Aeronautical Vestpocket Handbook, Pratt & Whitney, 22nd Edition, Sep 1991

AERONAUTICAL VEST POCKET HANDBOOK

e

UNITED TECHNOLOGIES PRATT&WHITNEY

.Jommercial Engine Business Government Engines and Space Propulsion Operations Pratt & Whitney Canada

Part No. P&W 79500

Twenty-Second Edition - First Printing September 1991 Printed in U.S.A.

Personal Data

Name Home Address

Home Telephone No. Business Address

Business Telephone No. In case of accident or serious, illness, please notify:

Telephone No.

Table of Contents Conversion Tables

Conversion Factors............

. ............. 11

Miscellaneous Conversions, Weights and Measures ............. 24 Heat and Temperature. ... ..... . . ............. ..26 Drill Sizes ................................................. 27 Metric System.... .. ... .. ............................ 28 Prefix Multiples...........................................33

Standard Atmosphere

Definition of Standard Atmosphere... ....................34 Geopotential Altitude. ........... ....................35 ICAO and U.S. Standard Atmosphere, British Units ...........36 ICAO and U.S. Standard Atmosphere, Metric Units. ....42

Compressible Flow

Compressible Flow Functions .......

One Dimensional Isentropic Compressible Flow

. .. 46

Functions ............................................... SO

One Dimensional Normal Shock Functions.................... 62 Inlet Pressures and Temperatures............................72 MIL-E-S007D Inlet Pressure Recovery........ ........ ..... 89

Air and Gas Properties

General Properties of Air...................................90 Normal Composition of Air............................. .91 General Properties of Gases.. ..92 Psychrometric Chart...... .............. .. .......93 Atmospheric Viscosity. .. ... .. .... .. ... .. . ....94 Specific Heats of Air at Low Pressures............ ......95 Specific Heats of Products of Combustion ..96 lOOOJo, 2000Jo, 4000Jo Theoretical Air.......

Physical Properties

Density and Weights of Fuels.............. ...99 Specific Gravity and Weights of Oils......... ..99 Applicable Fuel and Oil MIL Specifications........... ....99 Weights of Gases..........................................99 .....................100 Physical Constants.. ....... Density - Temperature Variation of Aviation Fuels.......... 101 Oil Viscosity Range... .......................103 Properties of Elements....................................104 Properties of Materials (Nonmetallics)......... .......112 Properties of Materials (Metars and Alloys). .............114

Rocket Engines

Liquid Rocket Engine Symbols .............................120 Rocket Engine Equations .................................. 123 Rocket Engine Formulas ................................... 124 Cryogenic Liquid Rocket Fuels ............................. 126 Liquid Rocket Engine Cycles ............................... 127 Theoretical Rocket Engine Propellant Summary .............. 131 Vapor Pressure of Liquid Propellants ....................... 133 Specific Gravities of Liquid Propellants ..................... 134

Gas Turbine Engines

Gas Turbine Engine Symbols Used by P&W.................135 Gas Turbine Engine Subscripts .............................137 Gas Turbine Parameter Correction Procedures ...............138 Inlet and Jet Wake Danger Areas ...........................139 Theta (0) Tables .......................................... 140 Gas Turbine Engine Station Designations .................... 148 Thrust - Horsepower Conversion ..........................155 Turbojet and Turbofan Engine Noise .......................156

Aircraft Performance

Aerodynamic Relationships ................................163 Airspeed Relationships and Corrections ......................164

Miscellaneous

Personal Data ..............................................3 A Brief History of Pratt & Whitney ...........................6 Greek Alphabet ........................................ .49 Climatic Data for Selected U.S. Cities .......................171 P&W Commercial Engine Designations ......................173 U.S. Military Aircraft Designations .........................173 U.S. Military Engine Designations ..........................175 Rocket and Missile Designations ............................179 Aircraft National Registration Marks ........................180 Designation Codes of Selected Airlines......................182 Major International Airports of the World...................188 Engines Designed by P&W .................................192 Absolute Records for Aircraft ..............................194 Inch - Millimeter Scales..................................195 P&W Offices - Addresses and Telephones ..................196

A Brief History of Pratt & Frederick Brant Rentschler arrived in Hartford in 1925 with a small group of men whose goal was to produce an air-cooled radial aircraft engine superior to any predecessor. To accomplish that goal, they formed a new company - Pratt & Whitney Aircraft - in July 1925. Some five months later, on December 29, 1925, Rentschler and his men succeeded in testing their first engine, the Wasp1!1 . The Wasp began a new era in American aviation. Rentschler and Pratt & Whitney Aircraft played a key role in that new industry. Their commitment to technological advancement was obvious; each new engine model incorporated important technical improvements. The Wasp and the Hornet® soon became the main power source for the nationts new military aircraft and for the developing air transport industry. The 1930s were a challenging time for aviation. Many milestones were achieved by Pratt & Whitney during that decade. Pratt & Whitney engines powered 90 percent of the nation's commercial transports. The company also played a major role in aviation history. For exarnpl� a Thin \Vasp® powered Martin China Qipper introduced trans-Pacific air travel in 1935. Significant technical advances were made in aircraft design that required new advanced engines that simultaneously combined higher horsepower with increased reliability. Pratt & Whitney met those challenges with engines that set the majority of records for speed and distance. While Pratt & Whitney was involved exploring new frontiers, the company was also unknowingly preparing for one of its greatest challenges; supplying the power that would help the U.S. and its Allies attain air supremacy in World War II. During World War II, the challenge for Pratt & Whitney was to produce and improve upon air�cooled reciprocating engines for the Military. Pratt & Whitney met the challenge by producing more than half the total aircraft horsepower used by the U.S. and its Allies. During that period, turbine engine to emerge as an aircraft however, the & Whitney's were tied; the company was powerpfant. committed to the war effort and could only observe gas turbine deve1opment.

At war's end, prospects in the gas turbine field turned brighter for Pratt & Whitney. A first peacetime step the company took toward leadership in thot area was its creation of the WiUgoos Turbine Laboratory, named for Andrew Willgoos, a P&W founder and its first chief engineer. The 'Lab', the world•s largest privately owned engine test facility, became an essential tool in jeL engine developmenL. One of the first engines developed at the Willgoos Lab was the J57, the first Pratt & Whiu,ey designed turbojet engine released to production. That engine, a dual-rotor, axial-now Lurbojet, produced 10.000 pounds of thrust and was the first to power an aircraft at supersonic speed in level flight. The JS7 also made aviation history by winning the Collier Trophy. The J57 powered the B-52 bomber, the backbone of American strategic power in the 1950s. The JS7, along with its more powerful ruccessort the 175 1 powered the U.S. 'century series' fighter aircraft. Commercial version.s of those engines. the JT3 and JT4 ins ta.lied in 707s and DC-Ss, ushered in the jet age for U.S. air travelers. The JT3D, P&W's first production turbofan, was developed by taking the service-proven JT3 (J57) gas generator nnd adding a two-stage front fan. In the mid 1950s, Pratt & Whitney began work with liquid hydrogen fuel for aerospace engines. A 157 was converted to operate on liquid hydrogen and a prototype turbofan engine, the 304, designed to fly at 100,000 feet, was tested in 1957 at the Florida Research and Development Center (FRDC). The expander cycle, used in the 304 was adopted for the RLIO liquid rocket engine. The 1960s saw continuing development of improved turbofans. The JT8D, selected as the powerplant for Boeing 727, 737, Douglas DC-9, and Aerospatiale Caravelle passenger aircraft met the rigorous requirements of short-to-medium range service where takeofrs and landings occur as o!len as hourly. Continued uprating of its initial 14,000 pounds of takeoff thrust made growth possible in aircraft payloads, increased range,. shortened takeoff distances, and produced higher rates of climb for reduced community noise levels. The RL!O began its highly rnccessful launch history in 1963 with the injection of a test payload into orbit. Since that time, this engine has launched all of the spacecraft for planeiary exploration, and most of

7

the communication satellites placed in 24 hour orbit. The sixties also saw the development of high chamber pressure rocket engine technlogy at P&W, which included oxygen and hydrogen turbopumps and culminated in test firings of the quarter million pound thrust XLR-129 at the FRDC facility. This technology was subsequently adopted for the Space Shuttle main engine. The JT9D introduced advances in turbofan technology i n the late 1960s and 1970s which made possible a whole new generation of wide-bodied commercial transports - Boeing 747, McDonnell Douglas DC.JO Series 40, and Airbus Industrie A300 airliners. The JT9D's initial power rating was 43,600 pounds of thrust, but standard series JT9D engine models soon offered up to 56,000 pounds of takeoff thrust. Military arterburning turbofans developed and produced by P&W in the 1970s included the TF30 which powers the Air Force F-Jll and the Navy F·l4, and the FIOO which powers the Air Force f.15 and F-16. Pratt & Whitney Canada introduced the PT6 turboprop engine in 1%4, and since its service introduction, it has become the world�s most popular powerplant in the 475 1424 shaft horsepower class. It powers more than 127 different business, commuter, and helicopter aircraft. The JT15D turbofan, first test run in September 1967, produced 2,200 to 2,900 pounds of takeoff thrust, and received certification in May 1971 from the Canadian Department of Transport. It powers the Cessna Citations I, !!, S/II, Cessna Navy Citation T-47A, Aerospatiale Corvette, Mitsubishi Diamonds I and IA, Beechjet, and SIA! Marchetti S2ll. Turbofan engine development in the 1970s emphasized greater energy efficiency and reduced levels of noise and emissions. The derivative JT8D-200 series engines, retaining the JT8D's high pressure rotor replaced the JT8D's two-stage fan with a larger diameter single-stage fan and added an exhaust mixer for reduced noise levels. JT8D-200 series engines have made the McDonnell Douglas advanced medium-range MD-80 series aircraft among the most fuel-efficient and quietest commercial jetliners now flying in its class. During the 1970s, the RLIO launched thirty-four critical payloads, including the Voyagers which completed the Grand Tour of the solar system in 1989. In the Helios mission, launched on a Titan/Centaur, the RLIOA-3-3 demonstrated its capability for multiple relights in space

with each engine being started seven times to inject the spacecraft into an orbit which passed within 0.29 AV from the sun. The JT9D-7R4 engine series, incorporating technical advances based on millions of JT9D engine flight hours' experience, made it possible for commercial operators in the late 1970s to satisfy many wide-body powerplant requirements with a single family of engines. JT9D-7R4 technology advances included a wide-chord, single-shroud fan, single· crystal turbine blades, and an electronic engine control. JT9D-7R4s power the Boeing 767 and stretched-upper-deck 747-300, and the Airbus A300-600. The PW2037, first engine in the PW2000 engine series, whose development began in the mid-!970s, powers the Boeing 757, an advanced technology single-aisle transport designed for maximum economy on short-to-medium range routes. Rated at 38,250 pounds of takeoff thrust, the PW2037 design features controlled diffusion airfoils, high-strength supera!loy disks, full-authority digital electronic control, and active clearance control for reduced fuel consumption. The PW2037 (F117-PW.JOO) was also selected as the powerplant for the Air Fon:e C-17 military transport. In early 1980, Pratt & Whitney Canada unveiled a new turboprop engine family, the PW!OO series, whose models offer about 15 percent lower specific fuel consumption than other turboprops. Providing 1,500 to 2,570 shaft horsepower, PWIOO models have been ,elected to power a new generation of commuter airliners; the de Havilland Dash 8, the Embraer Brasillia EMB-120, the Aerospatiale·Aeritalia ATR42, the British Aerospace ATP, and the Fokker 50. In 1983 P&WC announced the development of the PW200 series, an advanced technology 500-1,000 shp fuel efficient turboshaft engine for the new generation of light twin helicopters. The first model is the PW209T, a twin turboshaft. P&WC announced in the mid-1980s, development of the new PW300 series turbofan engines for business and commuter aircraft; this series will produce 4,500 to 6,000 pounds of takeoff thrust. The PW 4000 is a radically new large commercial jet engine series designed for advanced versions on the Boeing 747 and 767, the Airbus A300 and A310, as well a, the McDonnell Douglas MD-11. It offers takeoff thrnst of 50,000 to 62,000 pounds, with growth to over 76,000 pounds, at a marked increase in fuel efficiency. The PW4000 features 9

an almost SO percent reduction in engine parts for substantially reduced spare parts and labor maintenance costs. Development of the PW4000 was launched in late 1982, with commercial service introduced in

June 1987.

Development of the V2500 turbofan began in late 1983 by a five-nation consortium (P&W; Rolls-Royce of Great Britian; JAEC of Japan; MTU of West Germany; and, Fiat of Italy) to produce engines in the 18,000-30,000 pound takeoff thrust class for new Airbus, Boeing, and McDonnell Douglas 150-passenger medium-range jetliners. In the mid 1980s, P&W introduced the PJOO-PW-220 afterburning turbofan, which brought a new level of reliability and durability to P-15 and P-16 aircraft. It was followed, late in the decade, by the PIOO-PW-229, an increased performance member of P&W's PIOO family of fighter engines with 29,000 pounds of thrust for advanced P-15s and P-16s. At the same time, P&W was progressing with development of the Fll9, the company's candidate to power the Air Force's Advanced Tuctical Fighter of the future. Also during the 1980s, P&W began deliveries of the F!17 for the Air Force's McDonnell Douglas C-17 Airlifter. The Fll7 is a military version of the PW2040 series commercial engine. A major increase in the number of propulsion systems using hydrogen

fuel has occurred at P&W during the 1980s. The RLIO has been selected to power the commercial versions of the Atlas/Centaur and the Titan­ IV Centaur. More engines are now on order than have flown over the

last three decades. Alternate turbopumps which will provide full life to the space shuttle main engine are under development for NASA. Advanced technology rocket engine components are being developed for the Advanced Launch System for the USAF /NASA, and developmnent is underway on the powerplant for the National Aero­ Space Plane (NASP). The objective of the NASP program is to establish the technological base for an aircraft capable of single stage to orbit from a horizontal takeoff.

IO

Conversion Factors To obtain

Multiply

By

acre

4.3560 4.0469 4.0469 1.5625 4.8400

x x x x x

104 10-1 11)3 10-J 103

square feet

atmosphere (atm) (1962)

7.6000 2.9921 1.0332 1.0133 1.4696

x x x X x

10 10 104 10s 10

centimeters of mercury

bar

9.8962 x 10-1 1.0000 x 1()6

dynes/square

7.5006 x 102 1.0000 X 105 1.4504 x 10

newtons I square meter pounds I square inch

barn

1.0000 x 10-24

square centimeters (nuclear cross-section)

barrel, liquid (U.S.)

