Class 39 - 41 Introduction to Missile Dynamics

System Modeling Coursework

P.R. VENKATESWARANFaculty, Instrumentation and Control Engineering,

Manipal Institute of Technology, ManipalKarnataka 576 104 INDIAPh: 0820 2925154, 2925152

Fax: 0820 2571071Email: [email protected], [email protected]

Web address: http://www.esnips.com/web/SystemModelingClassNotes

Class 39 -

41: Introduction to Missile dynamics

mailto:[email protected]

mailto:[email protected]

http://www.esnips.com/web/SystemModelingClassNotes

July – December 2008 prv/System Modeling Coursework/MIT-Manipal 2

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.


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.


Components of a missile

•

Propulsion system•

Warhead section

•

Guidance system•

Control surfaces

Choice is between a guided and a non guided missile!


Components of a guided missile

•

Airframe •

Guidance

•

Motor (or propulsion)•

Warhead


Airframe

•

The type and size depends on–

Guidance characteristics

–

Motor size–

Warhead size


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.


Motor

•

The motor characteristics depends on–

Guidance requirements

–

The threat–

Airframe characteristics


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.


Common missile structure


Basic Weapon construction


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.


Factors affecting motor type selection

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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.


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.


Types of Missile Motors: All Sustain

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It has low acceleration, resulting in lower aerodynamic drag and longer time of flight, for a given range.

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It can be used in a look up engagement, and to provide sufficient velocity for maneuvering at high altitude.

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The motor is suitable for head on engagements, or in look-up engagements at high altitudes


Types of missile motors: Boost Sustain

•

The boost sustain motor represents an attempt to combine the best features of the all-boost and all-

sustain designs.


Missile development stages


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)


Skid to turn (STT) missile

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It is the commonly used in analysis and design of surface to air and air to air weapon systems

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The reason is the inertial cross coupling between roll, pitch and yaw is negligible.

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Both aerodynamics and rigid body dynamics are highly non linear


Comparison of weapon system characteristics


Response of the system

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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


Typical Pitch –

Yaw network


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.


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


Load factor command system


Dynamics of load factor in pitch plane

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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


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.


Load factor command system


The Missile Guidance system model

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Guidance is the means by which a missile steers, or is steered, to a target.

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A guided missile is guided according to a certain guidance law.

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The inputs are target location and missile to target separation.

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The desired output is that the missile have the same location as the target


Major subsystems of Missile Guidance System


A typical roll stabilized missile guidance/kinematic loop


General Problems of Guidance System Design

1.

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

2.

Sources of miss distance•

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)


General Problems of Guidance System Design

2.

Preserve stability of the parasitic attitude loop3.

Filtering

• Limit power consumption and saturation of the actuators

• Prevent noise from excessive hitting of dynamic range limits, such as auto pilot g

limits


Functions of the missile seeker subsystem

1.

Provide the measurements of target motion required to mechanise

the guidance law.

2.

Track the target with the antenna or other energy receiving device (eg. Radar, infrared, laser or optical)

3.

Track the target continuously after acquisition4.

Measure the LOS (Line of sight) angular rate dλ/dt.

5.

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.6.

Measure the closing velocity Vc

.


Missile seeker showing geometry


Typical block diagram of a seeker subsystem


References

•

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


And, before we break…

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Nothing is permanent in this wicked world. Not even our troubles.–

Charlie Chaplin

•

Thanks for listening…

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Class 39 - 41 Introduction to Missile Dynamics

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