1 This military manual is approved for use by all Department of the Army activities and agencies and is available for use by all Departments and Agencies of the Department of Defense. The size of the protected area and the capabilities of the threat have a major impact on the speed, maneuverability and lethality requirements of the missile system.
INTRODUCTION
1-1 BACKGROUND
1-1.1 DESCRIPTION OF A MISSILE FLIGHT SIMULATION
For example, a simulation of a specific type of missile usually has descriptive data built into the missile model, but simulations of generic missiles or not yet fully defined missiles can be arranged so that parameters that are subject to change are inputs. Typical missile flight simulation outputs include the missile's flight path history and resulting miss distance.
1-1.2 PUROSE OF A MISSILE FLIGHT SIM- ULATION
Examples of inputs are initial conditions such as missile and target positions and velocities at the time the simulation starts, programmed target maneuvers, and countermeasures control parameters. Environmental conditions, eg atmospheric density as a function of altitude, are usually included in the simulation; however, a non-standard atmosphere or other variable environmental conditions can be resolved by an appropriate choice of input.
1-1.3 IMPLEMENTATION OF A MISSILE FLIGHT SIMULATION
A spectrum of methods for determining missile performance (CRT) displays of the instruction lines are readily available. Inputs or changes to the simulation can be easily made by typing them into the computer using a keyboard.
1-2 PURPOSE OF THE HANDBOOK
Typically, 'hybrids are used in applications that require real-time results and in which the simulated functions contain high-frequency spectral components that would be difficult or impossible to produce with current digital equipment alone. The need for real-time computation is usually a result of using the actual rocket hardware in the simulation, which, of course, must operate in real-time (Refs. 2, 3, and 4).
1-3 SCOPE OF THE HANDBOOK
BIBLIOGRAPHY
MISSILE SYSTEM DESCRIPTION
2-0 LIST OF SYMBOLS
2-1 INTRODUCTION
The distance between the missile and the target at the closest approach of the missile to the target is the miss distance. As the missile approaches the target, the fuse senses the presence of the target and detonates the warhead.
2-2 MISSILE
The missile fire control system monitors the position of the target and gives an indication of the time when the target enters the launch range. The tracking system continues to track the target and provide information on the target's position and movement relative to the missile.
2-2.1 SEEKER
2-8(B), the circular path of the target image is no longer concentric with the reticle. When the target is positioned exactly on the lobe axis, the magnitude of the target return signal is greatest.
2-2.3 CONTROL
The design of the autopilot depends on the aerodynamics of the rocket airframe and the type of controls used. The magnitude of the aerodynamic moment is proportional to the lift L acting on the control surface.
2-2.4 WARHEAD AND FUZE
The angular position of the control surface can be sensed and fed back to the amplifier to form a feedback loop. Subtracting the target velocity vector gives the velocity of the fragment relative to the target, as shown by the dynamic pattern in Figure 1.
2-2.5 PROPULSION
Other boost and sustain designs use the same rocket nozzle for both thrust stages, with the change in thrust level achieved by grain configuration and combustion chamber layout. Specific impulse is one of the most important parameters used to describe the performance of a rocket motor (ref. 10).
2-2.6 AIRFRAME
This increases the static margin and therefore reduces maneuverability in the later parts of the flight. In contrast, the projectile's rotational inertia is reduced as the propellant grain burns, allowing for a faster response to control commands.
2-3 GUIDANCE
GUIDANCE IMPLEMENTATION (Ref
Current homing applications typically only measure line-of-sight angular velocity from the missile to the target. The voltage required to generate this torque is proportional to the line-of-sight angular velocity to the target.
2-3.2 GUIDANCE LAWS
The guidance sensor measures one or more parameters of the projectile's trajectory relative to the target. During the early part of the projectile's acceleration phase, the projectile's velocity is relatively low.
2-4 LAUNCHER
2-4.1 SOURCE OF INITIAL CONDITIONS
2-4.2 LAUNCHER POINTING DIRECTION
BIBLIOGRAPHY CONTROL (CLASSICAL)
Brown, Ballistic Missile and Space Vehicle Systems, John Wiley & Sons, Inc., New York, NY,. Brown, Ballistic Missile and Space Vehicle Systems, John Wiley & Sons, Inc., New York, NY,.