3.1500 x 10 1.1924 x 10-1

British thermal unit (Btu)

2.5180 7.7817 1.0551 3.9301 1.0551 1.0551 2.9302 1.0551

x x x x x x x x

4.1999 1.7548 1.2970 2.3581 1.7548 1.7931 1.7548

x JOB x 10 x 10-2 x 10

British thermal

unit/minute

(Btu/min)

102 102 1010 10-4 103 103 10-4 103

x 10

hectares square meters

square miles

square yards inches of mercury kilograms/ square meter newtons/square meter

pounds/ square inch

atmospheres

centimeter

millimeters of mercury

gallons

cubic meters

calories (post-1956 !ST) foot-pounds

ergs horsepower-hours

joules

newton-meters kilowatt-hours watt-seconds calories/second

ergs/ second

foot-pounds/second

horsepower

joules/second

kilogram-meters I second watts

11

Conversion Factors (continued) To obtain 107 10-6 ca.Jorie I second (cal/sec)

centimeter (cm)

2.3810 x 10-1 4.1868 x J07 3.0880 4.1868 3.2808 3.9370 1.0000 1.0000 1.0936

x x x x x

10-2 10-1 10-, 10-2 10-2

3.2808 x 10-2 3.9370 x 10-1 ],0000 x 10-2 x 10-•

chain (surveyor)

6.7197 J.6001) l.0000 2.21)1)1) 6.6000 2.0117

cord

1.2800 x 102

centipoise

x x x x

cubic centimeter J.0000 X 3.5315 x (cml) 6.1024 x J.0000 x J.3080 x cubic decimeter 1.01)1)1) x 3.5)15 x (literl 6.1024 x (dm3) 1.0000 x 1.3080 x 12

102 JO 10 JO

British thermal units foot-pounds ergs joules kilowatt-hours watt-seconds British thermal units/minute ergs/second foot-pounds/second joules I second feet inches kilometers meters yards feet/second inches Isecond meters/ second pounds (mass)/second-foot kilograms I hour�meter links yards feet meters cubic feet

Conversion Factors (continued) By

Multiply

To obtain

2.8317 x 2.8317 x 1.7280 x 2.8317. x 3. 7037 x

cubic foot (ft3)

104 10 103 10-2 10-2

H2 0 6.2366 x 10

cubic centimeters cubic decimeters cubic inches cubic cubic pounds

cubic inch (in3)

1.6387 1.6387 5.7870 1.6387 2.1433

x x x x x

10 10-2 10-4 10-s 10-5

cubic centimeters cubic decimeters cubic feet cubic cubic

cubic meter (m3)

1.0000 1.0000 3.5315 6.1024 1.3080

x x x x

106 103 10 104

cubic centimeters cubic decimeters cubic feet cubic inches cubic yards

cubic yard (yd3)

7.6455 7.6455 2.7000 4.6656 7.6455

x x x x x

to5 102 10 104 10-1

cubic centimeters cubic decimeters cubic feet cubic inches cubic meters

curie

3.7000 x 1010

disintegrations/second

degree (deg)

6.0000 1.7453 2.7778 3.6000

x x x x

10 10-2 10-3 J03

minutes radians revolutions seconds

dyne

1.0197 1.0197 1.0000 3.5970 2.2481

x x x x x

10-6 10-s 10-5 10-6

10-3

grams kilograms newtons ounces pounds

dyne/square centimeter

2.9530 1.0197 7.5006 1.0000 1.4504

x x x x x

10-5 10-2 10-4 10 10-s

inches of mercury kilograms/square meter millimeters of mercury newtons/square meter pounds I square inch 13

Conversion Factors (continued) Multiply

By

To obtain

electron volt

3.8268 x 10-20 1.6022 x 10-12 1.0000 x 10-6

MeV(mega electron volts)

9.4782 2.3885 1.0000 7.3756 1.0000

x 10-11 x 10-8

British thermal units calories dyne-centimeters foot-pounds joules

erg/second

5.6869 2.3885 7.3756 1.0000 1.0000

x x x x x

flow rate, fuel

4.5359 x 10-1

kilograms/hour

foot (ft)

3.0480 1.2000 3.0480 3.0480 1.8939 3.3333

x x x x x x

centimeters inches kilometers meters miles yards

foot-pound

1.2851 1.3558 5.0505 1.3558 3.7662 1.3558

x 10-3 x 101 x 10-1

7.7104 3.2383 1.8182 1.3558 1.3826 1.3558

x 10-2 x 10-t x 10-3

3.0480 1.0973 5.9248 3.0480 6.8182

x 10

(eV)

erg

(lb/hr)

(ft-lb)

foot-pound/

second

(ft-lb/sec)

foot/second

(fps)

14

x 10-8 x 10-1 10-9 10-8 10-8 10-1 10-1

10 10 10-4 10-t 10-4 10-t

x 10-1

x 10-t

calories ergs

British thermal units/minute calories/second foot-pounds/second joules/second watts

British thermal units

ergs

horsepower-hours joules kilowatt-hours newton-meters British thermal units/minute calories/second horsepower joules/second kilogram-meters I second watts

x 10-1 x 10-t x 10-t

centimeters I second kilometers/hour knots meters I second miles/hour

Conversion Factors (continued) Multiply

By

To obtain

furlong

1.0000 x 10 2.2000 x 102 2.0117 x 102

chains yards meters

gallon (U.S.) (gal)

1.3368 x 10-1 3.7854 3.7854 x I0-3 8.0000 4.0000

cubic feet liters cubic meters pints quarts

gram (gm)

1.0000 3.5274 2.2046 9.8067 9.8067

kilograms ounces pounds dynes newtons

hectare

2.4711 1.0000 x 102 J.0000 x 104 3.8610 x 10-3

acres ares

4.2436 x 10 104 102 10 102

British thermal units/minute foot-pounds/ second foot-pounds/ minute joules/ second kilogram-meters/ second watts

103 106 106 10-1

British thermal units foot-pounds joules kilowatt-hours

horsepower (hp)

x x x x x

10-3 10-2 l0-3 102 I0-3

5.5000 x 102

3.3000 7.4570 7.6040 7.4570

x x x x

horsepower-hour 2.5461 x 1.9800 x (hp hr) 2.6845 x 7.4570 x hour (hr)

6.0000 3.6000 4.1781 4.1667 1.1416

x x x x x

imperial gallon

2.7742 x 102 1.2009 4.5460

meters miles

10 lo3 10-2 10-2 I0-4 cubic inches gallons (U.S.) liters

15

Conversion Factors (continued) To obtain

inch (in)

2.5400 8.3333 x 10-2 2.S400 x 10-2 2.7778 x 10-2

inch of mercury 3.3421 x 3.3864 x at O'C 3.3864 x (in Hg) 1.3595 x 2.5400 x 3.3864 x 7.(1727 x 4.9116 x

10-2 10-2 104 JO 10 103 10 10-1

centimeters feet atmospheres bars

dynes/square centimeter

inches of water millimeters of mercury

newtons/ square meter

pounds/square feet

pounds/square inch

inch/second

8.3333 x 10-2 2.5400 2.5400 x 10-2

feet/second

inch of water at 4'C (in H20)

2.4584 7.3556 l.8683 2.4910 3.6128

x JQ-3 x 10-2

atmospheres inches of mercury millimeters of mercury newtons Isquare meter

joule

9.4771 2.3889 l.0000 1.0000 7.3756 l.0000 1.0000

x x x x x

1.0000 3.5274 2.2046 6.8521 9.8067 7.9290

x J03 x 10

(ips)

(J)

kilogram (k g)

kilogram/ square meter (kg/m2J

16

x 102 x 10-2 10-4 10-1 107 107 10-1

centimeters/ second meters/second

pounds/square inch

British thermal units calories dyne�centimeters

ergs foot-pounds

newton�meters

watt�seconds

x 10-2 x 10

9.6783 x 10-s 9.8067 x 10-s 2.8959 x 10-3 9.8067

atmospheres bars

inches of mercury

newtons/ square meter

Conversion Factors (continued) Multiply

By

To obtain

kilogram/

6.5895 2.0482 x 10-1 1.4223 x 10-J

pounds I square inch

square meter

(kg/m2)

kilogram-meter

(kgm)

9.2938 x 10-3 7.2330 9.8067 9.8067 2.7232 x 10-6

kilogram-meter/ 3.3458 x 10

second

poundals I square foot pounds/square foot

British thermal units foot-pounds

joules

newton-meters kilowatt-hours British thermal units/hour calories/second

2.3423 7.2330 9.8067 1.3151 x 10-2 9.8067 x 10-3

joules/second horsepower kilowatts

kilometer

3.2808 3.9370 1.0000 6.2137 1.0936

x x x x x

103 ]()4 103 10-1 103

feet inches meters miles yards

kilometer/hour (km/hr)

9.1130 5.3960 6.2137 2.7778

x x x x

10-1 10-1 10-1 10-1

miles/hour meters/second

kilo newton

2.2481 x 102

pounds

kilowatt hour

3.4128 2.6560 1.3414 3.6000 3.6721 3.6000

x 103 x 106

British thermal units

x 106 x 105 x 106

joules kilogram-meters watt-seconds

(kgm/sec)

(km)

foot-pounds/ second

feet/ second

knots

(kN)

(kWh)

foot-pounds horsepower-hours

knot (kt)

1.6878 1.1516 1.8532 5.1480 x 10-1

feet/ second miles/hour kilometers/hour

league (U.S.)

3.0000

nautical miles

meters I second

17

Conversion Factors (continued) To obtain light year

3.1040 x 1016 5.8786 x J0 12 9 .4608 x 101s

liter

6.1024 3.5315 2.6417 1.0000 2.1134 1.0567

x x x x

meter

1.0000 3.2808 3.9370 1.0000 6.2137 1.0936

x 10'

centimeters

x JO x J0-3 x 10-4

inches kilometers miles yards

(l)

(m)

meter/second (m/sec)

mile (mi)

10 10-2 10-1 10-J

feet

miles meters cubic inches cubic feet gallons (U.S. liquid) cubic meters pints (U.S. liquid) quarts (U.S. liquid) feet

3.2808 3.6000 1.9438 2.2369

feet/second kilometers/hour knots miles/hour

9.8632 x JO-I 1.3550 x 10-1

kilowatts

5.2800 6.3360 1.6093 J.6093 3.2000 1.7600

x J03 x 104 x 103 x 10' x 103

horsepower

feet inches kilometers meters rods

yards

mile/hour (mph)

1.4667 1.6093 8.6898 x 10-1 4.4704 x 10-1

feet/second kilometers/hour knots meters/second

millimeter of mercury at O'C (torr) (mm Hg)

l.3332 3.9370 5.3526 1.3332 1.9337

dynes/square centimeter inches of mercury (O'C) inches of water {4'C) newtons/square meter pounds/ square inch

18

x x x x x

103 10-2 10-1 102 10-2

Conversion Factors (continued) Multiply

By

minute (angle) (min)

1.6667 2.9089 4.6296 6.0000

x x x x

10-2 10-•

10-s

degrees radians revolutions

minute (time)

1.6667 6.0000 6.9444 1.9026

x x x x

10-2 10 10-• 10-6

hours seconds solar days solar years

nautical mile (international)

6.0761 x 103 1.8520 x 103

feet

newton

1.0000 1.0197 1.0197 2.2481 7.2330

x x x x

102 10-t 10-1

dynes grams

9.8692 1.0000 2.9530 1.0197 6.7200 2.0885 1.4504

x x x x x x x

10-6 10 10-• 10-1 10-1 10-2 10-•

2.8349 2.8349 6.2500 1.9428 2.7801

x x x x x

10 10-2 10-2 10-J 104

(min)

(nmi) (N)

newton/

square meter

(pascal (Pa)) (N/m2)

ounce (oz)

To obtain

10

10s

seconds

meters

kilograms

pounds

poundals

atmospheres

dynes/square centimeter

inches of mercury (O'C)

kilograms/square meter poundals/square foot pounds/ square foot pounds/square inch

grams kilograms pounds

· slugs

dynes

1.9163 x 1013 3.0857 x 1016

miles meters

pieze

1.0000 x 103

newtons/square meter

pint (U.S.) (pt)

1.6710 1.2500 4.7317 4.7317 5.0000

parsec

x x x x x

10-2 10-1 10-1 10-• 10-1

cubic feet

gallons

liters cubic meters quarts 19

Conversion Factors (continued)

pound (force) (lbt) pound/ square foot (pst)

pound/ square inch (psi)

poundal poundal/ square foot

4.7254 4.7880 4.7880 1.4139 4.8824 4.7880 3.2174 6.9444 6.8046 6.8948 2.0360 2.7681 7.0307 6.8948 4.6333 1.4400 1.4098 1.3825 3.1081 l.5174 1.4882 3.1081 2.1583

x 10-1 x 10-J 10 x J0-4 x J0-4 x 102 x 10-2 x x x x x

JO 10 J0-3 10-2 104

x x x x x x x x x x x x

10 ]02 J03 IQ3 J02 10-2 10-1 10-2 10-1 10-1 10-2 J0-4

x x x x

10 103 10-1 !Ol

newtons dekanewtons kilonewtons poundals atmospheres bars dynes/square centimeter inches of mercury (O"C) kilograms/square meter newtons/square meter poundals/square foot pounds I square inch atmospheres dynes/square centimeter inches of mercury (O'C) inches of water (4'C) kilograms/square meter newtons/square meter poundals /square foot pounds/square foot kilograms

newtons pounds kilograms/square meter newtons/ square meter pounds/square foot pounds/square inch

quart (U.S.) liquid (qt)

radian

(rad)

20

5.7296 3.4378 1.5916 2.0626

degrees minutes revolutions seconds

Conversion Factors (continued) Multiply

By

To obtain

revolution (rev)

3.6000 x 1()2 2.1600 x 1()4 6.2832 1.2960 x 106

degrees minutes radians seconds

second (angle) (sec)

2.7778 1.6667 4.8481 7.7160

degrees minutes radians revolutions

second (time) (sec)

2.7778 x 10-4 1.6667 x 10-2 1.1574 x 10-s

slug

1.4594 1.4594 5.1478 3.2174

x x x x

solar day

2.4000 1.4400 8.6400 1.0027 2.7379

x 10 x 103 x 104

solar year

x 10-3 8.7658 x J03 3.6624 x 102 3.6524 x 1()2

square centimeter (cm2)

1.0764 1.5500 1.0000 1.0000

x x x x

square foot (ft2)

2.2957 9.2903 1.4400 9.2903 3.5870 1.1111

x x x x x x

x x x x

10-4 10-2 10-6 J0-7

104

10 1()2 10

J0-3 10-1 l0-4 102 10-s 102 102 10-2 10-s 10-1

grams kilograms ounces pounds

acres

21

Conversion Factors (continued) To obtain 10-J J0-4 102 !Oli lQ-4 square kilometers (km2)

2.4711 1.0764 1.0000 3.8610

x x x x

102 J07 J06 10-1

square meter (m2)

2.4711 1.0000 1.0000 1.0764 1.5500 3.8610 l.1960

x x x x x x

io-4 10-4 104 10 J03 10-7

square mile (mi2)

6.4000 2.5900 2.7878 2.5900 2.5900 3.0976

x 102 x 102 x J07

square yard (yd2)

2.0661 9.0000 1.2960 8.3613 3.2283

x 10-•

thcrmie

4.1868 x J06

acres square feet square meters square miles acres hectares

x J06 x 10• x J03 x 10-1 x 10- 7

thrust specific 1.0197 fuel consumption (TSFC) J.0197 x J02 (lb/hr/lb Fn)

22

circular mils square centimeters square feet

acres

feet inches meters miles

kilograms/hour/ dekanewton kilograms IhourI kilonewton

Conversion Factors (continued) To obtain watt (joule/ second) (W)

3.4121 5.6869 2.3900 1.0000 7.3756 1.3410 1.0197

x x x x x x

10-2 10-1 101 10-1 10-3 10-1

British thermal units/hour British thermal units/minute calories/ second ergs I second foot-pounds/ second horsepower kilogram-meters/ second

watt second (Wsec)

9.4782 x 10-4 7.3756 x 10-1 J.0000 2.7778 x 10-7

British thermal units foot-pounds joule kilowatt-hours

yard (yd)

9.1440 3.0000 3.6000 9.1440 9.1440 5.6818 1.8182

centimeters feet inches kilometers meters miles rods

x 10 x x x x x

10 10-4 10-1 10-4 10-1

23

Miscellaneous Conversions w,,;011,t., and Measures Liquid Measure:

4 gills • 1 pint 2 pints • I quart 4 quarts = I gallon 31 v, gallons - l barrel 2 barrels = I hogshead l U.S. gallon = 0.833 imperial gallon

Dry Measure:

2 pint = 1 quart 8 quarts = 1 peck 4 pecks • 1 bushel 36 bushels • I chaldron

Long Measure:

12 inches = 1 foot 3 feet = I yard 511 yards = 1 rod 40 rods = J furlong 8 = I statute mile

I

Cubic Measure:

- l.201 U.S.

1,728 cubic inches - J cubic foot 21 cubic feet • 1 cubic yard

128 cubic feet = I cord (wood) 231 cubic inches - 1 U.S.

