Class 39 - 41 Introduction to Missile Dynamics

System Modeling Coursework

Class 39 - 41: Introduction to Missile dynamics

P.R. VENKATESWARAN Faculty, Instrumentation and Control Engineering, Manipal Institute of Technology, Manipal Karnataka 576 104 INDIA Ph: 0820 2925154, 2925152 Fax: 0820 2571071 Email: [email protected], [email protected] Web address: http://www.esnips.com/web/SystemModelingClassNotes

WARNING! • I claim no originality in all these notes. These are the compilation from various sources for the purpose of delivering lectures. I humbly acknowledge the wonderful help provided by the original sources in this compilation. • For best results, it is always suggested you read the source material. July – December 2008

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Definition for a missile • A missile can be defined as an aerospace vehicle with varying guidance capabilities that is self propelled through space for the purpose of inflicting damage on a designated target. • Fabricated for air-to-air, surface to air and surface to surface roles.

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Components of a missile • • • •

Propulsion system Warhead section Guidance system Control surfaces Choice is between a guided and a non guided missile!

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Components of a guided missile • • • •

Airframe Guidance Motor (or propulsion) Warhead

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Airframe • The type and size depends on – Guidance characteristics – Motor size – Warhead size

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Guidance • Guidance is the means by which a missile steers or is steered to a target. • The type of guidance is also dependent on the motor, warhead and threat. • More specifically, the type of guidance chosen is dependent on the overall weapon system in which the missile will be used, on the type of threat the missile will be used against, the characteristics of the threat target, and other factors. July – December 2008

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Motor • The motor characteristics depends on – Guidance requirements – The threat – Airframe characteristics

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Warhead • Dependent on the threat and type of guidance • The common procedure is to size the guidance requirements (e.g. accuracy, response time, range capability) from the threat, select an airframe that can deliver the required aerodynamic performance, size the motor based on threat and airframe considerations and size the warhead from guidance and airframe considerations. July – December 2008

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Common missile structure

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Basic Weapon construction

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Basic factors affecting the missile design • • • •

Threat Operating environment Cost State of the art – Since the last three is normally known, the missile design centers on meeting the threat in the environment with the state of the art, at minimum cost.

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Factors affecting motor type selection • Aerodynamic heating due to the incremental missile velocity • Aerodynamic drag, which decreases missile velocity • Maximum altitude at which the missile must perform • Maximum and minimum intercept ranges required.

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Types of missile motors: All Boost • It typically will make the missile accelerate rapidly, causing high peak velocities. However, this causes high missile drag, high aerodynamic heating, and short time of flight, for a given range • This is suitable for a rear hemisphere, tail chase encounter. July – December 2008

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Types of Missile Motors: All Sustain • It has low acceleration, resulting in lower aerodynamic drag and longer time of flight, for a given range. • It can be used in a look up engagement, and to provide sufficient velocity for maneuvering at high altitude. • The motor is suitable for head on engagements, or in look-up engagements at high altitudes July – December 2008

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Types of missile motors: Boost Sustain • The boost sustain motor represents an attempt to combine the best features of the all-boost and allsustain designs.

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Missile development stages

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Missile speed • Guided tactical missiles are sometimes referred to according to their airspeed relative to the speed of sound and their type of propulsion system • The highest rate of airspeed that can be reached safely and still ensure correct operation is considered as that missile’s classification. The common classification are – – – –

Subsonic (airspeeds less than mach 1) Sonic (airspeeds equal to mach 1) Supersonic (airspeeds ranging between mach 1 and mach 5) Hypersonic (airspeeds exceeding mach 5)

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Skid to turn (STT) missile • It is the commonly used in analysis and design of surface to air and air to air weapon systems • The reason is the inertial cross coupling between roll, pitch and yaw is negligible. • Both aerodynamics and rigid body dynamics are highly non linear

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Comparison of weapon system characteristics

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Response of the system • The pitch/yaw plane rotational responses behave like a spring mass damper system. It is given as: • The equation can also be written as: where

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Typical Pitch – Yaw network

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Modeling drag and lift • For the purposes of control design, drag can be modeled by parabolic drag form • If Lift is considered as control, it is subjected to the constraint where W is the weight and gm(v) represents the load factor limit, which may arise due to a structural limit, control surface actuator, or autopilot stability considerations. In general, lift is a function of missile speed. July – December 2008

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Load factor expression

• The dynamics for the angle of attack (AOA), α, as well as dα/dt, load factor nz and pitch rate are commonly modeled after the short period approximations of longitudinal motion. • The short period of attack is given by the following transfer function

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Load factor command system

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Dynamics of load factor in pitch plane • The load factor and angle of attack transfer functions are identical in form. • Specifically, the dynamics for the load factor in the pitch plane, nz, can be modeled by the following transfer function

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Dynamics of load factor in pitch plane • The parameters ζ,ω and Tα can be found by linear analysis of the entire closed loop system. • This transfer function is valid provided that the laod factor being modeled is located at the centre of pressure, that is , the point ahead of the centre of gravity where the effect of pitch acceleration and horizontal tail force cancel.

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Load factor command system

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The Missile Guidance system model • Guidance is the means by which a missile steers, or is steered, to a target. • A guided missile is guided according to a certain guidance law. • The inputs are target location and missile to target separation. • The desired output is that the missile have the same location as the target July – December 2008

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Major subsystems of Missile Guidance System

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A typical roll stabilized missile guidance/kinematic loop

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General Problems of Guidance System Design 1.

Help to maximize the single shot kill probability (SSKP) by minimizing the miss distance Sources of miss distance

2. • • • • • • •

Initial heading error Acceleration bias Gyro drifts (if gyros are used in seeker stabilisation) Glint (scintillation noise) Receiver noise Fading noise Angle noise (due to varying refraction with frequency diversity)

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General Problems of Guidance System Design

2. Preserve stability of the parasitic attitude loop 3. Filtering • •

Limit power consumption and saturation of the actuators Prevent noise from excessive hitting of dynamic range limits, such as auto pilot g limits

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Functions of the missile seeker subsystem 1. 2. 3. 4. 5. 6.

Provide the measurements of target motion required to mechanise the guidance law. Track the target with the antenna or other energy receiving device (eg. Radar, infrared, laser or optical) Track the target continuously after acquisition Measure the LOS (Line of sight) angular rate dλ/dt. Stabilise the seeker against a missile pitching rate dθm/dt (also, yawing rate) that may be much larger than the LOS rate dλ/dt to be measured. Measure the closing velocity Vc.

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Missile seeker showing geometry

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Typical block diagram of a seeker subsystem

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References • Missile Guidance and Control Systems, George M. Siouris, Springer, 2004 ISBN 0387007261

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And, before we break… • Nothing is permanent in this wicked world. Not even our troubles. – Charlie Chaplin

• Thanks for listening… July – December 2008

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