MISSILE SIMULATION OVERVIEW
3-0 LIST OF SYMBOLS
3-1 INTRODUCTION
Careful and methodical procedures are in place to evaluate each phase of weapon system acquisition and to ensure that a sound technology base is available (Ref. 5). Procuring and operating high-quality, affordable, high-tech weapons requires effective testing and evaluation throughout the life cycle of a weapon system (Ref. 6).
3-2 MISSILE SIMULATION OBJECTIVES
Flight test success rates of better than 95% have been achieved through careful preparation and planning, using flight simulations to verify the missile design prior to flight testing and to predict the results of each test (Ref. 5). Developing a hierarchy of flight simulations to assist in various phases throughout a missile system's life cycle is now considered indispensable (Ref. 5).
3-2.1 MISSIE SIMULATION PERSPECTIVE
The simulation realism required to predict flight test results cannot be achieved instantaneously, nor are the requirements for simulation realism the same throughout the life cycle of a missile system. One of the important goals of rocket flight tests is to validate the simulation model.
3-2.2 OBJECTIVES OF SIMULATIONS AD- DRESSED IN THIS HANDBOOK
The actual target position is measured by test instruments and fed into the simulation in near real time. The simulation provides the training instructor with information about the expected outcome of the engagement as well as the causes of failed engagements.
3-3 ESSENTIALS OF MISSILE SIMULA- TIONS
Thus, large numbers of training exercises can be conducted at a small fraction of the cost of live fire. In this environment, a major cause of guided missile strike failures is launching the missile at a time when the combination of target position and velocity parameters are not within acceptable launch patterns.
3-3.1 SIMULATING MISSILE GUIDANCE AND CONTROL
The model of the target tracker requires target signature data and features from other sources in the target scene, such as background, decoys, and jammers. The outputs of the control system model (or transfer function) are the fin deflections.
3-3.2 SIMULATING MISSILE AND TARGET MOTION
Thus, the thrust magnitude is passed to the simulation in the form of a thrust table as a function of time at a given reference pressure. For rockets using other types of propulsion, thrust simulation may be more complex.
3-3.3 ROLE OF COORDINATE SYSTEMS
These angles are defined in the target body coordinate system defined for the missile. Not all target signature data is based on a coordinate system that is seen as rigidly attached to the same coordinate system definition; therefore, the same objective; therefore, it translates, tones, rotates, and rotates the user must transform the signature data if it is not the target.
3-3.4 COMPUTATIONAL CYCLE
At this point, all parameters have been updated to the end of the current calculation interval. Otherwise, the program returns to the atmospheric routine to begin the next calculation cycle.
3-4 LEVEL OF SIMULATION DETAIL
The projectile accelerations are integrated to determine the translational and rotational velocities and position vectors at the end of the current calculation interval. The time now increments to the start of the next interval in preparation for the next calculation cycle.
3-4.1 MODELING TO MATCH SIMULATION OBJECTIVES
Three degrees of freedom plus a technique to calculate dynamic angle of attack is usually sufficient for a generic missile. At least five degrees of freedom are required to support hardware-in-the-loop and may also be required to support a very detailed mathematical seeker model.
3-4.2 MODEL SOPHISTICATION REQUIRED TO SATISFY HANDBOOK OBJECTIVES
If the missile's roll rate is fast enough to significantly affect the missile's performance, six degrees of freedom may be required, or techniques for handling rolling airframes in non-rolling coordinate frames may be used. Eckenroth; 'Tlight Test Validation of the Patriot Missile Six-Degree-of-Freedom Aerodynamic Simulation Model', Automatic Control Theory and Applications 7, 1 (January 1979).
BIBLIOGRAHY SIMULATION
MISSILE DYNAMICS
The approach discussed in the previous chapters involves calculating the forces and moments acting on the missile and substituting them into the equations of motion to give the vehicle accelerations.