Mariner's Measure:

6 feet = I fathom 120 fathoms = I cable length 1 !!\ cablC'lengths = I mile 5,280 feet - l statute mile feet • l nautical mile

Apothecaries Measure:

60 minim • l liquid dram 8 drams = l liquid ounce 16 ounces I

Shipping Measure:

100 cubic feet - l register ton 40 cubic feet - I U.S. shipping ton 42 cubic feet - I British shipping ton

24

Miscellaneous Conversions Weights and Measures (continued) Weight:

16 drams • 437.5 grains • I oz 16 oz = 7000 grains • I lb 112 lb = I hundredweight 20 hundredweight • I long ton 2000 lb = I short ton 2240 lb - 1 long ton 2204.60 lb = I metric ton

Precious Stones:

1 carat • 200 milligrams

Troy:

24 grains = I pennyweight 20 pennyweights = I oz 12 oz = 5760 grains = I lb

Apothecaries:

20 grains = l scruple 3 scruples • I dram 8 drams = I ounce 12 oz = 5760 grains = 1 lb

Avoirdupois:

25

Heat and Temperature The tWO basic units of heat are the British thermal unit (Btu) and the French thermal unit (kilogram calorie). A British thermal unit is the quantity of heat necessary to raise the temperature of one pound of pure water one degree Fahrenheit (F). A French thermal unit is the quantity of heat necessary to raise the temperature of one kilogram of pure water one degree Centigrade (C) or Celsius. One kilogram calorie = 3.968 British thermal units = !000 gram calories. A point has been theoretically determined on the temperature measurement scale which is calted absolute zero, beyond which a further decrease in temperature is inconceivable. That point is -459.67° F or -273.l56C. A temperature measured from that point is called absolute temperature. Absolute temperature in °C is known as degrees Kelvin (K) and absolute temperature in °F is known as degrees Rankine {R). 'K = 'C + 273.15 'R • 'F + 459.67 Pure water freezes at 32'F or O'C and boils at 212'F or lOO'C at standard sea level atmospheric pressure. The following formulas may be used to convert temperatures from one scale lO another: 'F ·915 ('C) + 32 'C • 5/9 ('F

26

32)

Drill Sizes

Decimal Equivalents

Dia. In. .2280 .2210 .2130 c .2090 D 5 .2055 E 6 .2040 F .2010 7 G .1990 8 H 9 .1960 I 10 .1935 J .1910 11 K .1890 L 12 13 .1850 M .1820 14 N .1800 15 0 .1770 16 p .1730 17 Q .1695 R 18 s .1660 19 .1610 20 T .1590 u 21 v 22 .1570 .1540 23 w .1520 24 x .1495 25 y .1470 26 z .1440 27 28 .1405 .1360 29 .1285 30 .1200 31 32 .1160 .1130 33 34 .1110 .1100 35 .1065 36 .1040 37 38 .1015 .0995 39 .0980 40 Screw Dia. = (Screw No. x 0.013) + 0.060 Drill No. A B

Dia. In. .234 .238 .242 .246 .250 .257 .261 .266 .272 .277 .281 .290 .295 .302 .316 .323 .332 .339 .348 .358 .368 .377 .386 .397 .404 .413

Drill No. 1 2 3 4

Drill No. 41 42 43 44 45 46 47 48 49 50

51 52 53 54

55 56

57 58

59

60 61 62 63 64

65

66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

Dia. In. .0960 .0935 .0890 .0860 .0820 .0810 .0785 .0760 .0730 .D700 .0670 .0635 .0595 .0550

.0520 .0465 .0430 .0420 .0410 .0400 .0390 .0380 .0370 .0360 .0350 .0330 .0320 .0310 .0292 .0280 .0260 .0250 .0240 .0225 .0210 .0200 .0180 .0160 .0145 .0135

27

Metric System

Because of increased use of the metric system of measurement, a summary of the current definitions of the International System of Units (SI) is included in this handbook. T he seven base units and two supplementary units of the system are shown in Table I.

TABLE 1 Name length. mass2 time.. .. , ....•...... electric current .... thermodynamic temperature3 ...... amount of substance.. , .. luminous intensity, ...

metre (meterJt ....... , .m kilogram.,,, .......... kg second,, ••...... ,,..• . s ampere . .. . ....... A

plane angle..... solid angle.

radian .. , •............ rad steradian.... , ........ . sr

Kelvin. ... . ... . ... K mole ................. mol candela. .. . , .. , cd

Units for all other _quantities are derived from these nine untts. T he seventeen derived units with special names. all of which are products of the nine base and supplementary units, are listed in Table 2. All other SI units are derived from the 26 base, supplementary and special�name SI units in Tables I and 2. Examples of derived units are given in Tables 3 and 4. 28

Metric System (continued) TABLE 2 SI derived units with

Quantity

Name SI UNITS

frequency......... .... .

hertz ....... Hz newton ..•• , N pressure, stress. .. •. . .... pascal ...... Pa energy, work, quantity of heat. ...... joule ....... J power, radiant flux....... watt ........ w quantity of electricity, electric charge, ...., , .. coulomb .... c electric potential, potential difference, electromotive force.... . volt ........ V capadtance.......... . farad ....... F ohm ........ Q electric resistance.. , siemens ..... S conductance .. magnetic flux..........•. weber....... Wb magnetic flux density..... tesla ........ T inductance ............. . henry.......H luminous flux .......... . lumen ...... lm illuminance •.. , , ........ , Jux ......... lx activity (radio,active).... . becquerel . . Bq absorbed dose ........... gray ........ Gy force ................ ..

, -1 m·kg!s2 N/m2 N·m J/s A·s W/A C/V VIA A/Y Y·s Wb/m2 Wb/A cd·sr lm/m2 ,- 1 J/kg

29

Metric System (continued) TABLE 3 Exam1pli� of SI derived units, in terms of base units SJ Unit

Unit

area ................... . square metre., ........ m2 volume ................. cubic metre....• , ...• ,m3 speed, velocity, ••. , ,..,. , acceleration .• , .....

metre per s econd•...... mis metre per second squared. ,..... , ..... m/s2

wave n umber............ J per metre ........... m-l densitY1 mass density .... . kilogram per cubic metre.,, .......,.,, .kg/ml current density.......... . ampere per square metre... ......,.. A/m2 magnetic field strength, ampere per metre...... Alm concentration (of amount of substance)... ,.,,,,. mole per cubic metre... mol/m3 specific volume.......... cubic metre per kilogram,.•. , ....... m3 /kg luminance......• ,,, ..... candela per square metre............... cd/ m2

30

Metric System (continued) TABLE 4 Exam�les of SI derived units expressed by means of special names Unit Symbol

Quantity

Name

dynamic viscosity ........ moment of force ......... surface tension .......... heat flux density, irradiance ............. heat capacity, entropy .... specific heat capacity, specific entropy ........ specific energy ........... thermal conductivity ..... energy density ........... electric field strength ..... electric charge density ....

pascal second ..........Pa· s metre newton ..........N · m newton per metre ......Nim

electric flux density ..... .

watt per square metre ..Wlm2 joule per kelvin ........JIK joule per kilogram kelvin .............. Jl(kg·K) joule per kilogram .....Jlkg watt per metre kelvin ...Wl(m · K) joule per cubic metre ...Jlm3 volt per metre .........Vim coulomb per cubic metre ...............Clm3 coulomb per square metre ...............Clm2 farad per metre ........Flm henry per metre ........Him joule per mole .........Jlmol

permittivity ............. permeability ............. molar energy ............ molar entropy, molar heat capacity .......... joule per mole kelvin ...Jl(mol · K) The units listed below, although not a part of the SI, are so widely used that it is impractical to abandon them. They are expected to be retained for continued use in the United States, some only for a limited time, subject to future review. liter (1) degree (0) minute (min) minute (') metric ton hour (hr) day (d) second (") tonne gallon hectare nautical mile acre curie knot (kt) roentgen bar angstrom (A) standard atmosphere (atm) are rod A set of prefixes is provided to form multiples and sub-multiples of these metric units. They are listed on page 28. 31

TABLE 5 Metric Equivalents Metric Equivalents for Length:

J centimeter .., 0.394 inches 1 inch • 2.540 centimeters l meter = 3.281 feet I foot = 0.35 meters I meter = 1.0936 yards 1 yard = 0.9144 meters 1 kilometer • 0.6214 mile l mile x l.6094 kilometers

Metric Equivalents for Squares:

I sq. centimeter • 0.1550 sq. in 1 sq. inch • 6.452 sq. centimeters l sq. meter • 10.764 sq. feet I sq. foot = 0.09290 sq. meters I sq. meter = 1.196 sq. yards l sq. yard = 0.8361 sq. meters I sq. kilometer = 0.386 sq. mile I sq. mile • 2.59 sq. kilometers

Metric Equivalents for Volume:

1 1 I I 1 I 1 1 I I I I J I

cubic centimeter • 0.061 cubic inch cubic inch • 16.39 cu. centimeters cubic meter • 35.314 cubic feet cubic foot • 0.02832 cubic meters cubic meter • 1.308 cubic yards cubic yard • 0.7646 cubic meters liter (dry) = 0.908 quart quart (dry) = 1.101 liters liter (liquid) - l.0567 quarts quart (liquid) - 0.9463 liters U.S. gallon (liquid) • 3. 785 liters imperial gal. (liquid) • 4.546 liters liter (liquid) • 0.264 U.S. gallon liter (liquid) • 0.220 imperial gallon

l I l I l l

gram • 0.03527 ounce ounce • 28.35 grams kilogram = 2.2046 pounds pound • 0.4536 kilograms metric ton - 0.98421 English ton English ton • 1.016 metric ton

Metric Equivalents for Weight:

32

Prefix Multiples Multiple

Prefix

Symbol

J 0 18

cxa

E

!O il

peta

p

10 1 2

tera

T

109 J06

giga

G

mega

M

J 03

kilo

k

1()2

hecto

JO

deka

da

10-1

deci

d

10-2 J0-3

centi milti

m

JQ-6

micro

µ

JQ-9

nano

n

J0-12 10- 15

pico

p

femto

J

atto

a

10-rn

33

Standard Atmosphere Definition of Standard Atmosphere A standard atmosphere is a hypothetical vertical distribution of atmospheric temperature, pressure and density which, by international

or national agreement, is taken to be representative of the atmosphere for the purpose of altimeter calibrations, aircraft design, performance calculations, etc. The internationally accepted standard atmosphere is called the International Civil Aeronautical Organization (ICAO) Standard Atmosphere or the International Standard Atmosphere (ISA). The U.S. Standard Atmosphere, 1962 agrees with the ICAO Standard Atmosphere up to 65,000 feet altitude. It is ideal air devoid of moisture. water vapor, and dust, and obeys the perfect gas law. It is based upon

accepted standard values of sea level air density, temperature and pressure.

ICAO and U.S. Standard Atmospheres Standard Values al Sea level British Units

Metric Units

Pressure, P O

2116.22 lb/ft2 29.92 in. Hg

1.013250 x J05 N/m2 760 mm Hg

Temperature. T0

518.67'R 59.0'F

288.15'K 15.0'C

Acceleration due to gravity, g0

32.1741 ft/sec2

9.80665 m/sec2

Specific weight, Ko'2o 0.076474 lb/ft3

1.2250 kg/mJ

Density, '2o

0.0023769 lb-sec2/ft4 0.12492 kg sec2/m4

Kinematic viscosity, v0

1.5723 x 10-• ft 2/sec

1.4607 x 10-5 m2/sec

Absolute viscosity, µ0

1.2024 x 10-5 lb/ft sec

1.7894 x JQ-5 kg/m sec

34

Standard Values at Al!itude British Units

Metric Units

Isothermal altitude, Z;

36,089 ft

ll,000 m

Isothermal temperature, I

-69.7'F

-56.5'C

Temperature lapse rate (sea level to isothermal)

l,000 ft

-3.57'F/

-6.5'C/km

Geopotential Altitude Geopotential altitude is the standard measure of altitude generally used

in aircraft and refers to the distance that a given unit of energy will lift

a given unit of mass. The physical length of geopotential units is not constant but increases with higher elevations because the acceleration due to gravity decreases as elevation is increased. Thus, at 100,000 feet geometric altitude as would be measured by a yardstick. an aircraft altimeter calibrated in geopotential feet would indicate 99,523 feet. The following equation is used to relate the geopotentiat altitude to geometric altitude: H •

J'_g_

Q

g,,

dZ

where: H = geopotential altitude Z "" geometric altitude g0 = acceleration due to gravity at sea level g = accelertion due to gravity at altitude Z

35

U.S. Standard Atmosphere, 1976 (Geopotential Altitude) British Units

15.79 19.0 66.J 525.8 17.0 15.23 62.5 522.2 15.0 14.70 59.0 518.7 14.17 55.4 1000 515.1 13.0 13.66 51.9 511.6 2000 11.0 13.17 508.0 9.1 3000 48.3 44.7 7.1 12.69 504.4 4000 12.23 500.9 41.2 5.1 5000 11.78 37.6 3.1 6000 497.3 493.7 11.34 34.0 1.1 7000 -0.8 8000 490.2 10.92 30.5 26.9 9000 10.50 486.6 -2.8 483.0 23.3 -4.8 10000 !0.11 479.5 9.720 11000 -6.8 19.8 475.9 9.346 12000 16.2 -8.8 472.3 8.984 13000 12.6 -10.7 12.7 468.8 8.633 14000 9.1 -14.7 8.294 465.2 15000 5.5 1.9 461.6 -16.7 16000 7.965 7.647 J.6 458.l -18.7 17000 7.339 454.5 -5.2 -20.7 18000 450.9 -8.8 -22.6 7.041 19000 -24.6 6.754 20000 447.4 -12.3 443.8 21000 6.475 -26.6 -15.9 -28.6 6.207 22000 440.2 -19.5 5.947 23000 -23.0 -30.6 436.7 -26.6 433.1 5.696 24000 -32.5 429.5 -34.5 25000 5.454 -30.2 426.0 5.220 -33.7 -36.5 26000 4.994 -38.5 -37.3 422.4 27000 -40.5 -40.9 4.777 418.8 28000 -44.4 4.567 -42.4 415.3 29000 411.7 4.364 -44.4 -48.0 30000 Note: The lCAO atmos phere is identical to the U.S. Atmosphere for altitudes below 65,617 feet. -2000 -1000 0

36

32.15 31.02 29.92 28.86 27.82 26.82 25.84 24.90 23.98 23.09 22.23 21.39 20.58 19.79 19.03 18.29 17.58 16.89 16.22 15.57 14.94 14.34 13.75 13.18 12.64 12.11 11.60 11.10 10.63 10.17 9.725 9.298 8.886 Standard

0

ve

1.0138 1.0069 1.0000 .9932 .9863 .9794 .9725 .9657 .9588 .9519 .9450 .9382 .9313 .9244 .9175 .9107 .9038 .8969 .8900 .8831 .8763 .8694 .8625 .8556 .8488 .8419 .8350 .8281 .8213 .8144 .8075 .8006 .7938

1.0069 1.0034 1.0000 .9966 .9931 .9897 .9862 .9827 .9792 .9757 .9721 .9686 .9650 .9615 .9579 .9543 .9507 .9470 .9434 .9398 .9361 .9324 .9287 .9250 .9213 .9175 .9138 .9100 .9062 .9024 .8986 .8948 .8909

1.074 1.037 1.000 .9644 .9298 .8962 .8637 .8321 .8014 .7716 .7428 .7148 .6877 .6614 .6360 .6113 .5875 .5644 .5420 .5203 .4994 .4791 .4596 .4406 .4223 .4047 .3876 .3711 .3552 .3398 .3250 .3107 .2970

1.060 1.030 1.000 .9710 .9427 .9151 .8881 .8616 .8358 .8106 .7860 .7619 .7385 .7155 .6932 .6713 .6500 .6292 .6089 .5892 .5699 .5511 .5328 .5150 .4976 .4806 .4642 .4481 .4325 .4173 .4025 .3881 .3741

q!Ml lb/ft2

Sonic Velocity ft/sec kts

1592. 1536. 1481. 1429. 1377. 1328. 1279. 1233. 1187. 1143. 1100. 1059. 1019. 979.8 942.1 905.6 870.2 836.0 802.9 770.8 739.8 709.8 680.8 652.7 625.6 599.4 574.1 549.7 526.2 503.4 481.5 460.3 439.9

1124.1 1120.2 1116.4 1112.6 1108.7 1104.9 1101.0 1097.1 1093.2 1089.2 1085.3 1081.3 1077.4 1073.4 1069.4 1065.4 1061.3 1057.3 1053.2 1049.2 1045.1 1041.0 1036.8 1032.7 1028.5 1024.4 1020.2 1016.0 1011.7 1007.5 1003.2 988.9 994.6

666.0 663.7 661.5 659.2 656.9 654.6 652.3 650.0 647.7 645.4 643.0 640.7 638.3 636.0 633.6 631.2 628.8 626.4 624.0 621.6 619.2 616.7 614.3 611.9 609.4 606.9 604.4 601.9 599.4 596.9 594.4 591.9 589.3

37

U.S. Standard Atmosphere, 1976 (Geopotential Altitude) (continued) British Units

31000 32000 33000 34000 35000 36000 *36089 37000 38000 39000 40000 41000 42000 43000 44000 45000 46000 47000 48000 49000 50000 51000 52000 53000 54000 55000 56000 57000 58000 59000 60000 61000 62000 63000 64000 65000 38

-51.6 -55.l -58.7 -62.3 -65.8 -69.4 -69.7 -69.7 -69.7 -69.7 -69.7 -69.7 -69.7 -69.7 -69.7 -69.7 -69.7 -69.7 -69.7 -69.7

-69.7 -69.7 -69.7 -69.7 -69.7 -69.7 -69.7 -69.7 -69.7 -69.7 -69.7

408.l 404.6 401.0 397.4 393.9 390.3 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0 390.0

-46.4 -48.4 -50.4 -52.4 -54.3 -56.3 -56.5 -56.5 -56.5 -56.5 -56.5 -56.5 -56.5

-56.5 -56.5 -56.5 -56.5

-56.5 -56.5

-56.5 -56.5 -56.5 -56.5

-56.5 -56.5 -56.5

-56.5 -56.5 -56.5 -56.5 -56.5 -56.5 -56.5 -56.5

4.169 3.981 3.800 3.626 3.458 3.297 3.282 3.142 2.994 2.854 2.720 2.592 2.471 2.355 2.244 2.139 2.039 1.943 1.852 1.765 l.682 1.603 1.528 1.456 1.388 l.323 1.261 1.201 1.145 1.091 1.040

.9913 .9448 .9005 .8582 .8179

8.489 8.106 7.737 7.383 7.041 6.712 6.683 6.397 6.097 5.811 5.538 5.278 5.030 4.794 4.569

