4

Example for Rocket Baseline Wing AW = 2.82 SW = 2.55 ft2 SRef = 0.349 ft2 δ = 13 deg, α = 9 deg

3

M=2 { 1 +[ 8 / ( π A )]2 }1/2 = 1.35

2

1 0 0

30

60

Since M > 1.35, use linear wing theory + Newtonian theory α’ = αW = α + δ = 22° ( CN )Wing SRef / SW = 4 sin 22° cos 22° / ( 22 – 1 )1/2 + 2 sin2 22° = 1.083 ( CN )Wing = 1.08 ( 2.55 ) / 0.349 = 90 7.91

α’ = αW = α + δ , Wing Effective Angle of Attack for Rocket Baseline, Deg 2/24/2008

ELF

45

Aerodynamic Center of a Thin Surface ( e.g., Wing, Tail, Canard ) Varies with Mach Number ( xAC / cMAC )Surface = [ A ( M2 – 1 )1/2 – 0.67 ] / [ 2A ( M2 –1 )1/2 – 1 ], if M > ~ 2

XAC / CMAC, Surface Non-dimensional Aerodynamic Center

( xAC / cMAC )Surface = 0.25, if M < ~ 0.7

0.5 0.4

Note: Based on linear wing theory Thin wing ⇒ M ( t / c ) { 1 + [ 8 / ( π A )]2 }1/2 }( S W {[ x C ard l / rw ) W] ( fo C 5 •(CNα)T = (CNα)W = π A / 2, if M < { 1 + xA 2 ( . – - 0 [ 8 / ( π A )]2 }1/2 G = x C ) {[ f Example Rocket Baseline: / S Re W S ( l = 144 in, d = 8 in, SW = 2.55 ft2, SRef = /l} ] )W 0.349 ft2, AW = 2.82, (cMAC)W = 13.3 in, x AC ( – xMAC = 67.0 in from nose tip, burnout ) G x C g ( xCG = 76.2 in from tip ), Mmax = 3 n {[ wi t f (a (xAC)W = 0.49 ( 13.3 ) = 6.5 in from leading edge of MAC

(ST)Neutral / SRef, Neutral Stability Tail Area / Reference Area

3

2

1

(xAC)W = 6.5 + 67.0 = 73.5 in from nose

0 0

1

2

3

4

M, Mach Number

5

{[ xCG – (xAC)W ] / l } ( SW / SRef ) = 0.14 ( forward wing ) (ST)Neutral / SRef = 1.69 provides neutral stability (ST)Neutral = 1.69 ( 0.349 ) = 0.59 ft2

2/24/2008

ELF

72

Stability and Control Derivatives Conceptual Design Criteria | Clδr / Clδa | < 0.3 ( Roll Due to Rudder Deflection ) | Clφ / Clδa | < 0.5 ( Roll Due to Roll Angle ) Clδr z

x

Clδa

x

Clδa

Clφ

y

z

y

| Cnδa / Cnδr | < 0.2 ( Yaw Due to Aileron Deflection ) | Cmα / Cmδ | < 1 ( Pitch Due to α ) x

Cnδa

Cnδr

z

Cmα

Cmδ

y

z

2/24/2008

y

z

| Clβ / Clδa | < 0.3 ( Roll Due to Sideslip ) Clβ

x

x

| Cnβ / Cnδr | < 1 ( Yaw Due to Sideslip ) x

Cnβ

Clδa

Cnδr

y

z

y

Note: The primary control derivative ( larger bold font ) should be larger than the undesirable stability and control derivative. ELF

73

Most of the Rocket Baseline Body Buildup Normal Force Is Provided by the Wing ( CN )Total = ( CN )Wing-Body-Tail ≅ ( CN )Body + ( CN )Wing + ( CN )Tail 15

CN, Normal Force Coefficient of Rocket Baseline

Body + Wing + Tail

10

Body + Wing

5 Body 0

0

5

10

15

α, Angle of Attack, Deg

20

25 Note for figure: M = 2, δ = 0

Note: ( CD0 )Total = ( CD0 )Wing-Body-Tail ≅ ( CD0 )Body + ( CD0 )Wing + ( CD0 )Tail ( Cm )Total = ( Cm )Wing-Body-Tail ≅ ( Cm )Body + ( Cm )Wing + ( Cm )Tail 2/24/2008

ELF

74

Summary of Aerodynamics Conceptual Design Prediction Methods of Bodies and Surfaces Normal force coefficient Drag coefficient Aerodynamic center / pitching moment coefficient / hinge moment

Design Tradeoffs Diameter Nose fineness Boattail Lifting body versus axisymmetric body Wings versus no wings Tails versus flares Surface planform geometry Flight control alternatives Maneuver alternatives Roll orientation Static margin / time to converge or diverge Tail sizing 2/24/2008

ELF

75

Summary of Aerodynamics ( cont ) Stability and Control Design Criteria Static stability Control effectiveness Cross coupling

Body Buildup New Aerodynamics Technologies Faceted / window / multi-lens domes Bank-to-turn maneuvering Lifting body airframe Forward swept surfaces Neutral static margin Lattice fins Split canard control Free-to-roll tails

Discussion / Questions? Classroom Exercise 2/24/2008

ELF

76

Aerodynamics Problems 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 2/24/2008

Missile diameter tradeoffs include consideration of seeker range, warhead lethality, structural mode frequency, and d___. Benefits of a high fineness nose include lower supersonic drag and lower r____ c____ s______. Three contributors to drag are base drag, wave drag, and s___ f_______ drag. To avoid flow separation, a boatail or flare angle should be less than __ deg. A lifting body is most efficient at a d______ p_______ of about 700 psf. At low angle of attack the aerodynamic center of the body is on the n___. Subsonic missiles often have w____ for enhanced range. The aerodynamic center of the wing is between 25% and 50% of the m___ a__________ c____. Hinge moment increases with the local flow angle due to control surface deflection and the a____ o_ a_____. Increasing the surface area increases the s___ f_______ d___. ELF

77

Aerodynamics Problems ( cont ) 11. 12.

13. 14. 15. 16. 17. 18. 19. 20. 2/24/2008

Leading edge sweep reduces drag and r____ c____ s______. A missile with six control surfaces, four surfaces providing combined pitch / yaw control plus two surfaces providing roll control, has an advantage of good c______ e____________. A missile with two control surfaces providing only combined pitch / yaw control has advantages of lower c____ and good p________. A tail control missile has larger trim normal force if it is statically u_______. Lattice fins have low h____ m_____. Split canards allow higher maximum angle of attack and higher m______________. Two types of unconventional control are thrust vector control and r_______ j__ control. The most common type of TVC for tactical missiles is j__ v___ control. Three maneuver laws are skid to turn, bank to turn, and r______ a_______. Bank to turn maneuvering is usually required for missiles with a single wing or with a_________ inlets. ELF

78

Aerodynamics Problems ( cont ) 21. 22. 23. 24.

25.

2/24/2008

A missile is statically stable if the aero center is behind the c_____ o_ g______. Tail stabilizers have low drag while a f____ stabilizer has low aero heating and a relatively small shift in static stability. If the moments on the missile are zero the missile is in t___. Total normal force on the missile is approximately the sum of the normal forces on the surfaces ( e.g., wing, tail, canard ) plus normal force on the b___. Increasing the tail area increases the s_____ m________.

ELF

79

Outline Introduction / Key Drivers in the Design Process Aerodynamic Considerations in Tactical Missile Design Propulsion Considerations in Tactical Missile Design Weight Considerations in Tactical Missile Design Flight Performance Considerations in Tactical Missile Design Measures of Merit and Launch Platform Integration Sizing Examples Development Process Summary and Lessons Learned References and Communication Appendices ( Homework Problems / Classroom Exercises, Example of Request for Proposal, Nomenclature, Acronyms, Conversion Factors, Syllabus ) 2/24/2008

ELF

80

Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics Propulsion Weight

Resize / Alt Config / Subsystems / Tech

Trajectory Meet Performance?

No

Yes Measures of Merit and Constraints

No

Yes 2/24/2008

ELF

81

High Specific Impulse Is Indicative of Lower Fuel / Propellant Consumption ISP, Specific Impulse, Thrust / ( Fuel or Propellant Weight Flow Rate ), S

4,000 Turbojet: ISP typically constrained by turbine temperature limit 3,000

Ramjet: ISP typically constrained by combustor insulation temperature limit

2,000

Scramjet: ISP typically constrained by thermal choking

1,000

Solid Rocket: ISP typically constrained by safety

Ducted Rocket 0 0

2

4

6

8

10

12

Mach Number 2/24/2008

ELF

82

Cruise Range Is Driven by L/D, Isp, Velocity, and Propellant or Fuel Weight Fraction R = ( L / D ) Isp V In [ WL / ( WL – WP )] , Breguet Range Equation Typical Value for 2,000 lb Precision Strike Missile Parameter

Subsonic Turbojet Missile

Liquid Fuel Ramjet Missile

Hydrocarbon Fuel Scramjet Missile Solid Rocket

L / D, Lift / Drag

10

5

3

5

Isp, Specific Impulse

3,000 s

1,300 s

1,000 s

250 s

VAVG , Average Velocity

1,000 ft / s

3,500 ft / s

6,000 ft / s

3,000 ft / s

WP / WL, Cruise Propellant or Fuel Weight / Launch Weight R, Cruise Range

0.3

0.2

0.1

0.4

1,800 nm

830 nm

310 nm

250 nm

Note:

2/24/2008

Ramjet and Scramjet missiles booster propellant for Mach 2.5 to 4 take-over speed not included in WP for cruise. Rockets require thrust magnitude control ( e.g., pintle, pulse, or gel motor ) for effective cruise. Max range for a rocket is usually a semi-ballistic flight profile, instead of cruise flight. Multiple stages may be required for rocket range greater than 200 nm. ELF

83

( T / W )Max , ( Thrust / Weight )Max

Solid Rockets Have High Acceleration Capability 1,000

Solid Rocket .

TMax = 2 Pc At = m Ve 100

10

Ramjet

Turbojet

TMax = (π / 4 ) d2 ρ0 V02 [( Ve / V0 ) 1] 1 0

1

TMax = (π / 4 ) d2 ρ0 V02 [( Ve / V0 ) 1]

2

3

4

5

M, Mach Number Note: . Pc = Chamber pressure, At = Nozzle throat area, m = Mass flow rate d = Diameter, ρ0 = Free stream density, V0 = Free stream velocity, Ve = Nozzle exit velocity ( Turbojet: Ve ~ 2,000 ft / s, Ramjet: Ve ~ 4,500 ft / s, Rocket: Ve ~ 6,000 ft / s ) 2/24/2008

ELF

84

Turbojet Nomenclature Inlet

Compressor

Combustor

Turbine

Nozzle

0 Free Stream

1

2

3

Compressor Entrance

Compressor Exit

Inlet Entrance

2/24/2008

5 4

Turbine Exit

Turbine Entrance

ELF

85

High Temperature Compressors Are Required to Achieve High Pressure Ratio at High Speed T3, Compressor Exit Temperature, R

T3 ≈ T0 { 1 + [( γ0 - 1 ) / 2 ] M02 }( p3 / p2 )( γ3 - 1 ) / γ3 p3 / p2 = 1 p3 / p2 = 2 p3 / p2 = 5 p3 / p2 = 10

γ0 = 1.4, γ3 ≈ 1.29 + 0.16 e-0.0007 T3

3000

Note: Ideal inlet; ideal compressor; low subsonic, isentropic flow

2000 T3

1000

Example: M0 = 2, h = 60k ft ( T0 = 398 R ) p3 / p2 = 5 ⇒ T3 = 1118 R, γ3 = 1.36

0 0

1

2

3

4

M0, Free Stream Mach Number T3 = Compressor exit temperature in Rankine, T0 = free stream temperature in Rankine, γ = specific heat ratio, M0 = free stream Mach number, p3 = compressor exit pressure, p2 = compressor entrance pressure

2/24/2008

ELF

86

High Turbine Temperature Is Required for High Speed Turbojet Missiles T4,Turbojet Turbine Temperature, R

T4 ≈ T3 + ( Hf / cp ) f / a, T in R

T3 = 500 R T3 = 1000 R T3 = 2000 R T3 = 4000 R

cp4 ≈ 0.122 T40.109, cp in BTU / lb / R

5000 4000 3000

T4

2000

Example: M0 = 2, h = 60K ft ( T0 = 398 R ), p3 / p2 = 5 ⇒ T3 = 1118 R

1000 0 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

RJ-5 fuel ( Hf = 14,525 BTU / lb ), cp = 0.302 BTU / lb / R , f / a = 0.067 ( stochiometric ) ⇒ T4 = 1118 + ( 14525 / 0.302 ) 0.067 = 4,340 R

f / a, Fuel-to-Air Ratio T4 = Turbojet turbine entrance temperature in Rankine, T3 = compressor exit temperature in Rankine, Hf = heating value of fuel, cp = specific heat at constant pressure, f / a = fuel-to-air ratio

2/24/2008

ELF

87

Turbine Material Temperature Limit Is a Constraint for a High Speed Turbojet Missile Max Short Duration Temp

Turbine Material

Temperature Constrained Turbines for Mach 4 Cruise

ISP for Mach 4 Cruise

≈ 3,000R

Nickel Super Alloys

Very Highly Constrained Turbojet, Air Turbo Rocket, Turbo Ramjet

≈ 1,000 s

≈ 3,000R

Titanium Aluminides ( lighter weight than nickel super alloys )

Very Highly Constrained Turbojet, Air Turbo Rocket, Turbo Ramjet

≈ 1,000 s

≈ 3,500R

Single Crystal Nickel Aluminides

Highly Constrained Turbojet

≈ 1,200 s

≈ 4,000R

Ceramic Matrix Composites

Moderately Constrained Turbojet

≈ 1,500 s

≈ 4,500R

Rhenium Alloys

Moderately Constrained Turbojet

≈ 2,000 s

≈ 5,000R

Tungsten Alloys

Slightly Constrained Turbojet

≈ 2,500 s

Note: Constrained turbojet for Mach 4 cruise imposes a limit on turbine temperature that is less than ideal. Constraints could consist of a combination of: • Constraint on compressor pressure ratio to limit turbine temperature • Constraint on fuel-to-air ratio to limit turbine temperature • Use of afterburner to limit turbine temperature

2/24/2008

ELF

88

Turbine-Based Missiles Are Capable of Subsonic to Supersonic Cruise Turbojet

SS-N-19 Shipwreck Firebee II

Turbo Ramjet

Regulus II

SR-71

Air Turbo Rocket

2/24/2008

ELF

89

Compressor Pressure Ratio for Maximum Thrust Turbojet Is Limited by Turbine Temperature ( p3 / p2 )@Tmax ≈ {( T4 / T0 )1/2 / { 1 + [( γ0 - 1 ) / 2 ] M02 }}γ4 / ( γ4 - 1 )

( p3 / p2 )@Tmax

Assumptions: Ideal turbojet ( isentropic inlet, compressor, turbine, nozzle; low subsonic and constant pressure combustion; exit pressure = free stream pressure ) 100

10

Example: M0 = 2.0, h = 60k ft (T0 = 390 R ) , T4 = 3,000 R, γ4 = 1.31 ( p3 / p2 )@Tmax = {{ ( 3000 / 390 )1/2 / { 1 + [( 1.4 1 ) / 2 ] 2.02 }}1.31/ ( 1.31 – 1 ) = 6.31 1

Note: 0

0.5

1

1.5

2

2.5

3

M0, Mach Number T4 = 2000 R T4 = 4000 R

3.5

4

T0 = Free stream temperature T4 = Turbine entrance temperature

T4 = 3000 R T4 = 5000 R

γ = Specific heat ratio

Source: Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., New York, 1974

2/24/2008

ELF

90

Turbojet Thrust Is Limited by Turbine Maximum Allowable Temperature .

Note: .

( T / m )IdealMax = Ve – V0

Assumption: Ideal turbojet 20

Ve = { 2 cp T5t [ 1 – ( p0 / p5t )( γ5 - 1 ) / γ5 ]}1/2 T5t ≈ T4 – T3 + T2 T3 ≈ T2 ( p 3 / p 2 ) ( γ 3 - 1 ) / γ 3

15

=1

)

T2 ≈ T0 { 1 + [( γ0 - 1 ) / 2 ] M02 }

/p

2

p5t ≈ p4 ( T5 / T4 )γ4 / ( γ4 - 1 ) p4 = p 3

je t

(p

3

10

p2 ≈ p0 { 1 + [( γ0 - 1 ) / 2 ] M02 }γ0 / ( γ0 - 1 )

Ram

Tmax / [( p0 ) ( A0 )], Nondimensional Maximum Thrust

TIdealMax / ( p0 A0 ) = ( γ0 M0 / a0 ) ( T / m )IdealMax

p0 = Free stream static pressure

5

A0 = Free stream flow area into inlet T4 = Turbine entrance temperature

0 0

1

2

3

M0, Mach Number T4 = 2000 R T4 = 4000 R

T4 = 3000 R T4 = 5000 R

4

Example: M0 = 2, h = 60 k ft ( T0 = 390 R, p0 = 1.047 psi ), T4 = 3,000 R, γ4 = 1.31, ( p3 / p2 )@Tmax = 6.31, p2 = 8.19 psi, p3 = 51.7 psi, A0 = 114 in2, T2 = 702 R, T3 = 1133 R, γ3 = 1.36 p5t = 23.0 psi, Ve = T5t = 2569 R, γ5 = 1.32, . 4524 ft / s, ( T / m )IdealMax = 2588 ft / s, TIdealMax / p0 A0 = 7.49 TIdealMax = 7.49 ( 1.047 ) ( 114 ) = 894 lb

2/24/2008

ELF

91

Turbojet Specific Impulse Decreases with Supersonic Mach Number ( ISP )Ideal@Tmax gc cp T0 / ( a0 Hf ) = TIdealMax T0 / [( p0 A0 γ0 M0 ) ( T4 – T3 )]

( ISP )Ideal ( gc ) ( cp ) ( T0) / [ ( a0 ) ( Hf )], Nondimensional Ideal Specific Impulse

Assumptions: Ideal turbojet ( isentropic inlet, compressor, turbine, nozzle; flow, low subsonic, constant pressure combustion; exit pressure = free stream pressure), max thrust Example: 0.8

0.6

Ra mje

M0 = 2, h = 60k ft ( T0 = 390 R, a0 = 968 ft / s ), RJ-5 fuel ( Hf = 14,525 BTU / lbm ), T4 = 3,000 R, cp = 0.293 BTU / lbm / R, γ0 = 1.4 t(p

3

/p

0.4

2

=1

Calculate ( ISP )Ideal@Tmax gc cp T0 / ( a0 Hf ) = 0.559 ( ISP )Ideal@Tmax = 0.559 ( 968 ) ( 14525 ) / [ 32.2 ( 0.293 ) ( 390 )] = 2136 s

)

Note: gc = Gravitational constant = 32.2

0.2

cp = Specific heat at constant pressure T0 = Free stream temperature 0 0

1

2

3

M0, Mach Number T4 = 2000 R T4 = 4000 R

4

a0 = Free stream speed of sound Hf = Heating value of fuel TIdealMax = Ideal maximum thrust

T4 = 3000 R T4 = 5000 R

γ = Specific heat ratio T4 = Combustor exit temperature T3 = Compressor exit temperature

2/24/2008

ELF

92

Tactical Missile Ramjet Propulsion Alternatives Liquid Fuel Ramjet Rocket Boost Inboard Profile Ramjet Sustain Inboard Profile

Note: Booster Propellant Fuel

Solid Fuel Ramjet Boost Sustain

Solid Ducted Rocket Boost Sustain

2/24/2008

ELF

93

High Specific Impulse for a Ramjet Occurs Using High Heating Value Fuel at Mach 3 to 4

( ISP )Ideal gc cp T0 / ( a0 Hf ) = { M0 {{( T4 / T0 ) / { 1 + [( γ0 - 1 ) / 2 ] M02 }}1/2 - 1 } / {{ 1 + [( γ0 - 1 ) / 2 ] M02 } {( T4 / T0 ) / { 1 + [( γ0 - 1 ) / 2 ] M02 }} – 1 }

( ISP )Ideal ( gc ) ( cp ) ( T0) / [ ( a0 ) ( Hf )], Nondimensional Ideal Specific Impulse

Assumptions: Ideal ramjet, isentropic inlet and nozzle, low subsonic and constant pressure combustion, exit pressure = free stream pressure, φ ≤ 1 Example for Ramjet Baseline: 0.6 M = 3.5, h = 60k ft ( T0 = 390 R, a0 = 968 ft / s ), RJ-5 fuel ( Hf = 14,525 BTU / lbm ), T4 = 4,000 R, cp = 0.302 BTU / lbm / R, γ0 = 1.4 Calculate ( ISP )Ideal gc cp T0 / ( a0 Hf ) = { 3.5 {{( 4000 / 390 ) / { 1 + [( 1.4 - 1 ) / 2 ] 3.52 }}1/2 - 1 } / {{ 1 + [( 1.4 - 1 ) / 2 ] 3.52 } {( 4000 / 390 ) / { 1 + [( 1.4 - 1 ) / 2 ] 3.52 }} – 1 } = 0.372

0.4

( ISP )Ideal = 0.372 ( 968 ) ( 14525 ) / [ 32.2 ( 0.302 ) ( 390 ) = 1387 s

0.2

Note: gc = Gravitational constant = 32.2 cp = Specific heat at constant pressure

0 0

1

2

3

4

M0, Free Stream Mach Number T4 / T0 = 3 T4 / T0 = 10

T4 / T0 = 5 T4 / T0 = 15

5

T0 = Free stream temperature a0 = Free stream speed of sound Hf = Heating value of fuel γ = Specific heat ratio T4 = Combustor exit temperature

Source: Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., New York, 1974

2/24/2008

ELF

94

High Thrust for a Ramjet Occurs from Mach 3 to 5 with High Combustion Temperature TIdeal / ( φ p0 A0 ) = γ0 M02 {{[ T4 / T0 ] / { 1 + [( γ0 - 1 ) / 2 ] M02 }}1/2 - 1 } Assumptions: Ideal ramjet, isentropic inlet and nozzle, low subsonic and constant pressure combustion, exit pressure = free stream pressure, φ ≤ 1 T / [ PHI ( p0 ) (A0 ) ], Nondimimensional Thrust

25

Note: T4 and T0 in R

Example for Ramjet Baseline:

20

M0 = 3.5, α = 0 deg, h = 60k ft ( T0 = 390 R, p0 = 1.047 psi ), T4 = 4,000 R, ( f / a ) = 0.055, φ = 0.82, A0 = 114 in2, γ0 = 1.4

15

TIdeal / ( φ p0 A0 ) = 1.4 ( 3.5 )2 {{[ 4000 / 390 ] / { 1 + [( 1.4 – 1 ) / 2 ] ( 3.5 )2 }}1/2 – 1 } = 12.43 TIdeal = 12.43 ( 0.82 ) ( 1.047 ) ( 114 ) = 1216 lb

10

Note: ( T )Ideal = Ideal thrust p0 = Free stream static pressure

5

A0 = Free stream flow area into inlet γ0 = Free stream specific heat ratio

0 0

1

2

3

4

M0, Free Stream Mach Number T4 / T0 = 3 T4 / T0 = 10

T4 / T0 = 5 T4 / T0 = 15

5

M0 = Free stream Mach number T4 = Combustor exit temperature T0 = Free stream temperature φ = Equivalence ratio = fuel-to-air ratio / stochiometric fuel-to-air ratio

Source: Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., New York, 1974

2/24/2008

ELF

95

Ramjet Combustor Temperature Increases with Mach Number and Fuel Flow T4 ≈ T0 { 1 + [( γ0 - 1 ) / 2 ] M02 } + ( Hf / cp ) ( f / a )

T4, Combustor Exit Temperature for RJ-5 Fuel, Rankine

Assumptions: Low subsonic combustion. No heat transfer through inlet ( isentropic flow ). φ ≤ 1. T4 = combustor exit temperature in Rankine, T0 = free stream temperature in Rankine, γ = specific heat ratio, M0 = free stream Mach number, Hf = heating value of fuel, cp = specific heat at constant pressure, f / a = fuel-to-air ratio.

6000

Example: •M0 = 3.5

4000

•h = 60k ft ( T0 = 390 R ) •RJ-5 fuel ( Hf = 14,525 BTU / lb / R ) •f / a = 0.055

2000

•γ0 = 1.4 •cp = 0.122 T0.109 BTU / lbm / R. Note: cp ≈ 0.302 +/- 5% if 2500 R < T < 5000 R

0 0

1

2

3

4

5

•Then T4 = 390 { 1 + [( 1.4 – 1 ) / 2 ] ( 3.5 )2 } + [( 14525 ) / ( 0.302 )] 0.055 = 3,991 R

M0, Free Stream Mach Number f / a = 0.01 2/24/2008

f / a = 0.03

f / a = 0.05

f / a = 0.067

Note: ( f / a )φ = 1 ≈ 0.067 for stochiometric combustion of liquid hydrocarbon fuel, e.g., RJ-5. ELF

96

Ramjet Combustor Entrance Mach Number Should Be Low, to Avoid Thermal Choking ( M3 )TC = {{ - b + [ b2 – 4 γ32 ]1/2 } / ( 2 γ32 )}1/2 b = 2 γ3 + ( T4t / T0 )( 1 + γ4 )2 / {( 1 + 0.2 M02 )[ 1 + ( γ4 – 1 ) / 2 ]} Assumptions: Constant area combustion, [( γ 3 – 1 ) / 2 ] M32 2 and Inlet Start at Low Supersonic Mach number

External Compression Inlet ( with Spillage )

Spillage Shocks

Shocks Converge Outside Inlet Lip ( Results in Spillage Air )

External Compression Inlet ( w/o Spillage )

Shocks

Inlet Swallows 100% of the Free Stream Flow

2/24/2008

Shocks Converge at Inlet Lip ( Inlet Captures Maximum Free Stream Flow )

ELF

107

Shock Wave Angle Increases with Deflection Angle and Decreases with Mach Number tan ( α + δ ) = 2 cot θ2D ( M2 sin2 θ2D – 1 ) / [ 2 + M2 ( γ + 1 – 2 sin2 θ2D )] , for 2D flow, perfect gas

Theta, 2D Shock Wave Angle @ Gamma = 1.4, Degrees

Note: θ2D = 2D shock wave angle, M = Mach number, α = angle of attack, δ = body deflection angle, γ = specific heat ratio, θconical ≈ 0.81 θ2D

50 Example for Ramjet Baseline:

40

α

30

θ

20

δ = 17.7 deg, M = 3.5, α = 0 deg, γ = 1.4 ⇒ θ2D = 32 deg

10

θconical ≈ 0.81 θ2D = 0.81 ( 32 ) = 26 deg Approximate estimate of θ:

0 0

5

10

15

20

Alpha + Delta, Deflection Angle, Degrees Mach 2 ( Deltamax = 23 deg ) Mach 5 ( Deltamax = 41 deg ) 2/24/2008

δ

θ2D ≈ μ + α + δ = sin-1 ( 1 / M ) + α + δ θconical ≈ 0.81 θ2D = 0.81 [ sin-1 ( 1 / M ) + α+δ]

Mach 3 ( Deltamax = 34 deg )

ELF

108

Capture Efficiency of an Inlet Increases with Mach Number ( A0 / Ac )conical = ( h / l ) ( 1 + δ M + αM ) / [( 1 – 0.23δM + αM )( δ + h / l )] , conical nose with forward inlet ( A0 / Ac )2D = ( h / l ) ( 1 + δ M + αM ) / [( 1 + αM )( δ + h / l )] , 2D nose with forward inlet Note: A0 / Ac ≤ 1, AC = inlet capture area, A0 = free stream flow area, δ = defection angle in rad, h = inlet height, l = distance from nose tip to inlet

A0 / Ac, Baseline Ramjet Inlet Capture Efficiency

1

α

δ stream lin

A0

streamline Ac streamline

0.8

e

oblique shock

0.6

body h inlet stream lin

e

Example for baseline ramjet ( conical nose )

0.4

h = 3 in

0.2

l = 23.5 in h / l = 0.1277 AC = 114 in2

0 0

1

2

3

4

Alpha = 0 Deg

5

δ = 17.7 deg ( 0.3089 rad ) M = 3.5, α = 0 deg

M, Mach Number

2/24/2008

nose

Alpha = 10 Deg ELF

A0 / Ac = 0.81 ⇒ A0 = 92 in2 Spillage = Ac - A0 = 114 - 92 = 22 in2 109

Isentropic Compression Allows Inlet Start at Lower Mach Number AIT / A0 = 1.728 ( MIE )start [ 1 + 0.2 ( MIE )start2 )-3, Assumptions: 2-D inlet, Isentropic flow through inlet ( n = ∞ ), γ = 1.4 AIT / A0 = ( MIE )start {[ 0.4 ( MIE )start2 + 2 ] / [ 2.4 ( MIE )start2 ]3.5 }{[2.8 ( MIE )start2 – 0.4 ] / 2.4 }2.5 {[ 1.2 / ( 1 + 0.2 ( MIE )start2 ]}3, Assumptions: 2-D inlet, single normal shock ( n = 1 ), γ = 1.4

( M )IE, Inlet Entrance Start Mach Number

Note: AIT = inlet throat area, A0 = free stream flow area, ( MIE )start = inlet entrance start Mach number, γ = specific heat ratio, n = number of shocks 4 Example for ramjet baseline n=∞

3

AIT = 0.29 ft2

n=1

Ac = 114 in2 = 0.79 ft2 ⇒ AIT / Ac = 0.367 Process: 1. Assume ( MIE )start

2

2. Compute capture efficiency AIT / A0 3. Compute ( MIE )start and compare with assumed ( MIE )start

1

4. Iterate until convergence Limit for isentropic compression

0 0

0.2

0.4

0.6

0.8

AIT / A0 Inlet Start for Isentropic Compression Inlet Start for Single Normal Shock 2/24/2008

ELF

1

- From Prior Figure, A0 / Ac = 0.53 - Compute AIT / A0 = ( AIT / Ac ) / ( A0 / Ac ) = 0.367 / 0.53 = 0.69 ⇒ ( MIE )start = 1.8 Ramjet baseline has mixed compression with n = 5. Actual inlet start Mach number is ( MIE )start > 1.8 110

Forebody Shock Compression Reduces the Inlet Entrance Mach Number ( MIE )2D = {{ 36 M04 sin2 θ2D - 5 [ M02 sin2 θ2D - 1 ][ 7 M02 sin2 θ2D + 5 ]} / {[ 7 M02 sin2 θ2D - 1 ][ M02 sin2 θ2D + 5 ]}}1/2

tan ( α + δ ) = 2 cot θ2D ( M02 sin2 θ2D – 1 ) / [ 2 + M02 ( 2.4 – 2 sin2 θ2D )] Assumptions: 2D flow, perfect gas, γ = specific heat ratio = 1.4 Note: MIEt= inlet entrance Mach number, M0 = free stream Mach number, θ = oblique shock angle, α = angle of attack, δ = body deflection angle

( M )IE, Inlet Entrance Mach Number

4

Example for ramjet baseline

3

δ = 17.7 deg ( MIE )start = 1.8 ( from prior example )

2

Compute M0 = 2.55 Note: Ramjet baseline forebody is conical, not 2D

1

0 0

10

20

30

40

Alpha + Delta, Local Angle of Attack at Inlet Entrance, Deg M0 = 2 2/24/2008

M0 = 3

M0 = 5 ELF

111

Optimum Forebody Deflection Angle(s) for Best Pressure Recovery Increases with Mach Number Note: δTotal = Total deflection angle, δ1 = 1st deflection angle, δ2 = 2nd deflection, δ3 = 3rd deflection.

First External Shock Second External Shock

Optimum Total Deflection Angle, Deg

δ2

60

Optimum deflection angle provides equal loss in total pressure across each shock wave.

δTotal

Optimum deflection angles are nearly equal for M > 4.

δ1

12.1, 15.2, 19.4 11.1, 13.0, 15.5

40

16.1, 22.1

15.0, 18.8 7.6, 8.2, 8.2 10.4, 11.2

20

Example: Optimum forebody deflection angles for double wedge ( n = 3 ) at Mach 2: δ1 = 10.4 deg, δ2 = 11.2 deg ⇒ δtotal = 10.4 + 11.2 = 21.6 deg

0 0

1

2

3

4

M0, Free Stream Mach Number n=1 2/24/2008

n=2

n=3

n=4

Isentropic Compression

Reference: “Technical Aerodynamics Manual,” North American Rockwell Corporation, DTIC AD 723823, June 1970. ELF

112

Oblique Shocks Prior to the Inlet Normal Shock Are Required to Satisfy MIL-E-5008B MIL-E-5008B Requirement: ptInlet / pt0 = 1 – 0.075 ( M – 1 )1.35

PtInlet / pt0, Inlet Total Pressure Ratio

1

n = 1 ( Normal Shock ) n = 2 ( 1 Optimum Oblique Shock + Normal Shock ) n = 3 ( 2 Opt Oblique Shocks + Normal Shock ) n = 4 ( 3 Opt Oblique Shocks + Normal Shock Ideal Isentropic Inlet

0.1

MIL-E-5008B 0.01

Note: 2D flow assumed

0

1

2

3

4

M, Mach Number

5

pt

Inlet

= Inlet total pressure

pt = Free stream total pressure 0

Example: MIL-E-5008B requirement for Mach 3.5 ( pt / pt = ηinlet = 0.74 ) can be satisfied only if there are more Inlet 0 than three oblique shocks prior to inlet normal shock. Source for Optimum 2D Shocks: Oswatitsch, K.L., “Pressure Recovery for Missiles with Reaction Propulsion at High Supersonic Speeds”, NACA TM - 1140, 1947. 2/24/2008

ELF

113

High Density Fuels Provide Higher Volumetric Performance but Have Higher Observables Type Fuel

Density, lb / in3

Volumetric Performance, BTU / in3

Low Observables

Turbine ( JP-4, JP-5, JP-7, JP-8, JP-10 )

~ 0.028

559

Liquid Ramjet ( RJ-4, RJ-5, RJ-6, RJ-7 )

~ 0.040

581

HTPB

~ 0.034

606

Slurry ( 40% JP-10 / 60% carbon )

~ 0.049

801

Solid Carbon ( graphite )

~ 0.075

1132

–

Slurry ( 40% JP-10 / 60% aluminum )

~ 0.072

866

–

Slurry ( 40% JP-10 / 60% boron carbide )

~ 0.050

1191

–

Solid Mg

~ 0.068

1200

–

Solid Al

~ 0.101

1300

–

Solid Boron

~ 0.082

2040

–

2/24/2008

Superior

Above average ELF

Average

– Below average 114

Ducted Rocket Design Implications Excess Fuel from Gas Generator ~ 30 % ⇒ Behaves more like a rocket ( higher burn rate, higher burn temperature, lower ISP ) ~ 70 % ⇒ Behaves more like a ramjet ( higher ISP, lower burn rate, lower burn temperature )

Choice of Fuel Metal ( e.g., B, Al, Mg ) ⇒ Higher ISP, higher density, deposits, higher observables Carbon based ( e.g., C, HTPB ) ⇒ Lower observables, higher reliability, lower ISP

Choice of Oxidizer

AP ⇒ Higher burn rate, lower hazard, HCl contrail Min Smoke ( e.g., HMX, RDX ) ⇒ Lower Observables, lower heating value, lower burn rate, hazardous

Thrust Magnitude Control Approaches Pintle or valve in gas generator throat Retractable wires in grain 2/24/2008

ELF

115

High Propellant Fraction Increases Burnout Velocity 5000

ΔV = -gc Isp ln (1 - Wp / Wi) Assumption: T >> D, T >> W sin γ, γ = const

4000 Isp = 250 s ΔV, Missile

3000

Isp = 200 s

Incremental Burnout Velocity, 2000 ft / s

Example: Rocket Baseline Wi,boost = WL = 500 lb, Wp, boost = 84.8 lb ISP, boost = 250 s WP, boost / Wi = 84.8 / 500 = 0.1696 ΔV = -32.2 ( 250 ) ln ( 1 - 0.1696 ) = 1496 ft / s

1000

0

0

0.1

0.2

0.3

0.4

0.5

WP / Wi, Propellant Weight / Initial Missile Weight 2/24/2008

ELF

116

High Specific Impulse Requires High Chamber Pressure and Optimum Nozzle Expansion ISP = cd {{[ 2 γ2 / ( γ - 1 )] [ 2 / ( γ + 1 )] ( γ + 1 ) / ( γ - 1 ) [ 1 – ( pe / pc ) ( γ - 1 ) / γ ]}1/2 + ( pe / pc ) ε - ( p0 / pc ) ε } c* / gc .