4-0 LIST OF SYMBOLS
INTRODUCTION
It is assumed that gravity acts through the center of mass of the rocket and does not produce a moment around the center of mass. For many applications, however, the effects of structural deflections (aeroelasticity) and of the dynamics of the relative motion of the control surfaces are on the overall missile.
4-2 NOMENCLATURE AND CONVEN- TIONS
The position of the rocket's center of mass is given by the cartesian coordinates expressed in an inertial reference frame, such as the solid-earth frame (xe,ye,Ze). For this purpose, the origins of the two frames are overlaid on the missile's center of mass.
4-3.1 NEWTON’S SECOND LAW OF MOTION
However, when we consider the absolute rate of change of vector B, we must also consider the rate of change of the rotating frame of reference. Given the rate of change of position relative to the rotating frame Prot, the rate of change of position of the particle relative to an inertial frame Pinrtl is obtained by replacing P with B in Eq.
4-4 FORCES AND MOMENTS
The first term on the right Arot is the acceleration of the particle as seen by an observer in the rotating frame. The variable Vrot is the velocity of the particle as seen by an observer in the rotating frame.
4-4.1 AERODYNAMIC FORCES AND MO- MENTS
The second term on the right of x P comes from the angular acceleration of the rotating frame; this term vanishes when a rotating frame rotates at a uniform speed, such as a frame attached to a rotating earth. 4-12 with the mass of the body and setting the result equal to the sum of the forces on the body is a way of applying Newtonian mechanics to a rotating frame of reference.
4-4.2 THRUST FORCE AND MOMENT
These external forces are applied directly to the rocket body; therefore, they affect only the portion of the total system momentum attributable to the rocket. If the thrust vector FP passes through the rocket's center of mass, no torque is generated by the thrust.
4-4.3 GRAVITATIONAL FORCE
If the acceleration due to gravity at the surface of the earth go is known, the acceleration at any height. Thus, no rotational torque is generated and the force of gravity is considered to act through the center of mass of the missile.
4-5 EQUATIONS OF MOTION
In this case, the motion of the projectile relative to the earth is best approximated using the gravitational acceleration g. In general, the international standard value of g or the value selected from Table 4-2 for the appropriate latitude is considered to be sufficiently accurate for the acceleration due to gravity at the surface of the earth.
4-5.1 TRANSLATIONAL EQUATIONS
The goal at this point is to calculate the absolute velocity V of the rocket's center of mass. 4-32, this should be expressed in the coordinates of the chosen frame of reference, in this case the.
4-5.2 ROTATIONAL EQUATIONS
Ω = angular velocity vector of the rotor relative to the body coordinate system, p´ib + q'jb + r´kb, rad/s. The rates of change of the Euler angles are related to the angular velocity w of the body frame.
BIBLIOGRAPHY EQUATIONS OF MOTION
Etkin, Dynamics of Flight-Stability and Control, John Wiley & Sons, Inc., New York, NY, 1982. Wolverton, Flight Performance Handbook for Orbital Operations, John Wiley & Sons, Inc., New York NY, 1963.
GRAVITY
Dynamics of the Airframe, BU AER-rapport AE-61-4 H, Bureau of Aeronautics, Navy Department, Washington, DC, 1952. Jenkins, Missile Dynamics Equations for Guidance and Control Modeling and Analysis, Technical Report RG-84-17 , Direktorat for vejledning og kontrol, US Army Missile Laboratory, US Army Missile Command, Redstone Arsenal, AL april 1984.
RIGID BODY DYNAMICS
MISSILE AERODYNAMICS
5-0 LIST OF SYMBOLS
Q = dynamic pressure parameter, Pa S = aerodynamic reference surface, m2 Sb = body cross-sectional area, m2 Sw = wetted body surface, mz.
5-1 INTRODUCTION
Much of the effort of the National Advisory Committee for Aeronautics (NACA) - predecessor of the National Aeronautics and Space Administration (NASA) - was devoted to the investigation of aerodynamic forces and moments. The outputs of most of these tests and studies are in the form of aerodynamic coefficients related to very detailed descriptions of the geometry and motion of the vehicle and of the flow conditions.