4.355

4.151 3.956 3.770 3.593 3.425 3.264 3.111 2.965 2.826 2.693 2.567 2.446 2.321 2.222 2.118 2.018 1.924 1.833 1.747 1.665

El

ve

&

.7869 .7800 .7731 .7663 .7594 .7525 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519

.8871 .8832 .8793 .8754 .8714 .8675 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .867! .8671

.2837 .2709 .2586 .2467 .2353 .2243 .2234 .2138 .2038 .1942 .1851 .1764 .1681 .1602 .1527 .1455 .1387 .1322 .1260

.1201 .JJ45 .1091 .1040 .09909 .09444 ,09000 .08578 .08175 .07792 .07426 .07078 .06746 .06429 .06127 .05840 .05566

q!J.12

lb/ft2

.3605 .3473 .3345 .3220 .3099 .2981 .2971 .2843 .2710 .2583 .2462 .2346 .2236 .2131 .2031 .1936 .1845 .1758 .1676 .1597 .1522 .1451 .1383 .13!8 .1256 .JJ97 .1141 .!087 .1036 .09877 .09413

.08971 .08550 .08149 .07767 .07402

420.3 401.3 383.1 365.5 348.6 332.3 330.9 316.7 301.8 287.7 274.2 261.3 249.0 237.4 226.2 215.6 205.5 195.8 186.7 177.9 169.5 161.6 154.0 146.8 139.9 133.3 127.1 121.1 115.4 JJO.O 104.8 99.93 95.24 90.77 86.51 82.45

Sonic Velocity ft/sec kts 990.3 586.8 986.0 584.2 981.6 581.6 977.3 579.0 972.9 576.4 968.5 573.8 968.1 573.6 968.1 573.6 968.1 573.6 968.1 573.6 968.1 573.6 573.6 968.l 968.1 573.6 573.6 968.1 968.l 573.6 968.1 573.6 573.6 968.1 968.l 573.6 968.l 573.6 968.1 573.6 968.1 573.6 968.1 573.6 968.1 573.6 573.6 968.1 968.1 573.6 968.1 573.6 968.l 573.6 968.1 573.6 573.6 968.1 968.1 573.6 968.l 573.6 968.1 573.6 968.1 573.6 968.1 573.6 968.1 573.6 968.1 573.6 39

U.S. Standard Atmosphere, 1976 (Geopolenlial Altitude) (continued) British Units -56.5 1.617 390.0 .7941 -69.7 -55.2 1.311 392.4 .6437 -67.3 .5073 1.0333 -53.6 -64.6 395.I 80000 .8155 -52.l -61.8 .4005 397.9 .3167 -59.1 400.6 .6449 85000 -50.6 .5108 -49.1 403.4 90000 .2509 -56.3 -47.5 .4052 .1990 95000 406.1 -53.6 -46.0 .1581 .3220 -50.8 408.9 100000 411.6 .2563 .1259 '104987 -48.1 -44.5 .01893 .03854 21.0 480.7 150000 - 6.1 .01609 .03275 '154199 - 2.5 27.5 487.2 27.5 .00557 .01742 487.2 - 2.5 '170604 -30.4 200000 .002576 437.0 .005245 -22.7 .002578 436.8 -30.5 '200131 -22.9 .005249 *Boundary between atmosphere layers of constant thermal gradient

' 65617 70000 75000

NOTE: For intermediate altitudes up to and including 36,089 feet, ambient

pressure and temperature can be calculated as follows:

Temperature (degrees R) • 518.7 -[3.5662 x (Altitude (ft} x J0-3)]

40

.7519 .7565 .76l8 .7671 .7724 .7777 .7830 .7883 .7935 .9269 .9393 .9393 .8771 .8768

.8671 .8698 .8728 .8759 .8789 .8819 .8849 .8878 .8908 .9627 .9692 .9692 .9365 .9364

.05403 .04380 .03452 .02726 .02155 .01707 .01354 .01076 .008567 .001288 .0001095 .0005823 .0001807 .0001797

.07186 .05789 .04532 .03553 .02790 .02195 .01730 .0!365 .010800 .001390 .OOl 165 .0006199 .0002060 .0002050

80.04 64.88 51.14 40.37 31.93 25.29 20.06 15.94 12.69 1.908 1.622 .8626 .2677 .2662

968.1 971.0 974.4 977.8 981.2 984.5 987.9 991.2 994.5 1074.8 1082.0 1082.0 1045.5 1045.4

573.6 575.3 577.3 579.3 581.3 583.3 585.3 587.3 589.2 636.8 641.1 641.1 619.5 619.4

41

U.S. Standard Atmosphere, 1976 (Geopotential Altitude) Metric Units

2500 3000 3500

4000

4500 5000 5500 6000

6500 7000 7500 8000 8500

9000

9500 10000 10500 '11000 11500 12000 12500 13000 13500 14000 14500 15000 15500

42

1640 0 1640 3281 4921 6562 8202 9843 11483 13123 14764 16404 18045 19685 21325 22%6 24606 26247 27887 29528 31168 32808 34449 36089 37730 39370 41011 42651 44291 45932 47572 49213 50853 52493 54134

64.8 59.0 53.1 47.3 41.4 35.6 29.7 23.9 18.0 12.2 6.3 0.5 -5.4 -11.2 -17.l -22.9 -28.8 -34.6 -40.5 -46.3 -52.2 -58.0 -63.9 -69.7 -69.7 -69.7 -69.7 -69.7 -69.7 -69.7 -69.7

291.4 288.2 284.9 281.7 278.4 275.2 271.9 268.7 265.4 262.2 258.9 255.7 252.4 249.2 245.9 242.7 239.4 236.2 232.9 229.7 226.4 223.2 219.9 216.7 216.7 216.7 216.7 216.7 216.7 216.7 216.7 216.7 216.7 216.7 216.7

1.2 -4.5

-7.7

-11.0 -14.2 -17.5 -20.7 -24.0 -27.2 -30.5 -33.7 -37.0 -40.2 -43.5 -46.7 -50.0 -53.2 -56.5 -56.5 -56.5 -56.5 -56.5 -56.5 -56.5 -56.5

74683 70109 65765 61641 57729 54021 50508 47182 44036 41062 38252 35601 33100 30744 28525 26437 24475 22632 20916 19330 17865 16510 15258 14102 13032

0 l.0113 1.0000 .9888 .9775 .9662 .9549 .9436 .9324 .9211 .9098 .8985 .8872 .8760 .8647 .8534 .8421 .8309 .8196 .8083 .7970 .7857 .7745 .7632 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519 .7519

1{0 1.0056 l.0000 .9944 .9887 .9830 .9772 .9714 .9656 .9597 .9538 .9479 .9419 .9359 .9299 .9238 .9177 .9115 .9053 .8991 .8928 .8864 .8800 .8736 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671 .8671

1.061 1.0000 .9421 .8870 .8345 .7846 .7371 .6919 .6490 .6084 .5697 .5331 .4985 .4657 .4346 .4052 .3775 .3514 .3267 .3034 .2815 .2609 .2416 .2234 .2064 .1908 .1763 .1629 .1506 .1392 .1286 .1189 .1099 .1015 .09383 .08672

1.049 1.0000

.9528 .9074 .8637 .8216 .7811 .7421 .7047 .6687 .6341 .6009 .5691 .5385 .5093 .4812 .4544 .4287 .4042 .3807 .3583 .3369 .3165 .2971 .2745 .2537 .2345 .2167 .2003 .1851 .1711 .1581 .1461 .1350 .1248 .1153

q!Ml N/ m2

Sonic Ve!.

75234 70927 66822 62912 59189 55647 52278 49076 46035 43149 40410 37815 35355 33027 30825 28743 26777 24921 23170 21520 19967 18506 17133 15842 14641 13531 12505 11557 10681 9871 9123 8431 7792 7201 6655 6151

342.2 340.3 338.4 336.4 334.5 332.5 330.6 328.6 326.6 324.6 322.6 320.5 318.5 316.4 314.4 312.3 310.2 308.1 305.9 303.8 301.6 299.5 297.3 295.1 295.l 295.1 295.l 295.1 295.l 295.1 295.1 295.1 295.1 295.l 295.1 295.1

m/sec

43

U.S. Standard Atmosphere, 1976 (Geopotential Altitude) (continued) Metric Units Altitude feet

meters 17500 18000 18500 19000 19500 '20000 25000 30000 *32000 35000

57415 59055 60696 62336 63976 65617 82021 98425 104987 114829 131234 147638 154199 164042 170604

'F -69.7 -69.7 -69.7 -69.7 -69.7 -69.7 -60.7 -51.7 -48.l -33.0 -7.8 17.4 27.5 27.5 27.5

Temperature 'K

•c

216.7 216.7 216.7 216.7 216.7 216.7 221.7 226.7 228.7 237.1 251.l 265.! 270.7 270.6 270.6

-56.5 -56.5 -56.5 -56.5 -56.5 -56.5 -51.5 -46.5 -44.5 -36.1

Press. N/m2 8120 7505 6936 6410 5924 5475 251! 1172 868 559 278 143 lll

76 59

• Boundary between atmosphere layers of constant thermal gradient. NOTE: The !CAO atmosphere is identical to the U.S. Standard Atmosphere for altitudes below 20 km.

44

e

ve

.7519 .7519 .7519 .7519 .7519 .7519 .7693 .7866 .7935 .8227 .8713 .9199 .9393 .9393 .9393 .9184 .8837 .8768

.8671 .8671 .8671 .8671 .8671 .8671 .8771 .8869 .8908 .9070 .9334 .9591 .9692 .9692 .9692 .9584 .9401 .9364

q!M2

N/m2 .08014 .07407 ,06845 .06326 .05846 .05403 .02478 .01157 .008567 .005516 .002739 .001413 .001095 .0007495 .0005823 .0003970 .0002056 .0001797

.1066 .09850

.09104

.08413 .Om6 .07186 .03222 .01470 .001080 .006705 .003144 .001536 .001165 .0007980 .0006199 .0004323 .0002327 .0002050

561!4 5253

4655

4487 4147

3832

1758

820

608 391 194 100 78 53 41 28 15 13

Sonic Vel.

m/sec 295.1 295.1 295.l 295.l 295.1 295.1 298.5 301.8 303.1 308.6 317.6 326.4 329.8 329.8 329.8 326.1 319.9 318.6

45

Compressible Flow Functions (For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat, cp , and Constant Specific Heat Ratio, y) Symbols A F M M'

P q R T

W WTAP

Stream tube cross-sectional area Impulse function Mach number (Velocity)/(Acoustic velocity at state where M Pressure Dynamic pressure Gas constant Temperature Mass flow rate Flow parameter Specific heat ratio Fluid density

Subscripts/Superscripts Static (stream) condition Total (isentropic stagnation) condition Condition at front of normal shock x y Condition behind normal shock Condition where M = 1.0

46

=

1.0)

1* +1

1. M* = M

2

1 + r....::...!,w 2

2, P,IPs =

+'; 1

(1

y

M2)-,-::T

5.AIA*=...L

M

[ I+r...=...!,w]~ r..:':..! 2(,-1)

2

2

8. WTAP=

J;LM R

~

y+1

A PI

(1

,1 )2(y-l) -+ --=---,w 2

47

2 9. My - J 2 + (y - 1) Mx

2yM,2 -y + 1

10. P,ylP,x - (yM/ + 1)/(yM/ + 1)

[ (rMx2 + 1) 12. P,/P1x (yM/ + I)

13. T,/Tsx -

(1

= (1

15 · PsyfPsx

=

48

1 + L!M, 2

(1

2

+

2

r..=..!.M2) x

2

-l + r..=..!.My2) 2

(yM,2 + 1)

(1

(yM,2

(1

+

1)

l

y 0

r.-=-!. Mi)-,=T

(1 + r..=..!_My2) 2

14. T5ylT1 x

16. T1y - Tix

+

y1 1 + 2M/

y-1 Myl) +2

y-1 Myl) 2 +-

Greek Alphabet A, a Alpha

N, v Nu

B, µ Beta

:::. � Xi

r. y Gamma

O. o Omicron

A. o Delta

n. rrPi

E, r. Epsilon

P. Q Rho

z. C Zeta

r. a,, Sigma

H. ry Eta

T. r Tau

e,

e Theta

I,, Iota

Y, u Upsilon

¢,+Phi

K, < Kappa

X, x Chi

A.,\ Lambda

'l', 'I' Psi

M,µ Mu

Q, w Omega

49

"' One Dimensional Isentropic Compressible Flow Functions 0

(For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat (cp), and Constant Specific Heat Ratio (y = 1.4)

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12

0.13

0.011 0.022 0.033 0.044 0.055 0.066 0.077 0.088 0.099 0.109 0.120 0.131 0.142

1.000 1.000 l.001 l.001 1.002 L003 L003 L004 L006 L007 1.008 1.010 1.012

1.000 1.000 1.000 1.000 1.000 1.001 LOOI LOOI L002 1.002 1.002 I.003 1.003

1.000 1.000 LOOO LOOI LOOI L002 1.002 L003 1.004 1.005 1.006 J.007 L008

A/A•

q!P1

F/F•

57 .874 28.942 19.300 14.481 11.591 9.666 8.292 7.262 6.461 5.822 5.299 4.864 4.497

0.000 0.000 0.001 0.001 0.002 0.003 0.003 0.004 0.006 0.007 0.008 0.010 0.012

45.649 22.834 15.232 11.435 9.158 7.643 6.562 5.753 5.125 4.624 4.215 3.875 3.588

WTAP

.0092 .0184 .0276 .0367 .0459 .0550 .0641 .0732

.0823 .0913 .1003 .1093 .1182

0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44

0.218 0.229 0.240 0.251 0.261 0.272 0.283 0.294 0.304 0.315 0.326 0.336 0.347 0.358 0.368 0.379 0.389 0.400 0.410 0.421 0.431 0.442 0.452 0.463 0.473

1.028 1.031 1.034 1.038 1.041 1.044 1.048 1.052 1.056 1.060 1.064 1.069 1.074 1.078 1.083 1.088 1.094 1.099 1.105 1.111 1.117 1.123 1.129 1.136 1.142

1.008 1.009 1.010 !.Oil

1.012 1.012 1.014 1.015 1.016 1.017 1.018 1.019 1.020 1.022 1.023 1.024 1.026 1.027 1.029 1.030 1.032 1.034 1.035 1.037 1.039

1.020 1.022 1.024 1.027 1.029 1.032 1.034 1.037 1.040 1.043 1.046 1.049 1.052 1.055 1.059 1.062 1.066 1.070 1.074 1.078 1.082 1.086 1.091 1.095 1.100

2.964 2.829 2.708 2.597 2.496 2.403 2.317 2.238 2.166 2.098 2.035 1.977 1.922 1.871 1.823 1.778 1.736 1.696 1.659 1.623 1.590 1.559 1.529 1.501 1.474

0.027 0.030 0.033 0.036 0.039 0.042 0.045 0.049 0.052 0.056 0.059 0.063 0.067 0.071 0.075 0.079 0.083 0.087 0.091 0.096 0.100 0.105 0.109 0.114 0.119

2.400 2.298 2.205 2.120 2.043 1.973 1.909 1.850 1.795 1.745 1.698 1.655 1.614 1.577 1.542 1.509 1.479 1.450 1.424 1.398 1.375 1.353 1.332 1.312 1.294

.1794 .1879 .1964 .2048 .2131 .2213 .2295 .2375 .2455 .2535 .2613 .2690 .2767 .2842 .2917 .2991 .3063 .3135 .3206 .3275 .3344 .3412 .3478 .3543 .3608

"' One Dimensional Isentropic Compressible Flow Functions N

(For Perfect Gas, Con stan t Molecular Weight, Con stan t Pressure Specific Heat (cp), and Constant Specific Heat Ratio (y = 1.4) (continued)

0.565

1.156 1.163 1.171 1.178 1.186 1.194 1.202 l.211

1.042 1.044 1.046 1.048 1.050 1.052 1.054 1.056

1.109 1.114 1.119 1.124 1.130 1.135 1.141 1.146

1.425 1.402 1.380 1.359 1.340 1.321 1.303 1.286

0.128 0.133 0.138 0.143 0.148 0.152 0.157 0.162

1.260 1.244 1.230 1.216 1.203 1.190 l.179 1.168

.3733 .3793 .3853 .3911 .3969 .4025 .4080 .4133

0.595 0.605 0.615 0.625

1.237 1.247 1.256 1.266

1.063 1.065 1.067 1.070 1.072 1.074 1.077

1.164 1.170 l.177 1.183

1.240 1.226 1.213 1.200 1.188 1.177 1.166

0.177 0.182 0.187 0.193 0.198 0.203 0.208 0.213

1.138 1.129 1.121 1.113

.4287 .4336 .4384 .4430

0.46 0.47 0.48 0.49 0.50 0.51 0.52 0.53

0.494 0.504 0.514 0.524 0.535

0.56 0.57 0.58 0.59

�"'

0.65 0.66 0.67 0.68 0.69 0.70 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.80 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89

0.684 0.693 0.703 0.713 0.722 0.732 0.741 0.751 0.760 0.770 0.779 0.788 0.798 0.807 0.816 0.825 0.834 0.843 0.852 0.861 0.870 0.879 0.888 0.897 0.906

1.328 1.340 1.351 1.363 1.375 1.387 1.400 1.412 1.425 1.439 1.452 1.466 1.480 1.495 1.509 1.524 1.540

1.555

1.571 1.587 1.604 1.621 1.638 1.655 1.673

1.084 J.087 J.090 1.092 1.095 1.098 I.IOI 1.104 1.107 1.110 1.112 1.116 1.119 1.122 1.125 1.128 1.131 1.134 1.138 1.141 1.144 1.148 1.151 1.155 1.158

1.225 1.232 1.240 1.247 1.255 1.263 1.271 1.280 1.288 1.297 1.305 1.314 1.323 1.333 1.342 1.351 1.361 1.371 1.381 1.391 1.401 1.412 1.422 1.433 1.444

1.136 1.127 1.118 1.110 1.102 1.094 1.087 1.081 1.074 1.068 1.062 1.057 1.052 1.047 1.043 1.038 1.034 1.030 1.027 1.024 1.021 1.018 1.015 1.013 I.Oil

0.223 0.228 0.233 0.238 0.242 0.247 0.252 0.257 0.262 0.266 0.271 0.276 0.280 0.285 0.289 0.294 0.298 0.303 0.307 0.311 0.315 0.319 0.323 0.327 0.331

1.073 1.068 1.063 1.058 1.053 1.049 1.045 1.041 1.038 1.034 1.031 1.028 1.026 1.023 1.021 1.019 1.016 1.015 1.013 1.011 1.010 1.008 1.007 1.006 1.005

.4682 .4720 .4757 .4792 .4826 .4859 .4891 .4921 .4950 .4978 .5005 .5031

.5055

.5079 .5101 .5122 .5142 .5160 .5178 .5194 .5210 .5224 .5237 .5250 .5261

�....