T = w p ISP = ( gc / c* ) pc At ISP Isp, Specific Impulse of Rocket Baseline, s

ε = {[ 2 / ( γ + 1 )]1 / ( γ - 1 ) [( γ -1 ) / ( γ + 1 )]1/2 } / {( pe / pc )1 / γ [ 1 - ( pe / pc ) ( γ - 1 ) / γ ]1/2 } Note: ε = nozzle expansion ratio pe = exit pressure pc = chamber pressure p0 = atmospheric pressure . w P = propellant weight flow rate At = nozzle throat area ( minimum, sonic, choked ) γ = specific heat ratio = 1.18 in figure cd = discharge coefficient = 0.96 in figure c* = characteristic velocity = 5,200 ft / s in figure h = 20k ft, p0 = 6.75 psi in figure Example for Rocket Baseline:

300

250

ε = Ae / At = 6.2 ⇒ pe / pc = 0.02488, At = 1.81 in2

200 0

10

20

30

Nozzle Expansion Ratio pc = 300 psi pc = 2000 psi

( pc )boost = 1769 psi, pe = 44 psi, ( ISP )boost = 257 s ( ISP )ε = 6.2 / ( ISP )ε = 1 = 257 / 200 = 1.29 ( T )boost = ( 32.2 / 5200 ) ( 1769 ) (1.81 )( 257 ) = 5096 lb

pc = 1000 psi pc = 3000 psi

( pc )sustain = 301 psi, pe = 7.49 psi, ( ISP )sustain = 239 s ( ISP )ε = 6.2 / ( ISP )ε = 1 = 240 / 200 = 1.20 ( T )sustain = ( 32.2 / 5200 ) ( 301 ) (1.81 )( 240 ) = 810 lb

2/24/2008

ELF

117

High Propellant Weight Flow Rate Requires High Chamber Pressure and Large Nozzle Throat .

(pc)At, Chamber Pressure x Nozzle Throat Area, lb

w p = gc pc At / c*

100000

10000

c* = 4800 ft / s c* = 5200 ft / s c* = 5600 ft / s

1000

Rocket Baseline At for Boost: c* = 5200 ft / s ( pc )boost = 1,769 psi

100

.

w p = Wp / tb = 84.8 / 3.69 = 23.0 lb / s

1

10

100

Propellant Weight Flow Rate, lb / s

.

pc At = c* w p / gc = 5200 ( 23.0 ) / 32.2 = 3,714 lb At = 3714 / 1769 = 2.10 in2

.

2/24/2008

Note: At = nozzle throat area, c* = characteristic velocity, w p = propellant weight flow rate, gc = gravitational constant, pc = chamber pressure ELF

118

Ab, Rocket Baseline Propellant Burn Area, in2

High Chamber Pressure Requires Large Propellant Burn Area and Small Nozzle Throat 600

Ab = gc pcAt / ( ρc*r )

Example Ab for Rocket Baseline:

r = rpc=1000 psi ( pc / 1000 )n

At= 1.81 in2 ρ = 0.065 lb / in3 n = 0.3 rp

400

c = 1000 psi

= 0.5 in / s

c* = 5,200 ft / s Tatmosphere = 70 °F For sustain ( pc = 301 psi ): •r = 0.5 ( 301 / 1000 )0.3 = 0.35 in / s

200

•Ab = 149 in2 For boost ( pc = 1,769 psi ) •r = 0.59 in / s •Ab = 514 in2

0 0

500

1000

1500

2000

Pc, Rocket Baseline Motor Chamber Pressure, psi Note: Ab = propellant burn area, gc = gravitation constant, At = nozzle throat area, ρ = density of propellant, c* = characteristic velocity, r = propellant burn rate, rp =1000 psi = propellant burn rate at pc = 1,000 psi, pc = chamber pressure, n = burn rate exponent c

2/24/2008

ELF

119

Conceptual Design Sizing Process for a Rocket Motor 1. Define Altitude and Required Thrust-time

New Value ( s )

2. Assume Propellant ( Characteristic Velocity, Nominal Burn Rate, Burn Rate Exponent ), Chamber Pressure, Burn Area, and Nozzle Geometry ( Expansion Ratio, Throat Area )

New Value ( s )

3. Compute ISP and Thrust OK? Yes

No

4. Compute Propellant Weight Flow Rate and Propellant Used OK? Yes

No

5. Determine Diameter and Length to Satisfy wp and Ae OK? Yes 2/24/2008

ELF

No 120

Conventional Solid Rocket Thrust-Time Design Alternatives with Propellant Cross-Section

•Climb at ≈ constant dynamic pressure •Fast launch – ≈ cruise •Fast launch – ≈ cruise – high speed terminal

Thrust ( lb ) Thrust ( lb )

•Dive at ≈ constant dynamic pressure

Thrust ( lb )

•≈ Cruise

Thrust Profile Thrust ( lb ) Thrust ( lb )

Example Mission

Example Web Cross Section / Volumetric Loading

Constant Thrust

~ 82%

Burning Time ( s )

End Burner

~90% Radial Slotted Tube

~ 79%

Regressive Thrust Burning Time ( s )

~ 87%

Progressive Thrust Burning Time ( s )

Production of Star Web Propellant.

~ 85% Photo Courtesy of BAE

Boost-Sustain Burning Time ( s ) Boost-Sustain-Boost

~ 85%

Burning Time ( s ) Note: High thrust and chamber pressure require large surface burn area.

2/24/2008

~95%

ELF

Medium Burn Rate Propellant High Burn Rate Propellant

121

Conventional Rocket Has Fixed Burn while Thrust Magnitude Control Can Vary Burn Interval Conventional Fixed Burn Interval ( Boost )

End Burning

Radial Burning

Conventional Fixed Burn Interval ( Boost – Sustain )

Concentric Radial Burning High Burn Rate Boost Low Burn Rate Sustain

Radial Boost End Burning Sustain Simultaneous Burning

Pulse Motor TMC Variable Burn Interval ( Boost – Coast – Boost / Sustain - Coast )

1st Pulse: Radial Boost 2nd Pulse: End Burning Sustain Separate Burning ( Pulsed Motor )

1st Pulse: Radial Boost 2nd Pulse: Radial Sustain / Boost Separate Burning ( Pulsed Motor )

Note: Each pulse increases motor cost approximately 40%. 2/24/2008

ELF

Boost Propellant Sustain Propellant 122

Tactical Rocket Motor Thrust Magnitude Control Alternatives Solid Pulse Motor ☺ High ISP Limited Pulses

Solid Pintle Motor Thermal or Mechanical Barriers

☺ Continuously Select Up to 40:1 Variation in Thrust ☺ Reduce MEOP on Hot Day Good ISP Only If Burn Rate Exponent n → 1

Pintle

Bi-propellant Gel Motor ☺ High ISP

Pressurization

☺ Duty Cycle Thrust

Gelled Oxidizer

Gelled Fuel

Combustion Chamber

☺ Insensitive Munition Lower Max Thrust Toxicity 2/24/2008

ELF

123

Solid Rocket Propellant Alternatives Burn ρ, ISP, Rate @ Specific Density, 1,000 psi, Safety Observables Impulse, s lb / in3 in / s

Type • Min Smoke. No Al fuel or AP oxidizer. Either Composite with Nitramine Oxidizer ( CL-20, ADN, HMX, RDX ) or Double Base. Very low contrail (H2O).

–

–

– 220 - 255

0.055 - 0.062

250 - 260

0.062

0.25 - 2.0

• Reduced Smoke. No Al ( binder fuel ). AP oxidizer. Low contrail ( HCl ).

0.1 - 1.5

–

• High Smoke. Al fuel. AP oxidizer. High smoke ( Al2O3 ).

Superior 2/24/2008

260 - 265

Above Average

0.065

Average ELF

0.1 - 3.0

– Below Average 124

Steel is the Most Common Motor Case Material Type

Temperature

Volumetric Efficiency

Weight

IM

Airframe / Launcher Attachment

Cost

Steel Aluminum

–

–

Strip Steel / Epoxy Laminate

–

–

Composite Titanium Superior 2/24/2008

Above Average ELF

–

–

–

–

Average – Below Average 125

Heat Transfer Drives Rocket Nozzle Materials, Weight, and Cost Dome Closeout

Exit Cone Housing Throat

2/24/2008

Rocket Nozzle Element

High Heating ( High Chamber Pressure or Long Burn ) ⇒ High Cost / Heavy Nozzle

Low Heating ( Low Chamber Pressure or Short Burn ) ⇒ Low Cost / Light Weight Nozzle

♦ Housing Material Alternatives

♦ Steel

♦ Cellulose / Phenolic ♦ Aluminum

♦ Throat Material Alternatives

♦ Tungsten Insert ♦ Rhenium Insert ♦ Molybdenum Insert

♦ ♦ ♦ ♦

♦ Exit Cone, Dome Closeout, and Blast Tube Material Alternatives

♦ Silica / Phenolic Insert ♦ Graphite / Phenolic Insert ♦ Silicone Elastomer Insert

♦ No Insert ♦ Glass / Phenolic Insert

ELF

Cellulose / Phenolic Insert Silica / Phenolic Insert Graphite Insert Carbon – Carbon Insert

126

Summary of Propulsion Emphasis Turbojet propulsion Ramjet propulsion Rocket propulsion

Conceptual Design Prediction Methods Thrust Specific impulse

Design Trades Turbojet turbine material, compressor ratio, and cycle Ramjet engine / booster / inlet integration Ramjet fuel Propellant burn area requirement Nozzle throat area Nozzle expansion ratio Rocket motor grain Thrust magnitude control 2/24/2008

ELF

127

Summary of Propulsion ( cont ) Design Trades ( cont ) Solid propellant alternatives Motor case material alternatives Nozzle materials

New Propulsion Technologies Hypersonic turbojet Ramjet / ducted rocket Scramjet Combined cycle propulsion High temperature turbine materials High temperature combustor Oblique shock airframe compression Mixed compression inlet Low drag inlet High density fuel / propellant Endothermic fuel 2/24/2008

ELF

128

Summary of Propulsion ( cont ) New Propulsion Technologies ( cont ) Solid rocket thrust magnitude control High burn exponent propellant Low observable fuel / propellant

Discussion / Questions? Classroom Exercise ( Appendix A )

2/24/2008

ELF

129

Propulsion Problems 1. 2. 3. 4. 5. 6. 7. 8. 9. 2/24/2008

An advantage of turbojets compared to ramjets is s_____ thrust. The specific impulse of a turbojet is often limited by the maximum allowable temperature of the t______. The specific impulse of a ramjet is often limited by the maximum allowable temperature of the c________. Ducted rockets are based on a fuel-rich g__ g________. A safety advantage of solid rocket propulsion over liquid propulsion is less t_______. A rocket boost to a take-over Mach number is required by ramjets and s________. Parameters that enable the long range of subsonic cruise turbojet missiles are high lift, low drag, available fuel volume, and high s_______ i______. High thrust and high acceleration are achievable with s____ r_____ propulsion. In a turbojet the power to drive the compressor is provided by the t______. ELF

130

Propulsion Problems ( cont ) 10. 11. 12. 13. 14. 15. 16. 17.

2/24/2008

The compressor exit temperature is a function of the flight Mach number and the compressor p_______ r____. Compressor exit temperature, fuel heating value, and fuel-to-air ratio determine the turbojet t______ temperature. Three types of turbine based propulsion are turbojet, turbo ramjet, and a__ t____ r_____. Mach number and fuel-to-air ratio determine the ramjet c________ temperature. An example of a ramjet with low drag and light weight is an i_______ r_____ ramjet. Russia, France, China, United Kingdom, Taiwan, and India are the only countries with currently operational r_____ missiles. 100% inlet capture efficiency occurs when the forebody shock waves intercept the i____ l__. Excess air that does not flow into the inlet is called s_______ air. ELF

131

Propulsion Problems ( cont ) 18. 19. 20. 21. 22. 23. 24. 25. 26.

2/24/2008

Starting a ramjet inlet at lower supersonic Mach number requires a larger area of the inlet t_____. Optimum pressure recovery across shock waves is achieved when the total pressure loss across each shock wave is e____. The specific impulse and thrust of a ramjet are a function of the efficiency of the combustor, nozzle, and i____. High density fuels have high payoff for v_____ limited missiles. The specific impulse of a ducted rocket with large excess fuel from the gas generator can approach that of a r_____. High speed rockets require large p_________ weight. At the throat, the flow area is minimum, sonic, and c_____ . For an optimum nozzle expansion the nozzle exit pressure is equal to the a__________ pressure. High thrust and chamber pressure are achievable through a large propellant b___ area. ELF

132

Propulsion Problems ( cont ) 27. 28. 29. 30. 31.

2/24/2008

Three approaches to solid rocket thrust magnitude control are pulse motor, pintle motor, and g__ motor. A high burn exponent propellant allows a large change in thrust with only a small change in chamber p_______. Three tradeoffs in selecting a solid propellant are safety, observables, and s_______ i______. A low cost motor case is usually based on steel or aluminum material while a light weight motor case is usually based on c________ material. Rockets with high chamber pressure or long burn time may require a t_______ throat insert.

ELF

133

Outline Introduction / Key Drivers in the Design Process Aerodynamic Considerations in Tactical Missile Design Propulsion Considerations in Tactical Missile Design Weight Considerations in Tactical Missile Design Flight Performance Considerations in Tactical Missile Design Measures of Merit and Launch Platform Integration Sizing Examples Development Process Summary and Lessons Learned References and Communication Appendices ( Homework Problems / Classroom Exercises, Example of Request for Proposal, Nomenclature, Acronyms, Conversion Factors, Syllabus ) 2/24/2008

ELF

134

Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics Propulsion Weight

Resize / Alt Config / Subsystems / Tech

Trajectory Meet Performance?

No

Yes Measures of Merit and Constraints

No

Yes 2/24/2008

ELF

135

Designing Light Weight Missile Has High Payoff Production cost Logistics cost Size Firepower Observables Mission flexibility Expeditionary warfare 2/24/2008

ELF

136

Flight Performance ( Range, Speed, Maneuverability ) Sensitive to Subsystem Weight Dome -

Seeker -

Structure

Guidance and Control -

Power Supply

High Sensitivity 2/24/2008

Propulsion

Warhead

Low Sensitivity ELF

Wings

Insulation

Data Link -

Stabilizers

Flight Control

- Minor Sensitivity 137

Missile Range is a Function of Launch Weight, Propellant Weight, and Specific Impulse ΔV ≈ -gc Isp ln ( 1 - WPropellant / Wi ) 1000

Assumptions: θI = Launch Incidence Angle = 45 deg for max range

R ≈ V2 sin ( 2θi ) / gc

Rmax, Maximum Range, nm

Thrust Greater Than Drag and Weight Flat, Non-rotating Earth For Two-Stage Missile with ( Wi )Min : ΔV1 = ΔV2 Example: Two-Stage Missile with Minimum Weight and Rmax = 200 nm = 1.216 x 106 ft

100

Assume ISP = 250 sec, WPayload = 500 lb, WInert = 0.2 WPropellant V = [( 32.2 ) ( 1.216 x 106 )]1/2 = 6251 ft / s ΔV1 = ΔV2 = V / 2 = 3125 ft / s Wi,SecondStage = WPayload + WInert + WPropellant = 814 lb Wi, FirstStage = WInert + WPropellant = 85 + 427 = 512 lb

10 100

1000 Wi, Example Initial Launch Weight, lb Single-Stage Missile

2/24/2008

10000 Wi = Wi,FirstStage + Wi,SecondStage = 1326 lb Compare: Single-Stage Missile, R = 200 nm

Two-Stage Missile ELF

ΔV = 6251 = - 32.2 ( 250 ) ln [ 1 – WPropellant / ( WPropellant + 0.2 WPropellant + 500 )] ⇒ Wp = 767 ⇒ Wi = 1420 lb 138

Missile Weight Is a Function of Diameter and Length WL = 0.04 l d2

WL, Missile Launch Weight, lb

10000

Units: WL( lb ), l ( in ), d ( in )

1000

100

10 100

1000

10000

100000

1000000

ld2, Missile Length x Diameter2, in3

2/24/2008

FIM-92

SA-14

Javelin

RBS-70

Starstreak

Mistral

HOT

Trigat LR

LOCAAS

AGM-114

Roland

RIM-116

Crotale

AIM-132

AIM-9M

Magic 2

Mica

AA-11

Python 3

AIM-120C

AA-12

Skyflash

Aspide

AIM-9P

Super 530F

Super 530D

AGM-65G

PAC-3

AS-12

AGM-88

Penguin III

AIM-54C

Armat

Sea Dart

Sea Eagle

Kormoran II

AS34

AGM-84H

MIM-23F

ANS

MM40

AGM-142

AGM-86C

SA-10

BGM-109C

MGM-140

SSN-22

Kh-41

ELF

139

Most Subsystems for Tactical Missiles Have a Density of about 0.05 lb / in3 Guidance: Flight Control: 0.04 lb / in3 0.04 lb / in3

Dome Material: 0.1 lb / in3

2/24/2008

Warhead: 0.07 lb / in3

Propellant: 0.06 lb / in3

Structure and Motor Case: 0.10 ( Al ) to 0.27 ( steel ) lb / in3

ELF

Data Link: 0.04 lb / in3

Aero Surfaces: 0.05 ( built-up Al ) to 0.27 ( solid steel ) lb / in3

140

Modeling Weight, Balance, and Moment-of-Inertia Is Based on a Build-up of Subsystems Example Missile Configuration Nose G&C

Wing Section With Fuel

Inlet Section Engine With Fuel Fuel Plug

Warhead

Inlet

Model

+z +x Legend

Assume Uniform Weight Distribution For a Given Segment Structure and Subsystems

Engine Structure and Subsystems

Warhead and Structure

Fuel

Inlet Structure and Subsystems

Aero Surfaces

xCG = Σ ( xsubsystem1 Wsubsystem1 + xsubsystem2 Wsubsystem2 + … ) / Wtotal 2/24/2008

IY = Σ [ ( Iy,subsystem1 )local + Wsubsystem1 ( xsubsystem1 - xCG )2 / gc + ( Iy,subsystem2 )local + Wsubsystem2 ( xsubsystem2 - xCG )2 / gc + … ] ELF

141

( Iy,local ) g / ( W d2 ), Nondimensional Yaw Local Momen of Inertia

Moment-of-Inertia Is Higher for High Fineness Ratio Body ( Iy,cylinder )local = [ W d2 / gc ] [( 1 / 16 ) + ( 1 / 12 ) ( l / d )2 ]

100

( Iy,cone )local = [ W d2 / gc ] [ ( 3 / 80 ) + ( 3 / 80 ) ( l / d )2 ] er d n i l Cy

Cone

10 Example for Ramjet Baseline at Launch ( xcg = 8.04 ft ) Assume missile can be approximated as a conical nose-cylinder

1

For the cone, d = 1.25 ft, l / d = 1.57, Wcone = 15.9 lb, xcg,cone = 1.308 ft For the cylinder, l / d = 7.22, d = 1.698 ft, Wcylinder = 2214 lb, xcg,cylinder = 8.09 ft Iy = ( Iy,cone )local + Wcone ( xcg,cone - xCG )2 / gc + ( Iy,cylinder )local + Wcylinder ( xcg,cylinder xCG )2 / gc

0.1

( Iy,cone )local = [ 15.9 ( 1.25 )2 / 32.2 ] [ 0.0375 + 0.0375 ( 1.57 )2 ] = 0.10 slug-ft2 ( Iy,cylinder )local = [ 2214 ( 1.698 )2 / 32.2 ] [ 0.0625 + 0.0833 ( 7.22 )2 ] = 872 slug-ft2 Iy = 0.10 + 22.4 + 872 + 0.16 = 895 slug-ft2

0.01 0

10

20

30

l / d, Length / Diameter 2/24/2008

ELF

142

Structure Design Factor of Safety Is Greater for Hazardous Subsystems / Flight Conditions Pressure Bottle ( 2.50 / 1.50 ) Ground Handling Loads ( 1.50 / 1.15 ) 3.0

Captive Carriage and Separation Flight Loads ( 1.50 / 1.15 ) Motor Case ( MEOP ) ( 1.50 / 1.10 ) Free Flight Loads ( 1.25 / 1.10 )

2.0 FOS, Factor of Safety ( Ultimate / Yield )

Δ Castings ( 1.25 / 1.25 ) Δ Fittings ( 1.15 / 1.15 ) Thermal Loads ( 1.00 / 1.00 )

1.0

Note: 0 • MIL STDs include environmental ( HDBK-310, NATO STANAG 4370, 810F, 1670A ), strength and rigidity ( 8856 ), and captive carriage ( 8591 ). •The entire environment ( e.g., manufacturing, transportation, storage, ground handling, captive carriage, launch separation, post-launch maneuvering, terminal maneuvering ) must be examined for driving conditions in structure design. •FOS Δ for castings is expected to be reduced in future as casting technology matures. •Reduction in required factor of safety is expected as analysis accuracy improves will result in reduced missile weight / cost.

2/24/2008

ELF

143

Structure Concepts and Manufacturing Processes for Low Parts Count Structure Manufacturing Process Alternatives Composites Metals

Structure Vacuum Vacuum Concept Compression Filament Thermal Assist Bag / Alternatives RTM Mold Wind Pultrusion Form Autoclave Cast

Geometry Alternatives

High Speed Strip Machine Forming Laminate

Monocoque

Lifting Body Airframe

Axisymmetric Airframe

Integrally Hoop Stiffened

–

Integrally Longitudinal Stiffened

–

Monocoque Integrally Hoop Stiffened Integrally Longitudinal Stiffened

Surface

Solid Sandwich

Note: Manufacturing process cost is a function of recurring cost ( unit material, unit labor ) and non-recurring cost ( tooling ).

Note: 2/24/2008

Very Low Parts Count

Low Parts Count ELF

Moderate Parts Count – High Parts Count 144

Low Parts Count Manufacturing Processes for Complex Airframes Vacuum Assisted RTM Resin

Pump

3D Fiber Orientation

Filament Wind

Helical wind versus radial wind

Pultrusion ………………………………….

2D Fiber Orientation ( 0-±45-90 deg )

Pour Cup Vent

Metal Casting

Riser Mold Cavity Parting Line

2/24/2008

ELF

145

Tactical Missile Airframe Material Alternatives Type

Tension ( σTU / ρ )

Material

Metallic Aluminum 2219 Increasing Steel PH 15-7Mo Cost

Buckling Max Stability Short – Life Temp ( σBuckling / ρ )

–

Thermal Stress

Joining

Cost

Weight

–

–

–

Titanium 6Al-4V

–

Composite S994 Glass / Increasing Epoxy and S994 Glass / Polyimide Cost Glass or Graphite Reinforce Molding

–

Graphite / Epoxy and Graphite Polyimide

Note: 2/24/2008

–

Superior

Above Average ELF

Average

–

– Below Average 146

Strength – Elasticity of Airframe Material Alternatives σt = P / A = E ε Kevlar Fiber w / o Matrix Graphite Fiber w / o Matrix ( 400 – 800 Kpsi )

400

Glass Fiber w / o Matrix

300 Very High Strength Stainless Steel ( PH 15-7 Mo, CH 900 ) High Strength Stainless Steel ( PH 15-7 Mo, TH 1050 )

σt, Tensile Stress, 103 psi 200

Titanium Alloy ( Ti-6Al-4V )

100

Aluminum Alloy ( 2219-T81 )

0 0

1

2

3

4

ε, Strain, 10-2 in / in 2/24/2008

ELF

5

Note: • High strength fibers are: – Very small diameter – Unidirectional – High modulus of elasticity – Very elastic – No yield before failure – Non forgiving failure • Metals: – Ductile, – Yield before failure – Allow adjacent structure to absorb load – Resist crack formation – Resist impact loads – More forgiving failure

E, Young’s modulus of elasticity, psi P, Load, lb ε, Strain, in / in A, Area, in2 Room temperature 147

Structural Efficiency at High Temperature of Short Duration Airframe Material Alternatives Graphite / Polyimide ( ρ = 0.057 lb / in3 ), 0-±45-90 Laminate Graphite / Epoxy ( ρ = 0.065 lb / in3 ) 0-±45-90 Laminate Ti3Al ( ρ = 0.15 lb / in3 )

σTU / ρ, Ultimate Tensile Strength / Density, 105 In.

12.0 10.0

Ti-6Al-4V Annealed Titanium ( ρ = 0.160 lb / in3 )

8.0

PH15-7 Mo Stainless Steel ( ρ = 0.277 lb / in3 ). Note: Thin wall steel susceptible to buckling.

6.0 Graphite

4.0

Glass Chopped Epoxy 2219-T81 Composites, Random Orientation Aluminum ( ρ = 0.101 lb / in3 ) ( ρ = 0.094 lb / in3 )

2.0 0

0

200

400

600

800

1,000

Short Duration Temperature, ° F 2/24/2008

ELF

148

Hypersonic Missiles without External Insulation Require High Temperature Structure ( Tmax )Titanium Aluminide ≈ 2,500 °F ) r=

1 r= 0 r = .9 0 .8

Tr = T0 ( 1 + 0.2 r M2 )

Tr, Recovery Temperature, °F

2,000

( Tmax )Single Crystal Nickel Aluminides ≈ 3,000 °F ( Tmax )Ceramic Matrix Composite ≈ 3,500 °F

( Tmax )Nickel Alloys ( e.g., Inconel, Rene, Hastelloy, Haynes )

1,500

Note: • (T ) max Steel

• γ = 1.4

• • •

1,000

• Tr = Recovery Temperature, R

( Tmax )Ti Alloy

• T0 = Free stream temperature, R • Tmax = Max temperature capability

( Tmax )Graphite Polyimide

• No external insulation assumed

• • • ( Tmax )Al Alloy

500

• • • • • •

( Tmax )Graphite Epoxy

0 2/24/2008

0

1

2

3

4

M, Mach Number

ELF

5

6

r is recovery factor h = 40k ft ( TFree Stream = 390 R ) Stagnation r = 1 Turbulent boundary layer r = 0.9 Laminar boundary layer r = 0.8 Short-duration flight ( less than 30 m ), but with thermal soak 149

Structure / Insulation Trades for Short Duration Flight Example Structure / Insulation Concepts

Mach Tmax Increasing

k

c

ρ

α

Hot Metal Structure ( e.g., Al ) without Insulation

600

0.027

0.22

0.101

0.000722

Hot Metal Structure ( e.g., Al )

600

0.027

0.22

0.101

0.000722

Internal Insulation ( e.g., Min-K )

2000

0.0000051 0.24

0.012

0.00000106

Self-insulating Composite Structure ( e.g., Graphite Polyimide )

1100

0.000109

0.27

0.057

0.00000410

Ext Insulation ( e.g., Micro-Quartz Paint )

1200

0.0000131 0.28

0.012

0.00000226

Cold Metal Structure ( e.g., Al )

600

0.027

0.22

0.101

0.000722

Internal Insulation ( e.g., Min-K )

2000

0.0000051 0.24

0.012

0.00000106

Note: • • • • 2/24/2008

Tactical missiles use passive thermal protection ( no active cooling ) Small thickness allows more propellant / fuel for diameter constrained missiles ( e.g., VLS launcher ) Weight and cost are application specific Tmax = max temp capability, ° F; k = thermal conductivity, BTU / s / ft2 / ° F / ft; c = specific heat or thermal capacity, BTU / lbm / ° F; ρ = density, lbm / in3; α = thermal diffusivity = k / ( ρ c ), ft2 / s ELF

150

External Insulation Has High Payoff for Short Duration Flight 1,000

Example Airframe Temperature with No External Insulator – Steel Airframe Selected.

Example Temperature ° F

900 800

4.0

Mach

700 3.0

600

Mach Number

500

2.0

400 300

Example Airframe Temperature with 0.012 in Insulator – Aluminum Airframe Acceptable for Short Duration.

200

Note: Short Range Air-to-Air Missile Launch ~ 0.9 Mach at 10k ft Altitude Atmosphere ~ Hot Day ( 1% Risk ) Mil-HDBK-310

100 0

1.0

0

2

4

6

8

10

12

14

Time After Launch ~ s 2/24/2008

ELF

151

Phenolic Composites Are Good Insulators for High Temperature Structure and Propulsion Graphites • Burn • ρ ~ 0.08 lb / in3 • Carbon / Carbon

6,000 5,000

Bulk Ceramics • Melt • ρ ~ 0.20 lb / in3 • Zirconium Ceramic, Hafnium Ceramic

4,000 Tmax, Max Temperature Capability, R

Porous Ceramics • Melt • Resin Impregnated • ρ ~ 0.12 lb / in3 • Carbon-Silicon Carbide

3,000 2,000

Low Density Composites • Char • ρ ~ 0.03 lb / in3 • Micro-Quartz Paint, GlassCork-Epoxy, Silicone Rubber

Plastics • Sublime • Depolymerizing • ρ ~ 0.06 lb / in3 • Teflon

1,000 0

Medium Density Phenolic Composites • Char • ρ ~ 0.06 lb / in3 • Nylon Phenolic, Silica Phenolic, Glass Phenolic, Carbon Phenolic, Graphite Phenolic

0

1

2

3

4

Insulation Efficiency, Minutes To Reach 300° F at Back Wall 2/24/2008

Note:

Assumed Weight Per Unit Area of Insulator / Ablator = 1 lb / ft2 ELF

152

A “Thermally Thin” Surface ( e.g., Metal Airframe ) Has Uniform Internal Temperature Example for Rocket Baseline Airframe:

( dT / dt )t = 0 = ( Tr - Tinitial ) h / ( c ρ z )

Aluminum skin w/o external insulation

dT / dt, Initial Skin Temperature Rate for Rocket Baseline, Deg F / sec

T = Tr – ( Tr – Tinitial ) e – h t / ( c ρ z )

c = 0.215 BTU / lb / R, ρ = 0.10 lb / in3 = 172.8 lb / ft3, z = 0.16 in = 0.0133 ft, k = 0.027 BTU / s / ft2 / R / ft

h = k NNU / x

1000

x = 1.6 ft

Thermally thin ⇒ h ( z / k )surface < 0.1

Assume Mach 2 sustain flight, 20k ft altitude ( T0 = 447 R , k = 3.31 x 10-6 BTU / s / ft2 / R / ft ), Turbulent boundary layer, x = 1.6 ft

100

Rex = ρ0 M a0 x / μ0 = 12.56 x 106 NNU = 0.0271 Re0.8 = 12947 h = k NNU / x = 0.0268 BTU / s / ft2 / R

10

Test: h ( z / k )surface = 0.0132 < 0.1 ⇒ thermally thin Calculate Tr = T0 [ 1 + 0.2 r M2 ] = 447 [ 1 + 0.2 ( 0.9 ) ( 2 )2 ] = 769 R

1 0

1

2

3

4

5

M, Mach Number

6

At t = 0, Assume Tinitial = 460 R, or 0° F ( dT / dt )t = 0 = ( 769 - 460 ) ( 0.0268 ) / [( 0.215 ) (172.8 ) ( 0.01333 )] = 17°F / s

At a sustain time t = 10 s, T = 769 - ( 769 – 460 ) e – 0.0268 ( 10 ) / [ 0.215 ( 172.8 ) ( 0.0133 )] = 589 R, or 129° F Note: No external insulation; thermally thin structure ( uniform internal temperature ); “Perfect” insulation behind airframe; 1-D heat transfer; Turbulent boundary layer; Radiation neglected; dT / dt = Temperature rate, R / s; Tr = Recovery ( max ) temperature, R; h = Convection heat transfer coefficient, BTU / s / ft2 / R; c = Specific heat, BTU / lb / R; ρ = Density, lb / ft3; z = Thickness, ft; k = Conductivity, BTU / s / ft2 / R / ft; Re = Reynolds number; NNU = Nusselt number Reference: Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design, D. Van Nostrand Company, Inc., Princeton, New Jersey, 1960 h = sea level

2/24/2008

h = 20K ft

h = 50K ft

h = 80K ft

ELF

153

A “Thermally Thick” Surface ( e.g., Radome ) Has a Large Internal Temperature Gradient [ T ( z, t ) - Tinitial ] / [ Tr – Tinitial ] = erfc { z / [ 2 ( α t )1/2 ]} – e( h z / k ) + h2 α t / k2 erfc { z / [ 2 ( α t )1/2 ] + h ( α t )1/2 / k } [ T ( 0, t ) - Tinitial ] / [ Tr – Tinitial ] = 1 - eh2 α t / k2 erfc [ h ( α t )1/2 / k ] Applicable for thermally thick surface: z / [ 2 ( α t )1/2 ] > 1

Example: Rocket Baseline Radome

.1 =0

Mach 2, 20k ft alt ( T0 = 447 R ), Turbulent boundary layer, x = 19.2 in = 1.6 ft, t = 10 s, Tr = 769 R, Tinitial = 460 R

/k1 0

k=1

00

⇒ h = 0.0268 BTU / s / ft ⇒ ( h / k )( α t )1/2 = 0.491 Test: z / [ 2 ( α t )1/2 ] = 0.0208 / { 2 [ 1.499x10-5 ( 10 )]1/2 } = 0.849 < 1 ⇒ not quite thermally thick Inner wall ⇒ h z / k = 0.935

hz/

hz

0.5

α = 1.499 x 10-5 ft2 / s

/k

k=

1 hz

hz

/k

=0

X = 1.6 ft z = 0.25 in = 0.0208 ft, k = 5.96 x 10-4 BTU / s / ft / R,

hz/

[ T ( z, t ) - ( T )initial ] / [( T )r – ( T )initial ]

1

[ T ( 0.0208, 10 ) - Tinitial ] / [ Tr – Tinitial ] = 0.0608 T ( 0.0208, 10 ) = 479 R ( Note: Tinner ≈ Tinitial ) Surface ⇒ h z / k = 0

0 0.1

1

( h / k )( α t )1/2

10

100

[ T ( 0, 10 ) - Tinitial ] / [ Tr – Tinitial ] = 0.372 T ( 0, 10 ) = 575 R

Note: T ( z,t ) ∼ ( T )initial; 1-D heat transfer; Radiation neglected; Turbulent boundary layer; Tr = Recovery temperature, R; h = Heat transfer coefficient, BTU / ft2 / s / R; k = Thermal conductivity of material, BTU / s / ft2 / R / ft; α = Diffusivity of material, ft2 / s; zmax = Thickness of material, ft; erfc = Complementary error function Reference: Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design, D. Van Nostrand Company, Inc., Princeton, New Jersey, 1960

2/24/2008

ELF

154

Internal Insulation Temperature Can Be Predicted Assuming Constant Flux Conduction [ T ( z, t ) – Tinitial ] / [ T ( 0, t ) – Tinitial ] = e- z2 / ( 4 α

t)–

Applicable for thermally thick surface: z / [ 2 ( α t )1/2 ] > 1 1

( π / α t )1 / 2 ( z / 2 ) erfc { z / [ 2 ( α t )1/2 ]} Example for Rocket Baseline Airframe Insulation:

[ T ( z, t ) – Tinitial ] / [ T ( 0, t ) – Tinitial ]