5-2 AERODYNAMIC COEFFICIENTS
Analytical equations and data for estimating aerodynamic forces and moments have been developed, partly on theory and partly on wind tunnel measurements on a wide variety of model configurations and flow conditions. This work included extensive wind tunnel testing and analytical studies aimed at providing methods for evaluating the variation of forces and moments with changes in flow type and changes in vehicle configurations (Ref. 2).
5-2.1 APPLICATION OF AERODYNAMIC COEFFICIENTS
The value of the aerodynamic force coefficient for a given body configuration is primarily influenced by the shape of the body (including any deflections of the control surface), the orientation of the body within the flow (angle of attack) and the flow conditions. The reference range takes into account the relative size of the body in aerodynamic force calculations.
5-2.2 DRAG COEFFICIENTS
For example, if the slope of the curve relating the lift coefficient to the angle of attack is given as C, of attack by CL = CLa a. For most surface-to-air missile flight simulations, the quadratic form of the parabolic polar (x =2 ) applicable.
5-2.3 LIFT COEFFICIENTS
5-2.4 MOMENT COEFFICIENTS
The instantaneous location of the center of mass xcm depends on the shape and combustion characteristics of the propellant grain. These equations include the torque 1., the aerodynamic contribution of which is calculated from the torque coefficient C1 using Eq.
5-3 AERODYNAMIC STABILITY DERIV- ATIVES
5-3.1 LIFT CURVE SLOPE
5-32 STATIC PITCH STABILITY DERIVA- TIVE
5-3.3 DYNAMIC STABILITY DERIVATIVES
The Cma derivative is very important in pitch dynamics because it contributes most of the damping of the aircraft's response to commands. A negative value of this derivative contributes to the damping of the aircraft's response to commands.
5-4 DETERMINATION OF AERODY- NAMIC COEFFICIENTS
When the direction of the effective control surface deviation causes a positive roll moment, C18 is positive. When the airframe rolls at an angular rate p, a rolling moment opposing the rotation is produced by the angular rate of the wings and fins.
5-3.4 ROLL STABILITY DERIVATIVES
If the airspeed is sufficiently high that aeroelastic effects are significant, the sign of Cmq may be positive or negative depending on the nature of the aeroelastic effects (Ref. 11). As wings and fins rotate about the longitudinal axis of the missile, individual components of angles of attack are produced by these surfaces.
5-4.1 ANALYTICAL PREDICTION
In the meantime, approximate and empirical analytical techniques provide estimates used in preliminary missile design. However, because the accuracy of the estimates is uncertain, aerodynamic estimates are always improved early in a rocket's development phase through wind tunnel testing.
5-4.2 WIND TUNNEL TESTING
For example, one method used to measure the derivatives of pitch damping is to place the model in a conventional wind tunnel so that the model is allowed to oscillate in pitch. Therefore, a less conventional wind tunnel design was used to measure the damping derivative Cmq.
5-4.3 FLIGHT TESTING
Wind tunnel data is not always as accurate as might be desired, and the results must be interpreted by experienced analysts. It is essential to understand the sources, significance, and correction of errors in the interpretation of wind tunnel test results.
5-5 ATMOSPHERIC PROPERTIES
The simulation has provisions for table lookup of the atmospheric data corresponding to the altitude of the simulated missile at each computational step. The standard height corresponding to the ambient density actually experienced is called the density height.
5-6.2 COEFFICIENTS
5-6.3 SIMPLIFICATIONS
5-7 ROLLING AIRFRAME CONSIDER- ATIONS
Since the lift coefficient varies with the roll orientation of the fins relative to the plane of the missile maneuver, the lift coefficient is often averaged over all roll angles.