One Dimensional Isentropic Compressible Flow Functions (For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat (cp), and Constant Specific Heat Ratio (y = 1.4) (continued) M

0.90 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09

M•

0.915 0.923 0.932 0.941 0.949 0.958 0.966 0.975 0.983 0.992 1.000 1.008 1.017 1.025 1.033 1.041 1.049 1.057 1.065 1.073

P,IP5

1.691 1.710 1.729 1.748 1.767 1.787 1.808 1.828 1.850 1.871 1.893 1.915 1.938 1.961 1.985 2.009 2.033 2.058 2.083 2.109

T/T5

e/es

A/A•

q!P,

FIF•

WTAP

1.162 1.166 1.169 1.173 1.177 1.180 1.184 1.188 1.192 1.196 1.200 1.204 1.208 1.212 1.216 1.220 1.225 1.229 1.233 1.238

1.456 1.467 1.478 1.490 1.502 1.514 1.526 1.539 1.552 1.564 1.577 1.591 1.604 1.618 1.632 1.646 1.660 1.674 1.689 1.704

1.009 1.007 1.006 1.004 1.003 1.002 1.001 1.001 1.000 1.000 1.000 1.000 1.000 1.001 1.001 1.002 1.003 1.004 1.005 1.006

0.335 0.339 0.343 0.346 0.350 0.353 0.357 0.360 0.363 0.367 0.370 0.373 0.376 0.379 0.382 0.384 0.387 0.389 0.392 0.394

1.004 1.003 1.002 1.002 1.001 1.001 1.001 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.001 1.001 1.001 1.002 1.002 1.003

.5271 .5280 .5288 .5295 .5301 .5306 .5310 .5313 .5316 .5317 .5317 .5317 .5316 .5314 .5311 .5307 .5302 .5297 .5290 .5283

1.10 1.ll 1.12 1.13 1.14 I.IS

1.16 1.17 l.!8

v, v,

1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.30 l.31 1.32 l.33

1.081 1.089 1.097 1.105 1.113 l.120 1.128 1.136 1.143 1.151 1.158 1.166 1.173 l.181 1.188 1.195 1.202 1.210 1.217 1.224

2.135 2.162 2.189 2.217 2.245 2.274 2.303 2.333 2.363 2.394 2.425 2.457 2.489 2.522 2.556 2.590 2.625 2.661 2.697 2.733 2.771 2.809

l.242 1.246 1.251 1.255 1.260 1.264 1.269 1.274 1.278 1.283 1.288 1.293 1.298 1.303 1.308 1.312 1.318 1.323 1.328 1.333

1.719 1.734 1.750 1.766 1.782 1.798 1.814 1.831 1.848 1.865 1.883 1.900 1.918 1.936 1.955 J.974 1.992 2.012 2.031 2.051

1.008 1.010 1.0!1 1.013 1.015 1.017 1.020 1.022 1.025 1.028 1.030 1.033 1.037 1.040 1.043 1.047 1.050 1.054 1.058 1.062

0.397 0.399 0.401 0.403 0.405 0.407 0.409 0.411 0.413 0.414 0.416 0.417 0.419 0.420 0.421 0.422 0.423 0.424 0.425 0.426 0.427 0.428 0.428 0.429

1.003 1.004 1.004 1.005 1.006 1.006 1.007 1.008 1.009 1.010 1.011 1.012 1.013 1.014 1.015 1.016 l.017 l.018 1.019 1.021

.5276 .5267 .5258 .5248 .5238 .5226 .5214 .5202 .5189 .5175 .5160 .5145 .5130 .5114 .5097 .5080 .5062 .5044

.5026 .5006

"' One Dimensional lsentropic Compressible Flow Functions u.

(For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat (cp), and Constant Specific Heat Ratio (y = 1.4) (continue d)

M

1.35 1.36 1.37 l.38 l.39 1.40 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.50 1.51 1.52 l.53 1.54

M•

1.266 1.273 l.280 l.286 1.293 1.300 1.306 1.313 1.320 1.326 1.333 1.339 1.346 1.352 1.358 1.365 1.371 1.377 l.383 1.389

P1!P,

T,tT,

2.967 3.009 3.051 3.094 3.138 3.182 3.227 3.273 3.320 3.368 3.416 3.465 3.515 3.566 3.618 3.671 3.724 3.779 3.834 3.891

1.364 1.370 1.375 l.381 1.386 1.392 1.398 1.403 1.409 1.415 1.420 1.426 1.432 1.438 1.444 1.450 1.456 1.462 1.468 1.474

Q,te, 2.175 2.196 2.218 2.241 2.263 2.286 2.309 2.333 2.356 2.380 2.405 2.430 2.455 2.480 2.506 2.532 2.558 2.585 2.612 2.639

A/A* 1.089 1.094 1.099 1.104 1.109 1.115 1.120 1.126 1.132 1.138 1.144 1.150 1.156 1.163 1.169 1.176 1.183 1.190 l.197

1.204

q!P,

FIF*

0.430 0.430 0.431 0.431 0.431 0.431 0.431 0.431 0.431 0.431 0.431 0.431 0.430 0.430 0.430 0.429 0.429 0.428 0.427 0.427

1.028 1.029 L031 1.032 1.033 1.035 l.036 l.037 1.039 1.040 1.042 1.043 1.044 1.046 1.047 1.049 l.050 1.052 l.053 1.055

WTAP .4883 .4861 .4838 .4816 .4793 .4769 .4746 .4722

.4698 .4673

.4648

.4623 .4598 .4573 .4547 .4521 .4495 .4469 .4442 .4416

1.55

-.,

1.56 1.57 1.58 1.59 1.60 1.61 1.62 1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.70 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79

1.395 1.401 1.408 1.414 1.419 1.425 1.431 1.437 1.443 1.449 1.454 1.460 1.466 1.471 1.477 1.482 1.488 1.493 1.499 1.504 1.510 1.515

1.520 1.526 1.531

3.943 4.007 4.066 4.126 4.188 4.250 4.314 4.378 4.444 4.511 4.579 4.648 4.718 4.789 4.862 4.936 5.011 5.087

5.165

5.243 5.324

5.405

5.488 5.572 5.658

1.480 1.487 1.493 1.499 1.506 1.512 1.518 1.525 1.531 1.538 1.544 1.551

1.558 1.564 1.571 1.578 1.585 1.592 1.599 1.605

1.612 1.619 1.627 1.634 1.641

2.667 2.695 2.723 2.752 2.781 2.811 2.841 2.871 2.902 2.933 2.964 2.996 3.029 3.061 3.094 3.128 3.162 3.196 3.231 3.266 3.302 3.338 3.374 3.411 3.448

1.212 1.219 1.227 1.234 1.242 1.250 1.258 1.267 1.275 1.284 1.292 1.301 1.310 1.319 1.328 1.338 1.347 1.357 1.366 1.376 1.386 1.397 1.407 1.417 1.428

0.426 0.425 0.424 0.423 0.423 0.422 0.421 0.420 0.418 0.417 0.416 0.415 0.414 0.413 0.411 0.410 0.408 0.407 0.406 0.404 0.403 0.401 0.400 0.398 0.396

1.056 1.058 1.059 1.060 1.062 1.063 1.065

1.066 1.068 1.069 1.071 1.072 1.074 1.075 1.077 1.079 1.080 1.082 1.083 1.085 1.086 1.088 1.089 1.091 1.092

.4389 .4362 .4335 .4308 .4281 .4253 .4226 .4198 .4171 .4143 .4115 .4087 .4059 .4031 .4004 .3976 .3948 .3919 .3891 .3863 .3835 .3807 .3779 .3751 .3723

�

One Dimensional Lsentropic Compressible Flow Functions

00

(For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat (cp), and Constant Specific Heat Ratio (y = 1.4) (continued) M

M*

PtfPs

TtfTs

etfes

1.80 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.90 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99

1.536 1.541 1.546 1.551 1.556 1.561 1.566 1.571 1.576 1.581 1.586 1.591 1.596 1.600 1.605 1.610 1.615 1.619 1.624 1.628

5.745 5.834 5.924 6.015 6.108 6.203 6.299 6.397 6.496 6.597 6.700 6.804 6.910 7.018 7.128 7.239 7.352 7.467 7.584 7.703

1.648 1.655 1.662 1.670 1.677 1.684 1.692 1.699 1.707 1.714 1.722 1.730 1.737 1.745 1.753 1.760 1.768 1.776 1.784 1.792

3.486 3.525 3.563 3.603 3.642 3.683 3.723 3.764 3.806 3.848 3.891 3.934 3.978 4.022 4.067 4.112 4.158 4.204 4.251 4.299

A/A*

1.439 1.450 1.461 1.472 1.484 1.495 1.507 1.519 1.531 1.543

1.555

1.568 1.580 1.593 1.606 1.619 1.633 1.646 1.660 1.673

q!P1

FIF*

0.395 0.393 0.391 0.390 0.388 0.386 0.384 0.383 0.381 0.379 0.377 0.375 0.373 0.372 0.370 0.368 0.366 0.364 0.362 0.360

1.094 1.095 1.096 1.098 1.099 I.IOI

1.102 1.104 1.105 1.107 1.108 l.IIO

I.Ill 1.113 1.114 1.116 1.117 1.118 1.120 1.121

WTAP

.3695 .3668 .3640 .3612 .3584 .3557 .3529 .3501 .3474 .3447 .3419 .3392 .3365 .3336 .3311 .3284 .3257 .3231 .3204 .3178

"'�

2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.10 3.20 3.30 3.40 3.50

l.633 l.655 1.677 1.698 1.718 1.737 1.756 1.775 1.792 1.809 1.826 1.842 1.857 1.872 1.887 1.900 1.914 1.927 1.940 1.952 1.964 1.987 2.008 2.028 2.047 2.064

7.824 8.457 9.144 9.887 10.691 11.562 12.503 13.520 14.613 15.804 17.084 18.464 19.951 21.554 23.280 25.137 27.135 29.282 31.590 34.068 36.728 42.641 49.430 57.211 66.109 76.262

1.800 1.840 1.882 1.924 1.968 2.012 2.058 2.104 2.152 2.200 2.250 2.300 2.352 2.404 2.458 2.512 2.568 2.624 2.682 2.740 2.800 2.922 3.048 3.178 3.312 3.450

4.347 4.595 4.859 5.138 5.433 5.745 6.075 6.424 6.793 7.182 7.593 8.026 8.483 8.964 9.471 10.005 10.567 11.158 11.779 12.432 13.118 14.593 16.218 18.003 19.961 22.106

1.687 1.760 1.837 1.918 2.005 2.096 2.193 2.295 2.403 2.517 2.637 2.763 2.896 3.036 3.183 3.337 3.500 3.670 3.849 4.037 4.234 4.657 5.121 5.628 6.183 6.789

0.358 0.348 0.338 0.327 0.317 0.306 0.296 0.286 0.276 0.266 0.256 0.247 0.237 0.228 0.219 0.211 0.202 0.194 0.186 0.179 0.172 0.158 0.145 0.133 0.122 0.112

l.123 1.130 1.137 1.143 1.150 1.156 1.163 1.169 1.175 1.181 1.187 1.192 l.198 1.203 1.208 1.213 1.218 1.223 1.228 1.232 1.237 1.245 1.253 1.260 1.268 1.274

.3151 .3022 .2895 .2772 .2652 .2537 .2425 .2317 .2213 .2113 .2017 .1925 .1836 .1752 .1671 .1593 .1519 .1449 .1381 .1317 .1256 .1142 .1038 .0945 .0860 .0783

°' One Dimensional lsentropic Compressible Flow Functions 0

(For Perfect Gas, Constant Molecular Weig ht, Constant Pressure Specific Heal (cp), and Constant Specific Heal Ratio (y = 1.4) (continued) M

M•

3.60 3.70 3.80 3.90 4.00 4.10 4.20 4.30 4.40 4.50 4.60 4.70 4.80 4.90

2.081 2.096 2.111 2.125 2.138 2.150 2.162

5.40 5.60 5.80 6.00

2.263 2.275 2.286 2.295

2.173

2.184 2.194 2.203

2.212 2.220 2.228

P1!P5

T/Ts

e1les

A/A•

q!P,

FIF'

87.825 100.967 115.874 132.749 151.816 173.318 197.523 224.720 255.224 289.379 327 .555

24.451 27.012 29.804 32.844 36.148 39.735 43.624 47.835 52.388 57.305 62.608 68.322 74.470 81.079

7.449 8.168 8.950 9.798 10.718 11.714 12.791 13.954 15.209 16.561 18.016 19.581 21.262 23.065

0.103

1.281 l .287 l.292 l.298 1.303 1.308 1.312

470.404

3.592 3.738 3.888 4.042 4.200 4.362 4.528 4.698 4.872 5.050 5.232 5.418 5.608 5.802

833.428 1036.907 1282.884 1578.712

6.832 7.272 7.728 8.200

121.993 142.594 166.010 192.532

34.172 39.737 46.046 53.176

0.095 0.087 0.080 0.074 0.068 0.063 0.058 0.053 0.049 0.045 0.042 0.039 0.036 0.024 0.021

O.QJ8

0.016

WTAP

1.317

l.321 1.325 l.328 1.332 l.335 1.339

.0714 .0651 .0594 .0543 .0496 .0454 .0416 .0381 .0350 .0321 .0295 .0272 .0250 .0231

1.352 1.357 1.362 1.365

.0156 .0134 .0115 .0100

6.50

7.00 7.50 8.00 9.00 10.00 11.00

2.316 2.333 2.347 2.359 2.377 2.390 2.400

2593.995 4139.453 6433.371 9762.039 21101.633 42436.316 80329.500

9.450 10.800 12.250 13.800 17.200 21.000 25.200

274.505 383.293 525.187 707.412 1226.868 2020.820 3187.739

75.129 104.136 141.833 190.098 327.171 535.911 841.370

0.011 0.008 0.006 0.005 0.003 0.002 0.001

1.374 1.381 1.387 1.391 1.399 1.404 1.408

.0071 .0051 .0037 .0028 .0016 .0010 .0006

a, N

One Dimensional Normal Shock Functions (For Perfect Gas, Constan t Molecular Weight, Constant Pressure Specific Heat (cp), and Constant Specific Heat Ratio (y = 1.4) Mx

My

1.00 I.OJ 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10

1.0000 0.9901 0.9805 0.9712 0.9620 0.9531 0.9444 0.9360 0.9277 0.9197 0.9118 0.9041 0.8966 0.8892 0.8820 0.8750 0.8632 0.8615 0.8549 0.8485