0.10 in Min-K Internal Insulation behind 0.16 in aluminum Skin Aluminum 0.16 in X = 1.6 ft 0.10 in Min-K z Assume M = 2, 20k ft alt, x = 1.6 ft, Tinitial = 460 R, t = 10 s, zMin-K = 0.10 in = 0.00833 ft, αMin-K = 0.00000106 ft2 / s, k = 5.96 x 10-4 BTU / s / ft, h = 0.0268 BTU / s / ft

0.5

Test: z / [ 2 ( α t )1/2 ] = 0.00833 / {2 [ 0.00000106 ( 10 )]1/2} = 1.279 > 1 ⇒ thermally thick ( α t )1/2 / z = [ 0.00000106 ( 10 ) ]1/2 / 0.00833 = 0.3907 [ TMin-K ( 0.0217, 10 ) – 460 ] / [ TMin-K ( 0, 10 ) – 460 ] = 0.0359 Assume ( Tinner )aluminum = ( Touter )Min-K From prior example, ( Tinner )aluminum = 569 R at = 10 s Then, ( Touter )Min-K = 569 R at t = 10 s

0 0.1

1

( α t )1/2 / z

10

100

Compute, ( Tinner )Min-K = 460 + ( 569 – 460 ) 0.0338 = 460 + 4 = 464 R

Note: 1-D conduction heat transfer, Radiation neglected, Constant heat flux input, T ( z,t ) = Inner temperature of insulation at time t, Tinitial = Initial temperature, T ( 0, t ) = Outer temperature of insulation at time t, α = Diffusivity of insulation material, ft2 / s; zmax = Thickness of insulation material, ft; erfc = Complementary error function Reference: Carslaw, H. S. and Jaeger, J. C., Conduction of Heat in Solids, Clarendon Press, 1989 2/24/2008

ELF

155

A Sharp Nose Tip / Leading Edge Has High Aerodynamic Heating hr, Stagnation Heat Transfer Coeff for Rocket Baseline at h = 20k ft, BTU / ft2 / s / R

hr = NNUr kr / dNoseTip 0.6

Example for Rocket Baseline Nose Tip:

NNUr = 1.321 RedNoseTip0.5 Pr0.4

Assume M = 2, 20k ft alt, stagnation ( Tr = 805 R ) for a sharp nose tip ( e.g., 1% blunt )

0.5 0.4

dNoseTip / dRef = 0.01 ⇒ dNoseTip = 0.01 ( 8 in ) = 0.08 in = 0.00557 ft

0.3

RedNoseTip = ρ0 V0 dNoseTip / μr = 3.39 x 104

0.2

NNUr = 223 hr = 0.1745 BTU / ft2 / s / R

0.1

Outer surface temperature after 10 s heating in sustain flight ( M = const, Tr = const ):

0

2

0

1

2

3

4

5

M, Mach Number 1% Bluntness 5% Bluntness

2% Bluntness 10% Bluntness

6

2

[ T ( 0, t ) - Tinitial ] / [ Tr – Tinitial ] = 1 – e h αt / k erfc { h ( α t )1/2 / k }

[ T ( 0, 10 ) - 460 ] / [ 805 – 460 ] = 1 – e [( 0.1745 ) ( 1.499 x 10-5 ) ( 10 ) / ( 5.96 x 10-4 )2 ] erfc { ( 0.1745 ) [ 1.499 x 10-5 ( 10 )]1/2 / ( 5.96 x 10-4 )]} = 0.845

2

T ( 0, 10 ) = 460 + 345 ( 0.845 ) = 752 R

Note: 1-D conduction heat transfer; Laminar boundary layer; Stagnation heating; Radiation neglected; hr = Convection heat transfer coefficient for stagnation recovery, BTU / s / ft2 / R; NNUr = Nusselt number for stagnation recovery; kr = Air thermal conductivity at stagnation recovery ( total ) temperature, BTU / s / ft / R; dNoseTip = Nose tip diameter, ft; RedNoseTip = Reynolds number based on nose tip diameter, Pr = Prandtl number Reference: Allen, J. and Eggers, A. J., “A Study of the Motion and Aerodynamic Heating of Ballistic Missiles Entering the Earth’s Atmosphere at High Supersonic Speeds”, NACA Report 1381, April 1953. 2/24/2008

ELF

156

Tactical Missile Radiation Heat Loss Is Usually Small Compared to Convective Heat Input QRad = 4.76 x 10-13 ε T4

100

QRad in BTU / ft2 / s, T in R Example: Ramjet Baseline Assume:

10 Radiation Heat Flux at Equilibrium Temperature, BTU / ft2 / s

•Titanium skin with emissivity ε = 0.3 •Long duration ( equilibrium ) heating at Mach 4

1

•h = 80k ft, T0 = 398 R •Turbulent boundary layer ( r = 0.9 ) ⇒ T = Tr = T0 ( 1 + 0.2 r M2 ) = 1513 R

0.1

Calculate: QRad = 4.76 x 10-13 ( 0.3 ) ( 1513 )4 = 0.748 BTU / ft2 / s

0.01 0

1

2

3

4

5

6

Cruise Mach Number Emissivity = 0.1 2/24/2008

Emissivity = 1 ELF

157

Design Concerns for Localized Aerodynamic Heating and Thermal Stress Flare / Wedge Corner Flow Body Joints Hot missile shell Cold frames or bulkheads Causes premature buckling

Shock wave – boundary layer interaction Separated Flow High heating at reattachment

Leading Edges

IR Domes / RF Radomes

Hot stagnation temperature on leading edge Small radius prevents use of external insulation Cold heat sink material as chord increases in thickness leads to leading edge warp Shock wave interaction with adjacent body structure

Large temp gradients due to low thermal conduction Thermal stress at attachment Low tensile strength Dome fails in tension

Note: σTS = Thermal stress from restraint in compression or tension = α E ΔT α = coefficient of thermal expansion, E = modulus of elasticity, ΔT = T2 – T1 = temperature difference. Example: Thermal Stress for Rocket Baseline Pyroceram Dome, α = 3 x 10-6, E = 13.3 x 106 psi Assume M = 2, h = 20k ft alt, t = 10 s. Based on prior figure, ΔT = TOuterWall – TInnerWall = 102 R Then σTS = 3 x 10-6 ( 13.3 x 106 ) ( 102 ) = 4,070 psi 2/24/2008

ELF

158

Examples of Aerodynamic Hot Spots Nose Tip

Leading Edge Flare 2/24/2008

ELF

159

WBS,Body Structure Weight, lb

Tactical Missile Body Structure Weight Is about 22% of the Launch Weight WBS / WL ≈ 0.22

1000

100 Example for 500 lb missile WL = 500 lb WBS = 0.22 ( 500 ) = 110 lb

10 100

1000

10000

WL, Launch Weight, lb

Hellfire ( 0.22 ) Sidewinder ( 0.23 ) Sparrow ( 0.18 ) Phoenix ( 0.19 ) Harpoon ( 0.29 ) SM 2 ( 0.20 ) SRAM ( 0.21 ) ASALM ( 0.13 ) SETE ( 0.267 ) Tomahawk ( 0.24 ) TALOS ( 0.28 )

Note: WBS includes all load carrying body structure. If motor case, engine, or warhead case carry external loads then they are included in WBS. WBS does not include tail, wing, or other surface weight. 2/24/2008

ELF

160

Body Structure Thickness Is Based on Considering Many Design Conditions Structure Design Conditions That May Drive Airframe Thickness Manufacturing Transportation Carriage Launch Fly-out Maneuvering

Contributors to Required Thickness for Cylindrical Body Structure Minimum Gage for Manufacturing: t = 0.7 d [( pext / E ) l / d ]0.4. t ≈ 0.06 in if pext ≈ 10 psi Localized Buckling in Bending: t = 2.9 r σ / E Localized Buckling in Axial Compression: t = 4.0 r σ / E Thrust Force: t = T / ( 2 π σ r ) Bending Moment: t = M / ( π σ r2 ) Internal Pressure: t = p r / σ

High Risk ( 1 ), Moderate Risk ( 2 ), and Low Risk ( 3 ) Estimates of Required Thickness 1. 2. 3. 2/24/2008

t = FOS x Max ( tMinGage , tBuckling,Bending , tBuckling,AxialCompression , tAxialLoad , tBending , tInternalPressure ) t = FOS x ( t2MinGage + t2Buckling,Bending + t2Buckling,AxialCompression + t2AxialLoad + t2Bending + t2InternalPressure )1/2 t = FOS x ( tMinGage + tBuckling,Bending + tBuckling,AxialCompression + tAxialLoad + tBending + tInternalPressure ) ELF

161

Localized Buckling May Be A Concern for Thin Wall Structure σBuckling,Bending / E ≈ 0.35 ( t / r )

Nondimensional Buckling Stress

σBuckling,AaxialCcompression / E ≈ 0.25 ( t / r )

t

r

Bending Axial Compression Note: Thin wall cylinder with local buckling

0.1

σBuckling / E = Nondimensional buckling stress σBucklingBending = Buckling stress in bending σBucklingAxialCompression = Buckling stress in axial compression

0.01

E = Young’s modulus of elasticity t = Airframe thickness

0.001

r = Airframe radius Min thickness for fab and handling ≈ 0.06 in

0.0001 0.001

Example for Rocket Baseline in Bending:

0.01

0.1

t / r, thickness / radius

4130 steel motor case, E = 29.5 x 106 psi σyield = 170,000 psi t = 0.074 in, r = 4 in t / r = 0.0185

Note: Actual buckling stress can vary +/- 50%, depending upon typical imperfections in geometry and the loading. 2/24/2008

ELF

σBuckling,Bending / E ≈ 0.35 ( 0.0185 ) = 0.006475 σbuckling,Bending ≈ 191,000 psi σbuckling,Bending ~ σyield 162

Process for Captive and Free Flight Loads Calculation Captive Flight Free Flight

Max Aircraft Maneuver Per MIL-A-8591

Maneuver Per Design Requirements

Carriage Load

Weight load of bulkhead section Air Load

Weight load of bulkhead section

Air Load Obtained By Wind Tunnel

2/24/2008

Air Load

Note: MIL-A-8591 Procedure A assumes max air loads combine with max g forces regardless of angle of attack. Example of αmax Calculated by MIL-A-8591 Using Procedure A for F-18 Aircraft Carriage: αmax = 1.5 nz,max Wmax / ( CLα q SRef )aircraft αmax = 1.5 ( 5 ) ( 49200 ) / [ 0.05 ( 1481 ) ( 400 )] = 12.5 deg

ELF

163

Maximum Bending Moment Depends Upon Load Distribution Example for Rocket Baseline: c = 4, ejection load l = 144 in

MB = N l / c C = 8 for uniform loading w = load per unit length

⇒ N = 10,000 lb ( 20 g ) ⇒ MB = 360,000 in-lb Total Load 100,000 N

50,000 40,000 30,000 20,000 10,000

Length l Max Bending Moment MB

Coefficient C 8 7.8 6 4

100

2,000 3,000 4,000 5,000

2,000

10,000

1,000

20,000 30,000 40,000 50,000

500 400 300

10

100

4 2/24/2008

0 l C = 4 for load at center ( e.g., ejection load ) N = Normal Force l/2

100,000 200,000 300,000 400,000 500,000

200

1

3

100

1,000,000

200

2,000,000

2

5

l

C = 6 for linear loading to center w

1,000

5,000 4,000 3,000

C = 7.8 for linear loading w 0

200 300 400 500

1

l = length

0

ELF

0 l C = 1 for load at end ( e.g., control force ) N = Normal Force l 0

l

164

Bending Moment May Drive Body Structure Weight t

t r MB

t = MB ( FOS ) / [ π r2 σMax ]

A=2πrt Iz = IY = π r3 t

Note / Assumptions: Thin cylinder Circular cross section

Example for Rocket Baseline: • Body has circular cross section • 2219-T81 aluminum skin ( σult = 65,000 psi ) • r = 4 in • Ejection load = 10,000 lb ( 20 g ) • MB = 360,000 in ⋅ lb • FOS = 1.5 • t = 360,000 ( 1.5 ) / [ π ( 4 )2 ( 65,000 )] = 0.16 in

2/24/2008

ELF

Solid skin Longitudinal strength Axial load stress and thermal stress assumed small compared to bending moment stress σ = MB r / IZ = MB r / (π r3 t ) = MB / (π r2 t )

165

Tactical Missile Propellant Weight Is about 72% of Rocket Motor Weight WP / WM ≈ 0.72

WP, Propellant Weight, lb

10000

1000

100

Example for Rocket Baseline WM = 209 lb WP = 0.72 ( 209 ) = 150 lb

Increased propellant fraction if: High volumetric loading

10 10

100

1000

WM, Total Motor Weight, lb Note: WM includes propellant, motor case, nozzle, and insulation. 2/24/2008

Hellfire ( 0.69 ) Sidewinder ( 0.61 ) Sparrow ( 0.64 ) Phoenix ( 0.83 ) ASALM ( 0.86 ) SM-2 ( 0.76 ) SRAM ( 0.71 ) TALOS ( 0.66 )

ELF

10000

Composite case Low chamber pressure Low flight loads Short burn time 166

Motor Case Weight Is Usually Driven By Stress from Internal Pressure Assume motor case is axisymmetric, with a front ellipsoid dome and an aft cylinder body Motor Case Cylinder Hoop Stress Case Dome

Nozzle

Case Cylinder

π/2

p

p b

Motor Dome Ellipsoid Longitudinal Stress

σt t = - 0∫ p r sinθ dθ ( σt )Hoop Stress = p r / t

( σt )Longitudinal Stress = [ 2 + ( a / b )2 ] p ( a b )1/2 / ( 6 t ) 2a

If a = b ( hemi dome of radius r ), then ( σt )Longitudinal Stress = p r / ( 2 t )

With metals – the material also reacts body bending In composite motor designs, extra ( longitudinal ) fibers must usually be added to accommodate body bending 2/24/2008

ELF

167

A Composite Motor Case Is Usually Lighter Weight Calculate Maximum Effective Operating Pressure ( Burst Pressure ) pburst = pBoost, Room Temp x eπk Δ T x ( Design Margin for Ignition Spikes, Welds, Other Design Uncertainty ) Assume Rocket Motor Baseline: diameter = 8 in., length = 55 in, ellipsoid dome a / b = 2, pBoost,RoomTemp = 1769 psi, πk = ( Δp / ΔT ) / pc = 0.14% / °F Assume Hot day T = 160° F ⇒ eπk ΔT = e0.0014 ( 160 - 70 ) = 1.134. Uncertainty factor is 1.134, 1σ Assume a 3σ uncertainty design margin is provided by, pburst ≈ 1769 x ( 1.134 )3 = 2,582 psi

Assume Ultimate Factor of Safety FOS = 1.5 Rocket Baseline Steel Case ( σt )ult = 190,000 psi tHoop = ( FOS ) x pburst x r / σt = 1.5 x 2582 x 4.0 / 190,000 = 0.082 in tDome = ( FOS ) x pburst x ( a b )1/2 x [ 2 + ( a / b )2 ] / ( 6 σt ) = 1.5 x 2582 x [ 4 x 2 ]1/2 x [ 2 + ( 2 )2 ] / [ 6 x 190,000 ] = 0.058 in Weight = WCylinder + WDome = ρ π d tHoop l + ρ ( 2 π a b ) tDome = 30.8 + 0.8 = 31.6 lb for steel case

Try Graphite Fiber at σt = 450,000 psi Ultimate, Assume 60% Fiber / 40% Epoxy Composite tHoop = 1.5 x 2582 x 4.0 / [ 450,000 ( 0.60 )] = 0.057 in radial fibers for internal pressure load tDome = 0.041 in, for internal pressure load Weight = 11.1 lb for composite case ( w/o insulation, attachment, aft dome, and body bending fiber ) Must also add about 0.015 in of either longitudinal fibers or helical wind to counteract body bending load

2/24/2008

ELF

168

WSurface σmax1/2 / ( ρ S Nmax1/2 ), Non-dimensional Weight

A Low Aspect Ratio Delta Wing Allows Lighter Weight Structure 3

WSurface σmax1/2 / [ ρ S Nmax1/2 ] = [ A ( 1 + 2 λ )]1/2

Note:

WSurface = ρ S tmac

Surface is 2 panels ( Cruciform wing has 4 panels ) WSurface = Surface weight sized by bending moment

troot = [ FOS Nmax A ( 1 + 2 λ ) / σmax,]1/2

ρ = Density

Assumption: Uniform loading

σmax = Maximum allowable ( ultimate ) stress tmac = Thickness of mean aero chord cmac

2

troot = Thickness of root chord croot Nmax = Maximum load A = Aspect ratio λ = Taper ratio

1

Example for Rocket Baseline Wing ( 2219-T81 Aluminum ): A = 2.82, λ = 0.175, cr = 19.4 in, σmax = σult = 65k psi Assume M = 2, h = 20k ft, α + δ = 22 deg From prior example, Nmax = 7525 lb

0 0

1

Calculate t = [ 1.5 ( 7525 ) ( 2.82 ) [ 1 + 2 ( 0.175 ) / 3 65000 ]1/2 =root0.813 in

2 A, Aspect Ratio

Taper Ratio = 0

2/24/2008

Taper ratio = 0.5

troot / croot = 0.813 / 19.4 = 0.0419 = tmac / cmac

Taper Ratio = 1

ELF

tmac = 0.0419 ( 13.3 ) = 0.557 in Wwing σmax1/2 / [ ρ S Nmax1/2 ] = [ A ( 1 + 2 λ )]1/2.= 1.95 Wwing = 20.6 lb for 1 wing ( 2 panels )

169

Dome Material Is Driven by the Type of Seeker and Flight Environment Seeker Dome Material RF-IR Seeker Zinc Sulfide ( ZnS ) Zinc Selenide ( ZnSe ) Sapphire / Spinel Quartz / Fused Silica ( SiO2 ) Silicon Nitride ( Si3N4 ) Diamond ( C ) RF Seeker Pyroceram Polyimide IR Seeker Mag. Fluoride ( MgF2 ) Alon ( Al23O27N5 ) Germanium ( Ge )

2/24/2008

Density ( g / cm3 )

Dielectric Constant

MWIR / LWIR Bandpass

Transverse Strength ( 103 psi )

Thermal Expansion ( 10-6 / ο F )

Max ShortErosion, Knoop ( kg Duration 2 / mm ) Temp ( ο F )

4.05

8.4

18

4

350

700

5.16

9.0

8

4

150

600

3.68

8.5

28

3

1650

1800

2.20

3.7

8

0.3

600

2000

3.18

6.1

90

2

2200

2700

3.52

5.6

400

1

8800

3500

2.55 1.54

5.8 3.2

25 17

3 40

700 70

2200 400

3.18

5.5

7

6

420

1000

3.67

9.3

44

3

1900

1800

5.33

- 16.2

15

4

780

200

Superior

-

-

Above Average

ELF

Average

Below Average

-

Poor 170

topt / ( N λ0 ), Non-dimensional Optimum Thickness

Radome Weight May Be Driven by Optimum Thickness Required for Efficient Transmission 1

WOptTrans = ρ Swet tOptTrans

Note:

tOptTrans = 0.5 n λ0 / ( ε - sin2 θi )1/2

WOptTrans = Weight at Optimum Transmission

θ

δ

ρ = Density

90 deg

θi

Swet = Surface wetted area tOptTrans = Optimum thickness for 100% transmission

d

n = Integer ( 1, 2, … )

l

λ0 = Wavelength in air ε = Dielectric constant θi = Radar signal incidence angle = 90 deg - δ - θ θ = Surface local angle δ = Seeker look angle Example for Rocket Baseline Pyroceram Radome: ε = 5.8, ρ = 0.092 lb / in3, λ0 = 1.1 in, n = 1, tangent ogive, l = 19.2 in, d = 8 in, Swet = 326 in2 10 δ = 0 deg ⇒ ( θI )avg ≈ 90 – 0 - 11.8 = 78.2 deg

0.1 1

ε, Dielectric Constant Incidence Angle = 0 deg Incidence Angle = 80 deg

Incidence Angle = 40 deg

tOptYtans = 0.5 ( 1 ) ( 1.1 ) / ( 5.8 – 0.96 )1/2 = 0.25 in WOptTrans = 0.092 ( 326 ) ( 0.25 ) = 7.5 lb

2/24/2008

ELF

171

Missile Electrical Power Supply Alternatives W = WE E + WP P Measure of Merit

Power Supply Generator

Lithium Battery

Thermal Battery

Storage Life Cost WE, Weight / Energy ( kg / kW-s )

0.0007

0.0012

0.0125

WP, Weight / Power ( kg / kW )

1.4

1.5

0.3

Voltage Stability Superior

Above Average

Average

Below Average

Example for Thermal battery: If E = 900 kW–s, P = 3 kW ⇒ W = WEE + WPP = 0.0125 ( 900 ) + 0.3 ( 3 ) = 12.2 kg Note: Generator provides highest energy with light weight for long time of flight ( e.g., cruise missile ). Lithium battery provides nearly constant voltage suitable for electronics. Relatively high energy with light weight. Thermal battery provides highest power with light weight ( may be required for actuators ). 2/24/2008

ELF

172

Electromechanical Actuators Are Light Weight and Reliable W = WT TS Measure of Merit

EM

Cold Gas Pneumatic

Hydraulic

WT, Weight / Stall Torque ( lb / in-lb )

0.0025

0.0050

0.0034

Rate ( deg / s )

Up to 800

Up to 600

Up to 1000

Bandwidth ( Hz )

Up to 40

Up to 20

Up to 60

Reliability Cost Superior

Above Average

Average

Note:

Below Average

Schematic of Cold Gas Pneumatic Actuation

•Actuation system weight based on four actuators. •Cold gas pneumatic actuation weight includes actuators, gas bottle, valves, regulator, and supply lines. •Hydraulic actuation weight includes actuators, gas generator or gas bottle, hydraulic reservoir, valves, and supply lines. •Stall torque ≈ 1.5 maximum hinge moment of single panel. Example weight for rocket baseline hydraulic actuation at Mach 2, 20k ft alt, α = 9 deg, with max control deflection of wing ( δ = 13 deg ) ⇒ Hinge moment of one panel = 11,500 in-lb. TS = 1.5 ( 11500 ) = 17,250 in-lb ⇒ W = WTTS = 0.0034 ( 17250 ) = 59 lb 2/24/2008

ELF

173

Examples of Electromechanical Actuator Packaging Canard ( Stinger ) ……………

Tail ( AMRAAM ) …………………………………………………………………

Jet Vane / Tail ( Javelin ) ……

Movable Nozzle ( THAAD ) ……………………………………………………………

2/24/2008

ELF

174

Summary of Weight Conceptual Design Weight Prediction Methods and Weight Considerations Missile system weight, cg, moment of inertia Factors of safety Aerodynamic heating Structure Dome Propulsion Insulation Power supply Actuator

Manufacturing Processes for Low Parts Count, Low Cost Precision castings Vacuum assisted RTM Pultrusion / Extrusion Filament winding 2/24/2008

ELF

175

Summary of Weight ( cont ) Design Considerations Airframe materials Insulation materials Seeker dome materials Thermal stress Aerodynamic heating

Technologies MEMS Composites Titanium alloys High density insulation High energy and power density power supply High torque density actuators

Discussion / Questions? Classroom Exercise ( Appendix A ) 2/24/2008

ELF

176

Weight Problems 1. 2. 3. 4. 5. 6. 7. 8. 9. 2/24/2008

Propulsion system and structure weight are driven by f_____ o_ s_____ requirements. For a ballistic range greater than about 200 nautical miles, a t__ s____ missile is lighter weight. Tactical missile weight is proportional to v_____. Subsystem d______ for tactical missiles is about 0.05 lb / in3 Modeling weight, balance, and moment-of-inertia is based on a build-up of s_________. Missile structure factor of safety for free flight is usually about 1.25 for ultimate loads and about 1.10 for y____ loads. Manufacturing processes that can allow low parts count include vacuum assisted resin transfer molding of composites and c______ of metals. Low cost airframe materials are usually based on aluminum and steel while light weight airframe materials are usually based c________ materials. Graphite fiber has high strength and high m______ o_ e_________. ELF

177

Weight Problems ( cont ) 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 2/24/2008

The recovery factors of stagnation, turbulent boundary layer, and laminar boundary layer are 1.0, 0.9, and ___ respectively. The most popular types of insulation for temperatures greater than 4,000 R are charring insulators based on p_______ composites. Tactical missiles experience transient heating, and with increasing time the temperature approaches the r_______ temperature. The inner wall temperature is nearly the same as the surface temperature for a t________ t___ structure. A thermally thick surface is a good i________. A low conductivity structure is susceptible to thermal s_____. The minimum gauge thickness is often set by the m____________ process. A very thin wall structure is susceptible to localized b_______. Ejection loads and flight control loads often result in large b______ moment. An approach to increase the tactical missile propellant / motor weight fraction over the typical value of 72% would be c________ motor case. ELF

178

Weight Problems ( cont ) 20. 21. 22. 23. 24.

2/24/2008

The required rocket motor case thickness is often driven by the combustion chamber p_______. A low aspect ratio delta wing has reduced w_____. For low speed missiles, a popular infrared dome material is z___ s______. A thermal battery provides high p____. The most popular type of actuator for tactical missiles is an e________________ actuator.

ELF

179

Outline Introduction / Key Drivers in the Design Process Aerodynamic Considerations in Tactical Missile Design Propulsion Considerations in Tactical Missile Design Weight Considerations in Tactical Missile Design Flight Performance Considerations in Tactical Missile Design Measures of Merit and Launch Platform Integration Sizing Examples Development Process Summary and Lessons Learned References and Communication Appendices ( Homework Problems / Classroom Exercises, Example of Request for Proposal, Nomenclature, Acronyms, Conversion Factors, Syllabus ) 2/24/2008

ELF

180

Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics Propulsion Weight

Resize / Alt Config / Subsystems / Tech

Trajectory Meet Performance?

No

Yes Measures of Merit and Constraints

No

Yes 2/24/2008

ELF

181

Flight Envelope Should Have Large Max Range, Small Min Range, and Large Off Boresight

Off Boresight Flyout Envelope / Range •Max •Min

Forward Flyout Envelope / Range •Max •Min

Examples of Max / Min Range Limitations: Fire Control System Range and Off Boresight Seeker Range, Gimbal Angle, and Tracking Rate Maneuver Capability Time of Flight Closing Velocity 2/24/2008

ELF

182

Conceptual Design Modeling Versus Preliminary Design Modeling Conceptual Design Modeling 1 DOF [ Axial force ( CDO ), thrust, weight ] 2 DOF [ Normal force ( CN ), axial force, thrust, weight ] 3 DOF point mass [ 3 aero forces ( normal, axial, side ), thrust, weight ] 3 DOF pitching [ 2 aero forces ( normal, axial ), 1 aero moment ( pitching ), thrust, weight ] 4 DOF [ 2 aero forces ( normal, axial ), 2 aero moments ( pitching, rolling ), thrust, weight ]

CDO CN CA CN CA CN

2/24/2008

ELF

Cm

CA CN

Cm

Cl

CN

Cm

Cl

CA

Preliminary Design Modeling 6 DOF [ 3 aero forces ( normal, axial, side ), 3 aero moments ( pitching, rolling, yawing ), thrust, weight ]

CY

CA

Cn

CY 183

1-DOF Coast Equation May Have Good Accuracy Near Zero Angle of Attack 2.0 1.5 •

•

( V )2-DOF / ( V )1-DOF, Predicted Deceleration 1.0 Comparison for Rocket Baseline 0.5 0 Note: – – – – – 2/24/2008

0

2 4 6 8 αTrim, Trim Angle of Attack, Deg

10

. ( V. )2-DOF = Two-degrees-of-freedom deceleration ( V )1-DOF = One-degree-of-freedom deceleration Rocket baseline during coast Mach 2, h = 20,000 ft αTrim ≈ 0.3 deg for 1-g flyout ELF

184

3-DOF Simplified Equations of Motion Show Drivers for Configuration Sizing + Normal Force

+ Thrust

+ Moment

θ

α Cm , Iy small ( W small ), q large α Large / Fast Heading Change ⇒ CN large, W small, q large High Speed / Long Range ⇒ Total Impulse large, CA small, q small

Note: Based on aerodynamic control 2/24/2008

ELF

185

For Long Range Cruise, Maximize V Isp, L / D, and Weight Fraction of Fuel / Propellant R = ( V Isp ) ( L / D ) ln [ WBC / ( WBC - WP )] , Breguet Range Equation

R, Cruise Range, ft

1.00E+08

ith Wing w t e j o b r onic Tu s b rframe i u A S l c i a r c t i e Typ xisymm A h t i w t Ramje Typical Airframe c i r t e m th Axisym i w t e k c o Typical R

1.00E+07

1.00E+06

Example: Ramjet Baseline at Mach 3 / 60k ft alt R = 2901 ( 1040 ) ( 3.15 ) ln [ 1739 / ( 1739 - 476 )] = ( 9,503,676 ) ln [ 1 / ( 1 - 0.2737 )] = 3,039,469 ft = 500 nm

1.00E+05 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

WP / WBC, Propellant or Fuel Weight / Weight at Begin of Cruise ( V ISP )( L / D ) = 2,000,000 ft ( V ISP )( L / D ) = 25,000,000 ft

( V ISP )( L / D ) = 10,000,000 ft

Note: R = cruise range, V = cruise velocity, ISP = specific impulse, L = lift, D = drag, WBC = weight at begin of cruise, WP = weight of propellant or fuel 2/24/2008

ELF

186

Efficient Steady Flight Is Enhanced by High L / D and Light Weight Steady Level Flight L D

T=D L=W T

Steady Climb T–D L γC

D

W T=W/(L/D) Note:

D–T

T

V∞

L γD

D γC

W SIN γc = ( T – D ) / W = Vc / V∞ Vc = ( T – D ) V∞ / W RC = Δh / tan γC = Δh ( L / D )

• Small Angle of Attack • Equilibrium Flight • VC = Velocity of Climb • VD = Velocity of Descent • γC = Flight Path Angle During Climb • γD = Flight Path Angle During Descent • V∞ = Total Velocity • Δh = Incremental Altitude • RC = Horizontal Range in Steady Climb • RD = Horizontal Range in Steady Dive ( Glide )

2/24/2008

Steady Descent ( Glide )

VC

T

W VD

γD

V∞

SIN γD = ( D – T ) / W = VD / V∞ V D = ( D – T ) V ∞/ W RD = Δh / tan γD = Δh ( L / D )

Reference: Chin, S.S., “Missile Configuration Design,” McGraw Hill Book Company, New York, 1961 ELF

187

Flight Trajectory Lofting / Shaping Provides Extended Range Apogee or Cruise

Climb

Altitude

Glide Rapid Pitch Up Line-Of-Sight Trajectory RMAX

Range

RMAX

Lofted Trajectory Design Guidelines for Horizontal Launch:

– High thrust-to-weight ≈ 10 for safe separation – Rapid pitch up minimizes time / propellant to reach efficient altitude – Climb at α ≈ 0 deg with thrust-to-weight T / W ≈ 2 and q ≈ 700 psf to minimize drag / propellant – Apogee at q ≈ 700 psf, followed by either ( L / D )MAX cruise or ( L / D )MAX glide

2/24/2008

ELF

188

Small Turn Radius Using Aero Control Requires High Angle of Attack and Low Altitude Flight .

RT = V / γ ≈ 2 W / ( gc CN SRef ρ ) Assumption: Horizontal Turn RT, Example Instantaneous Turn Radius, ft

1000000

Note for Example Figure: W = Weight = 2,000 lb a / b = 1 ( circular cross section ), No wings CN = sin 2 α cos ( α / 2 ) + 2 ( l / d ) sin2 α l / d = Length / Diameter = 10 SRef = 2 ft2 CDO = 0.2 ( L / D )Max = 2.5 q( L / D ) ≈ 700 psf Max α( L / D ) = 15 deg Max T( L / D ) = 740 lb

100000

10000

Max

Example: Δ α = 10 deg CN = 0.94

1000 0

5

10

15

Delta Alpha, Deg h = sea level h = 60k ft 2/24/2008

h = 20k ft h = 80k ft

20 h = 40k ft ( ρ = 0.000585 slug / ft3 )

RT = 2 ( 2,000 ) / [( 32.2 ) ( 0.94 ) ( 2 ) ( 0.000585 )] = 112,000 ft h = 40k ft

ELF

Note: Require ( RT )Missile ≤ ( RT )Target, for small miss distance 189

High Turn Rate Using Aero Control Requires High Angle of Attack and High Velocity .