5-7.1 ROLLING REFERENCE FRAMES
5-7.2 NEGLECTING LOW ROLL RATES
5-7.3 AVERAGING AERODYNAMIC COEFFI- CIENTS
One method to deal with this problem in a simulation is to average the aerodynamic coefficients over all roll angles. Typically, wind tunnel data is measured with one set of fins in the same plane as the angle of attack—Ø = O deg for an angle of attack in the xz plane—and with the body rotated so that the plane of the angle of attack is midway between the sets of fins ( Ø = 45 degrees).
5-7.4 MAGNUS EFFECT
Common practice is to prepare input aerodynamic coefficient data by averaging the values over the two roll angles.
5-7.5 MODULATION OF FIN DEFLECTION ANGLE
BIBLIOGRAPHY AERODYNAMICS
FLIGHT TEST WIND TUNNELS
ROLLING AIRFRAME
MISSILE PROPULSION
6-0 LIST OF SYMBOLS
6-1 INTRODUCTION
6-2 TYPES OF PROPULSION
6-2.1 SOLID PROPELLANT ROCKET MOTOR
In addition to the thrust history, histories of the mass of the missile and the distribution of mass are needed. The mass distribution is defined by the location of the center of mass and the moments of inertia.
6-2.2 AIR-AUGMENTED ROCKET MOTOR
The missile mass at any time is used in the simulation to calculate missile acceleration (Eq. 4-37). The center of mass is used to calculate the aerodynamic moments (Eq. 5. 12), and the moments of inertia are used to calculate the rotational response of the missile (Eq. 4-45).
6-2.3 LIQUID PROPELLANT ROCKET MOTOR
Methods used to model solid propellant rocket motors in missile deterrence simulations are discussed in par.
6-2.4 TURBOJET ENGINE
6-2.5 RAMJET ENGINE
6-3 SIMULATION OF THRUST AND MASS PARAMETERS
6-3.1 GRAIN TEMPERATURE
6-3.2 REFERENCE CONDITIONS
6-3.3 MASS CHANGE
6-3.4 TUBE LAUNCH
6-4 PROPULSION FORCE AND MOMENT VECTORS
If the thrust line is misaligned from the rocket axis by angles y] and y2, as shown in Fig. Quarterly Progress Report, 1 April-30 June 1966, AFRPL-TR-66-193, Air Force Rocket Propulsion Laboratory, Research and Technology Division, Air Force Systems Command, Edwards Air Force Base, CA, August 1966.
MISSILE AND TARGET MOTION
7-0 LIST OF SYMBOLS
Methods of determining the values of gravitational, aerodynamic, and propulsive forces to substitute into these equations of motion are given in Chapters 4, 5, and 6. Integration of the differential equations of motion yields the translational and rotational velocity and position history of the vehicle throughout the simulated flight.
7-2 COORDINATE SYSTEMS
The equations of motion apply to any vehicle, including the missile and the target. The translational and rotational equations of motion of the vehicle are usually solved in the body coordinate system if the simulation has five or six degrees of freedom.
7-3 MISSILE MOTION
The motions of missiles and targets are calculated in a simulation using the equations of motion from Chapter 4, using values of the various forces acting on the vehicle. In three degrees of freedom simulations, rotational motion is not explicitly computed, and the translational equations of motion are most easily solved in the Earth reference frame.
7-3.1 INITIAL CONDITIONS
The equations are usually simplified for target motion calculations and can also be simplified for missile motion calculations, depending on the objectives of the simulation. In simulating target motion, the goal is to provide the means to study the flight response of missiles to the target's flight characteristics.
7-3.2 MISSILE FLIGHT
The angle of attack and sideslip angle required to look up the coefficients in the table are calculated using . In a three-degree-freedom simulation, the components of the gravity vector Fg are obtained directly from Eqs.
7-4 TARGET MOTION
7-4.2 MANEUVERING FLIGHT
Thus, the maneuver load factor is the lift acceleration, expressed in units of the acceleration due to gravity (called g's). The maximum occupancy rate and the period of the maneuver are set by input to the simulation.
The roll attitude (bank angle) of the target is often required in a simulation to determine the attitude of the target reference frame. If the first-order transfer function is not used, e.g. when the cosine weave is simulated, ATach in Eq.