I.II

1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19

P5ylPsx 1.0000 1.0234 1.0471 1.0710 1.0952 1.1196 1.1442 1.1690 1.1941 1.2194 1.2450 1.2708 1.2968 1.3230 1.3495 1.3762 1.4032 1.4303 1.4578 1.4854

P1ylP1x

1.0000 1.0000 1.0000 1.0000 0.9999 0.9999 0.9998 0.9996 0.9994 0.9992 0.9989 0.9986 0.9982 0.9978 0.9973 0.9967 0.9961 0.9953 0.9946 0.9937

P5ylP1x 0.5283 0.5344 0.5403 0.5462 0.5519 0.5574 0.5628 0.5681 0.5732 0.5782 0.5831 0.5878 0.5924 0.5968 0.6011 0.6053 0.6093 0.6132 0.6170 0.6206

T5ylTsx 1.0000 1.0066 1.0132 1.0198 1.0263 1.0328 1.0393 1.0457 1.0522 1.0586 1.0649 1.0713 1.0776 1.0840 1.0903 1.0966 1.1029 1.1092 1.1154 1.1217

T5ylT1x 0.8333 0.8361 0.8387 0.8413 0.8438 0.8462 0.8486 0.8509 0.8531 0.8553 0.8574 0.8595 0.8615 0.8635 0.8654 0.8672 0.8690 0.8708 0.8725 0.8741

QsylQsx

1.0000 1.0167 1.0334 1.0502 1.0671 1.0840 1.1009 1.1179 1.1349 1.1520 1.1691 1.1862 1.2034 1.2206 1.2378 1.2550 1.2723 1.2896 1.3069 1.3242

l.20

l.21

1.22 1.23 1.24 !.25 1.26

1.27 1.28 l.29 1.30 1.31 1.32 1.33 l.34 1.35 1.36 1.37 1.38 1.39 1.40

1.41 J.42 1.43

0.8422 0.8360 0.8300 0.8241 0.8183 0.8126 0.8071 0.8017 0.7963 0.7911 0.7860 0.7809 0.7760 0.7712 0.7664 0.7618 0.7572 0.7527 0.7483 0.7440 0.7397 0.7355 0.7314 0.7274

1.5133

l.5414 l.5698 l.5983 1.6271 1.6562 1.6855 1.7150 1.7447 1.7747 1.8049 1.8354 1.8661 1.8970 1.9281 1.9595 1.9911 2.0230 2.0550 2.0874 2.1199 2.1527 2.1857

0.9928 0.9918 0.9907 0.9896 0.9884 0.9871 0.9857 0.9842 0.9827 0.9811 0.9794 0.9776 0.9758 0.9738 0.9718 0.9697 0.9676 0.9653 0.9630 0.9600 0.9582 0.9557 0.9531 0.9504

0.624! 0.6274 0.6306 0.6337 0.6366 0.6394 0.6421 0.6446 0.6470 0.6493 0.6514 0.6535 0.6554 0.657! 0.6588 0.6603 0.6617 0.6630 0.6642 0.6652

1.1280 1.1343 1.1405 l.1468

1.1531

1.1594 1.1656 1.1719 1.1782 1.1845 l.1909 1.1972 1.2035 1.2099 l.2162 1.2226 1.2290 1.2354 1.2418 1.2482

0.8758 0.8774 0.8789 0.8804 0.8819 0.8833 0.8847 0.8861 0.8874 0.8888 0.8900 0.8913 0.8925 0.8937 0.8949 0.8960 0.8971 0.8982 0.8993 0.9003 0.9014 0.9024 0.9033 0.9043

1.3416 1.3590 !.3763 1.3937 l.4lll 1.4285 1.4460

1.4634 1.4808 1.4982 1.5157 1.5331 1.5505 1.5679 1.5853 !.6027 1.6201 1.6375 1.6549 !.6723 1.6896 1.7069 J.7243 1.7415

i One Dimensional Normal Shock Functions (For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat (cp), and Constant Specific Heat Ratio (y) = 1.4) (continued) Mx 1.45 1.46 1.47 1.48 1.49 1.50 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.60 1.61 1.62 1.63 1.64

My 0.7196 0.7158 0.7120 0.7083 0.7047 0.7011 0.6976 0.6941 0.6907 0.6874 0.6841 0.6809 0.6777 0.6746 0.6715 0.6685 0.6655 0.6625 0.6596 0.6568

PsylPsx 2.2861 2.3201 2.3543 2.3887 2.4233 2.4582 2.4933 2.5287 2.5642 2.6001 2.6361 2.6724 2.7089 2.7456 2.7826 2.8198 2.8573 2.8950 2.9329 2.9710

P,1!P1x 0.9448 0.9420 0.9390 0.9360 0.9329 0.9298 0.9266 0.9233 0.9200 0.9166 0.9132 0.9097 0.9062 0.9026 0.8989 0.8952 0.8915 0.8877 0.8838 0.8799

PsylPrx 0.6692 0.6695 0.6697 0.6698 0.6698 0.6697 0.6694 0.6691 0.6687 0.6682 0.6677 0.6670 0.6662 0.6654 0.6645 0.6635 0.6624 0.6612 0.6600 0.6587

TsylTsx 1.2872 1.2937 1.3003 1.3069 1.3135 1.3202 1.3269 1.3335 1.3403 1.3470 1.3538 1.3605 1.3674 1.3742 1.3811 1.3879 1.3949 1.4018 1.4088 1.4157

Tsyl T1x 0.9062 0.9071 0.9079 0.9088 0.9097 0.9105 0.9113 0.9121 0.9129 0.9137 0.9144 0.9151 0.9159 0.9166 0.9173 0.9180 0.9186 0.9193 0.9199 0.9206

esylesx 1.7761 1.7933 1.8105 1.8277 1.8449 1.8620 1.8791 1.8962 1.9132 1.9303 1.9472 1.9642 1.9811 1.9980 2.0149 2.0317 2.0484 2.0652 2.0819 2.0985

1.65 l.66 l.67 1.68 l.69 1.70 l.71 1.72 1.73 1.74 l.75 1.76 1.77 1.78 l.79 1.80 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89

0.6540 0.6512 0.6485 0.6458 0.6432 0.6406 0.6380 0.6355 0.6330 0.6305 0.6281 0.6257 0.6234 0.6211 0.6188 0.6165 0.6143 0.6121 0.6099 0.6078 0.6057 0.6036 0.6016 0.5996 0.5976

3.0094 3.0480 3.0869 3.1259 3.1653 3.2048 3.2446 3.2846 3.3248 3.3653 3.4060 3.4470 3.4882 3.5296 3.5712 3.6131 3.6552 3.6975 3.7401 3.7829 3.8260 3.8693 3.9128 3.9565 4.0005

0.8760 0.8720 0.8680 0.8640 0.8599 0.8557 0.8516 0.8474 0.8431 0.8389 0.8346 0.8303 0.8259 0.8215 0.8171 0.8127 0.8033 0.8038 0.7993 0.7948 0.7903 0.7857 0.7812 0.7766

o.mo

0.6573 0.6558 0.6543 0.6527 0.6510 0.6493 0.6475 0.6457 0.6438 0.6418 0.6398 0.6377 0.6356 0.6334 0.6312 0.6289 0.6266 0.6242 0.6218 0.6193 0.6168 0.6142 0.6117 0.6090 0.6064

1.4228 1.4298 1.4369 1.4440 1.4511 1.4583 1.4655 1.4727 1.4800 1.4872 l.4945 1.5019 1.5092 1.5166 1.5241 1.5315 1.5390 1.5465 1.5541 1.5617 1.5693 1.5770 1.5846 1.5923 1.6001

0.9212 0.9218 0.9224 0.9230 0.9236 0.9242 0.9247 0.9253 0.9258 0.9263 0.9269 0.9274 0.9279 0.9284 0.9289 0.9294 0.9298 0.9303 0.9307 0.9312 0.9316 0.9321 0.9325 0.9329 0.9333

2.1152 2.1317 2.1483 2.1648 2.1812 2.1976 2.2140 2.2303 2.2466 2.2628 2.2790 2.2951 2.3112 2.3272 2.3432 2.3591 2.3750 2.3908 2.4066 2.4223 2.4380 2.4536 2.4692

2.4847 2.5002

"' One Dimensional Normal Shock Functions °'

(For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat (cp), and Constant Specific Heat Ratio (y) = 1.4) (continued)

M, 1.90 1.91 1.92 1.93

My

1.95

0.5956 0.5937 0.5918 0.5899 0.5880 0.5862

1.98 1.99 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09

0.5826 0.5808 0.5791 0.5774 0.5757 0.5740 0.5723 0.5707 0.5691 0.5675 0.5659 0.5643 0.5628

1.94

1.96 1.97

0.5844

P,/Psx

P,/P,x

P,/Ptx

T,/Tsx

T,/Ttx

Q,ylQsx

4.0447 4.0892 4.1338 4.1787 4.2239 4.2693 4.3149 4.3607 4.4008 4.4531 4.4997 4.5464 4.5935 4.6407 4.6882 4.7359 4.7838 4.8320 4.8804 4.9291

0.7674 0.7628 0.7582 0.7535 0.7489 0.7442 0.7396 0.7349 0.7302 0.7256 0.7209 0.7162 0.7116 0.7069 0.7022 0.6975 0.6929 0.6882 0.6835 0.6789

0.6037 0.6010 0.5982 0.5954 0.5926 0.5898 0.5869 0.5840 0.5811 0.5781 0.5751 0.5722 0.5691 0.5661 0.5631 0.5600 0.5569 0.5538 0.5507 0.5476

1.6079 l.6157 1.6235 1.6314 1.6393 1.6472 1.6552 1.6632 1.6713 1.6793 1.6874 1.6956 1.7038 1.7120 1.7202 1.7285 1.7368 1.7451 1.7535 1.7619

0.9337 0.9341 0.9345 0.9349 0.9353 0.9357 0.9361 0.9364 0.9368 0.9371 0.9375 0.9378 0.9382 0.9385 0.9388 0.9392 0.9395 0.9398 0.9401 0.9404

2.5156 2.5309 2.5462 2.5615 2.5766 2.5918 2.6068 2.6219 2.6368 2.6517 2.6666 2.6813 2.6961 2.7!07 2.7254 2.7399 2.7544 2.7688 2.7832 2.7975

2.10 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.20 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.30 2.31 2.32 2.33 2.34

0.5613 0.5598 0.5583 0.5568

0.5554 0.5540

0.5526 0.5512 0.5498 0.5484 0.5471 0.5457 0.5444 0.5431 0.5418 0.5406 0.5393 0.5381 0.5368 0.5356 0.5344 0.5332 0.5321 0.5309 0.5298

4.9779 5.0271 5.0764 5.1260 5.1758 5.2258 5.2761 5.3266 5.3774 5.4283 5.4796 5.5310 5.5827 5.6346 5.6867 5.7391 5.7917 5.8446 5.8976 5.9510 6.0045 6.0583 6.1123 6.1665 6.2210

0.6742 0.6696 0.6650 0.6603 0.6557 0.6511 0.6465 0.6419 0.6373 0.6327 0.6282 0.6236 0.6191 0.6146 0.6101 0.6056 0.6011 0.5966 0.5922 0.5878 0.5833 0.5789 0.5746 0.5702

0.5659

0.5444 0.5413 0.5381 0.5349 0.5318 0.5286 0.5254 0.5222 0.5190 0.5157 0.5125 0.5093 0.5061 0.5029 0.4996 0.4964 0.4932 0.4899 0.4867 0.4835 0.4803 0.4770 0.4738 0.4706 0.4674

1.7704 1.7789 1.7874 1.7959 1.8045 1.8131 1.8218 1.8305 1.8392 1.8480 1.8568 1.8656 1.8745 1.8834 1.8923 1.9013 1.9103 1.9194 1.9284 1.9376 1.9467 1.9559 1.9651 1.9744 1.9837

0.9407 0.9410 0.9413 0.9416 0.9419 0.9422 0.9425 0.9427 0.9430 0.9433 0.9435 0.9438 0.9440 0.9443 0.9445 0.9448 0.9450 0.9453

0.9455

0.9457 0.9460 0.9462 0.9464 0.9466 0.9469

2.8118 2.8260 2.8401 2.8542 2.8682 2.8822 2.8961 2.9099 2.9237 2.9374 2.9511 2.9647 2.9782 2.9917 3.0051 3.0185 3.0318 3.0451 3.0582 3.0714 3.0844 3.0974 3.1104 3.1233 3.1361

g;

One Dimensional Normal Shock Functions (For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat (cp), and Constant Specific Heat Ratio (y) = 1.4) (continued) M, 2.35 2.36 2.37 2.38 2.39 2.40 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.50 2.51 2.52 2.53 2.54

My 0.5286 0.5275 0.5264 0.5253 0.5242 0.5231 0.5221 0.5210 0.5200 0.5189 0.5179 0.5169 0.5159 0.5149 0.5140 0.5130 0.5120 0.5111 0.5102 0.5092

P5ylPsx 6.2757 6.3307 6.3858 6.4412 6.4969 6.5528 6.6089 6.6652 6.7218 6.7786 6.8356 6.8929 6.9504 7.0082 7.0662 7.1244 7.1828 7.2415 7.3004 7.3595

P1ylP1x 0.5615 0.5572 0.5529 0.5487 0.5444 0.5402 0.5360 0.5318 0.5276 0.5235 0.5194 0.5153 0.5112 0.5071 0.5031 0.4991 0.4951 0.4911 0.4871 0.4832

PsylP1x 0.4642 0.4610 0.4578 0.4546 0.4514 0.4483 0.4451 0.4420 0.4388 0.4357 0.4325 0.4294 0.4263 0.4232 0.4201 0.4170 0.4140 0.4109 0.4079 0.4048

T5ylTsx 1.9930 2.0024 2.0118 2.0212 2.0307 2.0402 2.0498 2.0594 2.0690 2.0787 2.0884 2.0981 2.1079 2.1177 2.1275 2.1374 2.1473 2.1573 2.1673 2.1773

T5ylT1x 0.9471 0.9473 0.9475 0.9477 0.9479 0.9481 0.9483 0.9485 0.9487 0.9489 0.9491 0.9493 0.9495 0.9496 0.9498 0.9500 0.9502 0.9503 0.9505 0.9507

ClsylQsx

3.1488 3.1615 3.1742 3.1868 3.1993 3.2118 3.2242 3.2365 3.2488 3.2610 3.2732 3.2853 3.2974 3.3094 3.3213 3.3332 3.3450 3.3568 3.3685 3.3802

2.55 2.56 2.57 2.58 2.59 2.60 2.61 2.62 2.63 2.64 2.65 2.66 2.67 2.68 2.69 2.70 2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79

0.5083 0.5074 0.5065 0.5056 0.5048 0.5039 0.5030 0.5022 0.5013 0.5005 0.4997 0.4988 0.4980 0.4972 0.4964 0.4956 0.4949 0.4941 0.4933 0.4926 0.4918 0.4911 0.4903 0.4896 0.4889

7.4189 7.4785 7.5384 7.5984 7.6588 7.7193 7.7801 7.8411 7.9023 7.9638 8.0255 8.0875 8.1496 8.2120 8.2747 8.3376 8.4007 8.4{;40 8.5276 8.5914 8.6554 8.7197 8.7842 8.8490 8.9139

0.4793 0.4754 0.4716 0.4{;78 0.4{;40 0.4602 0.4564 0.4527 0.4490 0.4453 0.4416 0.4380 0.4343 0.4307 0.4272 0.4236 0.4201 0.4166 0.4131 0.4097 0.4063 0.4029 0.3995 0.3961 0.3928

0.4018 0.3988 0.3958 0.3928 0.3899 0.3869 0.3840 0.3811 0.3781 0.3752 0.3724 0.3695 0.3666 0.3638 0.3610 0.3582 0.3554 0.3526 0.3498 0.3471 0.3444 0.3416 0.3389 0.3363 0.3336

2.1873 2.1974 2.2076 2.2178 2.2280 2.2382 2.2485 2.2588 2.2692 2.2796 2.2900 2.3005 2.3110 2.3216 2.3321 2.3428 2.3534 2.3641 2.3748 2.3856 2.3964 2.4073 2.4182 2.4291 2.4400

0.9509 0.9510 0.9512 0.9514 0.9515 0.9517 0.9518 0.9520 0.9521 0.9523 0.9524 0.9526 0.9527 0.9529 0.9530 0.9532 0.9533 0.9534 0.9536 0.9537 0.9539 0.9540 0.9541 0.9542 0.9544

3.3917 3.4033 3.4148 3.4262 3.4375 3.4488 3.4601 3.4713 3.4824 3.4935 3.5045 3.5155 3.5264 3.5373 3.5481 3.5589 3.5696 3.5802 3.5908 3.6013 3.6118 3.6222 3.6326 3.6429 3.6532

.....