γ = gc CN ρ V SRef / ( 2 W ), rad / s Assumption: Horizontal Turn

n= g 100

Example Gamma Dot, Turn Rate, deg / s

20

15

10

5

0 0

1000

2000

3000

Velocity, ft / s Alpha = 15 deg Alpha = 90 deg 2/24/2008

Alpha = 30 deg

ELF

Example for Lifting Body at Altitude h = 20,000 ft: Assume: • W = Weight = 2,000 lb • a / b = 1 ( circular cross section ) • No wings • Negligible tail lift • Neutral static stability CN = sin 2 α cos ( α / 2 ) + 2 ( l / d ) sin2 α • SRef = 2 ft2 • l / d = Length / Diameter = 10 • α = 15 deg • V = 2000 ft / s Then: • N = Normal Force = CN q SRef CN = sin [ 2 ( 15 )] cos ( 15 / 2 ) + 2 ( 10 ) sin2 ( 15 ) = 0.50 + 1.34 = 1.835 q = Dynamic Pressure = 0.5 ρ V2 = 0.5 ( 0.001267 ) ( 2000 )2 = 2534 psf N = 1.835 ( 2534 ) ( 2 ) = 9,300 lb N / W = 9300 / 2000 = 4.65 g . γ = 32.2 ( 1.835 ) ( 0..001267 ) ( 2000 ) ( 2 ) / [ 2 ( 2000 )] = 0.0749 rad / s = 4.29 deg / s 190

For Long Range Coast, Maximize Initial Velocity and Altitude and Minimize Drag Coefficient V / Vi = { 1 – [( gc sin γ ) / Vi ] t } / { 1 + {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t } {[ gc ρAVG SRef ( CD0 )AVG ] / ( 2 W )} R = ln { 1 – [ gc2 ρAVG SRef ( CD0 )AVG / ( 2 W )] [ sin γ ] t2 + {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t }

1

V / Vi @ γ = 0 deg

Note: Based on 1 DOF coast

0.8

dV / dt = - gc CD0 SRef q / W – gc sin γ Assumptions:

0.6

• γ = constant

0.4

• α ≈ 0 deg

0.2

{[ gc ρAVG SRef (CD0 )AVG ] / ( 2 W )} R

• D > W sin γ

@ γ = 0 deg

V = velocity during coast

0

Vi = initial velocity ( begin coast )

0

0.5

1

1.5

[( gc ρ SRef CD Vi ) / ( 2W )] t, Non-dimensional Coast Time 0

2 R = coast range Vx = V cos γ, Vy = V sin γ Rx = R cos γ, Ry = R sin γ

Example for Rocket Baseline:

•W = WBO = 367 lb, SRef = 0.349 ft2, Vi = 2,151 ft / s, γ = 0 deg, ( CD )AVG = 0.9, h = 20,000 ft ( ρ = 0.00127 slug / ft3 ), t = 10 s 0

•[( gc ρ SRef ( CD )AVG Vi ) / ( 2 W )] t = {[ 32.2 ( 0.00127 ) ( 0.349 ) ( 0.9 ) ( 2151 )] / [ 2 ( 367 ) ]} 10 = 0.376 0

•V / Vi = 0.727 ⇒ V = 0.727 x 2151 = 1564 ft / s, {[( gc ρ SRef ( CD )AVG )] / ( 2 W )} R = 0.319 ⇒ Rcoast = 18,300 ft or 3.0 nm 0

2/24/2008

ELF

191

For Ballistic Range, Maximize Initial Velocity, Optimize Launch Angle, and Minimize Drag Vx / Vi = cos γi / { 1 + {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t } ( Vy + gc t ) / Vi = sin γi / { 1 + {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t }

1.2

{[ gc ρAVG SRef (CD0 )AVG ] / ( 2 W cos γi )} Rx

1 0.8

= ln { 1 + [ gc ( ρ )AVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t }

0.6

{[ gc ρAVG SRef (CD0 )AVG ] / ( 2 W sin γi )} ( h – hi + gc t2 / 2 ) = ln { 1 + {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W ) t }

0.4

Assumptions: Thrust = 0, α = 0 deg, D > W sin γ, flat earth

0.2 0 0

0.5

1

1.5

2

Nomenclature: V = velocity during ballistic flight, Vi = initial velocity, Rx = horizontal range, h = altitude, hi = initial altitude, Vx = horizontal velocity, Vy = vertical velocity

{[ gc ρAVG SRef ( CD )AVG Vi ] / ( 2 W )} t, Non-dimensional Time 0

Example for Rocket Baseline: •W = 367 lb, SRef = 0.349 ft2, Vi = VBO = 2,151 ft / s, γi = 0 deg, ( CD )AVG = 0.9, hi = 20,000 ft, ρAVG = 0.00182 slug / ft3, t = 35 s 0

•[ gc ρ SRef ( CD )AVG Vi / ( 2 W )] t = { 32.2 ( 0.00182 ) ( 0.349 ) ( 0.9 ) ( 2151 ) / [ 2 ( 367 ) ]} 35 = 1.821 0

•Vx / Vi = 0.354 ⇒ Vx = 762 ft / s, ( Vy + 32.2 t ) / Vi = 0.354 ⇒ Vy = - 1127 ft / s, {[ gc ρ SRef ( CD )] / ( 2 W cos γi )} Rx = 1.037 ⇒ 0 Rx = 42,900 ft or 7.06 nm, {[ gc ρAVG SRef ( CD )AVG ] / ( 2 W sin γi )} ( h – hi + 16.1 t2 ) = 1.037 ⇒ h = 0 ft

2/24/2008

0

ELF

192

High Propellant Weight, High Thrust, and Low Drag Provide High Burnout Velocity Delta V / ( g ISP ), Nondimensional Incremental Velocity

ΔV / ( gc ISP ) = - [ 1 – ( DAVG / T ) – ( WAVG sin γ / T )] ln ( 1 - Wp / Wi ) 0.7

Example for Rocket Baseline:

0.6

Assume γ = 0 deg Assume Mi = 0.8, h = 20k ft

0.5

Wi = WL = 500 lb

0.4

For boost, WP = 84.8 lb WP / WL = 0.1696

0.3

ISP = 250 s

0.2

TB = 5750 lb

0.1

Assume D = DAVG = 635 lb

0

DAVG / T = 0.110

0

0.1

0.2

0.3

0.4

0.5

Wp / Wi, Propellant Fraction DAVG / T = 0

DAVG / T = 0.5

ΔV / [( 32.2 ) ( 250 )] = - ( 1 - 0.110 ) ln ( 1 - 0.1696 ) = 0.1654 ΔV = ( 0.1654 ) ( 32.2 ) ( 250 ) = 1331 ft / s

DAVG / T = 1.0

Note: 1 DOF Equation of Motion with α ≈ 0 deg, γ = constant, Wi = initial weight, WAVG = average weight, WP = propellant weight, ISP = specific impulse, T = thrust, Mi = initial Mach number, h = altitude, DAVG = average drag, ΔV = incremental velocity, gc = gravitation constant, Vx = V cos γ, Vy = V sin γ, Rx = R cos γ, Ry = R sin γ 2/24/2008

Note: R = ( Vi + ΔV / 2 ) tB, where R = boost range, Vi = initial velocity, tB = boost time ELF

193

High Missile Velocity and Lead Are Required to Intercept High Speed Crossing Targets VM sin L = VT sin A, Proportional Guidance Trajectory

4

VM

Note: Proportional Guidance VM = Missile Velocity VT = Target Velocity A = Target Aspect L = Missile Lead Angle ≈Seeker Gimbal

3

VM / VT

L A

VT

2

A = 90° Example: 1

0

A = 45°

L = 30 deg A = 45 deg VM / VT = sin ( 45° ) / sin ( 30° ) = 1.42

0

10

20

30

40

50

L, Lead Angle, Deg 2/24/2008

ELF

194

Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics Propulsion Weight

Resize / Alt Config / Subsystems / Tech

Trajectory Meet Performance?

No

Yes Measures of Merit and Constraints

No

Yes 2/24/2008

ELF

195

Summary of Flight Performance Flight Performance Activity in Missile Design Compute range, velocity, time-to-target, off boresight Compare with requirements

Discussed in This Chapter Equations of motion Flight performance drivers Propulsion alternatives range comparison Steady level flight required thrust Steady climb and steady dive range prediction Cruise prediction Boost prediction Coast prediction Ballistic flight prediction Turn radius and turn rate prediction Target lead for proportional homing guidance 2/24/2008

ELF

196

Summary of Flight Performance ( cont ) Flight Performance Strongly Impacted by Aerodynamics Propulsion Weight

Discussion / Questions? Classroom Exercise ( Appendix A )

2/24/2008

ELF

197

Flight Performance Problems 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 2/24/2008

Flight trajectory calculation requires input from aero, propulsion, and w_____. Missile flight envelope can be characterized by the maximum effective range, minimum effective range, and o__ b________. Limitations to the missile effective range include the fire control system, seeker, time of flight, closing velocity, and m_______ capability. 1 DOF simulation requires modeling only the thrust, weight, and a____ f____. A 3 DOF simulation that models 3 aero forces is called p____ m___ simulation. A simulation that includes 3 aero forces ( normal, axial, side ), 3 aero moments ( pitch, roll, yaw ), thrust, and weight is called a _ DOF simulation.

.. The pitch angular acceleration θ is approximately equal to the second time derivative of the a____ o_ a_____. Cruise range is a function of velocity, specific impulse, L / D, and f___ fraction. If thrust is equal to drag and lift is equal to weight, the missile is in s_____ l____ flight. Turn rate is a function of normal force, weight, and v_______. ELF

198

Flight Performance Problems ( cont ) 11. 12. 13. 14. 15. 16. 17. 18.

2/24/2008

Coast range is a function of initial velocity, weight, drag, and the t___ of flight. Incremental velocity due to boost is a function of ISP, drag, and p_________ weight fraction. To intercept a high speed crossing target requires a high speed missile with a high g_____ angle seeker. An analytical model of a rocket in co-altitude, non-maneuvering flight can be developed by patching together the flight phases of boost and c____. An analytical model of a rocket in a short range, off-boresight intercept can be developed by patching the flight phases of boost and t___. An analytical model of a guided bomb in non-maneuvering flight can be developed from the flight phase of a steady d___. An analytical model of an unguided weapon can be developed from the b________ flight phase. An analytical model of a ramjet in co-altitude, non-maneuvering flight can be developed by patching the flight phases of boost and c_____. ELF

199

Outline Introduction / Key Drivers in the Design Process Aerodynamic Considerations in Tactical Missile Design Propulsion Considerations in Tactical Missile Design Weight Considerations in Tactical Missile Design Flight Performance Considerations in Tactical Missile Design Measures of Merit and Launch Platform Integration Sizing Examples Development Process Summary and Lessons Learned References and Communication Appendices ( Homework Problems / Classroom Exercises, Example of Request for Proposal, Nomenclature, Acronyms, Conversion Factors, Syllabus ) 2/24/2008

ELF

200

Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics Propulsion Weight

Resize / Alt Config / Subsystems / Tech

Trajectory Meet Performance?

No

Yes Measures of Merit and Constraints

No

Yes 2/24/2008

ELF

201

Measures of Merit and Launch Platform Integration Should Be Harmonized Launch Platform Integration / Firepower

Robustness

Lethality

Cost

Balanced Design Miss Distance

Reliability Other Survivability Considerations

2/24/2008

Carriage and Launch Observables

ELF

202

Tactical Missiles Must Be Robust Tactical Missiles Must Have Robust Capability to Handle

Robustness Launch Platform Integration / Firepower

Robustness

Cost

Lethality

Reliability

Miss Distance

Other Survivability Considerations

Carriage and Launch Observables

Adverse Weather Clutter Local Climate Flight Environment Variation Uncertainty Countermeasures EMI / EMP

This Section Provides Examples of Requirements for Robustness 2/24/2008

ELF

203

Adverse Weather and Cloud Cover Are Pervasive

North Pole Region

North Atlantic

NOAA satellite image of earth cloud cover

Annual Average 1.0 Fraction of Cloud Cover 0.8 Rising Air Rising Air Descending Air

South Pole Region

0.6

0.4

Argentina, Southern Africa and Australia Note: Annual Average Cloud Cover Global Average = 61% Global Average Over Land = 52% Global Average Over Ocean = 65%

0.2

0.0 65°N

45°N

25°N

5°N

Cloud Cover Over Land

Descending Air

Deserts ( Sahara, Gobi, Mojave )

85°N

Cloud Cover Over Ocean

0°

5°S

25°S

45°S

65°S

85°S

Latitude Zone Reference: Schneider, Stephen H. Encyclopedia of Climate and Weather. Oxford University Press, 1996. 2/24/2008

ELF

204

Radar Seekers Are Robust in Adverse Weather O2, H2O

1000

ATTENUATION (dB / km)

100

Note:

H2O H2O

O2

EO attenuation through cloud at 0.1 g / m3 and 100 m visibility EO attenuation through rain at 4 mm / h Humidity at 7.5 g / m3 Millimeter wave and microwave attenuation through cloud at 0.1 gm / m3 or rain at 4 mm / h

CO2

10

H2O O2

H2O, CO2

CO2

1

H2O

20° C 1 ATM

H2O

EO sensors are ineffective through cloud cover

O3

0.1 X Ku K Ka Q V W MILLIMETER RADAR

0.01 10 GHz 3 cm

100 3 mm

Radar sensors have good to superior performance through cloud cover and rain

Very Long Long Mid Short

1 THz 0.3 mm

VISIBLE

INFRARED

SUBMILLIMETER

10 30 µm

100 3.0 µm

1000 0.3 µm

Increasing Frequency Increasing Wavelength

Source: Klein, L.A., Millimeter-Wave and Infrared Multisensor Design and Signal Processing, Artech House, Boston, 1997 2/24/2008

ELF

205

Radar Seekers Are Desirable for Robust Operation within the Troposphere Cloud Cover 40

Cumulonimbus ( 2 – 36k ft ) Cirrus ( 16 – 32k ft )

30 h, Altitude, 103 ft

20

Altostratus ( 8 – 18k ft ) Altocumulus ( 9 – 19k ft )

10 Stratus ( 1 – 7k ft )

Cumulus ( 2 – 9k ft )

Fog

0

Note: •IR seeker may be able to operate “Under the Weather” at elevations less than 2,000 ft using GPS / INS midcourse guidance •IR attenuation through cloud cover greater than 100 dB per km. Cloud droplet size ( 0.1 to 50 μm ) causes resonance. •mmW has ~ 2 dB / km attenuation through rain. Typical rain drop size ( ∼ 4 mm ) is comparable to mmW wavelength. 2/24/2008

ELF

206

Precision Strike Missile Target Sensors Are Complemented by GPS / INS / Data Link Sensors Sensor

Adverse Weather Impact

ATR / ATA in Clutter

Range

Moving Target

Volume Search Time

Hypersonic Dome Compat.

Diameter Required

Weight and Cost

• SAR

-

• Active Imaging mmW • Passive Imaging mmW • Active Imaging IR (LADAR) • Active Nonimage IR (LADAR) • Active Nonimage mmW • Passive Imaging IR • Acoustic

-

-

2/24/2008

-

-

• GPS / INS / Data Link

Note:

-

-

-

Maturity

-

-

Superior

Good

Below Average ELF

- Poor 207

Imaging Sensors Enhance Target Acquisition / Discrimination Imaging LADAR

Passive Imaging mmW

2/24/2008

Imaging Infrared

Video of Imaging Infrared

ELF

SAR

Video of SAR Physics

208

Example of Mid Wave – Long Wave IR Seeker Comparison Assume Exo-atmospheric Intercept with Target diameter DT = 2 ft ( AT = 2919 cm2 ), temperature TT = 300 K, emissivity ε = 0.5 Diameter of seeker aperture do = 5 in ( Ao = 0.01267 m2 ) Diameter of pixel detector dp = 40 μm Spot resolution if diffraction limited = dspot = dp = 40 μm Temperature of pixel detector Td = 77 K Focal plane array size 256x256 FPA ( Ad = 1.049 cm2 ) Pixel detector bandwidth Δfp = 50 Hz ( tinteg = 0.00318 s ) Required signal-to-nose ratio for detection ( S / N )D = 5

First Calculate MWIR Seeker Detection Range RD = { ( IT )Δλ ηa Ao { D* / [( Δfp )1/2 ( Ad )1/2 ]} ( S / N )D-1 }1/2, m Radiant intensity of target within seeker bandwidth ( IT )Δλ = ε Lλ ( λ2 - λ1 ) AT, W sr-1 Spectral radiance of target Lλ = 3.74 x 104 / { λ5 { e[ 1.44 x 104 / ( λ TT )] – 1 }}, W cm-2 sr-2 μm-1 Assume λ = 4 μm, λ2 = 5 μm, λ1 = 3 μm, then Lλ = 0.000224 W cm-2 sr-2 μm-1, ( IT )Δλ = 0.643 W sr-1 Assume Hg0.67Cd0.33Te detector at λ = 4 μm and 77 K ⇒ D* = 8 x 1011 cm Hz1/2 W-1 RD = { ( 0.643 ) ( 1 ) ( 0.01267 ) {( 8 x 1011 ) / [( 50 )1/2 ( 1.049 )1/2 ]} ( 5 )-1 }1/2 = 13,480 m 2/24/2008

ELF

209

Example of Mid Wave – Long Wave IR Seeker Comparison ( cont ) Next, Calculate LWIR Seeker Detection Range RD = { ( IT )Δλ ηa Ao { D* / [( Δfp )1/2 ( Ad )1/2 ]} ( S / N )D-1 }1/2, m ( IT )Δλ = ε Lλ ( λ2 - λ1 ) AT, W sr-1 Lλ = 3.74 x 104 / { λ5 { e[ 1.44 x 104 / ( λ TT )] – 1 }}, W cm-2 sr-2 μm-1 Assume λ = 10 μm, λ2 = 13 μm, λ1 = 7 μm, then Lλ = 0.00310 W cm-2 sr-2 μm-1, ( IT )Δλ = 26.7 W sr-1 Assume Hg0.80Cd0.20Te detector at λ = 10 μm and 77 K ⇒ D* = 5 x 1010 cm1/2 Hz1/2 W-1 RD = { ( 26.7 ) ( 1 ) ( 0.01267 ) {( 5 x 1010 ) / [( 50 )1/2 ( 1.049 )1/2 ]} ( 5 )-1 }1/2 = 21,600 m ( λ )( Lλ )max = 2898 / TT, Wein’s Displacement Law, TT in K

15

Subsonic Airframe

I LW

10

Mach 4 Airframe

R

Wavelength for Max Spectral Radiance, Microns

MWIR Seeker Versus LWIR Seeker Selection Depends Upon Target Temperature

MW IR

5

Jet Engine Rocket Plume Flare

Example: TT = 300 K

0 0

500

1000

1500

TT, Target Temperature, K

2/24/2008

ELF

2000

( λ )( Lλ )max = 2898 / TT = 2898 / 300 = 10.0 μm 210

GPS / INS Provides Robust Seeker Lock-on in Adverse Weather and Clutter Target Image

480 Pixels

•

640 Pixels ( 300 m )

175 m

Seeker Lock-on @ 850 m to go ( 1 pixel = 0.47 m )

Seeker Lock-on @ 500 m to go ( 1 pixel = 0.27 m )

3 m GPS / INS error ⇒ nM

3 m GPS / INS error ⇒ nM

req

= 0.15 g, σ < 0.1 m

req

88 m

= 0.44 g, σ < 0.1 m

44 m

Seeker Lock-on @ 250 m to go ( 1 pixel = 0.14 m )

Seeker Lock-on @ 125 m to go ( 1 pixel = 0.07 m )

3 m GPS / INS error ⇒ nM

3 m GPS / INS error ⇒ nM

req

2/24/2008

= 1.76 g, σ = 0.9 m

req

= 7.04 g, σ = 2.2 m

Note: = Target Aim Point and Seeker Tracking Gate, GPS / INS Accuracy = 3 m, Seeker 640 x 480 Image, Seeker FOV = 20 deg, Proportional Guidance Navigation Ratio = 4, Velocity = 300 m / s, G&C Time Constant = 0.2 s. ELF

211

Data Link Update at Seeker Lock-on Reduces Moving Target Error Target Error at Seeker Lock-on, m

TESeekerLock-on = [ TLE2 + ( VT tLatency )2 ]1/2 1000

VT = 1 m / s VT = 10 m / s VT = 100 m / s VT = 1000 m / s

100

10 0.1

1

10

100

Target Latency at Seeker Lock-on, s

1000

Example: TLE = 10 m tSeekerLock-on = 100 s tUdate = 90 s VT = 10 m / s tLatency = tSeeker- tUdate = 100 – 90 = 10 s TESeekerLock-on = [ TLE2 + ( VT tLatency )2 ]1/2 = { 102 + [ 10 ( 10 )]2 ]1/2 = 100.5 m

Note: tSeekerLock-on = Seeker Lock-on time, tUdate = Data Link Update Time, VT = Target Velocity, TLE = Target Location Error at Update = 10 m 2/24/2008

ELF

212

Optimum Cruise Is a Function of Mach Number, Altitude, and Planform Geometry 120 Scramjet

h, Altitude, kft

100

q = 200 psf q = 500 psf q = 1,000 psf q = 2,000 psf q = 5,000 psf q = 10,000 psf q = 20,000 psf

Ramjet

80 60 40

Subsonic Turbojet with Low Aspect Ratio Wing

20

Note: q = 1 / 2 ( ρ V2 )

Wingless Subsonic Turbojet

0 0

1

2

3

4

5

6

7

M, Mach number Note: • U.S. 1976 Standard Atmosphere • For Efficient Cruise, ( L / D )Max for Cruising Lifting Body Typically Occurs for 500 < q < 1,000 psf • ( L / D )Max for Cruise Missile with Low Aspect Ratio Wing Typically Occurs for 200 < q < 500 psf 2/24/2008 • q ≈ 200 psf lower limit for aero control ELF

213

Missile Guidance and Control Must Be Robust for Changing Events and Flight Environment

Level Out Engine Start Transient

Cruise

Example High Performance Missile Has • Low-to-High Dynamic Pressure • Negative-to-Positive Static Margin • Thrust / Weight / cg Transients • High Temperature • High Thermal Load • High Vibration • High Acoustics

Booster Shutdown Transient at High Mach Pitch-Up at High Alpha

Engine Shutdown Transient

Climb Booster Ignition Air Launch at Low Mach ( high α ) / Deploy Compressed Carriage Surfaces 2/24/2008

Pitch-Over at High Alpha

Pitch-Over at High Alpha Dive Terminal at High Dynamic Pressure Precision Impact at α ≈ 0 Deg

Vertical Launch in Cross Wind ( high α ) / Deploy Compressed Carriage Surfaces ELF

214

Design Robustness Requires Consideration of Flight Altitude Troposphere ( h < 36,089 ft )

Stratosphere ( h > 36089 ft )

T / TSL = 1 – 6.875 x 10-6 h, h in ft

T = constant = 390 R

p / pSL = ( T / TSL )5.2561

p / pSL = 0.2234 e - ( h – 36089 ) / 20807

ρ / ρSL = ( T / TSL )4.2561

ρ / ρSL = 0.2971 e - ( h – 36089 ) / 20807

Characteristic at Altitude / Characteristic at Sea Level

1 0

20

40

60

80

100

Troposphere Stratosphere

Temperature Ratio Pressure Ratio Density Ratio Speed of Sound Ratio

0.1

0.01

h, Geometric Altitude, kft

U.S. Standard Atmosphere, 1976 – TSL = 519 R – pSL = 2116 lb / ft2 – ρSL = 0.00238 slug / ft3 – cSL = 1116 ft / s

Note: TSL = Temperature at sea level, pSL = pressure at sea level, ρSL = density at sea level, cSL = speed of sound at sea level, h = altitude in ft. 2/24/2008

ELF

215

Variation from Standard Atmosphere

Design Robustness Requires Consideration of Cold and Hot Atmospheres Ratio: Cold-to-Standard Atmosphere Ratio: Hot-to-Standard Atmosphere Ratio: Polar-to-Standard Atmosphere Ratio: Tropic-to-Standard Atmosphere

1.5 ( + 30 % )

1

( - 23% )

0.5

0

Temp

Density Speed of Sound

Note: • Based on properties at sea level •U. S. 1976 Standard Atmosphere: Temperature = 519 R, Density = 0.002377 slug / ft3, Speed of sound = 1116 ft / s 2/24/2008

ELF

216

Design Robustness Is Required to Handle Uncertainty Narrow Uncertainty ( e.g., SDD Flight Performance )

Example Normalized PDF

1

Broad Uncertainty ( e.g., Conceptual Design Flight Performance ) Skewed Uncertainty ( e.g., Cost, Weight, Miss Distance ) Bimodal Uncertainty ( e.g., Multi-mode Seeker Target Location ) Uniform Bias Uncertainty ( e.g., Seeker Aim Point Bias )

0.5

0 -20

-10

0

10

20

Typical % Error from Forecast Value Note for normal distribution: PDF = { 1 / [ σ ( 2 π )1/2 ]} e {[( x - μ ) / σ ] 2/24/2008

ELF

2/2}

217

Counter-Countermeasures by Missile Enhance Design Robustness Examples of CCM ( Missile )

Examples of CM ( Threat )

Imaging Seeker Multi-spectral / Multimode Seeker Temporal Processing Hardened GPS / INS

EOCM directed laser flare smoke

RFCM active radar jammer chaff

standoff acquisition Integrated GPS / INS directional antenna pseudolite / differential GPS

Decoy Low Observables Speed Altitude Maneuverability Lethal Defense

2/24/2008

ATR / ATA Speed Altitude Maneuverability Low Observables Saturation ELF

218

Examples of Countermeasure-Resistant Seekers IIR ( I2R AGM-130 ) ……………………………………………… Two Color IIR ( Python 5 ) Acoustic - IIR ( BAT ) ………………………………………….. IIR – LADAR ( LOCAAS ) ………………………………………

ARH – mmW ( AARGM ) ARH - IIR ( Armiger ) ……………………………………………. 2/24/2008

ELF

219

A Target Set Varies in Size and Hardness Lethality

Example of Precision Strike Target Set Air Defense ( SAMs, AAA )

Launch Platform Integration / Firepower

Robustness

Cost

Lethality

Reliability

Miss Distance

Other Survivability Considerations

Carriage and Launch Observables

Armor TBM/ TELs

Artillery Naval

C3II Counter Air Aircraft

Transportation Choke Points ( Bridges, Railroad Yards, Truck Parks )

Oil Refineries

Examples of Targets where Size and Hardness Drive Warhead Design / Technology •Small Size, Hard Target: Tank ⇒ Small Shaped Charge, EFP, or KE Warhead •Deeply Buried Hard Target: Bunker ⇒ KE / Blast Frag Warhead •Large Size Target: Building ⇒ Large Blast Frag Warhead 2/24/2008

Video Example of Precision Strike Targets ELF

220

76% of Baghdad Targets Struck First Night of Desert Storm Were C3 Time Critical Targets Targets: 1. Directorate of Military Intelligence; 2, 5, 8, 13, 34. Telephone switching stations; 3. Ministry of Defense national computer complex; 4. Electrical transfer station; 6. Ministry of Defense headquarters; 7. Ashudad

1 4

2 3 6 5 7

23 25 8 24 26 9 10 27 11 21 22

12 13 14 15

20

16 17

28

31 32

29 30

33 34 35 37

36 19 2/24/2008

18

highway bridge; 9. Railroad yard; 10. Muthena airfield ( military section ); 11. Air Force headquarters; 12. Iraqi Intelligence Service; 14. Secret Police complex; 15. Army storage depot; 16. Republican Guard headquarters; 17. New presidential palace; 18. Electrical power station; 19. SRBM assembly factory ( Scud ); 20. Baath Party headquarters; 21. Government conference center; 22. Ministry of Industry and Military Production; 23. Ministry of Propaganda; 24. TV transmitter; 25, 31. Communications relay stations; 26. Jumhuriya highway bridge; 27. Government Control Center South; 28. Karada highway bridge ( 14th July Bridge ); 29. Presidential palace command center; 30. Presidential palace command bunker; 32. Secret Police headquarters; 33. Iraqi Intelligence Service regional headquarters; 35. National Air Defense Operations Center; 36. Ad Dawrah oil refinery; 37. Electrical power plant Source: AIR FORCE Magazine, 1 April 1998 ELF

221

Type of Target Drives Precision Strike Missile Size, Speed, Cost, Seeker, and Warhead Anti-Fixed Surface Target Missiles ( large size, wings, subsonic, blast frag warhead ) AGM-154

Storm Shadow / Scalp

KEPD-350

BGM-109

AGM-142

Anti-Radar Site Missiles ( ARH seeker, high speed or duration, blast frag warhead ) AGM-88

AS-11 / Kh-58

ARMAT

Armiger

ALARM

Anti-Ship Missiles ( large size, KE / blast frag warhead, and high speed or low altitude ) MM40

AS-34 Kormoran

AS-17 / Kh-31

BrahMos

SS-N-22 / 3M80

Anti-Armor Missiles ( small size, hit-to-kill, low cost, shape charge, EFP, or KE warhead ) Hellfire

LOCAAS

MGM140

AGM-65

LOSAT

Anti-Buried Target Missiles ( large size, high fineness, KE / blast frag warhead ) 2/24/2008

CALCM

GBU-28

GBU-31 ELF

Storm Shadow

MGM-140

Permission of Missile Index. 222

Examples of Light Weight Air Launched MultiPurpose Precision Strike Weapons Weapon

Fixed Surface Targets(1)

Moving Targets(2)

Time Critical Targets(3)

Buried Targets(4)

Adverse Weather(5)

Firepower(6)

Example New Missile AGM-65 Small Diameter Bomb AGM-88

– –

–

–

Hellfire / Brimstone / Longbow LOCAAS

–

–

– –

(1) – Multi-mode warhead desired. GPS / INS provides precision ( 3 m ) accuracy. (2) - Seeker or high bandwidth data link required for terminal homing.

Note: Superior

(3) - High speed with duration required ⇒ High payoff of high speed / loiter and powered submunition.

2/24/2008

(4) - KE penetration warhead required ⇒ High impact speed, low drag, high density, long length.

Good

(5) - GPS / INS, SAR seeker, imaging mmW seeker, and data link have high payoff.

Average

(6) - Light weight required. Light weight also provides low cost ELF

–

Poor

223

Blast Is Effective at Small Miss Distance Delta p / p0, Overpressure Ratio to Undisturbed Pressure

Δ p / p0 = 37.95 / ( z p01/3 ) + 154.9 / ( z p01/3 )2 + 203.4 / ( z p01/3 )3 + 403.9 / ( z p01/3 )4 1000

z = r / c1/3 Note: Based on bare sphere of pentolite ( Ec1/2 = 8,500 ft / s ) Δp = overpressure at distance r from explosion

100

p0 = undisturbed atmospheric pressure, psi z = scaling parameter = r / c1/3 r = distance from center of explosion, ft c = explosive weight, lb

10

Example for Rocket Baseline Warhead: c = 38.8 lb h = 20k feet, p0 = 6.8 psi r = 10 ft z = 10 / ( 38.8 )1/3 = 2.95

1 0

2

4

6

8

10

z p01/3 = 5.58 Δp / p0 = 13.36

z ( p0 )1/3

Δp = 90 psi Reference: US Army Ordnance Pamphlet ORDP-2—290-Warheads, 1980 2/24/2008

ELF

224

Guidance Accuracy Enhances Lethality Rocket Baseline Warhead Against Typical Aircraft Target PK > 0.5 if σ < 5 ft ( Δ p > 330 psi, fragments impact energy > 130k ft-lb / ft2 ) PK > 0.1 if σ < 25 ft ( Δp > 24 psi, fragments impact energy > 5k ftlb / ft2 )

Note: Rocket Baseline 77.7 lb warhead C / M = 1, spherical blast, h = 20k ft. Video of AIM-9X Flight Test Missile Impact on Target ( No Warhead ) 2/24/2008

ELF

225

Warhead Blast and Fragments Are Effective at Small Miss Distance

2.4 m witness plate Roland 9 kg explosively formed warhead multi-projectiles are from preformed case

Hellfire 24 lb shaped charge warhead fragments are from natural fragmenting case

Video of Guided MLRS 180 lb blast fragmentation warhead 2/24/2008

ELF

226

Maximum Total Fragment Kinetic Energy Requires High Charge-to-Metal Ratio ( KE / Mwh ) / Ec, Non-dimensional Kinetic Energy

KE = ( 1 / 2 ) Mm Vf2 = Ec Mc / ( 1 + 0.5 Mc / Mm ) 0.4

Low K

Note: Based on Gurney Equation Cylindrical Warhead KE = Total Kinetic Energy Mm = Total Mass Metal Fragments Vf = Fragment Velocity Ec = Energy Per Unit Mass Charge Mc = Mass of Charge Mwh = Mass of Warhead = Mm + Mc

KE High

E

0.3

0.2

Example: Rocket Baseline Warhead

0.1

Mc = 1.207 slug Mm = 1.207 slug Mc / Mm = 1

0 0

0.5

1

1.5

2

Mc / Mm, Charge-to-Metal Ratio

2.5

3

Ec Mc = 52,300,000 ( 1.207 ) = 63,100,000 ft-lb KE = 63100000 / [1 + 0.5 ( 1 )] = 42,100,000 ft-lb

Reference: Carleone, Joseph (Editor), Tactical Missile Warheads (Progress in Astronautics and Aeronautics, Vol 155), AIAA, 1993. 2/24/2008

ELF

227

Multiple Impacts Are Effective Against Threat Vulnerable Area Subsystems

Pk, Probability of Kil

PK = 1 - ( 1 - Av / Atp )nhits Note: • Av = Target vulnerable area • Atp = Target presented area

1 0.9 0.8 0.7 0.6 0.5 0.4

Av / Atp = 0.1 Av / Atp = 0.5 Av / Atp = 0.9

0.3 0.2 0.1 0

Example: If Av / Ap = 0.1, nhits = 22 gives PK = 0.9 If Av / Ap = 0.9, nhits = 1 gives PK = 0.9

0

5

10

15

20

25

30

nhits, Number of Impacts on Target 2/24/2008

ELF

228

Small Miss Distance Improves Number of Warhead Fragment Hits nhits = nfragments [ AP / ( 4 π σ2 )]

Number of Fragment Hits

100

Wwh = 5 lb Wwh = 50 lb Wwh = 500 lb

80 60

Example for Rocket Baseline: WWH = 77.7 lb

40

Mc / Mm = 1, Wm = 38.8 lb = 17,615 g Average fragment weight = 3.2 g

20

nfragments = 17615 / 3.2 = 5505 AP = Target presented area = 20 ft2

0 0

20

40

60

80

Sigma, Miss Distance, ft

2/24/2008

100

σ = Miss distance = 25 ft nhits = 5505 { 20 / [( 4 π ) ( 25 )2 ]} = 14 Kinetic energy per square foot. = KE / ( 4 π σ2 ) = 42100000 / [ 4 π ( 25 )2 ] = 5,360 ft-lb / ft2

Note: • Spherical blast with uniformly distributed fragments • nhits = nfragments [ AP / ( 4 π σ2 )] • Warhead charge / metal weight = 1 • Average fragment weight = 50 grains ( 3.2 g ) • AP = Target presented area = 20 ft2 ELF

229

High Fragment Velocity Requires High Charge-toMetal Ratio Vf = ( 2 Ec )1/2 [ ( Mc / Mm ) / ( 1 + 0.5 Mc / Mm )]1/2

Vf, Fragment Velocity, ft / s

10000

HMX Explosive TNT Explosive

8000 6000

Note: Based on the Gurney equation for a cylindrical warhead

Example: Baseline Rocket Warhead

4000

HMX Explosive MC / Mm = 1

2000

Vf = 8,353 ft / s

HMX Explosive ( 2 EC )1/2 = 10,230 ft / s TNT Explosive ( 2 EC )1/2 = 7,600 ft / s Vf = Fragment initial velocity, ft / s Ec = Energy per unit mass of charge, ft2 / s2 Mc = Mass of charge Mm = Total mass of all metal fragments Mwh = Mass of warhead = Mm + Mc

0 0

1

2

3

Mc / Mm, Charge-to-Metal Ratio 2/24/2008

ELF

230

Small Miss Distance Improves Fragment Penetration Steel Perforation by Fragment ( in )

.5 150 Grains ( 9.7 g )

.375

50 Grains ( 3.2 g ) .25

.125 10

2/24/2008

20

30

40

50

60

70

80

Miss Distance ( ft )

90

100

110

120

Note: Typical air-to-air missile warhead • Fragments initial velocity 5,000 ft / s • Sea level • Average fragment weight 3.2 g • Fewer than 0.3% of the fragments weigh more than 9.7 g for nominal 3.2 g preformed warhead fragments • Small miss distance gives less reduction in fragment velocity, enhancing penetration ELF

231

Hypersonic Hit-to-Kill Enhances Energy on Target for Missiles with Small Warheads ET / EC, Total Energy on Target / Warhead Charge Energy

ET / EC = [( 1 / 2 ) ( WMissile / gc ) V2 + EC ( WC / gc )] / [ EC ( WC / gc )] 9

Weight of missile / Weight of charge = 20

Example for Rocket Baseline:

8

WMissile = 367 lb

7

WC = 38.8 lb

6

WMissile / WC = 9.46

5

Weight of missile / Weight of charge = 10

V = 2,000 ft / s

4

( 1 / 2 ) ( WMissile / gc ) V2 = 22.8 x 106 ft-lb )

3

EC ( WC / gc ) = 63.1 x 106 ft-lb

2

ET / EC = 1.36

Weight of missile / Weight of charge = 5

1 0 0

1000

2000

3000

4000

5000

Missile Closing Velocity, ft / s

6000

Weight of missile / Weight of charge = 2

Note: Warhead explosive charge energy based on HMX, ( 2 EC )1/2 = 10,230 ft / s. 1 kg weight at Mach 3 closing velocity has kinetic energy of 391,000 J ⇒ equivalent chemical energy of 0.4 lb TNT. 2/24/2008

ELF

232

Kinetic Energy Warhead Density, Length, and Velocity Provide Enhanced Penetration P / d = [( l / d ) – 1 ] ( ρP / ρT )1/2 + 3.67 ( ρP / ρT )2/3 [( ρT V2 ) / σT ]1/3

P / d, Target Penetration / Penetrator Diameter for Steel on Concrete

60 50 40 30 20 10 0 0

1000

2000

3000

V, Velocity, ft / s l/d=2

l/d=5

l / d = 10

4000

Note: V > 1,000 ft / s l/d>2 Non-deforming ( high strength, sharp nose ) penetrator l = Penetrator length d = Penetrator diameter V = Impact velocity ρP= Penetrator density ρT = Target density σT= Target ultimate stress Example for 250 lb Steel Penetrator l / d = 10 l = 48 in ( 4 ft ) d = 4.8 in ( 0.4 ft ) Concrete target ρP = 0.283 lb / in3 ( 15.19 slug / ft3 ) ρT = 0.075 lb / in3 ( 4.02 slug / ft3 ) V = 4,000 ft / s σT = 5,000 psi ( 720,000 psf ) P / d = [ 10 – 1 }( 15.19 / 4.02 )1/2 + 3.67 ( 15.19 / 4.02 )2/3 [ 4.02 ( 4000 )2 / 720000 ]1/3 = 57.3 P = ( 57.3 ) ( 0.4 ) = 22.9 ft

Source: Christman, D.R., et al, “Analysis of High-Velocity Projectile Penetration,” Journal of Applied Physics, Vol 37, 1966 2/24/2008

ELF

233

Examples of Kinetic-Kill Missiles

Standard Missile 3 ( NTW )

PAC-3

LOSAT 2/24/2008

THAAD

LOSAT Video ELF

234

CEP Approximately Equal to 1σ Miss Distance Miss Distance Launch Platform Integration / Robustness Firepower

Missile Circular Error Probable ( 50% of shots within circle )

Extreme Missile Trajectory

Cost

Lethality

Reliability

Miss Distance

Survivability

Observables

Missile 1σ Miss Distance ( 68% of shots within circle for a normal distribution of error ) Median Trajectory

Target

Presented Target Area Extreme Missile Trajectory

For a normal distribution of error: Probability < 1σ miss distance = 0.68 Probability < 2σ miss distance = 0.95 Probability < 3σ miss distance = 0.997

Hypothetical Plane Through Target

Source: Heaston, R.J. and Smoots, C.W., “Introduction to Precision Guided Munitions,” GACIAC HB-83-01, May 1983. 2/24/2008

ELF

235

A Collision Intercept Has Constant Bearing for a Constant Velocity, Non-maneuvering Target Example of Collision Intercept ( Line-of-Sight Angle Constant ) . ( Line-of-Sight Angle Rate L = 0 )

Example of Miss ( Line-of-Sight Angle Diverging ) . ( Line-of-Sight Angle Rate L ≠ 0 ) Overshoot Miss

t2 ( LOS L

)1 > (

LO S

t1 )0

Seeker Line-of-Sight

Missile

t1

A

Target

t0 Missile

( LOS )1 = ( LOS )0 L

Seeker Line-of-Sight

A

t0

Target

Note: L = Missile Lead A = Target Aspect

2/24/2008

ELF

236

A Maneuvering Target and Initial Heading Error Cause Miss Target A

Missile

Collision Point

L

γM

0

+Z Maneuvering : τ d2Z + dZ + N’ Z = – N’ cos A 1 a t2 T dt to – t to – t cos L 2 Target dt2 Initial Heading : τ d2Z + dZ + N’ Z = – VM γM 0 dt to – t Error dt2 Reference: Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design, D. Van Nostrand Company, Inc., Princeton, New Jersey, 1960 2/24/2008

Note: to - t = 0 at intercept, causing discontinuity in above equations. N’ = Effective navigation ratio = N [ VM / ( VM - VT cos A )] N = Navigation ratio = ( dγ / dt ) / ( dL / dt ) τ = Missile time constant, VM= Velocity of missile, γM = Initial flight 0 path angle error of missile, to = Total time of flight, aT = Acceleration of target, VT = Velocity of target ELF

237

Missile Time Constant Causes Miss Distance τ is a measure of missile ability to respond to target condition changes τ equals elapsed time from input of target return until missile has completed 63% or ( 1 – e-1 ) of corrective maneuver ( t = τ ) τ also called “rise time” Contributions to time constant τ Control effectiveness ( τδ ) Control dynamics ( e.g., actuator rate ) ( τδ. ) Dome error slope ( τDome ) Guidance and control filters ( τFilter ) Other G&C dynamics ( gyro dynamics, accelerometer, processor latency, etc ) Seeker errors ( resolution, latency, blind range, tracking, noise, glint, amplitude )

Approach to estimate τ τ = τδ + 2/24/2008

τδ.