7-5.1 RELATIVE POSITION
The time constant is selected and entered by the simulation user to provide a realistic representation of the time it takes the target to change direction of the maneuver. 7-33, however, is a convenient method used to calculate the instantaneous yaw angle without having to calculate the instantaneous load factor given by.
7-5.2 RELATIVE ATTITUDE
In simulations with a ground-based target tracker, the position of the target relative to this tracker is also determined by Eqs. 7-36 and 7-37, in which the Rearth variable is now defined as the vector from the ground tracker to the target.
7-5.3 MISS DISTANCE
When the miss distance is defined as the closest approach from the center of mass of the missile to the center of mass of the target, the closest approach occurs when the range vector R reaches a minimum. The missile's closest approach to the target usually occurs between the last two discrete computation times in digital simulations, as shown in Figure 2.
BIBLIOGRAPHY COORDINATE FRAMES
Crude criteria such as the kill radius are useful in studies of the relative effectiveness of alternative missile designs and of countermeasures, but they should not be regarded as accurate estimates of the true effectiveness of any given missile. Beaty, Simulation of the Flight of an Air Defense System Short Range Missile Before Radar Acquisition, Final Report, U.S. Army Research Office, Engineering Experiment Station, Auburn University, Auburn, AL, April 1977.
SIMULATING VEHICLE MOTION
GUIDANCE AND CONTROL MODELING
8-0 LIST OF SYMBOLS
8-1 INTRODUCTION
A missile seeker-in-the-loop simulation uses an actual hardware seeker and generates physical electromagnetic radiation for the seeker to see. A missile seeker electronics-in-the-loop simulation uses hardware from the electronic guidance and control circuitry, but does not generate actual physical radiation.
8-2 GUIDANCE MODELING
In missiles with infrared (IR) seekers, the navigation relationship can be determined intrinsically by the electrical, mechanical, and aerodynamic design of the search and control system, rather than by setting a gain in the autopilot. Application of hardware-in-the-loop is divided into two general categories, i.e. missile-seeker-in-the-loop simulations and missile-seeker-electronics-in-the-loop simulations.
8-2.1 SEEKER MODELING
The response weighting function takes into account all other factors that affect the relationship between the tracking speed of the requested seeker and the position of the signal source within the viewfinder's field of view. In an actual IR seeker, the commanded tracking speed is in the form of the seeker head gyro spin voltage.
8-2.2 GUIDANCE PROCESSOR MODELING
The usual approximation is to substitute the rocket axis for the direction of the rocket velocity vector in the guidance equation. Multiplying the system gain by the search angular velocity gives the steady state lateral acceleration of the missile.
8-2.3 AUTOPILOT MODELING
To simulate the guidance process when the system gain curves are unknown, a detailed simulation of the entire guidance and control sequence of events is required - the seeker output through the control servos and fin deflections to the aerodynamic response. 7-18 all the effects that the autopilot has on the natural frequency and damping ratio of the missile's response characteristics, and by including the commanded acceleration limit.
8-2.4 GROUND-BASED GUIDANCE MODEL- ING
This error is defined as the perpendicular distance from the missile to the centerline of the guide beam. Define a unit vector ugl to represent the direction of the guide line, i.e. the center line of the guide beam.
8-3 CONTROL SYSTEM MODELING
In this control system block diagram, only the servo is represented by a transfer function. 8-11(C) illustrates the use of a single transfer function to represent the control system consisting of both the servo and the feedback loop.
8-4 HARDWARE SUBSTITUTION
In this case, the input to the control servo is the difference between the output and the input to the control system. By a derivation similar to that given for the open-loop system, the transfer function for the entire closed-loop control system, not just the servo as in Fig.
8-4.1 DESCRIPTION OF MISSILE HARD- WARE SUBSTITUTION
Thus, the simulation of the missile seeker in the loop provides a high degree of realism and reliability for the simulation. 8-13 shows the form of the in-block simulation loop diagram for the loop missile search mode, and Fig.