0

One Dimensional Normal Shock Functions (For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat and Constant Specific Heat Ratio (y) = 1.4) (continued) Mx

2.80 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.90 2.91 2.92 2.93 2.94 2.95 2.96 2.97 2.98 2.99

(cp),

My

PsylPsx

P1ylP1x

PsylP1x

T5ylTsx

TsylTtx

QsylQsx

0.4882 0.4875 0.4868 0.4861 0.4854 0.4847 0.4840 0.4834 0.4827 0.4820 0.4814 0.4807 0.4801 0.4795 0.4788 0.4782 0.4776 0.4770 0.4764 0.4758

8.9791 9.0446 9.1103 9.1762 9.2423 9.3087 9.3753 9.4421 9.5092 9.5765 9.6441 9.7118 9.7799 9.8481 9.9166 9.9853 10.0542 10.1234 10.1928 10.2624

0.3895 0.3862 0.3830 0.3797 0.3765 0.3733 0.3702 0.3670 0.3639 0.3608 0.3578 0.3547 0.3517 0.3487 0.3457 0.3428 0.3399 0.3370 0.3341 0.3312

0.3309 0.3283 0.3257 0.3231 0.3205 0.3179 0.3154 0.3128 0.3103 0.3078 0.3053 0.3028 0.3004 0.2979 0.2955 0.2931 0.2907 0.2884 0.2860 0.2837

2.4510 2.4621 2.4731 2.4842 2.4954 2.5066 2.5178 2.5290 2.5403 2.5517 2.5630 2.5745 2.5859 2.5974 2.6089 2.6205 2.6321 2.6437 2.6554 2.6671

0.9545 0.9546 0.9548 0.9549 0.9550 0.9551 0.9552 0.9554

3.6634 3.6736 3.6837 3.6938 3.7038 3.7137 3.7236 3.7335 3.7433 3.7530 3.7627 3.7724 3.7820 3.7915 3.8010 3.8105 3.8199 3.8292 3.8385 3.8478

0.9555

0.9556 0.9557 0.9558 0.9559 0.9560 0.9562 0.9563 0.9564 0.9565 0.9566 0.9567

3.00 3.20 3.40 3.60 3.80 4.00 5.00 6.00 7.00 8.00

0.4752 0.4643 0.4552 0.4474 0.4407 0.4350 0.4152 0.4042 0.3974 0.3929

10.3323 11.7800 13.3200 14.9533 16.6800 18.5000 29.0000 41.8333 57.0000 74.5000

0.3284 0.2762 0.2322 0.1953 0.1645 0.1388 0.0617 0.0297 0.0154 0.0085

0.2813 0.2383 0.2015 0.1702 0.1439 0.1218 0.0548 0.0265 0.0138 0.0076

2.6788 2.9220 3.1802 3.4537 3.7426 4.0469 5.8000 7.9406 10.4694 13.3867

0.9568 0.9587 0.%02 0.9615 0.9626 0.9635 0.9667 0.9684 0.9694 0.9701

3.8570 4.0315 4.1884 4.3296 4.4568 4.5714 5.0000 5.2683 5.4444 5.5652

"'"'

Inlet Pressures and Temperatures U.S. Standard Atmosphere, 1962 (Geopotential) MIL-E-50070 Inlet Pressure Recovery Altitude O Feet Va

Mach 0.0 0.1 0.2 0.3 0.4

0.5 0.6 0.7 0.8 0.9 1.0 1.2

1.4 1.6 1.8 2.0 3.0

kts 0.0 66.1 132.3 198.4 264.5 330.7 396.8 462.9 529.J 595.2 661.4 793.6 925.9 1058.2 1190.4

1322.7 1984.l

PT/Po

Py/Po

1.000 1.007 1.028 l.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.425 3.182 4.250 5.746 7.824 36.733

1.000 1.007 1.028 1.064 1.117 l.186 1.276 1.387 1.524 1.691 1.893 2.404 3.113 4.090 5.427 7.238 29.710

TT2

PT2

psia

14.70 14.80 15.11 15.64 16.41 17.43 18.74 20.38 22.40 24.86 27.82 35.33 45.75 60.11 79.75 106.36 436.62

"T2

1.00000 1.00702 1.02828 1.06443 1.11655 l.18621 1.27550 1.38710 1.52434 l.69130 1.89293 2.40425 3.11299 4.09045 5.42693 7.23761 29.7099

'F 59.00 60.03 63.14 68.32 75.59 84.92 96.33 109.82 125.38 143.02 162.73 208.37 262.31 324.56 395.10 473.94 992.63

E>r2

1.000

1.002 1.008 1.018 1.032 1.050 !.072 1.098 1.128 1.162 1.200 1.288 l.392 l.512 1.648 1.800 2.800

Altitude = 5,000 Feet Mach

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 3.0

Va

kts

0.0 65.0 130.0 195.0 260.0 324.9 389.9 454.9 519.9 584.9 649.9 779.9 909.8 1039.8 1169.8 1299.8 1949.7

PT/Po

1.000 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.425 3.182 4.250 5.746 7.824 36.733

PT/Po

1.000 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.404 3.113 4.090 5.427 7.238 29.710

PT2 psia

12.23 12.31 12.57 13.02 13.65 14.50 15.60 16.96 18.64 20.68 23.15 29.40 38.06 50.02 66.36 88.50 363.29

TT dT

2

0.83205 0.83789 0.85558 0.88565 0.92902 0.98698 1.06128 1.15413 1.26832 1.40724 1.57500 2.00045 2.59015 3.40344 4.51546 6.02203 24.7200

'F

2

41.16 42.16 45.16 50.17 57.18 66.20 77.22 90.24 105.27 122.30 141.33 185.40 237.49 297.60 365.71 441.84 942.70

8T

2

0.966 0.968 0.973 0.983 0.997 1.014 1.035 1.060 1.089 1.122 1.159 1.244 1.344 1.460 1.591 1.738 2.704

,,.-..,

Inlet Pressures and Temperatures U.S. Standard Atmosphere, 1962 (Geopotential) MIL-E-50070 Inlet Pressure Recovery (continued) 10,000 Feet Altitude Mach

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 3.0

Va

kts 0.0 63.8 127.6 191.5 255.3 319.1 382.9 446.7 510.6 574.4 638.2 765.9 893.5 1021.1 1148.8 1276.4 1914.6

PT2

PT/Po 1.000 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.425 3.182 4.250 5.746 7.824 36.733

PT/Po 1.000 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.404 3.113 4.090 5.427 7.238 29.710

psia

10.11 10.18 10.39 10.76 11.28 11.99 12.89 14.02 15.41 17.09 19.13 24.30 31.46 41.34 54.85 73.15 300.26

TT2 dT2 0.68770 0.69253 0.70715 0.73201 0.76785 0.81576 0.87717 0.95391 1.04829 1.16311 1.30177 1.65341 2.14081 2.81301 3.73211 4.97732 20.4316

'F

23.33 24.29 27.19 32.02 38.78 47.48 58.10 70.66 85.15 101.58 119.93 162.44 212.67 270.64 336.33 409.75 892.77

0T2 0.931 0.933 0.939 0.948 0.961 0.978 0.998 1.023 1.050 1.082 1.117 1.199 1.2% 1.408 1.535 1.676 2.607

Altitude Mach 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 3.0

Va kts 0.0 62.6 125.3 187.9 250.5 313.2 375.8 438.4 501.1 563.7 626.3 751.6 876.8 1002.1 1127.4 1252.6 1879.0

PT/Po 1.000 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.425 3.182 4.250 5.746 7.824 36.733

PT/P0 1.000 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.404 3.113 4.090 5.427 7.238 29.710

15,000 Feet PT2 psia 8.29 8.35 8.53 8.83 9.26 9.84 10.58 11.50 12.64 14.03 15.70 19.94 25.82 33.92 45.01 60.03 246.40

dT2

0.56434 0.56830 0.58030 0.60070 0.63011 0.66943 0.71982 0.78280 0.86024 0.95447 1.06826 1.35681 1.75678 2.30840 3.06263 4.08447 16.7665

TT

'F

2

5.50

6.43 9.22 13.87 20.38 28.75 38.99 51.08 65.04 80.86 98.53 139.47 187.85 243.68 306.94 377.65 842.85

0T2 0.897 0.899 0.904 0.913 0.926 0.942 0.961 0.985 1.012 1.042 1.076 1.155 1.248 1.356 1.478 1.614 2.511

"""

Inlet Pressures and Temperatures U.S. Standard Atmosphere, 1962 (Geopotential) MIL·E-50070 Inlet Pressure Recovery (continued) Altitude = 20,000 Feet

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 l.O l.2 1.4 1.6 1.8 2.0

3.0

61.4 122.8 184.3 245.7 307.1 368.5 429.9 491.4 552.8 614.2 737.0 859.9 982.7 1105.6 1228.4 1842.6

l.007 1.028 l.064 1.117 1.186 1.276 l.387 l.524 1.691 l.893 2.425 3.182 4.250 5.746 7.824 36.733

1.007 1.028 1.064 1.117 l.186 1.276 l.387 l.524 1.691 1.893 2.404 3.1!3 4.090 5.427 7.238 29.710

6.80 6.94 7.19 7.54 8.01 8.61 9.37 10.29 11.42 12.78 16.24 21.02 27.62 36.65 48.88 200.64

0.46277 0.47254 0.48915 0.51310 0.54511 0.58615 0.63743 0.70050 0.77722 0.86988 1.10485 1.43055 1.87973 2.49390 3.32598 13.6529

-11.44 -8.76 -4.28 1.98 I0.03 19.87 31.51 44.93 60.14 77.14 116.51 163.03 216.72 277.56 345.56 792.92

0.864 0.869 0.878 0.890 0.906 0.925 0.947 0.973 1.002 !.035 I.Ill

1.201 1.304 l.421 1.552 2.415

Altitude = 25,000 Feet Mach 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 3.0

........

PT2

Va kts

PT/Po

PT/Po

psia

0.0 60.2 120.4 18o.6 240.7 300.9 361.1 421.3 481.5 541.7 601.8 722.2 842.6 962.9 1083.3 1203.7 1805.5

1.000 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 l.691 l.893 2.425 3.182 4.250 5.746 7.824 36.733

1.000 1.007 1.028 l.064 l.l17 1.186 1.276 1.387 1.524 l.691 1.893 2.404 3.113 4.090 5.427 7.238 29.710

5.45 5.49 5.61 5.80 6.09 6.47 6.96 7.56 8.31 9.22 10.32 13.ll 16.98 22.31 29.60 39.47 162.02

dTz

TT2 'F

0.37109 0.37369 0.38158 0.39500 0.41434 0.44019 0.47333 0.51474 0.56567 0.62763 0.70245 0.89219 1.15520 1.51792 2.01388 2.68581 11.0251

-30.17 -29.31 -26.73 -22.43 -16.42 -8.69 0.76 11.93 24.81 39.42 55.74 93.54 138.21 189.75 248.17 313.46 742.99

e Tz 0.828 0.830 0.835 0.843 0.855 0.870 0.888 0.909 0.934 0.962 0.994 1.067 1.153 1.252 1.365 l.491 2.319

_, Inlei Pressures and Temperatures

00

U.S. Standard Atmosphere, 1962 (Geopotential) MIL-E-50070 Inlet Pressure Recovery (continued) Altitude 30,000 Feet

Mach 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 3.0

Va kts 0.0 58.9 117.8 176.8 235.7 294.6 353.5 412.4 471.4 530.3 589.2 707.1 824.9 942.7 1060.6 1178.4 1767.6

PT/Po 1.000 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.425 3.182 4.250 5.746 7.824 36.733

PTz

PT/Po 1.000 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.404 3.113 4.090 5.427 7.238 29.710

psia

4.36 4.39 4.49 4.65 4.87 5.18 5.57 6.05 6.65 7.38 8.26 10.49 13.59 17.85 23.68 31.59 129.66

dTz 0.29696 0.29904 0.30536 0.31609 0.33157 0.35226 0.37877 0.41191 0.45267 0.50225 0.56212 0.71397 0.92443 1.21470 1.61158 2.14928 8.82265

TTz 'F -48.00 -47.17 -44.70 -40.59 -34.82 -27.41 -18.35 -7.65 4.70 18.70 34.34 70.57 113.39 162.79 218.79 281.37 693.07

eTz 0.794 0.795 0.800 0.808 0.819 0.833 0.851 0.872 0.895 0.922 0.952 1.022 1.105 1.200 1.308 1.429 2.222

Altitude = 35,000 Feet Mach 0,0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 l.4 1.6 1.8 2.0 3.0

Va kts 0.0 57.6 ll5.3 172.9 230.5 288.2 345.8 403.4 461.0 518.7 576.3 691.6 806.8 922.l 1037.4 IIS2.6 1728.9

PT{Po

PTlPo

1.000 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 l.691 1.893 2.425 3.182 4.250 5.746 7.824 36.733

1.000 1.007 1.028 1.064

l.117 l.186 1.276 1.387 1.524 1.691 1.893 2.404 3.113 4.090 5.427 7.238 29.710

P Tz psia

3.46 3.48 3.56 3.68 3.86 4.10 4.41 4.80 5.27 5.85

6.55

8.31 10.76 14.14 18.77 25.03 102.74

0Tz

0.23530 0.23696 0.24196 0.25046 0.26273 0.27912 0.30013 0.32639 0.35868 0.39797 0.44541 0.56573 0.73250 0.96250 l.27698 1.70304 6.99086

TT z "F

8r2

-65.83 -65.04 -62.68 -58.74 -53.22 -46.13 -37.47 -27.23 -15.41 -2.02 12.95 47.61 88.57 135.83 189.40 249.27 643.14

0.759 0.761 0.765 0.773 0.784 0.797 0.814 0.834 0.857 0.882 0.911 0.978 1.057 1.14$ 1.251 1.367 2.126

79

"' 0

Inlet Pressures and Temperatures U.S. Standard Atmosphere, 1962 (Geopotential) MIL-E-50070 Inlet Pressure Recovery (continued) Altitude 36,089 Feet Mach 0.0 0.1 0.2 0.3 0.4

0.5

0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6

1.8

2.0

3.0

Va

kts

o.o

57.3 114.7 172.0 229.4 286.7 344.1 401.4 458.8 516.1 573.5 688.2 802.8 917.5 1032.2 1146.9 1720.4

PTi1Po

PT/P0

1.000 1.007 1.028 1.064 1.117

1.000 1.007 1.028

l.186

1.276 1.387 1.524 1.691 1.893 2.425 3.182 4,250 5.746 7.824 36.733

1.064

1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.404 3.113 4.090 5.427 7.238 29.710

PT2

psia 3.28 3.31 3.38 3.49 3.67 3.89 4.19 4.55 5.00 5.55 6.21 7.89 10.22 13.43 17.81 23.76 97.52

&rz

0.22336 0.22493 0.22968 0.23775 0.24939 0.26495 0.28490 0.30982 0.34048 0.37777 0.42281 0.5370] 0.69532 0.91364 1.21216 1.61660 6.63602

TT2

'F

0T2

-69.71 -68.93 -66.59 -62.69 -57.23 -50.21 -41.63 -31.49 -19.79 -6.53 8.29 42.60 83.16 129.96 183.00 242.28 632.27

0.752 0.753 0.758 0.765

0.776

0.789 0.806 0.826 0.848 0.874 0.902 0.968 1.047 l.137 1.239

1.353

2.105

Altitude = 40,000 Feet Mach

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 3.0

�

PT

Ya

kts

0.0 57.3 114.7 172.0 229.4 286.7 344.1 401.4 458.8 516.1 573.5 688.2 802.8 917.5 1032.2 1146.9 1720.4

PT1/Po

PT/Po

1.000 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.425 3.182 4.250 5.746 7.824 36.733

1.000 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.404 3.113 4.090 5.427 7.238 29.710

2

psia

2.72 2.74 2.80 2.90 3.04 3.23 3.47 3.77 4.15 4.60 5.15 6.54 8.47 11.13 14.76 19.69 80.81

dT

TT 2

0.18508 0.18638 0.19032 0.19701 0.20666 0.21955 0.23607 0.25673 0.28213 0.31303 0.35035 0.44499 0.57616 0.75708 1.00444 1.33956 5.49883

'F

2

-69.71 -68.92 -66.59 -62.69 -57.23 -50.21 -41.63 -31.49 -19.79 -6.53 8.29 42.60 83.16 129.96 183.00 242.28 632.27

0T

2

0.752 0.753 0.758 0.765 0.776 0.789 0.806 0.826 0.848 0.874 0.902 0.968 1.047 1.137 1.239 1.353 2.105

.,""

Inlet Pressures and Temperatures U.S. Standard Atmosphere, 1962 (Geopotential) MIL-E-5007D Inlet Pressure Recovery (continued) Altitude = 45,000 Feet

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 3.0

57.3 114.7 172.0 229.4 286.7 344.1 401.4 458.8 516.l 573.5 688.2 802.8 917.5 1032.2 1146.9 1720.4