Input

Time ti

63% Output

ti

τ

Time

Acceleration Achieved = 1 – e- t / τ Acceleration Commanded Example for Rocket Baseline: M = 2, h = 20k ft, coast τ = τδ + τδ. + τDome

+ τDome

= 0.096 + 0.070 + 0.043 = 0.209 s ELF

238

Time Constant τδ for Control Effectiveness Is Driven by Static Margin Assumptions for τδ Control surface deflection limited Near neutral stability

αMax, δMax

Equation of motion is ..

αMax

α = [ ρ V2 S d Cmδ / ( 2 Iy ) ] δMax

Integrate to solve for αMax

τδ / 2

αMax= [ ρ V2 S d Cmδ / ( 8 Iy ) ] δMax τδ2

τδ is given by

τδ

– δMax

τδ = [ 8 Iy ( αMax / δMax ) / ( ρ V2 SRef d Cmδ )]1/2

Contributors to small τδ

Example for Rocket Baseline:

Low fineness ( small Iy / ( SRef d )) High dynamic pressure ( low altitude / high speed ) Large Cmδ

2/24/2008

W = 367 lb, d = 0.667 ft, SRef = 0.349 ft2, Iy = 94.0 slug-ft2, M = 2, h = 20k ft ( ρ = 0.001267 slug / ft3 ), αMax = 9.4 deg, δMax = 12.6 deg, Cmδ = 51.6 per rad, τδ = { 8 ( 94.0 ) ( 9.4 / 12.6 ) / [ 0.001267 ( 2074 )2 ( 0.349 ) ( 0.667 ) ( 51.6 ) ]}1/2 = 0.096 s ELF

239

Time Constant τδ. for Flight Control System Is Driven by Actuator Rate Dynamics α Max, δ Max

Assumptions for τδ.

.

.

δ

Control surface rate limited ( δ = δ Max ) Near neutral stability .

1

.

Equation of motion for δ = +/- δ Max

α Max

α Max

.

τδ

τδ.

.

...

α = [ ρ V2 S d Cmδ / ( 2 Iy ) ] δ Max

Equation of motion for “perfect” response . δ = ∞, δ = δMax ..

α = [ ρ V2 S d Cmδ / ( 2 Iy ) ] δMax

τδ. is difference between actual response to αMax and “perfect” ( τδ ) response Then

.

• δ Max = 360 deg / s, δMax = 12.6 deg

Note:

.

• τδ. = 2 ( 12.6 / 360 ) = 0. 070 s

Response for control rate limit Response for no control rate limit

τδ. = 2 δMax / δ Max

2/24/2008

- δ Max Example for Rocket Baseline

ELF

240

Time Constant τDome for Radome Is Driven by Dome Error Slope | R | = 0.05 ( lN / d – 0.5 ) [ 1 + 15 ( Δ f / f ) ] / ( d / λ ) τDome = N’ ( VC / VM ) | R | ( α / γ. ) α / γ. = α ( W / gc ) VM / { q SRef [ CN + CN / ( α / δ )]} α

δ

Example for Rocket Baseline at M = 2, h = 20k ft, q = 2725 psf Assume VT = 1,000 ft / s, giving VC = 3,074 ft / s Assume N’ = 4, f = 10 GHz or λ = 1.18 in, Δ f / f = 0.02 Configuration data are lN / d = 2.4, d = 8 in, SRef = 0.349 ft2, W = 367 lb, CN = 40 per rad, CN = 15.5 per rad, α / δ α δ = 0.75 Compute | R | = 0.05 ( 2.4 – 0.5 ) [ 1 + 15 ( 0.02 )] / ( 8 / 1.18 ) = 0.0182 deg / deg τDome = 4 ( 367 ) ( 3074 ) ( 0.0182 ) / [ 32.2 ( 2725 ) ( 0.349 ) ( 40 + 15.5 / 0.75 )] = 0.043 s

2/24/2008

|R| @ d / λ = 10, Radome Error Slope, Deg / Deg

Substituting gives τDome = N’ W VC | R | / { gc q SRef [ CNα + CNδ / ( α / δ )]}

ELF

0.03 Δ f / f = 0.05

0.02

Δ f / f = 0.02 Δf/f=0 Faceted or Window Dome

0.01

0

Tangent Ogive Dome

0

1 2 3 lN / d, Nose Fineness

Multi-lens Dome

241

High Initial Acceleration Is Required to Eliminate a Heading Error aM t0 / ( VM γM ) = N’ ( 1 – t / t0 ) N’ – 2

6

6

4

aM t0 / ( VM γM ), Non-dimensional Acceleration

4

Note: Proportional Guidance τ=0 t0 = Total Time to Correct Heading Error aM = Acceleration of Missile VM = Velocity of Missile γM = Initial Heading Error of Missile N’ = Effective Navigation Ratio

3 2.5 2 N’ = 2

0 0 2/24/2008

Example: Exoatmospheric Head-on Intercept, N’ = 4 Midcourse lateral error at t = 0 ( seeker lock-on ) = 200 m, 1 σ Rlock-on = 20000 m ⇒ γM = 200 / 20000 = 0.0100 rad VM = 5000 m / s, VT = 5000 ⇒ t0 = Rlock-on / ( VM + VT ) = 20000 / ( 5000 + 5000 ) = 2.00 s aM t0 / ( VM γM ) = 4 aM = 4 ( 5000 ) ( 0.0100 ) / 2.00 ) = 100 m / s2 nM = 100 / 9.81 = 10.2 g

0.2

0.6 0.4 t / t0, Non-dimensional Time ELF

0.8

1.0 242

Missile Minimum Range May Be Driven By 4 to 8 Time Constants to Correct Initial Heading Error σHE = VM γM t0 e-( t0 / τ ) j = 1∑N’ – 1 {( N’ - 2 )! [ - ( t0 / τ )]j / [( j – 1 )! ( N’ – j – 1 )! j! ]} If N’ = 3, σHE = VM γM t0 e-( t0 / τ ) [ ( t0 / τ ) - ( t0 / τ )2 / 2 ] If N’ = 4, σHE = VM γM t0 e-( t0 / τ ) [( t0 / τ ) - ( t0 / τ )2 + ( t0 / τ )3 / 6 ] If N’ = 5, σHE = VM γM t0 e-( t0/ τ ) [( t0 / τ ) – ( 3 / 2 ) ( t0 / τ )2 + ( t0 / τ )3 / 2 – ( t0 / τ )4 / 24 ] If N’ = 6, σHE = VM γM t0 e-( t0 / τ ) [( t0 / τ ) - 2 ( t0 / τ )2 + ( t0 / τ )3 - ( t0 / τ )4 / 6 + ( t0 / τ )5 / 120 ]

0.3

N’ = 3 0.2

Note: Proportional Guidance ( σHE )Max shown in figure is the envelope of adjoint solution ( σHE )Max = Max miss distance ( 1 σ ) from heading error, ft VM = Velocity of missile, ft / s γM = Initial heading error, rad t0 = Total time to correct heading error, s τ = Missile time constant, s N’ = Effective navigation ratio

N’ = 4

| ( σHE )Max / ( VM γM to ) |

N’ = 6

0.1

Example: Ground Target, N’ = 4, τ = 0.2, GPS / INS error = 3 m, Rlock-on = 125 m, γM = 3 / 125 = 0.024 rad, VM = 300 m / s, t0 = 125 / 300 = 0.42 s t0 / τ = 0.42 / 0.2 = 2.1, (σHE )Max / ( VM γM to ) = 0.12 ( σHE )Max = 0.12 ( 300 ) ( 0.024 ) ( 0.42 ) = 2.2 m

0 References:

0

2

tO / τ

4

6

8

10

•Donatelli, G.A., et al, “Methodology for Predicting Miss Distance for Air Launched Missiles,” AIAA-82-0364, January 1982 •Bennett, R.R., et al, “Analytical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952 2/24/2008

ELF

243

Required Maneuverability Is about 3x the Target Maneuverability for an Ideal ( τ = 0 ) Missile nM / nT = [ N’ / ( N’ – 2 )] [ 1 – ( 1 – t / t0 )N’ – 2 ] Where t = Elapsed Time t0 = Time to Target N’ = Effective Navigation Ratio

6 nM , nT

Assumptions: τ=0 VM > VT

N’ = 2 ∞ ↑ N’ = 2.5

Example: τ = 0, N’ = 3, t / t0 = 1

4

⇒ nM / nT = 3

3

Missile-to-Target Acceleration 2 Ratio 0

4 6

0

0.2

0.4

0.6

0.8

1.0

t / t0, Non-Dimensional Time 2/24/2008

ELF

244

Target Maneuvers Require 6 to 10 Time Constants to Settle Out Miss Distance 0.3

σMAN = gc nT τ2 e-( t0 / τ ) j = 2∑N’ – 1 {( N’ - 3 )! [ - ( t0 / τ )]j / [( j – 2 )! ( N’ – j – 1 )! j! ]} If N’ = 3, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 ] If N’ = 4, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 - ( t0 / τ )3 / 6 ] If N’ = 5, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 - ( t0 / τ )3 / 3 + ( t0 / τ )4 / 24 ] If N’ = 6, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 - ( t0 / τ )3 / 2 + ( t0 / τ )4 / 8 - ( t0 / τ )5 / 120 ]

N’ = 3

0.2 ( σMAN )Max gc nT τ2

Note: Proportional Guidance ( σMAN )Max is the envelope of adjoint solution ( σMAN )Max = Max miss ( 1 σ ) from target accel, ft nT = Target acceleration, g gc = Gravitation constant, 32.2 τ = Missile time constant, s N’ = Effective navigation ratio τ0 = Time of flight, s

N’ = 4 0.1 N’ = 6

0 References:

0

2

tO / τ

4

6

8

10

•Donatelli, G.A., et al, “Methodology for Predicting Miss Distance for Air Launched Missiles,” AIAA-82-0364, January 1982 •Bennett, R.R., et al, “Analytical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952 2/24/2008

ELF

245

An Aero Control Missile Has Reduced Miss Distance at Low Altitude / High Dynamic Pressure Note: Proportional guidance Target maneuver initiated for max miss ( t0 / τ = 2 ) ( σMan )Max in figure = Envelope of adjoint miss distance τ = Missile time constant, s N’ = Effective navigation ratio = 4 nT = Target acceleration, g gc = Gravitation constant = 32.2

Rocket Baseline Maximum Miss Due to Maneuvering Target, ft

( σMan )Max = 0.13 gc nT τ2 @ N’ = 4, t0 / τ = 2 100

10

h = SL h = 20k ft h = 40k ft h = 60k ft h = 80k ft

1

Example for Rocket Baseline at Mach 2, coasting Assume: • nT = 5g, VT = 1,000 ft / s, head-on intercept •h = 20k ft ⇒ τ = 0.209 s

0.1 0

2

4

6

8

10

( σMan )Max = 0.13 ( 32.2 )( 5 )( 0.209 )2 = 0.9 ft •h = 80k ft ⇒ τ = 1.17 s

Target Maneuverability, g

( σMan )Max = 0.13 ( 32.2 )( 5 )( 1.17 )2 = 28.7 ft 2/24/2008

ELF

246

Glint Miss Distance Driven by Seeker Resolution, Missile Time Constant, and Navigation Ratio Sigma / ( bT )Res, Nondimensional Miss Distance from Glint @ 2 Hz Bandwidth

σGlint = KN’ ( W / τ )1/2

Note: Proportional guidance Adjoint miss distance σGlint = Miss distance due to glint noise, ft W = Glint noise spectral density, ft2 / Hz τ = Missile time constant, s N’ = Effective navigation ratio ( bT )Res = Target span resolution at seeker blind range, ft B = Noise bandwidth, Hz ( 1 < B < 5 Hz )

KN’ = 0.5 ( 2 KN’ = 4 )N’ / 4

0.8

KN’ = 4 = 1.206 W = ( bT )Res2 / ( 3 π2 B )

0.6

0.4

Example: Rocket Baseline at Mach 2, h = 20k ft altitude ⇒ τ = 0.209 s Assume:

0.2

•N’ = 4 •B = 2 Hz •( bT )Res = bt = 40 ft ( radar seeker beam width resolution of target wing span )

0 0

0.2

0.4

0.6

0.8

Tau, Missile Time Constant, s

N' = 3

N' = 4

N' = 6

1

Calculate: W = ( 40 )2 / [ 3 π2 ( 2 )] = 27.0 ft2 / Hz σGlint / ( bT )Res = KN’ ( W / τ )1/2 / ( bt )Res = 1.206 ( 27.0 / 0.209 )1/2 / 40 = 0.343

σGlint = 0.343 ( 40 ) = 13.7 ft Reference: Bennett, R.R., et al, “Analytical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952 2/24/2008

ELF

247

Minimizing Miss Distance with Glint Requires Optimum Time Constant and Navigation Ratio σ = [( σMAN )Max2 + ( σGlint )2 ]1/2

Note: Proportional guidance Adjoint miss distance ( σMAN )Max = Max miss distance from target maneuver, ft σGlint = Miss distance from glint noise, ft τ = Missile time constant, s N’ = Effective navigation ratio

Rocket Baseline Miss Distance, ft

50 40 30

Example for Rocket Baseline at Mach 2, h = 20k ft altitude ⇒ τ = 0.209 s

20

Assume: 10

N’ = 4 •B = 2 Hz •( bT )Res = 40 ft

0 0

0.2

0.4

0.6

0.8

Tau, Missile Time Constant, s

N' = 3

N' = 4

N' = 6

1

•nT = 5g, VT = 1,000 ft / s, Head-on From prior figures: ( σMAN )Max = 0.9 ft, σGlint = 13.7 ft Calculate:

σ = [( σMAN )Max2 + ( σGlint )2 ]1/2 = 13.7 ft Reference: Bennett, R.R., et al, “Analytical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952 2/24/2008

ELF

248

Missile Carriage RCS and Launch Plume Are Considerations in Launch Platform Observables Launch Platform Integration / Firepower

Carriage and

Missile Carriage Alternatives

Robustness

Cost

Lethality

Reliability

Miss Distance

Survivability

Observables

Launch Observables

Internal Carriage: Lowest Carriage RCS Conformal Carriage: Low Carriage RCS Conventional External Pylon or External Rail Carriage: High Carriage RCS

Plume Alternatives Min Smoke: Lowest Launch Observables ( H2O Contrail ) Reduced Smoke: Reduced Launch Observables ( e.g., HCl Contrail from AP Oxidizer ) High Smoke: High Launch Observables ( e.g., Al2O3 Smoke from Al Fuel )

2/24/2008

ELF

249

Examples of Weapon Bay Internal Carriage and Load-out Center Weapon Bay Best for Ejection Launchers

F-22 Bay Loadout: 3 AIM-120C, 1 GBU-32

Video

AMRAAM Loading in F-22 Bay 2/24/2008

F-117 Bay Loadout: 1 GBU-27, 1 GBU-10

B-1 Bay Loadout: 8 AGM-69

Side Weapon Bay Best for Rail Launchers

F-22 Side Bay: 1 AIM-9 Each Side Bay ELF

RAH-66 Side Bay: 1 AGM-114, 2 FIM92, 4 Hydra 70 Each Side Bay

250

Minimum Smoke Propellant Has Low Observables

High Smoke Example: AIM-7

Reduced Smoke Example: AIM-120

Minimum Smoke Example: Javelin

Particles ( e.g., metal fuel ) at all atmosphere temperature.

Contrail ( HCl from AP oxidizer ) at T < -10° F atmospheric temperature.

Contrail (H2O ) at T < -35º F atmospheric temperature.

High Smoke Motor

Reduced Smoke Motor

Minimum Smoke Motor

2/24/2008

ELF

251

High Altitude Flight and Low RCS Enhance Survivability Pt, Radar Transmitted Power Required for Detection, W

Launch Platform Integration / Firepower

Other Survivability Considerations

Pt = ( 4 π )3 Pr R4 / ( Gt Gr σ λ2 )

10000000

Robustness

Cost

Lethality

Reliability

Miss Distance

Survivability

Observables

1000000 100000 Example for Pt = 50,000 W:

10000

Not detected if: h > 25k ft for σ = 0.001 m2

1000

h > 77k ft for σ = 0.1 m2

100 0

20

40

60

80

100

h, Geometric Altitude, kft RCS = 0.1 m2

2/24/2008

RCS = 0.01 m2

RCS = 0.001 m2

Note: Range Slant Angle = 20 deg, Gt = Transmitter Gain = 40 dB, Gr = Receiver Gain = 40 dB, λ = Wavelength = 0.03 m, Pr = Receiver Sensitivity = 10-14 W, σ = radar cross section ( RCS ) Based on Radar Range Equation with ( S / N )Detect = 1 and Unobstructed Line-of-Sight ELF

252

Mission Planning and High Speed Enhance Survivability Flyby

texp ( V / Rmax ), Non-dimensional Threat Exposure Time

texp = 2 ( Rmax / V ) cos [

sin-1

( yoffset / Rmax )] – treact

2 x

R ma

SAM Site

yoffset

texp V

1

Example: yoffset = 7 nm, Rmax = 10 nm = 60750 ft, yoffset / Rmax = 0.7, treact = 15 s

0 0

0.2

0.4

0.6

0.8

1

yoffset / Rmax, Non-dimensional Offset Distance from Threat treact ( V / Rmax ) = 0

treact ( V / Rmax ) = 1.0

Note: Based on assumption of constant altitude, constant heading flyby of threat SAM site with an unobstructed line-of-sight. texp = exposure time to SAM threat, Rmax = max detection range by SAM threat, V = flyby velocity, yoffset = flyby offset, treact = SAM site reaction time from detection to launch

2/24/2008

treact V

ELF

If V = 1000 ft / s, treact ( V / Rmax ) = 0.247 •texp ( V / Rmax ) = 2 cos [ sin-1 ( 7 / 10 )] – 15 ( 1000 / 60746 ) = 1.428 – 0.247 = 1.181 •texp = 1.181 ( 60746 / 1000 ) = 71.7 s If V = 4000 ft / s, treact ( V / Rmax ) = 0.988 •texp ( V / Rmax ) = 0.440 •texp = 0.440 ( 60746 / 4000 ) = 6.7 s 253

Low Altitude Flight and Terrain Obstacles Provide Masking from Threat hmask = ( hmask )obstacle + ( hmask )earth = hobstacle ( Rlos / Robstacle ) + ( Rlos / 7113 )2 hmask, Altitude that Masks Line-of-Sight Exposure to Surface Threat, ft

2000

hmask = altitude that allows obstacle and earth curvature to mask exposure to surface threat LOS, ft hobstacle = height of obstacle above terrain, ft

1500

Rlos = line-of-sight range to surface threat, ft Robstacle = range from surface threat to obstacle, ft

1000

Height of low hill or tall tree ≈ 100 ft Height of moderate hill ≈ 200 ft Height of high hill ≈ 500 ft

500

Height of low mountain ≈ 1000 ft Example:

0 0

10

20

30

Rlos, Line-of-Sight Range to Surface Threat, nm Rlos ( hobstacle / Robstacle ) = 100 ft Rlos ( hobstacle / Robstacle ) = 200 ft Rlos ( hobstacle / Robstacle ) = 500 ft Rlos ( hobstacle / Robstacle ) = 1000 ft 2/24/2008

ELF

40

hobstacle = 200 ft Robstaacle = 5.0 nm = 30395 ft Rlos = 10.0 nm = 60790 ft Rlos ( hobstacle / Robstaacle ) = 60790 ( 200 / 30395 ) = 400 ft hmask = 200 ( 60790 / 30395 ) + ( 60790 / 7113 )2 = 400 + 73 = 473 ft above terrain 254

Insensitive Munitions Improve Launch Platform Survivability Critical Subsystems

Rocket motor or fuel tank Warhead

Severity Concerns Ranking of Power Output - Type 1. 2. 3. 4. 5.

Detonation ( ~ 0.000002 s rise time ) Partial detonation ( ~ 0.0001 s rise time ) Explosion ( ~ 0.001 s rise time ) Deflagration or propulsion rise time ( ~ 0.1 s rise time ) Burning ( > 1 s )

Design and test considerations ( MIL STD 2105C )

2/24/2008

Fragment / bullet impact or blast Sympathetic detonation Fast / slow cook-off fire Drop Temperature Vibration Carrier landing ( 18 ft / s sink rate ) ELF

255

High System Reliability Is Provided by High Subsystem Reliability and Low Parts Count Typical System Reliability

Rsystem ≈ 0.94 = RArm X RLaunch X RStruct X RAuto X RAct X RSeeker X RIn Guid X RPS X RProp X RFuze X RW/H

Arm ( 0.995 – 0.999 )

Launch Platform Integration / Firepower

Robustness

Cost

Lethality

Reliability

Miss Distance

Survivability

Observables

Reliability

Launch ( 0.990 – 0.995 ) Structure ( 0.997 – 0.999 ) Autopilot ( 0.993 – 0.995 )

Typical Event / Subsystem

Actuators ( 0.990 – 0.995 ) Seeker ( 0.985 – 0.990 ) Inertial Guidance ( 0.995 – 0.999 ) Power Supply ( 0.995 – 0.999 ) Propulsion ( 0.995 – 0.999 ) Fuze ( 0.987 – 0.995 ) Warhead ( 0.995 – 0.999 )

0.90

0.92

0.94

0.96

0.98

1.00

Typical Reliability 2/24/2008

ELF

256

Sensors, Electronics and Propulsion Drive Missile Production Cost Cost

Dome

Seeker

Structure •Rocket – •Airbreather

Guidance and Control

Power – Supply

Very High ( > 25% Production Cost )

Propulsion •Rocket •Airbreather

Warhead – and Fuzing

High ( > 10% )

Wings –

Robustness

Lethality

Reliability

Miss Distance

Survivability

Observables

Stabilizers –

Aerothermal – Data Link Insulation

Moderate ( > 5% )

Launch Platform Integration / Firepower Cost

Flight Control

– Relatively Low ( < 5% )

Note: System assembly and test ~ 10% production cost Propulsion and structure parts count / cost of airbreathing missiles are higher than that of rockets 2/24/2008

ELF

257

Sensors and Electronics Occupy a Large Portion of a High Performance / High Cost Missile. Example: Derby / R-Darter Missile

Source: http://www.israeli-weapons.com/weapons/missile_systems/air_missiles/derby/Derby.html

2/24/2008

ELF

258

Cost Considerations Life Cycle System Development and Demonstration ( SDD ) Production Logistics

Culture / processes Relative Emphasis of Cost, Performance, Reliability, Organization Structure Relaxed Mil STDs IPPD Profit

Competition 2/24/2008

ELF

259

SDD Cost Is Driven by Schedule Duration and Risk CSDD = $20,000,000 tSDD1.90, ( tSDD in years )

CSDD, SDD Cost in Millions

10000

1000

Example: 5 year ( medium risk ) SDD program

100

Low

Moderate

High

Risk

Risk

Risk

SDD

SDD

SDD

CSDD = $20,000,000 tSDD1.90 = ( 20,000,000 ) ( 5 )1.90 = $426,000,000

10 0

2

4

6

8

10

12

14

tSDD, SDD Schedule Duration in Years AGM-142 SLAM AIM-120A

TOW 2 JDAM JSOW

SLAM-ER AGM-130 HARM

MLRS Harpoon Javelin

LB Hellfire ATACMS BAT

JASSM Tomahawk PAC-3

Hellfire II ESSM Patriot

Note: SDD required schedule duration depends upon risk. Should not ignore risk in shorter schedule. -- Source of data: Nicholas, T. and Rossi, R., “U.S. Missile Data Book, 1999,” Data Search Associates, 1999 – SDD cost based on 1999 US$ 2/24/2008

ELF

260

Light Weight Missiles Have Low Unit Production Cost C1000th ≈ $6,100 WL0.758, ( WL in lb ) C1000th, Cost of Missile Number 1000, U.S.$

10000000

Javelin Longbow Hellfire AMRAAM MLRS HARM JSOW Tomahawk

1000000

100000

Example:

10000

2,000 unit buy of 100 lb missile:

10

100 1000 WL , Launch Weight, lb

10000 C1000th ≈ $6,100 WL0.758 = 6100 ( 100 )0.758 = $200,000

Cost of 2,000 missiles = 2000 ( $200000 ) = $400,000,000

Note: -- Source of data: Nicholas, T. and Rossi, R., “U.S. Missile Data Book, 1999,” Data Search Associates, 1999 – Unit production cost based on 1999 US$ 2/24/2008

ELF

261

Learning Curve and Large Production Reduce Unit Production Cost Cx / C1st, Cost of Unit x / Cost of First Unit

Cx = C1st Llog2x, C2x = L Cx , where C in U.S. 99$ 1

L = 1.0

L = 0.9 0.1 Example: For a learning curve coefficient of L = 80%, cost of unit #1000 is 11% the cost of the first unit

0.01 1

10

100

L = 0.8 L = 0.7 1000

10000 100000 1E+06

x, Number of Units Produced Source of data: Nicholas, T. and Rossi, R., “U.S. Missile Data Book, 1999,” Data Search Associates, 1999 2/24/2008

ELF

Javelin ( L = 0.764, C1st = $3.15M, Y1 = 1994 ) Longbow HF ( L = 0.761, C1st = $4.31M, Y1 = 1996 ) AMRAAM ( L = 0.738, C1st = $30.5M, Y1 = 1987 ) MLRS ( L = 0.811, C1st = $0.139M, Y1 = 1980 ) HARM ( L = 0.786, C1st = $9.73M, Y1 = 1981 ) JSOW ( L = 0.812, C1st = $2.98M, Y1 = 1997 ) Tomahawk ( L = 0.817, C1st = $13.0M, Y1 = 1980 )

Labor intensive learning curve: L < 0.8 Machine intensive learning curve: L > 0.8 ) Contributors to the learning curve include: • More efficient labor • Reduced scrap • Improved processes 262

Parts Count, Hours, or Cost ( US$ )

Low Parts Count Reduces Missile Unit Production Cost 1000000 100000 10000 1000 100 10 Parts

Fasteners

Circuit Cards Connectors

Current Tomahawk

Assembly / Test Hours

Unit Production Cost ( US$ )

Tactical Tomahawk

Note: Tactical Tomahawk has superior flexibility ( e.g., shorter mission planning, in-flight retargeting, BDI / BDA, modular payload ) at lower parts count / cost and higher reliability. Enabling technologies for low parts count include: casting, pultrusion / extrusion, centralized electronics, and COTS. 2/24/2008

ELF

263

Tactical Missile Culture Is Driven by Rate Production of Sensors and Electronics Copperhead Seeker and Electronics Production

Patriot Control Section Production

Video of Hellfire Seeker and Electronics Production

2/24/2008

ELF

264

Logistics Cost Considerations Wartime Logistics Activity

Peacetime Logistics Activity

•Contractor Post-production Engineering •Training Manuals / Tech Data Package •Simulation and Software Maintenance •Configuration Management •Engineering Support •System Analysis •Launch Platform Integration •Requirements Documents •Coordinate Suppliers

•Deployment Alternatives •Airlift •Sealift

•Combat Logistics

•Storage Alternatives •Wooden Round ( Protected ) •Open Round ( Humidity, Temp, Corrosion, Shock )

•Reliability Maintenance

•Launch Platform Integration •Mission Planning •Field Tests •Reliability Data •Maintainability Data •Effectiveness Data •Safety Data

•Surveillance •Testing

•Maintenance Alternatives •First level ( depot ) •Two level ( depot, field )

•Disposal 2/24/2008

ELF

265

Logistics Cost Lower for Simple Missile Systems Simple: Stinger More Sophisticated: Hawk and SLAMRAAM

Very Complex: THAAD

2/24/2008

Complex: PAC-3

Video of Logistics Alternatives

ELF

266

Logistics Is Simpler for Light Weight Missiles

Support Personnel required for Installation

Support personnel for installation with 50 lb lift limit per person Support personnel for installation with 100 lb lift limit per person Machine lift for installation 6 4 2 0 10

100

1000

10000

Missile Weight, lb

Predator ( 21 lb ) 2/24/2008

Sidewinder ( 190 lb )

Sparrow ( 500 lb ) ELF

Video of Simple Logistics for a Light weight Missile

Laser Guided Bomb ( 2,500 lb ) 267

Small MEMS Sensors Can Provide Health Monitoring, Reducing Cost and Weight Micro-machined Electro-Mechanical Systems ( MEMS ) Small size / low cost semiconductor manufacturing process 2,000 to 5,000 sensors on a 5 in silicon wafer

Wireless ( RF ) Data Collection and Health Monitoring Distributed Sensors Over Missile Stress / strain Vibration Acoustics Temperature Pressure

Reduced Logistics Cost and Improved Reliability Health monitoring

Reduced Weight and Production Cost More Efficient Design 2/24/2008

ELF

268

Missile Carriage Size, Shape, and Weight Are Driven by Launch Platform Compatibility Launch Platform Integration / Firepower

US Launch Platform

Launcher

Carriage Span / Shape

Length

Weight Launch Platform Integration / Firepower

” 22

Submarines

263”

3400 lb

263”

3400 lb

~168”

~500 lb to 3000 lb

158”

3700 lb

70”

120 lb

Miss Distance

Survivability

Observables

22 ”

~

VLS

Lethality

Reliability

~

Surface Ships

Robustness

Cost

CLS 22”

2/24/2008

” 28

Helos

~

Vehicles

Launch Pods

~24” x 24”

Rail ELF

28 ”

Ground

Rail / Ejection

~

Fighters / Bombers / UCAVs

∼13” x 13”

269

F-18 C / E

5,000 lb

4,000 lb E, carry 1

E, carry 2

C, carry 1

C, carry 2 E, carry 3 C, carry 3

E, carry 2

Configuration for Day Operation with Bring-Back Load 2/24/2008

ELF

+ 2 Inbd Tk + 2 AIM-9

C, carry 2

+ CL Tk + 2 AGM-88

+ 2 Inbd Tk + 2 AIM-9

+ CL Tk + 2 AGM-88

+ CL Tk + 2 AIM-9

+ 2 Inbd Tanks

+ CL Tank

1,000 lb Clean

Outboard Asymmetric Bring-Back Load Limit

E, carry 1

+ CL Tk + 2 AIM-9

2,000 lb

C, carry 1

+ 2 Inbd Tanks

Inboard Asymmetric Bring-Back Load Limit

+ CL Tank

3,000 lb

Clean

Max Strike Weapon Weight

Light Weight Missiles Enhance Firepower

Configuration for Night Operation with Bring-Back Load 270

Launch Envelope Limitations in Missile / Launch Platform Physical Integration Off Boresight Seeker field of regard ⇒ potential obscuring from launch platform

Minimum Range Launcher rail clearance and aeroelasticity ⇒ miss at min range Helo rotor downwash ⇒ miss at min range

Safety Launcher retention ⇒ potential inadvertent release, potential hang-fire Launch platform local flow field α, β ⇒ potential unsafe separation Launch platform maneuvering ⇒ potential unsafe separation Handling qualities with stores ⇒ potential unsafe handling qualities Launch platform bay / canister acoustics ⇒ missile factor of safety Launch platform bay / canister vibration ⇒ missile factor of safety 2/24/2008

ELF

271

Store Separation Wind Tunnel Tests Are Required for Missile / Aircraft Compatibility

F-18 Store Compatibility Test in AEDC 16T

AV-8 Store Compatibility Test in AEDC 4T

Types of Wind Tunnel Testing for Store Compatibility - Flow field mapping with probe - Flow field mapping with store - Captive trajectory simulation - Drop testing Example Stores with Flow Field Interaction: Kh-41 + AA-10 2/24/2008

ELF

272

Examples of Rail Launched and Ejection Launched Missiles

Example Rail Launcher: Hellfire / Brimstone

Example Ejection Launcher: AGM-86 ALCM

Video of Hellfire / Brimstone Carriage / Launch

Video of AGM-86 Carriage / Launch

2/24/2008

ELF

273

Examples of Safe Store Separation

Laser Guided Bombs Drop from F-117

AMRAAM Rail Launch from F-16 2/24/2008

Video of Rapid Drop ( 16 Bombs ) from B-2 ELF

274

Examples of Store Compatibility Problems Unsafe Separation

2/24/2008

Hang-Fire

ELF

Store Aeroelastic Instability

275

MIL-STD-8591 Aircraft Store Suspension and Ejection Launcher Requirements Store Weight / Parameter

30 Inch Suspension

14 Inch Suspension

♦ Weight Up to 100 lb • Lug height ( in ) • Min ejector area ( in x in )

Not Applicable

Yes 0.75 4.0 x 26.0

♦ Weight 101 to 1,450 lb • Lug height ( in ) • Min lug well ( in ) • Min ejector area ( in x in )

Yes 1.35 0.515 4. 0 x 36.0

Yes 1.00 0.515 4.0 x 26.0

♦ Weight Over 1,451 lb • Lug height ( in ) • Min lug well ( in ) • Min ejector area ( in x in )

Yes 1.35 1.080 4.0 x 36.0

Not Applicable

Ejection Stroke

2/24/2008

ELF

276

MIL-STD-8591 Aircraft Store Rail Launcher Examples Rail Launcher

Forward Hanger

LAU-7 Sidewinder Launcher

2.260

LAU 117 Maverick Launcher

1.14

Aft Hanger 2.260

7.23

Note: Dimensions in inches. • LAU 7 rail launched store weight and diameter limits are ≤ 300 lb, ≤ 7 in •LAU 117 rail launched store weight and diameter limits are ≤ 600 lb, ≤ 10 in 2/24/2008

ELF

277

Compressed Carriage Missiles Provide Higher Firepower Baseline AIM-120B AMRAAM

Compressed Carriage AIM-120C AMRAAM ( Reduced Span Wing / Tail )

Baseline AMRAAM: Loadout of 2 AMRAAM per F-22 SemiBay Compressed Carriage AMRAAM: Loadout of 3 AMRAAM per F-22 Semi-Bay

17.5 in

17.5 in

12.5 in 12.5 in 12.5 in

Video of Longshot Kit on CBU-97

Note: Alternative approaches to compressed carriage include surfaces with small span, folded surfaces, wrap around surfaces, and planar surfaces that extend ( e.g., switch blade, Diamond Back, Longshot ). 2/24/2008

ELF

278

Example of Aircraft Carriage and Fire Control Interfaces

Folding Suspension Lug

Wing Deploy Safety Pin

Wing

Folding Suspension Lug

Fire Control / Avionics Umbilical Connector

Flight Control Access Cover

Electrical Safety Pin

Example: ADM-141 TALD ( Tactical Air-Launched Decoy ) Carriage and Fire Control Interfaces 2/24/2008

ELF

279

Example of Ship Weapon Carriage and Launcher, Mk41 VLS Cell Cell Before After Firing Firing

Canister Cell Hatch

Exhaust Hatch Ship Deck Missile Cover

Plenum

8 Modules / Magazine

Tomahawk Launch 2/24/2008

Module Gas Management

8 Canister Cells / Module ELF

Standard Missile Launch 280

Robustness Is Required for Carriage, Shipping, and Storage Environment Environmental Parameter Typical Requirement Surface Temperature

-60° F* to 160° F

Surface Humidity

5% to 100%

Rain Rate

120 mm / h**

Surface Wind

100 km / h steady***

Video: Ground / Sea Environment

150 km / h gusts**** Salt fog

3 g / mm2 deposited per year

Vibration

10 g rms at 1,000 Hz: MIL STD 810, 648, 1670A

Shock

Drop height 0.5 m, half sine wave 100 g / 10 ms: MIL STD 810, 1670A

Acoustic

160 dB

Note: MIL-HDBK-310 and earlier MIL-STD-210B suggest 1% world-wide climatic extreme typical requirement. * Lowest recorded temperature = -90° F. 20% probability temperature lower than -60° F during worst month of worst location. ** Highest recorded rain rate = 436 mm / h. 0.5% probability greater than 120 mm / h during worst month of worst location. *** Highest recorded steady wind = 342 km / h. 1% probability greater than 100 km / h during worst month of worst location. **** Highest recorded gust = 378 km / h. 1% probability greater than 150 km / h during worst month of worst location. 2/24/2008

ELF

281

Summary of Measures of Merit and Launch Platform Integration Measures of Merit Robustness Warhead lethality Miss distance Carriage and launch observables Other survivability considerations Reliability Cost

Launch Platform Integration Firepower, weight, fitment Store separation Launch platform handling qualities, aeroelasticity Hang-fire Vibration Standard launchers Carriage and storage environment

Discussion / Questions? Classroom Exercise ( Appendix A ) 2/24/2008

ELF

282

Measures of Merit and Launch Platform Integration Problems 1. 2. 3. 4. 5. 6. 7. 8. 9.