8-4.2 SEEKER HARDWARE SUBSTITUTION
8-4.3 AUTOPILOT HARDWARE SUBSTITU- TION
8-4.4 CONTROL HARDWARE SUBSTITU- TION
Mango, “Recent Experience in Simulated Missile Flight Hardware in Terminal Homing Applications”, Proceedings of the Society of Photo-Optical Instrumentation Engineers, Optics in Missile Engineering, SPIE Vol. Strittmatter, “A Seasonal Approach to Missile Target Simulators”, Proceedings of the Society of Photo-Optical Instrumentation Engineers, Optics in Missile Engineering, SPIE Vol.
BIBLIOGRAPHY AUTOPILOT SIMULATION
Hazel, “Monte Carlo Model Requirements for Hardware-Loop Rocket Simulations,” Proceedings of the 1976 Summer Conference on Computer Simulation, Washington, DC, July 1976, p. Sutherlin, "On an Application of Hybrid Simula- tion to Antiradiation Missiles," Proceedings of the 1976 Summer Computer Simulation Conference, Washington, DC, July 1976, p.
GUIDANCE SIMULATION
Hazel, "Implementation and Validation of an AD-10 Multiprocessor in a Hardware-in-the-Loop Missile Simulation", Summer Computer Simulation Conference, Toronto, Ontario, Canada, July.
TRANSFER FUNCTIONS
Brown, ballistisk missil- og rumfartøjssystem, John Wiley & Sons, Inc., New York NY, 1961. Smith, Mathematical Modeling and Digital Simulation for Engineers and Scientists, John Wiley & Sons, Inc., New York, NY, 1987.
SCENE SIMULATION
9-1 INTRODUCTION
9-2 SCENE ELEMENTS
9-2.1 TARGET
Sun glare from various surfaces of the target aircraft can affect the performance of the EO seeker. At long range, the receiver of scattered RF energy sees the target as a single-point scatterer.
9-2.2 SCENE BACKGROUND
In fact, it need not be limited to the physical range of the target and can be an important fiction of the time outside the target. This aiming drift, called glint, is perceived by the seeker as target movement and is a particularly important parameter in missile miss range investigations with RF seekers.
9-2.3 COUNTERMEASURES
At shorter distances, the apparent reflection center does not coincide with the target center. Changes in the target aspect with respect to the radar can cause the apparent center of radar reflections to wander from one point to another.
9-2.4 ATMOSPHERIC AND RANGE EFFECTS
Decoy-to-target trajectories are entered into the simulation as function tables or calculated by a flight simulation computer. Decoy release times and decoy trajectory parameters are transferred from the simulation computer to a scene simulator (physical or mathematical) in which the decoy signal is generated and assigned the required motion relative to the projectile seeker.
9-3 METHODS OF SCENE SIMULATION
The missile can track the decoy and allow the target to escape the field of view. The decoy intensities as functions of time - and the attenuation of the decoy signals - are also controlled by the flight simulation computer, and the appropriate parameters are passed to the scene simulation for controlling the decoy signal intensities presented to the simulation seeker.
9-3.1 MATHEMATICAL SCENE SIMULA- TION
9-3.2 PHYSICAL SCENE SIMULATION
During a simulation, RF signals are generated in real time and sent to the seeker mounted on a three-axis flight table (missile-positioning unit (MPU)). When the seeker is semi-active, radar pulses are emitted from the simulated target as if it were illuminated by an illuminator radar.
9-3.3 ELECTRONIC SCENE SIMULATION
9-4 EQUIPMENT FOR SCENE SIMULA- TION
9-4.1 ELECTRO-OPTICAL SCENES
Each scene in the TIS represents a target at a specific range and aspect angle relative to the missile. The success of this technique depends on the speed of the TIS and the host computer.
9-4.2 RADIO FREQUENCY SCENES
For each computation time step, a pair of scenes selected from memory are interpolated by the TIS to produce a scene corresponding to the range and aspect angle of the target at that step. Typical RF Scene Simulation Configuration (Adapted from Ref. 9) The RFSS operates over a frequency range of 2 to Levels of Fidelity.