1.007 1.028 1.064

1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.425 3.182 4.250 5.746 7.824 36.733

l.007

l.028 1.064 1.117 1.186

1.276 1.387 1.524 1.691 1.893 2.404 3.113 4.090 5.427 7.238 29.710

2.15 2.20 2.28 2.39 2.54 2.73 2.97 3.26 3.62 4.05 5.14 6.66

8.15 11.61

15.48 63.55

0.14657 0.14966 0.15492 0.16251 0.17265 0.18564 0.20189 0.22186 0.24616 0.27551 0.34993 0.45308 0.59535 0.78987 l.05340 4.32415

-68.93 -66.59 -62.69 -57.23 -50.21 -41.63 -31.49 -19.79 -6.53 8.29 42.60 83.16 129.96 183.00 242.28 632.27

0.753 0.758 0.765 0.776 0.789 0.806 0.826 0.848 0.874 0.902 0.968 1.047 1.137 1.239 1.353 2.105

Altitude = 50,000 Feet Mach

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 3.0

kts

PT/Po

PT/P0

PT z psia

0.0 57.3 114.7 172.0 229.4 286.7 344.1 401.4 458.8 516.1 573.5 688.2 802.8 917.5 1032.2 1146.9 1720.4

1.000 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.425 3.182 4.250 5.746 7.824 36.733

1.000 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.404 3.113 4.090 5.427 7.238 29.710

1.68 1.69 1.73 1.79 1.88 2.00 2.15 2.33 2.56 2.84 3.18 4.04 5.24 6.88 9.13 12.17 49.97

Va

dTz

0.11445 0.11526 0.11769 0.12183 0.12779 0.13577 0.14599 0.15876 0.17447 0.19358 0.21665 0.27518 0.35629 0.46817 0.62113 0.82837 3.40041

T Tz

"F

eT z

-69.71 -68.93 -66.59 -62.69 -57.23 -50.21 -41.63 -31.49 -19.79 -6.53 8.29 42.60 83.16 129.96 183.00 242.28 632.27

0.752 0.753 0.758 0.765 0.776 0.789 0.806 0.826 0.848 0.874 0.902 0.%8 1.047 1.137 1.239 1.353 2.105

83

:!'= Inlet Pressures and Temperatures

U.S. Standard Atmosphere, 1962 (Geopotential) MIL-E-50070 Inlet Pressure Recovery (continued) Altitude SS,000 Feet

Mach 0.0 0.1 0.2 0.3 0.4

0.5

0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 3.0

Va

kts

o.o

57.3 114.7 172.0 229.4 286.7 344.1 401.4 458.8 516.1 573.5 688.2 802.8 917.5 1032.2 1146.9 1720.4

PT/Po 1.000 1.007 1.028 1.064 1.117 1.186 1.276 l.387 1.524 1.691 1.893 2.425 3.182 4.250 5.746 7.824 36.733

PT/Po 1.000 1.007

1.028

1.064 1.117 1.186 1.276 l.387 1.524 1.691 1.893 2.404 3.113 4.090 5.427 7.238 29.710

PT2 psia 1.32 1.33 l.36 1.41 1.48 1.57 1.69 1.83 2.02 2.24 2.50 3.18 4.12 5.41 7.18 9.57 39.30

dTz 0.09000 0.09064 0.09255 0.09580 0.10049 0.10676 0.11480 0.12484 0.13720 0.15222 0.17037 0.21639 0.28018 0.36816 0.48844 0.65141 2.67401

TT2

'F

-69.71 -68.93

-66.59

-62.69 -57.23 -50.21 -41.63 -31.49 -19.79 -6.53 8.29 42.60 83.16 129.96 183.00 242.28 632.27

0-r2

0.752 0.753 0.758 0.765 0.776 0.789

0.806

0.826 0.848 0.874

0.902 0.968 1.047

1.137

1.239 1.353 2.105

Altitude Mach

0.0 0.1 0.2 0.3 0.4

0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 2.0 3.0

Va

60,000 Feet PT2

kts

PT/Po

PT/Po

psia

0.0 57.3 114.7 172.0 229.4 286.7 344.l 401.4 458.8 516.1 573.5 688.2 802.8 917.5 1032.2 1146.9 1720.4

1.000 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.425 3.182 4.250 5.746 7.824 36.733

1.000 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.404 3.113 4.090 5.427 7.238 29.710

1.04 1.05 1.07 1.11 1.16 1.23 1.33 1.44 1.59 1.76 1.97 2.50 3.24 4.25 5.64 7.53 30.90

dT

TT

2

2

'F

0.07078 0.07127 0.07278 0.07534 0.07903 0.08396 0.09028 0.09817 0.10789 0.11971 0.13398 0.17017 0.22033 0.28951 0.38410 0.51226 2.10278

-69.71 -68.93 -66.59 -62.69 -57.23 -50.21 -41.63 -31.49 -19.79 -6.53 8.29 42.60 83.16 129.96 183.00 242.28 632.27

9T

2

0.752 0.753 0.758 0.765 0.776 0.789 0.806 0.826 0.848 0.874 0.902 0.968 1.047 1.137 1.239 1.353 2.105

85

"' "'

Inlet Pressures and Temperatures U.S. Standard Atmosphere, 1962 (Geopotential) MIL-E-50070 Inlet Pressure Rewvery (continued) Altitude = 65,000 Feet

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 LO

1.2 1.4 1.6 1.8 2.0 3.0

57.3 114.7 172.0 229.4 286.7 344.1 401.4 458.8 516.l 573.5 688.2 802.8 917.5 1032.2 1146.9 1720.4

1.007 1.028 1.064

1.117 l.!86 1.276 1.387 1.524 1.691 1.893 2.425 3.182 4.250 5.746 7.824 36.733

1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.404 3.113 4.090 5.427 7.238 29.710

0.82 0.84 0.87 0.91 0.97 1.04 1.13 1.25 1.38 1.55 1.97 2.55 3.35 4.44 5.92 24.30

0.05605 0.05723 0.05924 0.06214 0.06602 0.07099 0.07720 0.08484 0.09413 0.10536 0.13381 0.17326 0.22766 0.30205 0.40283 1.65358

-68.93 -66.59 -62.69 -57.23 -50.21 -41.63 -31.49 19.79 -6.53 8.29 42.60 83.16 129.96 183.00 242.28 632.27

0.753 0.758 0.765 0.776 0.789 0.806 0.826 0.848 0.874 0.902 0.968 1.047 1.137 1.239

1.353 2.105

Altitude = 70,000 Feet Mach 0.0 0.1 0,2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8

2.0 3.0

Va

PT2

kts

PT/Po

PT /Po

psia

0.0 51.5 115.0 172.6 230.1 287.6 345.1 4-02.7 460.2 517.7 575.2 690.3 805.3 920.4 1035.4 1150.5 1725.7

1.00l 1.007 1.028

1.00) 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.404 3.113 4.090 S.427 7.238 29.710

0.64 0.65 0.66 0.69 0.72 0.76 0.82 0.89 0.98 1.09 1.22

1.064

1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.425 3.182 4.250 5.746 7.824 36.733

1.55

2.00 2.63 3.49 4.66 19.12

dT2

0.04380 0.04411 0.04504 0.04662 0.04890 0.05195 0.05587 0.06075 0.06676 0.074-08 0.08291 0.10530 0.13634 0.17916 0.23769 0.31700 1.30125

TT2 'F

-67.31 -66.52 -64.17 -60.24 -54.75 -47.69 -39.06 -28.85 -17.08 -3.74 11.17 45.70 86.51 133.60 186.96 246.61 639.00

0-r2

0.757 0.758 0.763 0.770 0.781 0.794 0.811 0.831 0.853 0.879 0.908 0.974 1.053 1.144

1.247 1.362 2.1!8

87

OQ

00

Inlet Pressures and Temperatures U.S. Standard Atmosphere, 1962 (Geopotential) MIL-E-50070 Inlet Pressure Recovery (continued) Altitude = 75,000 Feet Mach 0.0 0.! 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 l.2 1.4

l.6 l.8 2.0 3.0

Va

kts 0.0 57.7 115.4 173.2 230.9 288.6 346.3 404.l 461.8 519.5 577.2 692.7 808.l 923.6 1039.0 1154.5 1731.7

PT1/Po 1.000 1.007 1.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 l.893 2.425 3.182 4.250 5.746 7.824 36.733

PT/Po 1.000 l.007 I.028 1.064 1.117 1.186 1.276 1.387 1.524 1.691 1.893 2.404 3.113 4.090 5.427 7.238 29.710

PT2 psia

0.51 0.51 0.52 0.54 0.57 0.60 0.65 0.70 0.77 0.86 0.96 1.22 U8 2.08 2.75 3.67 15.07

r2

0.03452 0.03477 0.03550 0.03675 0.03855 0.04095 0.04403 0.04789 0.05262 0.05839 0.06535 0.08300 0.10747 0.14121 0.18735 0.24986 1.02567

TT2 'F -64.56 -63.77 -61.40 -57.45 -51.92 -44.81 -36.11 -25.84 -13.99 -0.55 14.46 49.23 90.33 137.74 191.48 251.54

646.68

eTz 0.762 0.763 0.768 0.776 0.786 0.800 0.817 0.836 0.859 0.885 0.914 0.981 l.060 1.152 1.255 1.371 2.133

MIL-E-50070 Inlet Pressure Recovery P121Pt1

I.DO from M = 0 to 1.0 I.DO - 0.076 (M -J)l.35 800 M4 + 935

from M > 1.0 to 5.0

M > 5.0

where: P12 = total pressure at compressor inlet Pu = free stream total pressure M = flight Mach number

89

General Properties of Air Speed of Sound in Air at Atmospheric Temperature Cfps = 49.02 VToR Cmph = 33.42 VTOR Ckts = 29.04 VToR

Cm/sec = 20.05 VTOR

Specific Weight of Air in Ibfft J go

~ .07647(~)(~) ~ 1.326(~i~~)

Density of Air in Ib sec 2fft 4 or slngfft J Q

~ .002377 (.!!..-)(~) ~ .041206 (~in. Po

T

Hg)

TOR

Air Density Ratio

o = ~ =(.!!..- )(~) Qo

Po

T

~

17.336

(Pin. Hg) TOR

Coefficient of Viscosity in Ibfft sec fie ~ p (TOR )3/2 TOR

+ S

where: S = 198.72 'R P = 7.3025 x 10- 7 ftfsee

v'R

Kinematic Viscosity in ft 2fsec v =

-&.. gp

Absolute Viscosity for Air in Ib-secfft1 10- 10 ~ ~ pv ~10.3170(T )3/2E-~-Yx ~ OR TOR + 216 ~

90

Specific Heat (Heat Capacity) of Air at S9•F at constant pressure cP = 0.240 at constant volume c" = 0.1715 Specific heat ratio, r

1.4

Gas Constant for Air R = 53.35

1 287.074-kg 'K

Normal Composition of Clean, Dry Atmospheric Air Near Sea Level Content, Percent Molecular Constituent Gas by Volume Weight' and Formula 78.084 28.0134 Nitrogen (Ni) 20.9476 31.9988 Oxygen (Ov 39.948 0.934 Argon (A) 0.0314 44.00995 Carbon dioxide (COv O.OOJ818 20.183 Neon (Ne) 0.000524 4.0026 Helium (He) 83.80 0.000114 Krypton (Kr) 0.0000087 131.30 Xenon (Xe) 2.01594 0.00005 Hydrogen (Hi) 0.0002 16.04303 Methane (Cl:;y) 0.00005 Nitrous oxide (N2 0) 44.0128 Summer: 0 to 0.000007 Ozone (03) 47.9982 47.9982 Winter: Oto 0.000002 Sulfur dioxide (SOi) 0to 0.0001 64.0628 46.0055 Oto 0.000002 Nitrogen dioxide (NOy 0to trace Ammonia (NH 3) 17.03061 28.01055 0to trace Carbon monoxide (CO) Oto 0.000001 253.8088 Iodine (ly •on basis of carboa-12 isotope scale for which ci2 = 12. 1 Molecular weight of air = 28.9644 lb 01 ( k/!01 )

!

91

General Properties of Gases Perfect Oas Law at constant temperature at constant pressure at constant volume

PV = mRT P1IP2 V2IV1 V1IV1 T1IT2 P1IP2 T1IT2

Reversible adiabatic process

!:.!. V1 y P2 =( !'.i) (

2g

)y

l

!:.!. =( Q2'51)' P1V1" P2V2" !'.J. ( !':l. 1-n V,) T2 P2

PoJytropic process

Steady-flow energy equation 2 q + hi + "i\ + Z1 = h2

�

+

Bernoulli equation (W (P2 - Pi) + QK where Z = altitude Flow per unit area

f =j1

Velocity of sound in a perfect gas c ,}ygRT

2 l'2

+

Z2

+

W

PSYCHROMETRIC CHART FOR SEA LEVEL BAROMETRIC PRESS. TO FIND Vp AT BT ADD /J. Vp TO S.L. Vp /J.V p

= (29.9

- (t d - tw) 2800 - 1.3 tw

SPECIFIC HUMIDITY W/A Vp BT td tw

=

V_p_ 0.622 (__ ) BT - Vp

= VAPOR PRESS. IN . HG = TRUE BAR. PRESS. IN. HG = ORY TEMP. DEG F = WET BULB TEMP. DEG F

"',! t-

� i:.5 �

2.5 2.3 .05

ENTER CHART WITH DRY AND WET BULB TEMP. AT INTERSECTION READ RELATIV E HUMIDITY, READ LEFT FOR DEW POINT, READ RIGHT FOR SPECIFIC HUMIDITY AND VAPOR PRESS

" If?

.06

0

1.9

a,

w

rr:

1.7

�

0

1.5

::::, Ii

::.

.03 CD ...J

1.3

15

�

:E

1.1

.02 I

0.9

0

0.7

::::,

u::

w a.

(/)

Qi.,

,S'

.01

,._Q} �"'

20

2.1

.04 -"'

Iii

ci I

� w

rr: ::::, (/) (/)

w

rr: a. rr: 0 a.

UJ a..

+300 l----+--1--+-+4' !l�'§���������....4l--1+� +760 '-::l,,,l�Pl"....i:--+-+-+-Fl"'��---p,�� +860 +400 +500 L.--J....-i-J...W...J.J..J.J.-..-'-�w............_-1-..J.....E::!loJ..l�-�l.-!...I...J..I..I.U +960 0.o1 0.1 1.0 10 100

VAPOR PRESSURE, ATM 133

VAPOR PRESSURE OF LIQUID PROPELLANTS

� UJ I-

�

TEMPERATURE, 0 R 1.6 1.4

160

60

260

360

460

-200

-100

0

560

660

+1 00

+200

LIQUID' FLUORINE

1.2

a:

(...'.;

0

u::

0

w

0.. (/)

1.0 0.8 0.6 0.4 0.2 -300

TEMPERATURE, °F SPECIFIC GRAVITIES OF LIQUID PROPELLANTS

Gas Turbine Engine Symbols Used By Pratt & Whitney A a c c CLB CON CRZ D EGT F f g hp H h I LHV m M M MCL MCR MCT N

n p p

Pr Q q q

cross-sectional area linear acceleration speed of sound specific heat coefficient, factor of proportionality, correction factor maximum climb rating maximum continuous rating maximum cruise rating diameter exhaust gas temperature 2.718281828459045 {the base of the natural system of logarithms) thrust, force frequency acceleration due to gravity horsepower enthalpy specific enthalpy length lower heating value of fuel mass moment mach number maximum climb rating maximum cruise rating maximum continuous rating rotational speed polytropic exponent pressure {absolute) pressure {gage) Prandtl number volume rate of flow quantity of heat {specific) dynamic pressure

135

Gas Turbine Engine Symbols Used By Pratt & Whitney (continued) R Re r

s

$ SFC TSFC T T t

t

TO TOD TOW u u

v v

v w w y

d Ii 11 e µ ll

136

gas constant Reynolds number radius entropy specific entropy specific fuel consumption (esfc, bsfc, equiv., brake) thrust specific fuel consumption torque temperature (absolute) temperature time takeoff rating dry takeoff rating wet takeoff rating internal energy (specific) linear gas velocity velocity volume specific volume weight weight rate of flow angle of attack angular acceleration ratio of specific heats (cplcv) relative pressure ratio, PIP0 finite difference efficiency relative temperature ratio, TIT0 absolute viscosity kinematic viscosity 3.141592653589793 (ratio of circumference of a circle to its diameter) density relative density ratio, QIe0 gross thrust parameter angular velocity

Gas Turbine Engine Subscripts 1 , 2, 3 , etc. a

AIB am av ax

b

bl

er

d

e

ej

f g H h j

m

n

o

p

px s T t

th w

engine station designations air (Va); added (qa) afterburner ambient