2/24/2008

IR signal attenuation is greater than 100 dB per km through a c____. GPS / INS enhances seeker lock-on in adverse weather and ground c______. A data link can enhance missile seeker lock-on against a m_____ target. An example of a missile counter-counter measure to flares is an i______ i_____ seeker. Compared to a mid-wave IR seeker, a long wave IR seeker receives more energy from a c___ target. High fineness kinetic energy penetrators are required to defeat b_____ targets. For the same lethality with a blast fragmentation warhead, a small decrease in miss distance allows a large decrease in the required weight of the w______. For a blast / frag warhead, a charge-to-metal ratio of about one is required to achieve a high total fragment k______ e_____. A blast fragmentation warhead tradeoff is the number of fragments versus the individual fragment w_____. ELF

283

Measures of Merit and Launch Platform Integration Problems ( cont ) 10. 11. 12. 13. 14. 15. 16. 17. 18.

2/24/2008

Kinetic energy penetration is a function of the penetrator diameter, length, density, and v_______. In proportional homing guidance, the objective is to make the line-of-sight angle rate equal to z___. Aeromechanics contributors to missile time constant are flight control effectiveness, flight control system dynamics, and dome e____ s____. Miss distance due to heading error is a function of missile navigation ratio, velocity, time to correct the heading error, and the missile t___ c_______. A missile must have about t_____ times the maneuverability of the target. Minimizing the miss distance due to radar glint requires a high resolution seeker, an optimum missile time constant and an optimum n_________ r____. Weapons on low observable launch platforms use i_______ carriage. Weapons on low observable launch platforms use m______ smoke propellant. For an insensitive munition, burning is preferable to detonation because it releases less p____. ELF

284

Measures of Merit and Launch Platform Integration Problems ( cont ) 19. 20. 21. 22. 23. 24. 25. 26. 27.

2/24/2008

Missile system reliability is enhanced by subsystem reliability and low p____ count. High cost subsystems of missiles are sensors, electronics, and p_________. Missile SDD cost is driven by the program duration and r___. Missile unit production cost is driven by the number of units produced, learning curve, and w_____. First level maintenance is conducted at a d____. A standard launch system for U.S. Navy ships is the V_______ L_____ S_____. Most light weight missiles use rail launchers while most heavy weight missiles use e_______ launchers. Higher firepower is provided by c_________ carriage. The typical environmental requirement from MIL-HDBK-310 is the _% worldwide climatic extreme.

ELF

285

Outline Introduction / Key Drivers in the Design Process Aerodynamic Considerations in Tactical Missile Design Propulsion Considerations in Tactical Missile Design Weight Considerations in Tactical Missile Design Flight Performance Considerations in Tactical Missile Design Measures of Merit and Launch Platform Integration Sizing Examples Development Process Summary and Lessons Learned References and Communication Appendices ( Homework Problems / Classroom Exercises, Example of Request for Proposal, Nomenclature, Acronyms, Conversion Factors, Syllabus ) 2/24/2008

ELF

286

Sizing Examples Rocket Baseline Missile Standoff range requirement Wing sizing requirement Multi-parameter harmonization Lofted range comparison

Ramjet Baseline Missile Range robustness Propulsion and fuel alternatives Velocity control

Computer Aided Conceptual Design Sizing Tools Soda Straw Rocket Design, Build, and Fly 2/24/2008

ELF

287

Air-to-Air Engagement Analysis Process and Assumptions F-pole range provides kill of head-on threat outside of threat weapon launch range Aircraft contrast for typical engagement C = 0.18

Typical visual detection range by target ( Required F-pole range ) RD = 3.3 nm

Typical altitude and speed of launch aircraft, target aircraft, and missile h = 20k ft altitude VL = Mach 0.8 = 820 ft / s VT = Mach 0.8 = 820 ft / s VM = 2 VT = 1,640 ft / s 2/24/2008

ELF

288

Assumed Air-to-Air Engagement Scenario for Head-on Intercept RL= VM tf + VT tf

t = 0 s (Launch Missile)

RF-Pole = VM tf - VL tf

Blue Aircraft ( 820 ft / s )

Red Aircraft ( 820 ft / s )

Blue Missile ( 1640 ft / s ) RL= Launch Range = 10.0 nm RF = Missile Flight Range = 6.7 nm

t = tf = 24.4 s ( Missile Impacts Target ) Blue Aircraft ( 820 ft / s )

Red Aircraft Destroyed R F-pole = 3.3 nm

2/24/2008

ELF

289

R, Visible Range for 50 ft2 Target, nm

Target Contrast and Size Drive Visual Detection and Recognition Range

2/24/2008

8

RD = 1.15 [ Atp ( C – CT )]1/2, RD in nm, Atp in ft2 RR = 0.29 RD

Visual Detection Range, nm Visual Recognition Range, nm

6

Note: RD = Visual detection range for probability of detection PD = 0.5 C = Contrast CT = Visual threshold contrast = 0.02 Atp = Target presented area = 50 ft2 RR = Visual recognition range θF = Pilot visual fovial angle = 0.8 deg Clear weather Pilot search glimpse time = 1 / 3 s

4 2

Example: If C = 0.18 RD = 3.3 nm RR = 1.0 nm

0 0.01

C = 0.01 C = 0.02

0.1

1

C, Contrast C = 0.05 C = 0.1 C = 0.2

ELF

C = 0.5 C = 1.0

290

High Missile Velocity Improves Standoff Range RF-Pole / RL = 1 – ( VT + VL ) / ( VM + VT )

Note: Head-on intercept RF-Pole = Standoff range at intercept RL= Launch range

F-Pole Range / Launch Range

1

VM = Missile average velocity VT = Target velocity

0.8

VL = Launch velocity

VL / VM = 0 VL / VM = 0.2 VL / VM = 0.5 VL / VM = 1.0

0.6 0.4 0.2 0 0

0.2

0.4

0.6

0.8

Target Velocity / Missile Velocity 2/24/2008

ELF

1

Example: • VL = VT • VM = 2 VT • Then VT / VM = VL / VM = 0.5 • RF-Pole / RL = 0.33 • RF-Pole = RD = 3.3 nm • RL = 3.3 / 0.33 = 10.0 nm 291

Missile Flight Range Requirement Is Greatest for a Tail Chase Intercept RF / RL, Missile Flight Range / Launch Range

( RF / RL )Head-on = ( VM / VT ) / [(VM / VT ) + 1 ] 3

( RF / RL )TailChase = ( VM / VT ) / [(VM / VT ) - 1 ]

2.5 2 ( RF / RL ) Head-on ( RF / RL ) Tail Chase

1.5

Examples:

1

•Head-on Intercept

0.5 0 0

1

2

3

4

VM / VT, Missile Velocity / Target Velocity

2/24/2008

ELF

5

• VM = 1,640 ft / s, VT = 820 ft / s • VM / VT = 1640 / 820 = 2 • RF / RL = 2 / ( 2 + 1 ) = 0.667 • RL = 10.0 nm • RF = 0.667 ( 10.0 ) = 6.67 nm •Tail Intercept at same conditions • RF / RL = 2 / ( 2 – 1 ) = 2.0 • RF = 2.0 ( 10.0 ) = 20.0 nm

292

Drawing of Rocket Baseline Missile Configuration STA 60.8 19.4

LEmac at STA 131.6 BL 8.0

3.4 LEmac at STA 67.0 BL 10.2

Λ = 45° 16.1

8.0 d cgBO

STA 125.4 18.5 12.0

cgLaunch Λ = 57° Rocket Motor

40.2 STA 0

19.2 Nose

46.1 Forebody

62.6 84.5 Payload Midbody Bay

Aftbody

138.6 143.9 Tailcone

Note: Dimensions in inches Source: Bithell, R.A. and Stoner, R.C., “Rapid Approach for Missile Synthesis, Vol. 1, Rocket Synthesis Handbook,” AFWAL-TR-81-3022, Vol. 1, March 1982.

2/24/2008

ELF

293

Mass Properties of Rocket Baseline Missile Component 1 3 2 4 5 6

2/24/2008

Weight, lb.

C.G. STA, in.

4.1 12.4 46.6 7.6 77.7 10.2 61.0 0.0 47.3 23.0 6.5 5.8 26.2 38.6

12.0 30.5 32.6 54.3 54.3 73.5 75.5 – 107.5 117.2 141.2 141.2 137.8 75.5

Burnout Total Propellant

367.0 133.0

76.2 107.8

Launch Total

500.0

84.6

Nose ( Radome ) Forebody structure Guidance Payload Bay Structure Warhead Midbody Structure Control Actuation System Aftbody Structure Rocket Motor Case Insulation ( EDPM – Silica ) Tailcone Structure Nozzle Fixed Surfaces Movable Surfaces

ELF

294

Rocket Baseline Missile Definition Body

Dome Material Airframe Material Length, in Diameter, in Airframe thickness, in Fineness ratio Volume, ft3 Wetted area, ft2 Nozzle exit area, ft2 Boattail fineness ratio Nose fineness ratio Nose bluntness Boattail angle, deg

Pyroceram Aluminum 2219-T81 143.9 8.0 0.16 17.99 3.82 24.06 0.078 0.38 2.40 0.0 7.5

Material Planform area, ft2 ( 2 panels exposed ) Wetted area, ft2 ( 4 panels ) Aspect ratio ( 2 panels exposed ) Taper ratio Root chord, in Tip chord, in Span, in ( 2 panels exposed ) Leading edge sweep, deg

Aluminum 2219-T81 2.55 10.20 2.82 0.175 19.4 3.4 32.2 45.0

Movable surfaces ( forward )

2/24/2008

ELF

295

Rocket Baseline Missile Definition ( cont ) Movable surfaces ( continued )

Mean aerodynamic chord, in Thickness ratio Section type Section leading edge total angle, deg xmac, in ymac, in ( from root chord ) Actuator rate limit, deg / s

13.3 0.044 Modified double wedge 10.01 67.0 6.2 360.0

Material Modulus of elasticity, 106 psi Planform area, ft2 ( 2 panels exposed ) Wetted area, ft2 ( 4 panels ) Aspect ratio ( 2 panels exposed ) Taper ratio Root chord, in Tip chord, in Span, in ( 2 panels exposed ) Leading edge sweep, deg Mean aerodynamic chord, in Thickness ratio Section type Section leading edge total angle, deg xmac, in ymac, in ( from root chord )

Aluminum 2219-T81 10.5 1.54 6.17 2.59 0.0 18.5 0.0 24.0 57.0 12.3 0.027 Modified double wedge 6.17 131.6 4.0

Fixed surfaces ( aft )

2/24/2008

ELF

296

Rocket Baseline Missile Definition ( cont ) References values Reference area, ft2 Reference length, ft Pitch / Yaw Moment of inertia at launch, slug-ft2 Pitch / Yaw Moment of inertia at burnout, slug-ft2

0.349 0.667 117.0 94.0

Rocket Motor Performance ( altitude = 20k ft, temp = 70° F ) Burning time, sec ( boost / sustain ) Maximum pressure, psi Average pressure, psi ( boost / sustain ) Average thrust, lbf ( boost / sustain ) Total impulse, lbf-s ( boost / sustain ) Specific impulse, lbf-s / lbm ( boost / sustain )

3.69 / 10.86 2042 1769 / 301 5750 / 1018 21217 / 11055 250 / 230.4

Propellant Weight, lbm ( boost / sustain ) Flame temperature @ 1,000 psi, °F Propellant density, lbm / in3 Characteristic velocity, ft / s Burn rate @ 1000 psi, in / s Burn rate pressure exponent 2/24/2008

84.8 / 48.2 5282 / 5228 0.065 5200 0.5 0.3 ELF

297

Rocket Baseline Missile Definition ( cont ) Propellant ( continued ) Burn rate sensitivity with temperature, % / °F Pressure sensitivity with temperature, % / °F

0.10 0.14

Rocket Motor Case Yield / ultimate strength, psi Material Modulus of elasticity, psi Length, in Outside diameter, in Thickness, in (minimum) Burst pressure, psi Volumetric efficiency Grain configuration Dome ellipse ratio

170,000 / 190,000 4130 Steel 29.5 x 106 psi 59.4 8.00 0.074 3140 0.76 Three slots + web 2.0

Nozzle Housing material Exit geometry Throat area, in2 Expansion ratio Length, in Exit diameter, in 2/24/2008

4130 Steel Contoured ( equiv. 15° ) 1.81 6.2 4.9 3.78 ELF

298

Rocket Baseline Missile Has Boost-Sustain Thrust - Time History 8

Boost Total Impulse = ∫Tdt = 5750 ( 3.69 ) = 21217 lb-s

6

Thrust – 1,000 lb 4

2 Sustain Total Impulse = ∫Tdt = 1018 ( 10.86 ) = 11055 lb-s

0

2/24/2008

0

4

Time – seconds ELF

8

12

16

Note: Altitude = 20k ft, Temperature = 70° F Total impulse drives velocity change 299

Normal Force ~ CN

Pitching Moment – Cm

Rocket Baseline Missile Aerodynamic Characteristics 0 -4.0

0.6

4.60

M = 1.2 and 1.5

-8.0

3.95

-12.0

2.35 2.0

-16.0 20

M 1.5

16

2.0 2.35 2.87 3.95 4.60

1.2 0.6

12 8 4 0

2/24/2008

SRef = 0.349 ft2, lRef = d = 0.667 ft, CG at STA 75.7, δ = 0 deg

0

4

8 12 16 α, Angle of Attack – Deg ELF

20

24 300

K1, K2 ~ Per Deg2

K2

.004

0.2

K1

.002

0.1

CA = CAα = 0 + K1 δ2 + K2 α δ

0

0 1.2

Power Off

0.8 Power On

1.2 0.8 0.4

δ

0.4 0

2/24/2008

.006

0.3

Cm at α = 0 deg, Per Deg

CA at α = 0 deg

δ

CN at α = 0 deg, Per Deg

Rocket Baseline Missile Aerodynamic Characteristics ( cont )

0

1

2 3 4 M, Mach Number

0

5 ELF

0

1

2 3 4 M, Mach Number

5 301

High Altitude Launch Enhances Rocket Baseline Range Burnout

Vmax = 2524 ft / s

40

Altitude ~ 103 ft

30

Boost / Sustain

Termination Mach = 1.5

Coast

Vmax = 2147 ft / s

20 ML = 0.7 CD

10

AVG

Vmax = 1916 ft / s

= 0.65

Constant Altitude Flight

0 0

5

10

15

20

25

Range ~ nm 2/24/2008

ELF

302

Low Altitude Launch and High Alpha Maneuvers Enhance Rocket Baseline Turn Performance 25

Alt.

α

1 10k ft 15° 2 10k ft 10° 3 40k ft 15° 4 40k ft 10°

Cross Range 1,000 ft.

20 15 4 10

3

5

1

Termination at M = 1.0 Marks at 2 s intervals

2 0

-10

-5

0

5

10

Down Range 1,000 ft. Note: Off boresight envelope that is shown does not include the rocket baseline seeker field-of-regard limit ( 30 deg ). 2/24/2008

ELF

303

Paredo Shows Range of Rocket Baseline Driven by ISP, Propellant Weight, Drag, and Static Margin 1.5 Note: Rocket baseline:

1

hL = 20k ft, ML = 0.7, MEC = 1.5 R@ ML = 0.7, hL = 20k ft = 9.5 nm

Nondimensional 0.5 Range Sensitivity to 0 Parameter

Example: 10% increase in propellant weight ⇒ 8.8% increase in flight range

Isp

Prop. Weight

CD0

-0.5

Drag- Static Thrust Inert Due-to- Margin Weight Lift

-1 Parameter 2/24/2008

ELF

304

Boost - Sustain Trajectory Assumptions Assumptions 1 degree of freedom Constant altitude

Simplified equation for axial acceleration based on thrust, drag, and weight nX = ( T – D ) / W

Missile weight varies with burn rate and time W = WL – WP t / tB

Drag is approximated by D = CDO q S

2/24/2008

ELF

305

Example of Rocket Baseline Axial Acceleration nX = ( T - D ) / W 15

Note: tf = 24.4 s ML = 0.8 hL = 20,000 ft TB = 5750 lb tB = 3.69 s TS = 1018 lb tS = 10.86 s D = 99 lb at Mach 0.8 D = 1020 lb at Mach 2.1 WL = 500 lb WP = 133 lb

nx, Axial Acceleration, g

Boost

10

5 Sustain

0 0

5

10

15

Coast

20

25

-5 t, Time, s 2/24/2008

ELF

306

Example of Rocket Baseline Missile Velocity vs Time ΔV / ( gc ISP ) = - ( 1 - DAVG / T ) ln ( 1 - Wp / Wi ), During Boost-Sustain V / VBO = 1 / { 1 + t / { 2 WBO / [ gc ρAVG SRef ( CD )AVG VBO ]}}, During Coast 0

V, Velocity, ft / s

3000

Sustain

2000

Coast

Boost

1000

Note: ML = 0.8 hL = 20k feet

0 0

5

10

15

20

25

t, Time, s 2/24/2008

ELF

307

Range and Time-to-Target of Rocket Baseline Missile Meet Requirements 10

R = Δ Rboost + Δ Rsustain + Δ Rcoast

R, Flight Range, nm

8 Coast

6 (RF)Req = 6.7 nm @ t =24.4 s

4

Sustain Note:

2

ML = 0.8

Boost

hL = 20k ft

0 0

5

10

15

20

25

t, Time, s 2/24/2008

ELF

308

Sizing Examples Rocket Baseline Missile Standoff range requirement Wing sizing requirement Multi-parameter harmonization Lofted range comparison

Ramjet Baseline Missile Range robustness Propulsion and fuel alternatives Velocity control

Computer Aided Conceptual Design Sizing Tools Soda Straw Rocket Design, Build, and Fly 2/24/2008

ELF

309

Example of Wing Sizing to Satisfy Required Maneuver Acceleration Size Wing for the Assumptions ( nZ )Required = 30 g to counter 9 g maneuvering target ) ( nZ ) = Δ ( nZ )Wing + Δ ( nZ )Body + Δ ( nZ )Tail

Rocket Baseline @ Mach 2 20,000 ft altitude 367 lb weight ( burnout )

From Prior Example, Compute

αWing = α’Max = ( α + δ )Max = 22 deg for rocket baseline Video of Intercept of Maneuvering Target

α = 0.75δ, αBody = αTail = 9.4 deg

Δ ( nZ )Body = q SRef ( CN )Body / W = 2725 ( 0.349 ) ( 1.28 ) / 367 = 3.3 g ( from body ) Δ ( nZ )Tail = q STail [( CN )Tail ( SRef / STail )] / W = 2725 ( 1.54 ) ( 0.425 ) / 367 = 4.9 g ( from tail ) Δ ( nZ )Wing = ( nZ )Required - Δ ( nZ )Body - Δ ( nZ )Tail = 30 – 3.3 – 4.9 = 21.8 g ( SW )Required = Δ ( nZ )Wing W / { q [( CN )Wing (SRef / SWing )]} = 21.8 ( 367 ) / {( 2725 ) ( 1.08 )} = 2.72 ft2 Note: ( SW )RocketBaseline = 2.55 ft2

2/24/2008

ELF

310

Wing Sizing to Satisfy Required Turn Rate Assume .

( γ )Required > 18 deg / s to counter 18 deg / s maneuvering aircraft

Rocket Baseline @ Mach 2 20,000 ft altitude 367 lb weight ( burnout ) γi = 0 deg

Compute .

γ = gc n / V = [ q SRef CNα α + q SRef CNδ δ - W cos ( γ ) ] / [( W / gc ) V ] α / δ = 0.75 α’ = α + δ = 22 deg ⇒ δ = 12.6 deg, α = 9.4 deg . γ = [ 2725 ( 0.349 )( 0.60 )( 9.4 ) +2725 ( 0.349 )( 0.19 )( 12.6 ) – 367 ( 1 )] / ( 367 / 32.2 )( 2074 ) = 0.31 rad / s or 18 deg / s

Note: ( SW )RocketBaseline ⇒ 18 deg / s Turn Rate

2/24/2008

ELF

311

Wing Sizing to Satisfy Required Turn Radius Assume Maneuvering Aircraft Target with .

γ = 18 deg / s = 0.314 rad / s V = 1000 ft / s . ( RT )Target = V / γ = 1000 / 0.314 = 3183 ft

Assume Rocket Baseline @ Mach 2 20,000 ft altitude 367 lb weight ( burnout )

Compute .

γ = 18 deg / s ( prior figure ) . ( RT )RocketBaselinet = V / γ = 2074 / 0.314 = 6602 ft

Note: ( RT )RocketBaselinet > ( RT )Target ⇒ Rocket Baseline Can Be Countermeasured by Target in a Tight Turn Counter-Countermeasure Alternatives Larger Wing Higher Angle of Attack Longer Burn Motor with TVC 2/24/2008

ELF

312

Sizing Examples Rocket Baseline Missile Standoff range requirement Wing sizing requirement Multi-parameter harmonization Lofted range comparison

Ramjet Baseline Missile Range robustness Propulsion and fuel alternatives Velocity control

Computer Aided Conceptual Design Sizing Tools Soda Straw Rocket Design, Build, and Fly 2/24/2008

ELF

313

Combined Weight / Miss Distance Drivers: Nozzle Expansion and Motor Volumetric Efficiency Parameter

Baseline

Fixed surface number of panels Movable surface number of panels Design static margin at launch Wing movable surface sweep ( deg ) Tail fixed surface sweep ( deg ) Wing movable surface thickness ratio Nose fineness ratio Rocket chamber sustain pressure ( psi ) Boattail fineness ratio ( length / diameter ) Nozzle expansion ratio Motor volumetric efficiency Propellant density ( lb / in3 ) Boost thrust ( lb ) Sustain thrust ( lb ) Characteristic velocity ( ft / s ) Wing location ( percent total length )

4 4 0.40 45.0 57.0 0.044 2.4 301 0.38 6.2 0.76 0.065 5,750 1,018 5,200 47.5

Sensitivity Variation 3 2 0.30 49.5 60.0 0.034 2.6 330 0.342 6.82 0.84 0.084 6,325 1,119 5,720 42.75 Note:

Baseline: Weight = 500 lb, Miss distance = 62.3 ft W* = weight sensitivity for parameter variation = ΔW / W

σ* = miss distance sensitivity for parameter variation = Δ σ / σ 2/24/2008

ELF

W*

σ*

+0.054 +0.071 +0.095 -0.205 +0.027 +0.041 -0.016 -0.076 +0.096 -0.114 -0.136 -0.062 +0.014 +0.088 -0.063 +0.181

+0.100 +0.106 +0.167 +0.015 +0.039 +0.005 -0.745 -0.045 +0.140 -0.181 -0.453 +0.012 -0.018 +0.246 -0.077 -0.036

Strong impact with synergy Strong impact Moderate impact with synergy Moderate impact 314

A Harmonized Missile Can Have Smaller Miss Distance and Lighter Weight Parameter Judicious changes Boost thrust ( lb ) Wing location ( percent missile length to 1/4 mac ) Wing taper ratio Nose fineness ratio Nose blunting ratio Nozzle expansion ratio Sustain chamber pressure ( psi ) Boattail fineness ratio Tail leading edge sweep ( deg ) Technology limited changes No. wing panels No. tail panels Wing thickness ratio Wing leading edge sweep ( deg ) Static margin at launch ( diam ) Propellant density ( lb / in3 ) Motor volumetric efficiency Measures of Merit Total weight ( lb ) Miss distance ( ft ) Time to target ( s ) Length ( in ) Mach No. at burnout Weight of propellant ( lb ) Wing area ( in2 ) Tail area ( in2 ) 2/24/2008

*Note:

Value of driving parameter

Baseline Value

Missile Configured for Minimum: Weight Miss Distance

Harmonized

5,750 47.5 0.18 2.4 0.0 6.2 301 0.38 57

3,382 47 0.2 3.2 0.05 15 1,000 0.21 50

3,382 44 0.2 2.55 0.05 15 1,000 0.21 50

3,382 46 0.2 2.6 0.05 15 1,000 0.21 50

4 4 0.044 45 0.4 0.065 0.76

2 3 0.030 55 0.0 0.084 0.84

2 3 0.030 55 0.0 0.084 0.84

2 3 0.030 55 0.0 0.084 0.84

500 62.3 21.6 144 2.20 133 368.6 221.8

385.9 63.1 23.8 112.7 2.08 78.3 175.5 109.1

395.0 16.2 23.6 114.7 2.09 85.4 150.7 134.5

390.1 16.6 23.8 114.9 2.07 85.9 173.8 112.0

ELF

315

Baseline Missile vs Harmonized Missile 144”

57°

45° 2.4 Nose Fineness; 2.6

Weight ( lb ); 500 390

Propellant Density 0.065 0.084 ( lb / in3 );

55°

Surfaces;

{ 2 wings / 3 tails 4 wings / 4 tails

50°

115” 2/24/2008

ELF

316

Sizing Examples Rocket Baseline Missile Standoff range requirement Wing sizing requirement Multi-parameter harmonization Lofted range comparison

Ramjet Baseline Missile Range robustness Propulsion and fuel alternatives Velocity control

Computer Aided Conceptual Design Sizing Tools Soda Straw Rocket Design, Build, and Fly 2/24/2008

ELF

317

Lofted Glide Trajectory Provides Extended Range Using Rocket Baseline, Compare Lofted Launch-Coast-Glide Trajectory Lofted Launch-Ballistic Trajectory Constant Altitude Trajectory

Assume for Lofted Launch-Coast-Glide Trajectory: γi = 45 deg γ = 45 deg during boost and sustain γ = 45 deg coast Switch to ( L / D )max glide at optimum altitude ( L / D )maxg glide trajectory after apogee hi = hf = 0 ft

Velocity, Horizontal Range, and Altitude During Initial Boost @ γ = 45 deg ΔV = - gc ISP [ 1 – ( DAVG / T ) - ( WAVG sin γ ) / T ] ln ( 1 - Wp / Wi ) = -32.2 ( 250 ) [ 1 - ( 419 / 5750 ) – 458 ( 0.707 ) / 5750 ] ln ( 1 - 84.8 / 500 ) = 1,303 ft / s ΔR = ( Vi + ΔV / 2 ) tB = ( 0 + 1303 / 2 ) 3.69 = 2,404 ft ΔRx = ΔR cos γi = 2404 ( 0.707 ) = 1,700 ft ΔRy = ΔR sin γi = 2404 ( 0.707 ) = 1,700 ft h = hi + ΔRy = 0 + 1700 = 1,700 ft 2/24/2008

ELF

318

Lofted Glide Trajectory Provides Extended Range ( cont ) Velocity, Horizontal Range, and Altitude During Sustain @ γ = 45 deg ΔV = - gc ISP [ 1 – ( DAVG / T ) – ( WAVG sin γ ) / T ] ln ( 1 - Wp / Wi ) = -32.2 ( 230.4 ) [ 1 – ( 650 / 1018 ) – 391 ( 0.707 ) / 1018 ] ln ( 1 - 48.2 / 415.2 ) = 81 ft / sec VBO = 1303 + 81 = 1,384 ft / s ΔR = ( Vi + ΔV / 2 ) tB = ( 1303 + 81 / 2 ) 10.86 = 14,590 ft ΔRx = ΔR cos γi = 14590 ( 0.707 ) = 10,315 ft ΔRy = ΔR sin γi = 14,590 ( 0.707 ) = 10,315 ft h = hi + ΔRy = 1700 + 10315 = 12,015 ft

Velocity, Horizontal Range, and Altitude During Coast @ γ = 45 deg to h@( L / D )max Vcoast = Vi { 1 – [( gc sin γ ) / Vi ] t } / { 1 + {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t } = 1384 { 1 – [( 32.2 ( 0.707 )) / 1384 ] 21 } / { 1 + {[ 32.2 ( 0.001338 ) ( 0.349 ) ( 0.7 ) ( 1384 )] / ( 2 ( 367 ))} 21 } = 674 ft / s Rcoast = { 2 W / [ gc ρAVG SRef ( CD0 )AVG )]} ln { 1 – [ gc2 ρAVG SRef ( CD0 )AVG / ( 2 W )] [ sin γ ] t2 + {[ gc ρAVG SRef ( CD0 )AVG Vi ] / ( 2 W )} t } = { 2 ( 367 ) / [ 32.2 ( 0.001338 ) ( 0.349 ) ( 0.7 )] ln { 1 – [ (32.2)2 ( 0.001338 ) ( 0.349 ) ( 0.7 ) / (( 2 ( 367 ))] [ 0.707 ] ( 21 )2 + {[ 32.2 ( 0.001338 ) ( 0.349 ) ( 0.7 ) ( 1384 )] / ( 2 ( 367 ))} 21 } = 17148 ft ( Rx )coast = ( Ry )coast = Rcoast sinγ = 17148 ( 0.707 ) = 12124 ft

2/24/2008

ELF

319

Lofted Glide Trajectory Provides Extended Range ( cont ) Flight Conditions At End-of-Coast Are: t = 35 s V = 674 ft / s h = 24,189 ft q = 251 psf M = 0.66 ( L / D )max = 5.22 α( L / D )max = 5.5 deg

Initiate α = α( L / D )max = 5.5 deg at h = 24,189 ft Incremental Horizontal Range During ( L / D )max Glide Is ΔRx = ( L / D ) Δh = 5.22 ( 24189 ) = 126,267 ft

Total Horizontal Range for Elevated Launch-Coast-Glide Trajectory Is Rx = ΣΔRx = ΔRx,Boost + ΔRx,Sustain + ΔRx,Coast + ΔRx,Glide = 1700 + 10315 + 12124 + 126267 = 150406 ft = 24.8 nm

2/24/2008

ELF

320

Lofted Glide Trajectory Provides Extended Range ( cont ) Note: Rocket Baseline

30

z End of boost

0

γ = 45 de g Ballis t ic

Gli de

s, h = 21,590 ft

ÊLofted coast apogee, t = 35 s, V = 674 ft / s, h = 24,189 ft

@

(L

/D

®Lofted ballistic impact, t = 68 s,

)m

²Lofted

ax

istic

Coas t@

20

γ = - 71 deg, V = 1368 ft / s

glide impact, t = 298 s, γ = - 10.8 deg, V = 459 ft / s

Ä Co-altitude flight impact, t = 115 s, V = 500 ft / s

„

Susta in

10

ÈLofted ballistic apogee, t = 35 s, V = 667 ft /

Ø È

Ball

h, Altitude, k ft

„ End of sustain

z z

0

Co-altitude

„

®

Ä

²

10

20

30

R, Range, nm

2/24/2008

ELF

321

Sizing Examples Rocket Baseline Missile Standoff range requirement Wing sizing requirement Multi-parameter harmonization Lofted range comparison

Ramjet Baseline Missile Range robustness Propulsion and fuel alternatives Velocity control

Computer Aided Conceptual Design Sizing Tools Soda Straw Rocket Design, Build, and Fly 2/24/2008

ELF

322

Ramjet Baseline Is a Chin Inlet Integral Rocket Ramjet ( IRR ) Sta 150.3 37°

11.6 11.5 16.5

Boost Nozzle

20.375 dia Guidance Chin Inlet Sta 0.