BIBLIOGRAPHY SCENE SIMULATION
Strittmatter, "A Seasoned Approach to Missile Target Simulators", Proceedings of the Society of Photo-Optical Instrumentation Engineers, Optics in Missile Engineering, SPIE Vol 133, Los Angeles, CA, januar 1978, s. Atherton, "A Missile Flight Simulator for Infrared Countermeasures Investigations”, Proceedings of the Society of Photo-Optical Instrumentation Engineers, Optics in Missile Engineering, SPIE Vol 133, Los Angeles, CA, januar 1978, pp.
TARGET SIGNATURE
IMPLEMENTATION
So far, the handbook has focused on the equations and algorithms that need to be programmed for a computer to construct a rocket flight simulation. This chapter covers (1) the selection of a computer system suitable for implementing the equations and algorithms, (2) the selection of a computer language to develop the simulation, (3) the application of numerical techniques required for digital solutions, and (4) special instructions to run missile flight simulations that include missile hardware in the simulation loop.
10-0 LIST OF SYMBOLS
10-1 INTRODUCTION
The differential equations used to model missile flight are sets of nonlinear differential equations with time-varying coefficients that cannot be solved analytically. Since the roots are matched, the difference equation cannot become unstable, provided that the differential equation is stable, regardless of the integration step size.
10-2 SELECTION OF COMPUTERS
One or more Compute Engines (CEs), using Motorola MC88110 microprocessors, are available to perform the non-hardware-in-the-loop portions of the simulation. There may be cases where compromises must be made in the simulation model in order to meet treatment requirements.
10-2.1 ASSESSING COMPUTER PROCESS- ING SPEED (BENCHMARKS)
It is important to make these compromises with minimal impact on the missile simulation objectives. Numerous simplifications and approximations have been discussed in previous chapters of this handbook that maintain a degree of fidelity in the missile simulation.
10-2.3 SECONDARY CONSIDERATIONS
Peripherals and input/output devices for the simulation computer system include control terminals, real-time display units, two eight-channel strip chart recorders, a line printer, and various disk drives. It is important to have enough ports for all the peripherals planned for the system.
10-3 SELECTION OF COMPUTER LAN- GUAGES
EAI developed the Starlight Interactive Simulation Language (SISL) to program the parallel part of the simulation. Standard compilers can be used for user-supplied FORTRAN, C, or Ada source code that is independently linked to DIAC to run alongside SISL code compiled and linked by Starlight Executive (SX) .
10-4 TECHNIQUES
The Starlight compiler then directly maps the SISL source into parallel machine code without the intermediate step of converting the code into sequentially executed FORTRAN or C. EAI claims that this direct, efficient conversion is one of the key reasons why the Starlight computer simulates high speed.
10-4.1 NUMERICAL SOLUTION OF DIFFER- ENTIAL EQUATIONS
One such rule (Ref. 12) is that if the numerical value of the quantity. A k-step difference equation uses the values of the dependent variable at the first k preceding steps.
10-4.2 DIGITAL SOLUTION OF TRANSFER FUNCTIONS
10-2(A) shows the response of the transfer function to a step input command applied at time zero. When the input is a unit step, the exact solution of the transfer function of Eq.
10-4.3 SPECIAL INSTRUCTIONS FOR HARD
When the sampling rate is reduced to about six times the damped natural frequency, the aliasing effect begins to introduce errors as shown in Fig. With a sampling rate of only three times the damped natural frequency, the aliasing error is pronounced, as shown in Fig. .
WARE-IN-THE-LOOP SIMULATIONS
Hamming, Numerical Methods for Scientists and Engineers, 2nd Ed., McGraw-Hill Book Company, Inc., Nju Jork. Rabinowitz, A First Course in Numerical Analysis, 2nd Ed., McGraw-Hill Book Company, Inc., Nju Jork, NY, 1978.
VERIFICATION AND VALIDATION
11-1 INTRODUCTION
11-2 VERIFICATION
11-3 VALIDATION
11-3.1 LEVELS OF CONFIDENCE