Ramjet Fuel

Warhead

Boost Propellant Booster, and Ramjet Engine

Transport Air Duct 23.5

43.5 Forebody

126.0

76.5 Payload Bay

Mid-body

Nose

Aft-body

Tail Cone 159.0

171.0

Note: Dimensions are in inches

Source: Bithell, R.A. and Stoner, R.C. “Rapid Approach for Missile Synthesis”, Vol. II, Air-breathing Synthesis Handbook, AFWAL TR 81-3022, Vol. II, March 1982. 2/24/2008

ELF

323

Mass Properties of Ramjet Baseline Missile Component

Weight, lb

Nose

CG Sta, in

15.9

15.7

Forebody Structure Guidance

42.4 129.0

33.5 33.5

Payload Bay Structure Warhead

64.5 510.0

60.0 60.0

Midbody Structure Inlet Electrical Hydraulic System for Control Actuation Fuel Distribution

95.2 103.0 30.0 20.0 5.0

101.2 80.0 112.0 121.0 121.0

Aftbody Structure Engine

44.5 33.5

142.5 142.5

Tailcone Structure Ramjet Nozzle Flight Control Actuators Fins ( 4 ) End of Cruise Ramjet Fuel ( 11900 in3 ) Start of Cruise Boost Nozzle ( Ejected ) Frangible Port End of Boost Boost Propellant 2/24/2008 Booster Ignition

31.6 31.0 37.0 70.0 1,262.6 476.0 1,738.6 31.0 11.5 1,781.1 449.0 2,230.1 ELF

165.0 165.0 164.0 157.2 81.8 87.0 83.2 164.0 126.0 84.9 142.5 96.5

324

Ramjet Baseline Missile Definition Inlet

Type Material Conical forebody half angle, deg Ramp wedge angle, deg Cowl angle, deg Internal contraction ratio Capture area, ft2 Throat area, ft2

Mixed compression Titanium 17.7 8.36 8.24 12.2 Percent 0.79 0.29

Dome Material Airframe Material Combustor Material Length, in Diameter, in Fineness ratio Volume, ft3 Wetted area, ft2 Base area, ft2 ( cruise ) Boattail fineness ratio Nose half angle, deg Nose length, in

Silicon nitride Titanium Insulated Inconel 171.0 20.375 8.39 28.33 68.81 0.58 N/A 17.7 23.5

Body

2/24/2008

ELF

325

Ramjet Baseline Missile Definition ( cont ) Tail ( Exposed )

Material Planform area ( 2 panels ), ft2 Wetted area ( 4 panels ), ft2 Aspect ratio ( 2 panels exposed ) Taper ratio Root chord, in Span, in. ( 2 panels exposed ) Leading edge sweep, deg Mean aerodynamic chord, in Thickness ratio Section type Section leading edge total angle, deg xmac, in ymac, in ( from root chord )

Titanium 2.24 8.96 1.64 0.70 16.5 23.0 37.0 14.2 0.04 Modified double wedge 9.1 150.3 5.4

Reference values Reference area, ft2 Reference length, ft 2/24/2008

2.264 1.698 ELF

326

Engine Nomenclature and Flowpath Geometry for Ramjet Baseline ( CD0 )Nose Corrected = ( CD0 )Nose Uncorrected x ( 1 - Ac / SREF )

Ac = Inlet capture area SRef = Reference area

20.375 in

Ac = 114 in2 120°

Ramjet Engine Station Identification SRef

0

1

2

3

4

5

6

Subscripts 0 Free stream flow into inlet ( Example, Ramjet Baseline at Mach 4, α = 0 deg ⇒ A0 = 104 in2. Note: AC = 114 in2 ) 1 Inlet throat ( Ramjet Baseline A1 = AIT = 41.9 in2 ) 2 Diffuser exit ( Ramjet Baseline A2 = 77.3 in2 ) 3 Flame holder plane ( Ramjet Baseline A3 = 287.1 in2 ) 4 Combustor exit ( Ramjet Baseline A4 = 287.1 in2 ) 5 Nozzle throat ( Ramjet Baseline A5 = 103.1 in2 ) 6 Nozzle exit ( Ramjet Baseline A6 = 233.6 in2 ) Ref Reference Area ( Ramjet Baseline Body Cross-sectional Area, SRef = 326 in2 ) 2/24/2008

ELF

327

Aerodynamic Characteristics of Ramjet Baseline SRef = 2.264 ft2 lRef = dRef = 1.698 ft Xcg @ Sta 82.5 in δ = 0 deg 4.0

Normal Force Coefficient, CN

Axial Force Coefficient, CA

.40 Mach .30

1.2 1.5 2.0

.20

3.0 4.0

.10

0 0

4

8

12

16

α, Angle of Attack ~ deg

Mach 3.0

1.2 1.5 2.0

2.0

3.0 4.0

1.0

0 0

4

8

12

16

α, Angle of Attack ~ deg

Source: Reference 27, based on year 1974 computer program from Reference 32.

2/24/2008

ELF

328

Aerodynamic Characteristics of Ramjet Baseline ( cont )

Pitching Moment Coefficient, Cm

+ .4

SRef = 2.264 ft2 lRef = dRef = 1.698 ft Xcg @ Sta 82.5 in δ = 0 deg

0

-.4 Mach 4.0

-.8

3.0

-1.2

2.0 1.5

-1.6

1.2

0

4

8

12

α, Angle of Attack ~ deg

16

Source: Reference 27, based on year 1974 computer program from Reference 32. 2/24/2008

ELF

329

-.4

SRef = 2.264 ft2 lRef = dRef = 1.698 ft Xcg @ Sta 82.5 in δ= 0 deg α = 0 deg.

.4

-.2

.3 C D

0

C

δ

m ~ per deg

Aerodynamic Characteristics of Ramjet Baseline ( cont )

0

.2

.1

.05

0

δ

N ~ per deg

.10

1

2

3

4

C

M, Mach Number 0 0

2/24/2008

0

1

2

3

M, Mach Number

4

Source: Reference 27, based on year 1974 computer program from Reference 32. ELF

330

Thrust Modeling of Ramjet Baseline

Tmax, Max Thrust, lb

100000

10000

h = Sea Level h = 20k ft h = 40k ft h = 60k ft h = 80k ft

Example: M = 3.5, h = 60k ft, ϕ = 1 ⇒ Max Thrust = 1,750 lb

1000

Note: Standard atmosphere T = Tmax ϕ

100 0

1

2

3

4

φ = 1 if stochiometric ( f / a = 0.0667 ) α = 0 deg

M, Mach Number Figure based on Reference 27 prediction 2/24/2008

ELF

331

Specific Impulse Modeling of Ramjet Baseline

ISP, Specific Impulse, s

1,500

•

Example: M = 3.5 ⇒ ISP = 1,120 s

1,000

• •

••

••

Note:

500

•

• •

Standard atmosphere ϕ≤1 ISP based on Reference 27 computer prediction. 0

0

1

2

3

4

M, Mach Number 2/24/2008

ELF

332

Rocket Booster Acceleration / Performance of Ramjet Baseline Boost Thrust ~ 1000 lb

30 ( ISP )Booster = 250 s 20

10

0 1.0

2.0

3.0

Time ~ s

Standard atmosphere ML = 0.80 Constant altitude flyout

2.0

Burnout Mach Number

Boost Range ~ nm

0

1.0

0 0

20

40

60

h, Altitude 1,000 ft 2/24/2008

ELF

4.0

5.0

6.0

0

20

40

3.0

2.5

2.0

60

h, Altitude 1,000 ft

80 333

Ramjet Baseline Has Best Performance at High Altitude 500

400

Range ~ nm

60,000 ft 300

200 40,000 ft 100

20,000 ft h = SL

0

0

1

2

3

4

M, Mach Number

Note: ML = 0.8, Constant Altitude Fly-out

Example, Mach 3 / 60k ft flyout ⇒ 445 nm. Breguet Range Prediction is R = V ISP ( L / D ) ln [ WBC / ( WBC - Wf )] = 2901 ( 1040 ) ( 3.15 ) ln ( 1739 / ( 1739 - 476 )) = 3,039,469 ft or 500 nm. Predicted range is 10% greater than baseline missile data. 2/24/2008

ELF

334

From Paredo Sensitivity, Ramjet Baseline Range Driven by ISP, Fuel Weight, Thrust, and CD0 Nondimensional Range Sensitivity to Parameter

1.5 Example: At Mach 3.0 / 60k ft altitude cruise, 10% increase in fuel weight ⇒ 9.6% increase in flight range

1 0.5 0 ISP

-0.5

Fuel Weight

Thrust

-1

CD0, Zero- CLA, LiftLift Drag CurveCoefficient Slope Coefficient

Inert Weight

Parameter Sea Level Flyout at Mach 2.3 40k ft Flyout at Mach 2.8 2/24/2008

ELF

20k ft Flyout at Mach 2.5 60k ft Flyout at Mach 3.0 335

Ramjet Baseline Flight Range Uncertainty Is +/- 7%, 1 σ Parameter

Baseline Value at Mach 3.0 / 60k ft

Uncertainty in Parameter

ΔR / R from Uncertainty

1. Specific Impulse

1040 s

+/- 5%, 1σ

+/- 5%, 1σ

2. Ramjet Fuel Weight

476 lb

+/- 1%, 1σ

+/- 0.9%, 1σ

3. Cruise Thrust ( φ = 0.39 )

458 lb

+/- 5%, 1σ

+/- 2%, 1σ

4. Zero-Lift Drag Coefficient

0.17

+/- 5%, 1σ

+/- 4%, 1σ

5. Lift Curve Slope Coefficient

0.13 / deg

+/- 3%, 1σ

+/- 1%, 1σ

6. inert Weight

1205 lb

+/- 2%, 1σ

+/- 0.8%, 1σ

Level of Maturity Based on Flight Demo of Prototype, Subsystem Tests, and Integration Wind tunnel tests Direct connect, freejet, and booster firing propulsion tests Structure test Mock-up Hardware-in-loop simulation Flight Test

Total Flight Range Uncertainty at Mach 3.0 / 60k ft Flyout ΔR / R = [ (ΔR / R )12 + (ΔR / R )22 + (ΔR / R )32 + (ΔR / R )42 + (ΔR / R )52 + (ΔR / R )62 ]1/2 = +/- 6.9%, 1σ 2/24/2008

R = 445 nm +/- 31 nm, 1σ

ELF

336

Sizing Examples Rocket Baseline Missile Standoff range requirement Wing sizing requirement Multi-parameter harmonization Lofted range comparison

Ramjet Baseline Missile Range robustness Propulsion and fuel alternatives Velocity control

Computer Aided Conceptual Design Sizing Tools Soda Straw Rocket Design, Build, and Fly 2/24/2008

ELF

337

Slurry Fuel and Efficient Packaging Provide Extended Range Ramjet Propulsion / Configuration

Fuel Type / Volumetric Performance (BTU / in3) / Density (lb / in3)

Fuel Volume (in3) / Fuel Weight (lb)

ISP (s) / Cruise Range at Mach 3.5, 60k ft (nm)

Liquid Fuel Ramjet

RJ-5 / 581 / 0.040

11900 / 476

1120 / 390

Ducted Rocket ( Low Smoke )

Solid Hydrocarbon / 1132 / 7922 / 594 0.075

677 / 294

Ducted Rocket ( High Performance )

Boron / 2040 / 0.082

7922 / 649

769 / 366

Solid Fuel Ramjet

Boron / 2040 / 0.082

7056 / 579

1170 / 496

Slurry Fuel Ramjet

40% JP-10, 60% boron carbide / 1191 / 0.050

11900 / 595

1835 / 770

2/24/2008

Note:

Flow Path

Available Fuel

ELF

Rcruise = V ISP ( L / D ) ln [ WBC / ( WBC - Wf )]

338

Sizing Examples Rocket Baseline Missile Standoff range requirement Wing sizing requirement Multi-parameter harmonization Lofted range comparison

Ramjet Baseline Missile Range robustness Propulsion and fuel alternatives Velocity control

Computer Aided Conceptual Design Sizing Tools Soda Straw Rocket, Design, Build, and Fly 2/24/2008

ELF

339

Example of Ramjet Velocity Control Through Fuel Control Ramjet Baseline Equivalence Ratio Ramjet Baseline Fuel Flow Rate, lb / s 10 T

Example for Ramjet Baseline: Mi = 4, h = sea level, T0 = 519R T+W-D=0

W

1

D

W = WBO = 1263 lb D = CD q SRef = 3353 CD MI2 = 3353 ( 0.14 ) 0 0 ( 4 )2 = 7511 lb Trequired = D - W = 7511 - 1263 = 6248 lb .

wf = T / ISP = 6248 / 1000 = 6.25 lb / s φ = Trequired / Tφ = 1 = 6248 / 25000 = 0.25

0.1 0

1

2

3

4

Note: Excess air provides cooling of combustor

Mi, Impact Mach Number at Sea Level Note: Ramjet baseline, vertical impact at sea level, steady state velocity at impact, T = thrust, W = weight, D = drag, WBO = burnout. weight, CD = zero-lift drag coefficient, Mi= impact Mach number, Trequired = required thrust for steady 0 state flight, wf = fuel flow rate, ISP = specific impulse, φ = equivalence ratio ( φ = 1 stochiometric )

2/24/2008

ELF

340

Sizing Examples Rocket Baseline Missile Standoff range requirement Wing sizing requirement Multi-parameter harmonization Lofted range comparison

Ramjet Baseline Missile Range robustness Propulsion and fuel alternatives Surface impact velocity

Computer Aided Conceptual Design Sizing Tools Soda Straw Rocket Design, Build, and Fly 2/24/2008

ELF

341

Computer Sizing Code Should Have Fast Turnaround and Be Easy to Use Objective of Conceptual Design Search Broad Solution Space Iterate to Design Convergence

Characteristics of Good Conceptual Design Sizing Code Fast Turnaround Time Easy to Use Directly Connect Predictions of Aeromechanics and Physical Parameters to Trajectory Code Simple, Physics Based Methods Includes Most Important, Driving Parameters Provides Insight into Relationships of Design Parameters Stable Computation Imbedded Baseline Missile Data Human Designer Makes the Creative Decisions 2/24/2008

ELF

342

Example of DOS-Based Conceptual Sizing Computer Code – ADAM Conceptual Sizing Computer Program Advanced Design of Aerodynamic Missiles ( ADAM ) PC compatible Written in DOS

Aerodynamic Module Based on NACA 1307 Calculates Static and dynamic stability derivatives Control effectiveness and trim conditions

3, 4, 5, and 6-DOF Simulation Modules Proportional guidance Input provided automatically by aerodynamic module

Configurations Benchmarked with Wind Tunnel Data Greater than 50 Input Parameters Available Defaults to benchmark configuration ( s )

2/24/2008

ELF

343

Example of Spreadsheet Based Conceptual Sizing Computer Code - TMD Spreadsheet Conceptual Sizing Computer Code Tactical Missile Design ( TMD ) Spreadsheet PC compatible Windows Excel spreadsheet

Based on Tactical Missile Design Short Course and Textbook Aerodynamics Propulsion Weight Flight trajectory Measures of merit

2/24/2008

ELF

344

Example of Spreadsheet Based Conceptual Sizing Computer Code, TMD Spreadsheet Define Mission Requirements [ Flight Performance ( RMax, RMin, VAVG ) , MOM, Constraints ] Establish Baseline ( Rocket

, Ramjet

)

Aerodynamics Input ( d, l, lN, A, c, t, xcg ) Aerodynamics Output [ CD , CN, xac, Cm , L / D, ST ] δ

0

Propulsion Input ( pc, ε, c*, Ab, At, A0, Hf, ϕ, T4, Inlet Type ) . Propulsion Output [ Isp, Tcruise, pt / pt , w , Tboost, Tsustain, ΔVBoost ] 2

Alt Mission Alt Baseline

Resize / Alt Config / Subsystems / Tech

0

Weight Input ( WL, WP, ρ, σmax ) Weight Output [ WL, WP, h, dT / dt, T, t, σbuckling, MB, σ, Wsubsystems, xcg, Iy ] Trajectory Input ( hi, Vi, Type ( cruise, boost, coast, ballistic, turn, glide ) Trajectory Output ( R, h, V, and γ versus time ) Meet Performance? Yes Measures of Merit and Constraints Yes 2/24/2008

ELF

No [ RMax, RMin, VAVG ] No [ pBlast, PK, nHit, Vfragments, PKE, KEWarhead, τTotal, σHE, σMAN, Rdetect, CSDD, C1000th, Cunit x ]

345

Example of TMD Spreadsheet Sizing Code Verification: Air-to-Air Range Requirement Example Launch Conditions hL = 20k ft ML = 0.8

Example Requirement RF = 6.7 nm with tf < 24.4 s

Solutions for Rocket Baseline ADAM: RF = 6.7 nm at tf = 18 s TMD Spreadsheet: RF = 6.7 nm at tf = 19 s 3 DOF using wind tunnel aero data: RF = 6.7 nm at tf = 21 s

Differences in Flight Time to 6.7 nm Mostly Due to Zero-Lift Drag Coefficient. For Example: ADAM prediction at Mach 2.0: ( CD0 )coast = 0.53 TMD Spreadsheet prediction at Mach 2.0: ( CD0 )coast = 0.57 Wind tunnel aero data at Mach 2.0: ( CD0 )coast = 1.05

Wind Tunnel Data / Baseline Missile Data Correction Required to Reduce Uncertainty in CD 0

2/24/2008

ELF

346

Sizing Examples Rocket Baseline Missile Standoff range requirement Wing sizing requirement Multi-parameter harmonization Lofted range comparison

Ramjet Baseline Missile Range robustness Propulsion and fuel alternatives Surface impact velocity

Computer Aided Conceptual Design Sizing Tools Soda Straw Rocket Design, Build, and Fly 2/24/2008

ELF

347

Example of Design, Build, and Fly Customer Requirements Objective – Design, Build, and Fly Soda Straw Rocket with: Flight Range Greater Than 90 ft Weight Less Than 2 g

Furnished Property Launch System Distance Measuring Wheel Weight Scale Micrometer Scale Engineer’s Scale Scissors

Furnished Material 1 “Giant” Soda Straw: 0.28 in Diameter by 7.75 in Length, Weight = 0.6 g 1 Strip Tabbing: ½ in by 6 in, Weight = 1.4 g 1 Ear Plug: 0.33 – 0.45 in Diameter by 0.90 in Length, Weight = 0.6 g 1 “Super Jumbo” Soda Straw: 0.25 in Diameter by 7.75 in Length 2/24/2008

ELF

348

Example of Design, Build, and Fly Customer Requirements ( cont ) Furnished Property Launch System with Specified Launch Conditions Launch Tube Diameter: 0.25 in Launch Tube Length ( e.g., 6 in ) Launch Pressure ( e.g., 30 psi ) Launch Elevation Angle ( e.g., 40 deg )

Predict Flight Trajectory Range and Compare with Test

2/24/2008

ELF

349

Soda Straw Rocket Launcher and Targeting 9. Rocket on Launcher 8. Launch Tube 7. Inclinometer 6b. Manual Valve Launcher ( 0.1 s average response ) 6a. Solenoid Valve Launcher ( 0.025 s average response ) 5. Launch Switch 4. Pressure Gauge 3. Air Hose 2. Pressure Tank

1. Pump 11. Rockets with Various Length, Tail Geometry, Nose Geometry, and Other Surfaces 2/24/2008

10. Laser Pointer Targeting Device

ELF

350

It Is Easy to Make a Soda Straw Rocket 1. Cut Large Diameter “Giant” Soda Straw to Desired Length 2. Twist and Squeeze Ear Plug to Fit Inside Soda Straw 3. Slide Ear Plug Inside Soda Straw

4. Cut Adhesive Tabs to Desired Height and Width of Surfaces

5. Apply Adhesive Tabs to Soda Straw 6. Wrap Front of Ear Plug and Straw with Tape 7. Slide Giant Soda Straw Rocket Over Smaller Diameter “Super Jumbo” Soda Straw Launch Tube

2/24/2008

ELF

351

Soda Straw Rocket Baseline Configuration

Ear Plug

Soda Straw

Strip Tabbing

0.25 in 0.28 in 0.5 in

lc = 6.0 in l = 7.0 in

2/24/2008

ELF

352

Soda Straw Rocket Baseline Weight and Balance Component Nose ( Plug ) Body ( Soda Straw ) Fins ( Four ) Total

2/24/2008

Weight, g 0.6 0.5 0.5 1.6

ELF

cg Station, in 0.5 3.5 6.75 3.39

353

Soda Straw Rocket Baseline Definition Body Material Type Material density, lb / in3 Material strength, psi Thickness, in Length, in Diameter, in Fineness ratio Nose fineness ratio

HDPE Plastic 0.043 4,600 0.004 7.0 0.28 25.0 0.5

Material Planform area, in2 ( 2 panels exposed ) Wetted area, in2 ( 4 panels ) Aspect ratio ( 2 panels exposed ) Taper ratio Chord, in Span ( exposed ), in Span ( total including body ), in Leading edge sweep, deg xmac, in

Plastic 0.25 1.00 1.00 1.0 0.5 0.5 0.78 0 6.625

Fins

2/24/2008

ELF

354

Soda Straw Rocket Baseline Definition ( cont ) Nose Material Type Material density, lb / in3 Average diameter Length

Foam 0.012 0.39 in 0.90 in

Reference Values Reference area, in2 Reference length, in

0.0616 0.28

Thrust Performance Inside cavity length, in Typical Pressure, psi Maximum thrust @ 30 psi pressure, lb Time constant, s ( standard temperature )

2/24/2008

6.0 30 1.47 0.025

ELF

355

Soda Straw Rocket Baseline Static Margin ( xAC )B xCG

d

xAC l

( xAC )T

For body-tail geometry, static margin given by ( xAC – xCG ) / d = - {( CN α )B {[ xCG – ( xAC )B ] / d } + ( CNα )T {[ xCG – ( xAC )T ] / d }( ST / SRef )} / [( CNα )B + ( CNα )T ST / SRef ]

For baseline soda straw configuration

xCG = 3.39 in, d = 0.28 in, ( CNα )B = 2 per rad, ST = 0.25 in2, SRef = 0.0616 in2 ( xAC )B = [( xAC )B / lN ] lN = 0.63 ( 0.14 ) = 0.09 in ( CNα )T = π AT / 2 = π ( 1 ) / 2 = 1.57 ( xAC )T = 6.5 + 0.25 ( cmac )T = 6.63

Substituting

( xAC - xCG ) / d = - { 2 ( 3.39 – 0.09 ) / 0.28 + [ 1.57 ( 3.39 – 6.63 ) / 0.28 ] [( 0.25 ) / 0.0616 ]} / [ 2 + 1.57 ( 0.25 ) / 0.0616 ] = 6.00 ( statically stable ) xAC = 6.00 ( 0.28 ) + 3.39 = 5.07 in from nose 2/24/2008

ELF

356

Soda Straw Rocket Has High Acceleration Boost Performance T = ( p – p0 ) A = pgauge ( 1 – e – t / τ ) A a ≈ 32.2 T / W, V = ∫ a dt, s = ∫ V dt

100

V, Velocity, fps

80

60

Note: Time Tics Every 0.01 s

40

20

0 0

2

4

6

8

10

s, Distance Traveled During Launch, Inches pgauge = 15 psi pgauge = 60 psi 2/24/2008

pgauge = 30 psi

ELF

Thrust ( T ) from Pressurized Tube of Area A T = ( p – p0 ) A = pgauge ( 1 – e – t / τ ) A A = ( π / 4 ) ( 0.25 )2 = 0.0491 in2, τ = Valve Rise Time Example: Assume pgauge = 30 psi, lt = 6 in, τ = 0.025 s ( Average for Solenoid Valve ), s = lc = 6 in Thrust Equation Is: T = 30 ( 1 - e – t / 0.025 ) ( 0.0491 ) = 1.4726 ( 1 - e – 40.00 t ) Note: Actual Boost Thrust Lower ( Pressure Loss, Boundary Layer, Launch Tube Leakage, Launch Tube Friction ) Equations for Acceleration ( a ), Velocity ( V ), and Distance ( s ) During Boost Are: a ≈ 32.2 T / W = 32.2 ( 1.4726 ) ( 1 - e – 40.00 t ) / 0.00352 = 13471.1 ( 1 - e – 40.00 t ) V = ∫ a dt = 13471.1 t + 336.78 e – 40.00 t – 336.78 s = ∫ V dt = 6735.57 t2 – 8.419 e – 40.00 t – 336.78 t + 8.419 End of Boost Conditions Are: s = lc = 6 in = 0.500 ft ⇒ t = 0.0188 s a = 7123 ft / s2 = 221 g V = 75.2 ft / s q = ½ ρ V2 = ½ ( 0.002378 ) ( 75.2 )2 = 6.72 psf M = V / c = 75.2 / 1116 = 0.0674 357

Most of the Soda Straw Rocket Drag Coefficient Is from Body Skin Friction CD0 = ( CD0 )Body,Friction + ( CD0 )Base,Coast + ( CD0 )Tail,Friction = 0.053 ( l / d ) [ M / ( q l )]0.2 + 0.12 + nT { 0.0133 [ M / ( q cmac )]0.2 } ( 2 ST / SRef )

CD0, Zero-Lift Drag Coefficient

1.5

1

0.5

0 0

2

4

6

8

10

ST / SRef, Tail Planform Area / Reference Area V = 40 fps 2/24/2008

V = 80 fps ELF

Example: V = 75.2 fps, ST = 0.00174 ft2, SRef = 0.000428 ft2 ⇒ ST / SRef = 4.07 Compute: CD0 = 0.053 ( 25.0 ){ 0.0674 / [( 6.72 ) ( 0. 583 )]}0.2 + 0.12 + 2 { 0.0133 { 0.0674 / [( 6.72 ) ( 0.0417 )]}0.2 }[ 2 ( 4.07 )] = 0.58 + 0.12 + 0.16 = 0.86 Note: • Above Drag Coefficient Not Exact • Based on Assumption of Turbulent Boundary Layer • Soda Straw Rocket Small Size and Low Velocity ⇒ Laminar Boundary Layer ⇒ Large Boundary Layer Thickness on Aft Body at Tails Compute Drag Force: Dmax = CD qmax SRef = 0.86 ( 6.72 ) ( 0.000428 ) = 0.00247 lb Compare Drag Force to Weight: Dmax / W = 0.00247 / 0.00352 = 0.70 Note: Drag Force Smaller Than Weight 358

Soda Straw Rocket Baseline Has a Ballistic Flight Range Greater Than 90 Feet Rx = { 2 W cos γi / [ gc ρ SRef CD0 ]} ln { 1 + t / { 2 W / [ gc ρ SRef CD0 Vi ]}}

h - hi, Height above Initial Launch Height, ft

h = { 2 W sin γi / [ gc ρ SRef CD ]} ln { 1 + t / { 2 0 W / [ gc ρ SRef CD0 Vi ]}} + hi - gc t2 / 2

Horizontal Range At Impact = Rx = { 2 (

40 Note: Time Tics every 0.5 s

30

0.00352 ) cos γi / [ 32.2 ( 0.002378 ) ( 0.000428 ) ( 0.86 )]} ln { 1 + t / { 2 ( 0.00352 ) / [ 32.2 ( 0.002378 ) ( 0.000428 ) ( 0.86 ) ( 75.2 )]}} = 249.8 cos γi ln ( 1 + 0.301 t )

= 249.8 ( 0.866 ) ln [ 1 + 0.301 ( 1.8 )] = 93.7 ft

20

Height At Impact = h = { 2 ( 0.00352 )

10 0 0

20

40

60

80

100

Rx, Horizontal Range, ft Gamma = 10 Deg 2/24/2008

Example, Assume lt = 6 in, pgauge = 30 psi, γi = 30 deg, τ = 0.025 sec, Soda Straw Baseline, t = timpact = 1.8 s

Gamma = 30 Deg

Gamma = 50 Deg ELF

sin γi / [ 32.2 ( 0.002378 ) ( 0.000428 ) ( 0.86 )} ln { 1 + t / { 2 ( 0.00352 ) / [ 32.2 ( 0.002378 ) ( 0.000428 ) ( 0.86 ) ( 75.2 )]}} + hi – 32.2 t2 / 2 = 249.8 sin γi ln ( 1 + 0.301 t ) + hi – 32.2 t2 / 2 = 249.8 ( 0.5 ) ln [ 1 + 0.301 ( 1.8 )] + hi – 32.2 ( 1.2 )2 / 2 = hi + 1.9 ft 359

Soda Straw Rocket Range Driven by Inside Chamber Length and Launch Angle 0.8

Example: 10% decrease in inside chamber length ⇒ 7.7% decrease in range at t = 1.8 s. Note: Result is nonlinear because inside chamber length = launcher length. Increase in lc also leads to decrease in range.

0.6

Nondimensional Range Sensitivity to Parameter

0.4

Note: Decreased chamber length ⇒ shorter duration thrust ( decreased total impulse ) ⇒ decreased end-ofboost velocity Soda Straw Rocket Baseline: W = Weight = 0.00423 lb lc = inside chamber length = 6 in τ = Time constant to open solenoid valve = 0.025 s pgauge = gauge pressure = 30 psi

0.2

γi = Initial / launch angle angle = 30 deg lt = 7 in 0

V = Launch velocity = 75.2 fps lc

Gamma pgauge

W

tau

CD0

CD0 = Zero-lift drag coefficient = 0.86 timpact = Time from launch to impact = 1.8 s

-0.2

Rx = Horizontal range = 94 ft 2/24/2008

ELF

360

Soda Straw Rocket Baseline Flight Range Uncertainty Is +/- 2.4%, 1 σ Parameter

Baseline Value

Uncertainty in Parameter

ΔR / R Due to Uncertainty

1. Inside Chamber Length

6 in

+/- 2%, 1 σ

+/- 1.5%, 1σ

2. Launch Angle

30 deg

+/- 3%, 1σ

+/- 1.7%, 1σ

3. Gauge Pressure

30 psi

+/- 3%, 1σ

+/- 0.5%, 1σ

4. Weight

1.6 g

+/- 6%, 1σ

+/- 0.4%, 1σ

5. Solenoid Time Constant

0.025 s

+/- 20%, 1σ

+/- 0.2%, 1σ

6. Zero-Lift Drag Coefficient

0.86

+/- 20%, 1σ

+/- 0.2%, 1σ

Estimate of Level of Maturity / Uncertainty of Soda Straw Rocket Baseline Parameters Based on Wind tunnel test Thrust static test Weight measurement Prediction methods

Total Flight Range Uncertainty for 30 psi launch at 30 deg ΔR / R = [ (ΔR / R )12 + (ΔR / R )22 + (ΔR / R )32 + (ΔR / R )42 + (ΔR / R )52 + (ΔR / R )62 ]1/2 = +/- 2.4%, 1σ R = 94 ft +/- 2.3 ft, 1σ 2/24/2008

ELF

361

House of Quality Translates Customer Requirements into Engineering Emphasis 0

Chamber Length

Tail Planform Area

Flight Range

7

8

2

Weight

3

6

4

74 = ( 7x8 + 3x6 )

26 = ( 7x2 + 3x4 )

1

2

Note: Based on House of Quality, inside chamber length most important design parameter. Note on Design Characteristics Sensitivity Matrix: ( Room 5 ):

1 - Customer Requirements 2 – Customer Importance Rating ( Total = 10 ) 3 – Design Characteristics 4 – Design Characteristics Importance Rating ( Total = 10 ) 5 – Design Characteristics Sensitivity Matrix 6 – Design Characteristics Weighted Importance 7 – Design Characteristics Relative Importance

++ Strong Synergy + Synergy 0 Near Neutral Synergy - Anti-Synergy - - Strong Anti-Synergy 2/24/2008

ELF

362

DOE Explores the Broad Possible Design Space with a Reasonably Small Set of Alternatives Design Space for Design of Experiments ( DOE ) Engineering Characteristics Range

lc, Inside Chamber Length, in

ST, Tail Planform Area, in2

Lower Value

4

0.125

Upper Value

6

0.25

Full Factorial DOE Based on Upper / Lower Values of k = 2 Parameters: Number of Combinations = 2k = 22 = 4 Concept

Sketch

lc, Inside Chamber Length, in

ST, Tail Planform Area, in2

“Big Kahuna”

6

0.25

“Shorty”

4

0.25

“Stiletto”

6

0.125

“Petite”

4

0.125

Note: DOE concepts should emphasize customer driving requirements and the driving engineering characteristics. 2/24/2008

ELF

363

Engineering Experience Should Guide the DOE Set of Alternatives and the Preferred Design As an Example, for the Soda Straw Rocket, from Experience We Know That Soda Straw Rocket Must Fit on Launcher Maximum Boost Velocity Occurs When Chamber Length = Launch Tube Length Three or Four Tails Best for Stability Tails That Are Too Small May Result in an Unstable Flight Tails That Are Too Large Add Weight and Cause Trajectory Dispersal Canards Require Larger Tails for Stability, Add Weight, and Cause Trajectory Dispersal Wings Add Weight, Add Drag, and Cause Trajectory Dispersal

2/24/2008

ELF

364

Engineering Experience Should Guide the DOE Set of Alternatives and Preferred Design ( cont )

As an Example, Soda Straw Rocket Geometry Should Be Comparable to an Operational Rocket with Near-Neutral Static Stability ( e.g., Hydra70 ) Concept

Sketch

l / d, Total Length / Diameter

b / d, Total Tail Span / Diameter

c / d, Tail Chord / Diameter

“Big Kahuna”

25

2.79

2

“Shorty”

17.9

2.79

2

“Stiletto”

25

1.89

2

“Petite”

17.9

1.89

2

Hydra 70

15.1

2.66

1

Note: For a subsonic rocket with the center-of-gravity in the center of the rocket, slender body theory and slender surface theory give total tail span and chord for neutral stability of bNeutralStability ≈ 2 d and cNeutralStability > ≈ d respectively. 2/24/2008

ELF

365

Optimum Design Should Have Balanced Engineering Characteristics As an Example, for the Soda Straw Rocket Design We Should Reflect Customer Emphasis of Requirements for Range Weight

Provide Balanced Emphasis of Most Important Engineering Characteristics Chamber Length Tail Size / Span

2/24/2008

ELF

366

Summary of Sizing Examples Rocket Powered Missile ( Sparrow Derived Baseline ) Standoff range requirement Wing area sizing requirements for maneuverability, turn rate, and turn radius Multi-parameter harmonization Ballistic versus lofted glide flight range

Ramjet Powered Missile ( ASALM Derived Baseline ) Robustness in range uncertainty Propulsion and fuel alternatives Surface target impact velocity

Computer Aided Sizing Tools for Conceptual Design ADAM Analytical prediction of aerodynamics Numerical solution of equations of motion 2/24/2008

ELF

367

Summary of Sizing Examples ( cont ) Computer Aided Sizing Tools for Conceptual Design ( cont ) TMD analytical sizing spreadsheet ( based on this text ) Analytical prediction of aero, propulsion, and weight Closed form analytical solution of simplified equations of motion

Soda Straw Rocket Design, Build, and Fly Static margin Drag Performance Sensitivity study House of Quality Design of Experiment ( DOE )

Discussion / Questions? Classroom Exercise ( Appendix A ) 2/24/2008

ELF

368

Sizing Examples Problems 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 2/24/2008

Required flight range is shorter for a head-on intercept and it is longer for a t___ c____ intercept. The rocket baseline center-of-gravity moves f______ with motor burn. The rocket baseline is an a_______ airframe. The rocket baseline thrust profile is b____ s______. The rocket baseline motor case and nozzle are made of s____. The rocket baseline flight range is driven by ISP, propellant weight fraction, drag, and s_____ m_____. Contributors to the maneuverability of the rocket baseline are its body, tail, and w___. Although the rocket baseline has sufficient g’s and turn rate to intercept a maneuvering aircraft, it needs a smaller turn r_____. Compared to a co-altitude trajectory, the rocket baseline has extended range with a l_____ glide trajectory. The ramjet baseline has a c___ inlet. The Mach 4 ramjet baseline has a t_______ airframe. ELF

369

Sizing Examples Problems ( cont ) 12. 13. 14. 15. 16.

17. 18. 19. 2/24/2008

Although the ramjet baseline combustor is a nickel-based super alloy, it requires insulation, due high temperature. The super alloy is i______. The flight range of the ramjet baseline is driven by ISP, weight, thrust, zero-lift coefficient, and the weight fraction of f___. Extended range for the ramjet baseline would be provided by more efficient packaging of subsystems and the use of s_____ fuels. A conceptual design sizing code should be based on the simplicity, speed, and robustness of p______ based methods. The House of Quality room for design characteristics weighted importance indicates which engineering design characteristics are most important in meeting the c_______ r___________. Paredo sensitivity identifies the design parameters that are most i________. DOE concepts should emphasize the customer driving requirements and the driving e__________ characteristics If the total tail span ( including body diameter ) is twice the body diameter, the missile is approximately n________ s_____. ELF

370

Outline Introduction / Key Drivers in the Design Process Aerodynamic Considerations in Tactical Missile Design Propulsion Considerations in Tactical Missile Design Weight Considerations in Tactical Missile Design Flight Performance Considerations in Tactical Missile Design Measures of Merit and Launch Platform Integration Sizing Examples Development Process Summary and Lessons Learned References and Communication Appendices ( Homework Problems / Classroom Exercises, Example of Request for Proposal, Nomenclature, Acronyms, Conversion Factors, Syllabus ) 2/24/2008

ELF

371

Relationship of Technology Assessment / Roadmap to the Development Process Technology Roadmap Establishes Time-phased Interrelationships for Technology development and validation tasks Technology options Technology goals Technology transition ( ATD, ACTD, DemVal, PDRR, SDD )

Technology Roadmap Identifies Key, enabling, high payoff technologies Technology drivers Key decision points Critical paths Facility requirements Resource needs 2/24/2008

ELF

372

Relationship of Design Maturity to the US Research, Technology, and Acquisition Process Research

Technology

Acquisition

6.1

6.2

6.3

6.4

6.5

Basic Research

Exploratory Development

Advanced Development

Demonstration & Validation

System Development and Demonstration

Production

System Upgrades

~ $0.1B

~ $0.3B

~ $0.9B

~ $0.5B

~ $1.0B

~ $6.1B

~ $1.2B

Maturity Level

Conceptual Design

Drawings ( type ) < 10 ( subsystems ) Technology Development ~ 10 Years

2/24/2008

Preliminary Design

Detail Design

Production Design

< 100 ( components )

> 100 ( parts )

> 1000 ( parts )

Technology Demonstration ~ 8 Years

Prototype Demonstration ~ 4 Years

Full Scale Development ~ 5 Years

First Limited Block ~ 2 Years ~ 5 Years

1-3 Block Upgrades ~ 5-15 Years

Production Note: Total US DoD Research and Technology for Tactical Missiles ≈ $1.8 Billion per year Total US DoD Acquisition ( SDD + Production + Upgrades ) for Tactical Missiles ≈ $8.3 Billion per year Tactical Missiles ≈ 11% of U.S. DoD RT&A budget US Industry IR&D typically similar to US DoD 6.2 and 6.3A ELF

373

Technology Readiness Level ( TRL ) Indicates the Maturity of Technology TRL 1- 3

TRL 4

TRL 5

TRL 6

TRL 7

Category 6.1

Category 6.2A

Category 6.2B

Category 6.3

Category 6.4

Basic research

Exploratory development of a component, conceptual design studies, and prediction methods

Exploratory development of a subsystem

Advanced tech demo of a subsystem

Prototype demonstration

Initial assessment ⇒ component test ⇒ 2/24/2008

subsystem test ⇒ integrated subsystems ⇒ integrated missile ELF

374

Typical Number of Alternative Concepts or Number of Design Drawings

Conceptual Design Has Broad Alternatives While Detail Design Has High Definition 1000

100 Number of Concepts Number of Drawings

10

1 0

5

10

15

Time ( Years )

2/24/2008

Conceptual

Prelim.

Detail

Production

Design

Design

Design

Design

ELF

375

US Tactical Missile Follow-On Programs Occur about Every 24 Years Short Range ATA, AIM-9, 1949 - Raytheon

AIM-9X ( maneuverability ), 1996 - Hughes

Medium Range ATA, AIM-7,1951 - Raytheon

AIM-120 ( autonomous, speed, range, weight ), 1981 - Hughes

Anti-radar ATS, AGM-45, 1961 - TI

Hypersonic Missile, > 2007

AGM-88 ( speed, range ), 1983 - TI Hypersonic Missile > 2007 PAC-3 (accuracy), 1992 - Lockheed Martin

Long Range STA, MIM-104, 1966 - Raytheon

Man-portable STS, M-47, 1970 - McDonnell Douglas Javelin ( gunner survivability, lethality, weight ), 1989 - TI Long Range STS, BGM-109, 1972 - General Dynamics

Long Range ATS, AGM-86, 1973 - Boeing

AGM-129 ( RCS ), 1983 - General Dynamics

Medium Range ATS, AGM-130, 1983 - Rockwell 1950 2/24/2008

1965

1970

1975

1980

1985

Year Entering SDD ELF

Hypersonic Missile > 2007

1990

JASSM ( cost, range, observables ), 1999 - LM 1995 > 2000 376

Missile Design Validation / Technology Development Is an Integrated Process Propulsion Propulsion Model

•Rocket Static •Turbojet Static •Ramjet Tests -Direct Connect -Freejet

Airframe Aero Model Guidance and Control

Wind Tunnel Tests

Model Digital Simulation Seeker

Lab Tests

IM Tests

Structure Test Hardware In-Loop Simulation Tower Tests

Flight Test Progression ( Captive Carry,Jettison, Separation, Unpowered Guided Flights, Powered Guided Flights, Live Warhead Flights )

Actuators / Initiators Sensors

Lab Tests

Autopilot / Electronics Power Supply Warhead 2/24/2008

Ballistic Tests

Environment Tests •Vibration •Temperature

Witness / Arena Tests ELF

IM Tests

Sled Tests 377

Examples of Missile Development Tests and Facilities Airframe Wind Tunnel Test ………………………………………………………

Propulsion Static Firing with TVC ……..

Propulsion Direct Connect Test …………………………………….

Propulsion Freejet Test …………

2/24/2008

ELF

378

Examples of Missile Development Tests and Facilities ( cont ) Warhead Arena Test ……………………………………………………….

Warhead Sled Test ………………………

Insensitive Munition Test ……………………………………………..

Structure Test …………………………………………..

2/24/2008

ELF

379

Examples of Missile Development Tests and Facilities ( cont ) Seeker Test ……………………………………………………….

Hardware-In-Loop ………

Environmental Test ……………………………………………..

Submunition Dispenser Sled Test …………………… 2/24/2008

ELF

380

Examples of Missile Development Tests and Facilities ( cont ) RCS Test ……………………………………………………………….

Store / Avionics Test

Flight Test ……………………………………………………………………….

Video of Facilities and Tests

2/24/2008

ELF

381

Missile Flight Test Should Cover Extremes of Flight Envelope Example: Ramjet Baseline Propulsion Test Validation ( PTV ) High L / D Cruise Flight 7 Flight 3

Booster Transition: Thrust - Drag

w Lo

m na y D

ic

su s e Pr

re

High Aero Heating Flight 7

Flight 1 Flight 7

Flight 7

Flight 3

Flight 7

a yn D h Hig

cP i m

re su s re

Flight 3

Note: Seven Flights from Oct 1979 to May 1980. Flight 1 failure of fuel control. As a result of the high thrust, the flight Mach number exceeded the design Mach number. 2/24/2008

ELF

382

Example of Aero Technology Development Conceptual Design ( 5 to 50 input parameters ) Prediction Preliminary Design ( 50 to 200 input parameters ) Prediction Missile DATCOM. Contact: AFRL. Attributes include: Low cost MISL3. Contact: NEAR. Attributes include: Modeling vortex shedding SUPL. Contact: NEAR. Attributes include: Paneling complex geometry AP02. Contact: NSWC. Attributes include: Periodic updates CFD. Contact: Georgia Tech. Attributes include: Model runs on Parallel Processing PCs

Preliminary Design Optimization Response Surface Model: Contact: Georgia Tech. Attributes include 10x more rapid computation Probabilistic Analysis: Contact: Georgia Tech. Attributes include an evaluation of design robustness

2/24/2008

ELF

383

Example of Aero Technology Development ( cont ) Wind Tunnel Test Verification Body buildup force and moment Control effectiveness and hinge moment Store carriage and separation Flow field ( may be required ) Pressure distribution ( may be required ) Plume, heat transfer, and dynamic stability ( usually not required ) Inlet ( if applicable )

3 to 6-DOF Digital Simulation Hardware-in-loop Simulation Detail Design ( over 200 input parameters ) Flight Test Validation 2/24/2008

ELF

384

Example of Missile Technology State-of-the-Art Advancement: Air-to-Air Missile Maneuverability Operational Angle of Attack, Deg

60 50

Controls Augmented with Propulsion Devices ( TVC, Reaction Jet )

40 30 20 10 0 1950

1960

1970

1980 Year IOC

2/24/2008

ELF

1990

2000

2010

AIM-7A AM-9B R530 AA-8 AIM-54 R550 Skyflash Python 3 AA-10 Aspide Super 530D AA-11 AIM-120 Python 4 AA-12 MICA AIM-132 AIM-9X

385

Mcruise, Cruise Mach Number

Example of Missile Technology State-of-the-Art Advancement: Ramjet Propulsion 7 6

Scramjet Ramjet

5 4 3 2 1 0 1950

1960

1970

1980

1990

2000

2010

Year Flight Demonstration Cobra RARE D-21 ALVRJ ANS HyFly 2/24/2008

X-7 Bloodhound CROW 3M80 Kh-41 SED

Vandal/Talos BOMARC SA-6 ASALM SLAT ELF

St-450 Typhon Sea Dart AS-17 / Kh-31 BrahMos

SE 4400 STATEX LASRM ASMP Meteor 386

Enabling Technologies for Tactical Missiles Dome Faceted / Window Multi-mode Multi-spectral Multi-lens

Electronics

G&C GPS / INS In-flight Optimize α, β Feedback ATR

Insulation Hypersonic High Density

COTS Central

Power

Data Link BDI / BDA In-flight Retarget Moving Target Phased Array

Flight Control EM and Piezoelectric TVC / Reaction Jet Dedicated Roll

MEMS

Seeker Multi-mode Multi-spectral SAR Strapdown Uncooled Imaging High Gimbal

Warhead High Energy Density Multi-mode High Density Penetrator Boosted Penetrator Smart Dispenser Powered Submunition 2/24/2008

Airframe Lifting Body Neutral Static Margin Lattice Fins Split Canard Low ΔxAC Wing / Low Hinge Moment Control Free-to-Roll Tails Compressed Carriage Low Drag Inlet Mixed Compression Inlet Single Cast Structure VARTM, Pultrusion, Extrusion, Filament Wind High Temperature Composites Titanium Alloy MEMS Data Collection Low Observable Shaping and Materials ELF

Propulsion Hypersonic Turbine-Based Liquid / Solid Fuel Ramjet Variable Flow Ducted Rocket Scramjet Combined Cycle Propulsion High Temperature Turbine High Temperature Combustor High Density Fuel / Propellant High Throttle Fuel Control Endothermic Fuel Composite Case Pintle / Pulsed / Gel Motor High Burn Rate Exponent Propellant Low Observable 387

Summary of Development Process Development Process Technology roadmap Development activities Time frame

Level of Design Maturity Related to Stage of Development Missile Follow-on Programs Subsystems Development Activities Subsystems Integration and Missile System Development Flight Test Activities Missile Development Tests and Facilities State-of-the-Art Advancement in Tactical Missiles New Technologies for Tactical Missiles Discussion / Questions? Classroom Exercise ( Appendix A ) 2/24/2008

ELF

388

Development Process Problems 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.

2/24/2008

A technology roadmap establishes the high payoff technologies g____. The levels of design maturity from the most mature to least mature are production, detail, preliminary, and c_________ design. Technology transitions occur from basic research to exploratory development, to advanced development, to d____________ and v_________. Approximately 11% of the U.S. RT&A budget is allocated to t_______ m_______. In the U.S., a tactical missile has a follow-on program about every __ years. Compared to the AIM-9L, the AIM-9X has enhanced m______________. Compared to the AIM-7, the AIM-120 has autonomous guidance, lighter weight, higher speed, and longer r____. Compared to the PAC-2, the PAC-3 has h__ t_ k___ accuracy. Guidance & control is verified in the h_______ in l___ simulation. Airbreathing propulsion ground tests include direct connect tests and f______ tests. Aerodynamic force and moment data are acquired in w___ t_____ tests. ELF

389

Outline Introduction / Key Drivers in the Design Process Aerodynamic Considerations in Tactical Missile Design Propulsion Considerations in Tactical Missile Design Weight Considerations in Tactical Missile Design Flight Performance Considerations in Tactical Missile Design Measures of Merit and Launch Platform Integration Sizing Examples Development Process Summary and Lessons Learned References and Communication Appendices ( Homework Problems / Classroom Exercises, Example of Request for Proposal, Nomenclature, Acronyms, Conversion Factors, Syllabus ) 2/24/2008

ELF

390

Evaluate Alternatives and Iterate the System-ofSystems Design • Mission / Scenario Definition

Update Initial

• Weapon Requirements, Trade Studies and Sensitivity Analysis • Launch Platform Integration

Revised Trades / Eval

Initial Reqs

Alt Concepts

Initial Carriage / Launch

Effectiveness / Eval

Baseline Selected Iteration

Refine Weapons Req

• Weapon Concept Design Synthesis

Alternate Concepts ⇒ Select Preferred Design ⇒Eval / Refine

• Technology Assessment and Dev Roadmap

Initial Tech

Tech Trades

Initial Revised Roadmap Roadmap

Note: Typical design cycle for conceptual design is usually 3 to 9 months 2/24/2008

ELF

391

Exploit Diverse Skills for a Balanced Design Customer ( requirements pull ) ⇒ mission / MIR weighting

Operations analysts ⇒ system-of-systems analysis System integration engineers ⇒ launch platform integration Missile design engineers ⇒ missile concept synthesis Technical specialists ( technology push ) ⇒ technology assessment / roadmap 2/24/2008

ELF

392

Utilize Creative Skills Use Creative Skills to Consider Broad Range of Alternatives Ask Why? of Requirements / Constraints Project into Future ( e.g., 5 – 15 years ) State-of-the-art ( SOTA ) Threat Scenario / Tactics / Doctrine Concepts Technology Impact Forecast

Recognize and Distill the Most Important, Key Drivers Develop Missile Concept that is Synergistic within a System-of-Systems Develop Synergistic / Balanced Combination of High Leverage Subsystems / Technologies

2/24/2008

ELF

393

Identify and Quantify the High Payoff Measures of Merit

Max / Min Range

Lethality

Time to Target

Reliability

Miss Distance

Observables

Survivability

2/24/2008

Robustness

ELF

Weight

394

Start with a Good Baseline

I would have used the wheel as a baseline.

2/24/2008

ELF

395

Conduct Balanced, Unbiased Tradeoffs Propulsion

Aerodynamics

Production

Structures Seeker

Guidance and Control Warhead – Fuze 2/24/2008

ELF

396

Evaluate Many Alternatives

AA- 8 / R-60

Python 4

Magic 550

U-Darter

Python 5

Derby / R-Darter

AIM-9L

Aspide

AA-10 / R-27

Skyflash

AIM-7

R-37

AA-12 / R-77

AIM-9x

Super 530D

AIM-132

AA-11 / R-73

AIM-54

AIM-120

Mica

IRIS-T

Meteor

A-Darter

Taildog

Note: Although all of the above are supersonic air-to-air missiles, they have different configuration geometry 2/24/2008

ELF

397

Search a Broad Design Solution Space ( Global Optimization vs Local Optimization )

Local Optimum ( e.g., Lowest Cost Only in Local Solution Space )

Local Optimum ( e.g., Lowest Cost Only in Local Solution Space )

Global Optimum ( e.g., Lowest Cost in Global Solution Space ) within Constraints

2/24/2008

ELF

398

Evaluate and Refine as Often as Possible

2/24/2008

ELF

399

Provide Balanced Emphasis of Analytical vs Experimental

Thomas Edison: "Genius is 1% inspiration and 99% perspiration."

Albert Einstein: "The only real valuable thing is intuition."

2/24/2008

ELF

400

Use Design, Build, and Fly Process, for Feedback That Leads to Broader Knowledge Prediction Satisfies Customer Requirements?

No

Build Is it Producible?

No

2/24/2008

Wisdom

Where is the wisdom we have lost in knowledge? Where is the knowledge we have lost in information?--T. S. Eliot ( The Rock )

Understanding

Knowledge comes by taking things apart: analysis. But wisdom comes by putting things together.--John A. Morrison

Knowledge

Information

Failure / Success

Fly ( Test ) Test Results Satisfy Customer Requirements and Consistent with Prediction?

Climb Ladder of Kn owledge

Design

No

We are drowning in information but starved for knowledge.--John Naisbitt ( Megatrends: Ten New Directions Transforming Our Lives ) We learn wisdom from failure much more than from success. We often discover what will do, by finding out what will not do; and probably he who never made a mistake never made a discovery.--Samuel Smiles ( Self Help )

Data

Yes ELF

401

Evaluate Technology Risk

2/24/2008

ELF

402

Keep Track of Assumptions and Develop RealTime Documentation It’s finally finished ! . . .

2/24/2008

ELF

403

Develop Good Documentation Technology Roadmap Unit production cost and developmen t cost Weight and balanc e

Three-view drawing of preferred concept( s ) Traceability of system driving MIRs Sensitivity of system / subsystem parameters Mission flight profiles of preferred concept( s ) Aero and propulsion characteristics Justification of ept(s) recommended conc rnative Sketches of alte concepts eighting MIRs W

2/24/2008

ELF

404

Utilize Group Skills Preliminary Design – 8%

Detail / Production Design – 30%

Conceptual Design – 2%

Other Than Design – 60% (Test, Analysis, Configuration Management, Software, Program Management, Integration, Requirements, etc.)

Source: Nicolai, L.M., “Designing a Better Engineer,” AIAA Aerospace America, April 1992 2/24/2008

ELF

405

Balance the Tradeoff of Importance vs Priority

Production Programs / Detail Design SDD Programs / Preliminary Design

2/24/2008

ELF

Advanced Programs / Conceptual Design

406

Evaluate Alternatives and Iterate the Configuration Design Define Mission Requirements Alt Mission Establish Baseline Alt Baseline Aerodynamics Propulsion Weight

Resize / Alt Config / Subsystems / Tech

Trajectory Meet Performance?

No

Yes Measures of Merit and Constraints

No

Yes 2/24/2008

ELF

407

Configuration Sizing Conceptual Design Guidelines: Aeromechanics Configuration Sizing Parameter

Aeromechanics Design Guideline

Body fineness ratio Nose fineness ratio Boattail or flare angle Efficient cruise dynamic pressure Missile homing velocity Ramjet combustion temperature Oblique shocks prior to inlet normal shock to satisfy MIL-E-5008B Inlet flow capture Ramjet Minimum cruise Mach number Subsystems packaging

2/24/2008

ELF

5 < l / d < 25 lN / d ≈ 2 if M > 1 < 10 deg q < 1,000 psf VM / VT > 1.5 > 4,000° F > 2 oblique shocks / compressions if M > 3.0, > 3 shocks / compressions if M > 3.5 Shock on cowl lip at Mmax cruise M > 1.2 x MInletStart , M > 1.2 MMaxThrust = Drag Maximize available volume for fuel / propellant

408

Configuration Sizing Conceptual Design Guidelines: Guidance & Control Configuration Sizing Parameter

G&C Design Guideline ωBB > 2 ωACT α/δ>1 If low aspect ratio, b / d ≈ 2, c / d > ≈ 1 < 30% τ < 0.2 s n M / nT > 3 3 < N’ < 5 < btarget . . γM> γT RTM < RTT

Body bending frequency Trim control power Neutral stability tail-body Stability & control cross coupling Airframe time constant Missile maneuverability Proportional guidance ratio Target span resolution by seeker Missile heading rate Missile turn radius

2/24/2008

ELF

409

Wrap Up ( Part 1 of 2 ) Missile design is a creative and iterative process that includes System considerations Missile concepts and sizing Flight trajectory evaluation

Cost / performance drivers may be “locked in” during conceptual design Missile design is an opportunity for a diverse group to work together for a better product Military customer ⇒ mission / scenario definition Operations analysts ⇒ system-of-systems modeling System integration engineers ⇒ launch platform integration Missile design engineers ⇒ missile concept synthesis Technical specialists ⇒ technology assessment / technology roadmap 2/24/2008

ELF

410

Wrap Up ( Part 2 ) The missile conceptual design philosophy requires Iteration, iteration, iteration Evaluation of a broad range of alternatives Traceable flow-down allocation of requirements Starting with a good baseline Paredo sensitivity analysis to determine the most important, driving parameters Synergistic compromise / balanced subsystems and technologies that are high leverage Awareness of technology SOTA / technology assessment Technology impact forecast Robust design Creative design decisions made by the designer ( not the computer ) Fast, simple, robust, physics-based prediction methods 2/24/2008

ELF

411

Outline Introduction / Key Drivers in the Design Process Aerodynamic Considerations in Tactical Missile Design Propulsion Considerations in Tactical Missile Design Weight Considerations in Tactical Missile Design Flight Performance Considerations in Tactical Missile Design Measures of Merit and Launch Platform Integration Sizing Examples Development Process Summary and Lessons Learned References and Communication Appendices ( Homework Problems / Classroom Exercises, Example of Request for Proposal, Nomenclature, Acronyms, Conversion Factors, Syllabus ) 2/24/2008

ELF

412

References 1. “Missile.index,” http://missile.index.ne.jp/en/ 2. AIAA Aerospace Design Engineers Guide, American Institute of Aeronautics and Astronautics, 1993 3. Bonney, E.A., et al, Aerodynamics, Propulsion, Structures, and Design Practice, “Principles of Guided Missile Design”, D. Van Nostrand Company, Inc., 1956 4. Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design, “Principles of Guided Missile Design”, D. Van Nostrand Company, Inc., 1960 5. Chin, S.S., Missile Configuration Design, McGraw-Hill Book Company, 1961 6. Mason, L.A., Devan, L., and Moore, F.G., “Aerodynamic Design Manual for Tactical Weapons,” NSWCTR 81-156, 1981 7. Pitts, W.C., Nielsen, J.N., and Kaattari, G.E., “Lift and Center of Pressure of Wing-Body-Tail Combinations at Subsonic, Transonic, and Supersonic Speeds,” NACA Report 1307, 1957 8. Jorgensen, L.H., “Prediction of Static Aerodynamic Characteristics for Space-Shuttle-Like, and Other Bodies at Angles of Attack From 0° to 180°,” NASA TND 6996, January 1973 9. Hoak, D.E., et al., “USAF Stability and Control DATCOM,” AFWAL TR-83-3048, Global Engineering, 1978 10. “Nielsen Engineering & Research (NEAR) Aerodynamic Software Products,” http://www.nearinc.com/near/software.htm 11. Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., 1974 12. Anderson, John D. Jr., “Modern Compressible Flow,” Second Edition, McGraw Hill, 1990 13. Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319 and AFWAL TR 80-2003, June 1980 14. “Technical Aerodynamics Manual,” North American Rockwell Corporation, DTIC AD 723823, June 1970 15. Oswatitsch, K.L., “Pressure Recovery for Missiles with Reaction Propulsion at High Supersonic Speeds”, NACA TM 1140, 1947 16. Carslaw, H.S. and Jaeger, J. C., Conduction of Heat in Solids, Clarendon Press, 1988 2/24/2008

ELF

413

References ( cont ) 17. Allen, J. and Eggers, A.J., “A Study of the Motion and Aerodynamic Heating of Ballistic Missiles Entering the Earth’s Atmosphere at High Supersonic Speeds”, NACA Report 1381, April 1953. 18. Schneider, S.H., Encyclopedia of Climate and Weather, Oxford University Press, 1996 19. Klein, L.A., Millimeter-Wave and Infrared Multisensor Design and Signal Processing, Artech House, Boston, 1997 20. US Army Ordnance Pamphlet ORDP-20-290-Warheads, 1980 21. Carleone, J. (Editor), Tactical Missile Warheads, “AIAA Vol. 155 Progress in Astronautics and Aeronautics,” American Institute of Aeronautics and Astronautics, 1993 22. Christman, D.R. and Gehring, J.W., “Analysis of High-Velocity Projectile Penetration Mechanics,” Journal of Applied Physics, Vol. 37, 1966 23. Heaston, R.J. and Smoots, C.W., “Precision Guided Munitions,” GACIAC Report HB-83-01, May 1983 24. Donatelli, G.A. and Fleeman, E.L., “Methodology for Predicting Miss Distance for Air Launched Missiles,” AIAA-820364, January 1982 25. Bennett, R.R. and Mathews, W.E., “Analytical Determination of Miss Distances for Linear Homing Navigation Systems,” Hughes Tech Memo 260, 31 March 1952 26. Nicholas, T. and Rossi, R., “US Missile Data Book, 1996,” Data Search Associates, 1996 27. Bithell, R.A. and Stoner, R.C., “Rapid Approach for Missile Synthesis,” AFWAL TR 81-3022, March 1982 28. Fleeman, E.L. and Donatelli, G.A., “Conceptual Design Procedure Applied to a Typical Air-Launched Missile,” AIAA 811688, August 1981 29. Hindes, J.W., “Advanced Design of Aerodynamic Missiles ( ADAM ),” October 1993 30. Frits, A.P., et al, “A Conceptual Sizing Tool for Tactical Missiles, “ AIAA Missile Sciences Conference, November 2002 31. Bruns, K.D., Moore, M.E., Stoy, S.L., Vukelich, S.R., and Blake, W.B., “Missile DATCOM,” AFWAL-TR-91-3039, April 1991 2/24/2008

ELF

414

References ( cont ) 32. Moore, F.G., et al, “The 2002 Version of the Aeroprediction Code”, Naval Surface Warfare Warfare Center, March 2002 33. Nicolai, L.M., “Designing a Better Engineer,” AIAA Aerospace America, April 1992

2/24/2008

ELF

415

Bibliography of Other Reports and Web Sites System Design Fleeman, E.L., “Tactical Missile Design,” American Institute of Aeronautics and Astronautics, 2006 “DoD Index of Specifications and Standards,” http://stinet.dtic.mil/str/dodiss.html “Periscope,” http://www.periscope1.com/ Defense Technical Information Center, http://www.dtic.mil/ NATO Research & Technology Organisation, http://www.rta.nato.int/ “Missile System Flight Mechanics,” AGARD CP270, May 1979 Hogan, J.C., et al., “Missile Automated Design ( MAD ) Computer Program,” AFRPL TR 80-21, March 1980 Rapp, G.H., “Performance Improvements With Sidewinder Missile Airframe,” AIAA Paper 79-0091, January 1979 Nicolai, L.M., Fundamentals of Aircraft Design, METS, Inc., 1984 Lindsey, G.H. and Redman, D.R., “Tactical Missile Design,” Naval Postgraduate School, 1986 Lee, R.G., et al, Guided Weapons, Third Edition, Brassey’s, 1998 Giragosian, P.A., “Rapid Synthesis for Evaluating Missile Maneuverability Parameters,” 10th AIAA Applied Aerodynamics Conference, June 1992 Fleeman, E.L. “Aeromechanics Technologies for Tactical and Strategic Guided Missiles,” AGARD Paper presented at FMP Meeting in London, England, May 1979 Raymer, D.P., Aircraft Design, A Conceptual Approach, American Institute of Aeronautics and Astronautics, 1989 Ball, R.E., The Fundamentals of Aircraft Combat Survivability Analysis and Design, American Institute of Aeronautics and Astronautics, 1985 “National Defense Preparedness Association Conference Presentations,” http://www.dtic.mil/ndia

2/24/2008

ELF

416

Bibliography of Other Reports and Web Sites ( cont ) System Design ( continued ) Eichblatt, E.J., Test and Evaluation of the Tactical Missile, American Institute of Aeronautics and Astronautics, 1989 “Aircraft Stores Interface Manual (ASIM),” http://akss.dau.mil/software/1.jsp “Advanced Sidewinder Missile AIM-9X Cost Analysis Requirements Description (CARD),” http://deskbook.dau.mil/jsp/default.jsp Wertz, J.R and Larson W.J., Space Mission Analysis and Design, Microprism Press and Kluwer Academic Publishers, 1999 “Directory of U.S. Military Rockets and Missiles”, http://www.designation-systems.net/ Fleeman, E.L., et al, “Technologies for Future Precision Strike Missile Systems,” NATO RTO EN-018, July 2001 “The Ordnance Shop”, http://www.ordnance.org/portal/ “Conversion Factors by Sandelius Instruments”, http://www.sandelius.com/reference/conversions.htm “Defense Acquisition Guidebook”, http://akss.dau.mil/dag/ Aerodynamics “A Digital Library for NACA,” http://naca.larc.nasa.gov/ Briggs, M.M., Systematic Tactical Missile Design, Tactical Missile Aerodynamics: General Topics, “AIAA Vol. 141 Progress in Astronautics and Aeronautics,” American Institute of Aeronautics, 1992 Briggs, M.M., et al., “Aeromechanics Survey and Evaluation, Vol. 1-3,” NSWC/DL TR-3772, October 1977 “Missile Aerodynamics,” NATO AGARD LS-98, February 1979 “Missile Aerodynamics,” NATO AGARD CP-336, February 1983 “Missile Aerodynamics,” NATO AGARD CP-493, April 1990 “Missile Aerodynamics,” NATO RTO-MP-5, November 1998 Nielsen, J.N., Missile Aerodynamics, McGraw-Hill Book Company, 1960 2/24/2008

ELF

417

Bibliography of Other Reports and Web Sites ( cont ) Aerodynamics ( continued ) Mendenhall, M.R. et al, “Proceedings of NEAR Conference on Missile Aerodynamics,” NEAR, 1989 Nielsen, J.N., “Missile Aerodynamics – Past, Present, Future,” AIAA Paper 79-1818, 1979 Dillenius, M.F.E., et al, “Engineering-, Intermediate-, and High-Level Aerodynamic Prediction Methods and Applications,” Journal of Spacecraft and Rockets, Vol. 36, No. 5, September-October, 1999 Nielsen, J.N., and Pitts, W.C., “Wing-Body Interference at Supersonic Speeds with an Application to Combinations with Rectangular Wings,” NACA Tech. Note 2677, 1952 Spreiter, J.R., “The Aerodynamic Forces on Slender Plane-and Cruciform-Wing and Body Combinations”, NACA Report 962, 1950 Simon, J.M., et al, “Missile DATCOM: High Angle of Attack Capabilities, AIAA-99-4258 Burns, K.A., et al, “Viscous Effects on Complex Configurations,” WL-TR-95-3060, 1995 Lesieutre, D., et al, “Recent Applications and Improvements to the Engineering-Level Aerodynamic Prediction Software MISL3,’’ AIAA-2002-0274 Moore, F.G., Approximate Methods for Weapon Aerodynamics, American Institute of Aeronautics and Astronautics, 2000 “1976 Standard Atmosphere Calculator”, http://www.digitaldutch.com/atmoscalc/ “Compressible Aerodynamics Calculator”, http://www.aoe.vt.edu/~devenpor/aoe3114/calc.html Ashley, H. and Landahl, M., Aerodynamics of Wings and Bodies, Dover Publications, 1965 John, James E.A., Gas Dynamics, Second Edition, Prentice Hall, 1984 Zucker, Robert D., Fundamentals of Gas Dynamics, Matrix Publishers, 1977 Propulsion Chemical Information Propulsion Agency, http://www.cpia.jhu.edu/ St. Peter, J., The History of Aircraft Gas Turbine Engine Development in the United States: A Tradition of Excellence, ASME International Gas Turbine Institute, 1999 2/24/2008

ELF

418

Bibliography of Other Reports and Web Sites ( cont ) Propulsion ( continued ) Mahoney, J.J., Inlets for Supersonic Missiles, American Institute of Aeronautics and Astronautics, 1990 Sutton, G.P., Rocket Propulsion Elements, John Wiley & Sons, 1986 “Tri-Service Rocket Motor Trade-off Study, Missile Designer’s Rocket Motor handbook,” CPIA 322, May 1980 Humble, R.W., Henry, G.N., and Larson, W.J., Space Propulsion Analysis and Design, McGraw-Hill, 1995 Jenson, G.E. and Netzer, D.W., Tactical Missile Propulsion, American Institute of Aeronautics and Astronautics, 1996 Durham, F.P., Aircraft Jet Powerplants, Prentice-Hall, 1961 Bathie, W.W., Fundamentals of Gas Turbines, John Wiley and Sons, 1996 Hill, P.G. and Peterson, C.R., Mechanics and Thermodynamics of Propulsion, Addison-Weshley Publishing Company, 1970 Mattingly, J.D., et al, Aircraft Engine Design, American Institute of Aeronautics and Astronautics, 1987 Materials and Heat Transfer Budinski, K.G. and Budinski, M.K., Engineering Materials Properties and Selection, Prentice Hall, 1999 “Matweb’s Material Properties Index Page,” http://www.matweb.com “NASA Ames Research Center Thermal Protection Systems Expert (TPSX) and Material Properties Database”, http://tpsx.arc.nasa.gov/tpsxhome.shtml Harris, D.C., Materials for Infrared Windows and Domes, SPIE Optical Engineering Press, 1999 Kalpakjian, S., Manufacturing Processes for Engineering Materials, Addison Wesley, 1997 MIL-HDBK-5J, “Metallic Materials and Elements for Aerospace Vehicle Structures”, Jan 2003 “Metallic Material Properties Development and Standardization ( MMPDS )”, http://www.mmpds.org

2/24/2008

ELF

419

Bibliography of Other Reports and Web Sites ( cont ) Materials and Heat Transfer ( continued ) Mallick, P.K., Fiber-Reinforced Composites: Materials, Manufacturing, and Design, Second Edition, Maecel Dekker, 1993 Chapman, A.J., Heat Transfer, Third Edition, Macmillan Publishing Company, 1974 Incropera, F.P. and DeWitt, D.P., Fundamentals of Heat and Mass Transfer, Fourth Edition, John Wiley and Sons, 1996 Guidance, Navigation, Control, and Sensors Zarchan, P., Tactical and Strategic Missile Guidance, “AIAA Vol. 124 Progress in Astronautics and Aeronautics,” American Institute of Aeronautics and Astronautics, 1990 “Proceedings of AGARD G&C Conference on Guidance & Control of Tactical Missiles,” AGARD LS-52, May 1972 Garnell, P., Guided Weapon Control Systems, Pergamon Press, 1980 Locke, A. S., Guidance, “Principles of Guided Missile Design”, D. Van Nostrand, 1955 Blakelock, J. H., Automatic Control of Aircraft and Missiles, John Wiley & Sons, 1965 Lawrence, A.L., Modern Inertial Technology, Springer, 1998 Siouris, G.M., Aerospace Avionics Systems, Academic Press, 1993 Stimson, G.W., Introduction to Airborne Radar, SciTech Publishing, 1998 Lecomme, P., Hardange, J.P., Marchais, J.C., and Normant, E., Air and Spaceborne Radar Systems, SciTech Publishing and William Andrew Publishing, 2001 Wehner, D.R., High-Resolution Radar, Artech House, Norwood, MA, 1995 Donati, S., Photodetectors, Prentice-Hall, 2000 Jha, A.R., Infrared Technology, John Wiley and Sons, 2000 Schlessinger, M., Infrared Technology Fundamentals, Marcel Decker, 1995

2/24/2008

ELF

420

Follow-up Communication I would appreciate receiving your comments and corrections on this text, as well as any data, examples, or references that you may offer. Thank you, Gene Fleeman Tactical Missile Design E-mail: [email protected] Web Site: http://genefleeman.home.mindspring.com

2/24/2008

ELF

421

Outline Introduction / Key Drivers in the Design Process Aerodynamic Considerations in Tactical Missile Design Propulsion Considerations in Tactical Missile Design Weight Considerations in Tactical Missile Design Flight Performance Considerations in Tactical Missile Design Measures of Merit and Launch Platform Integration Sizing Examples Development Process Summary and Lessons Learned References and Communication Appendices ( Homework Problems / Classroom Exercises, Example of Request for Proposal, Nomenclature, Acronyms, Conversion Factors, Syllabus ) 2/24/2008

ELF

422