In 1993, while teaching at the United States Military Academy, I was engaged in a post-Desert Storm reliability analysis of the Patriot missile system. My understanding of the dynamics of missile flight was limited, so I endeavored to educate myself. From 1994 through 2007, I began working on missile defense studies for the Department of Defense (DoD). In 2008, I began work for the Missile Defense Agency (MDA) on verification and validation of missile flight simulations and threat missile modeling. Over the course of the last five years, I have been compiling what I have learned into this book.
Chapter 1 provides background information is furnished regarding the need for missile flight simulations, and brief descriptions are given of their character, purpose, and implementation. The purpose, scope and organization of the book are described.
Chapter 2 describes in general terms the missile subsystems and functions that are important to the simulation of missile flight. These include in section 2-2 the subsystems of the physical missile-seeker autopilot, control, warhead and fuze propulsion, and airframe; in section 2-3 the various types of guidance; and in section 2-4 specific considerations of missile launch that are applicable to missile flight simulation.
An overview of missile flight simulation is given in Chapter 3. The four primary objectives of flight simulations-establishing requirements, designing and operating missiles, assessing missile performance, and training—are discussed. The essentials of simulating missile guidance and control and the motions of the missile and target are described; a discussion of the role of coordinate systems is included. Appropriate levels of simulation detail, to match simulation objectives, are discussed.
Chapter 4 begins development of the specific mathematical techniques employed in missile flight simulations. The approach discussed in the previous chapters includes calculating the forces and moments acting on the missile and substituting them into the equations of motion to yield vehicle accelerations. Chapter 4 expands on this approach by beginning with a more general statement of Newton’s second law of motion and proceeds through development of equations for translational and rotational motions, for expressing these equations relative to rotating reference frames, and for handling the gyroscopic moments of internal rotors.
Simulation of missile flight requires calculation of the forces and moments that act on the missile. The particular forces and moments contributed by aerodynamics are addressed in detail in Chapter 5. The various sources of aerodynamic data are discussed; representation of aerodynamic data in the form of force and moment coefficients is presented; and stability derivatives are defied. Methods and equations for employing the data in the calculation of the aerodynamic force vector F ?_A and the aerodynamic moment vector M ?_A are described. Effects of atmospheric properties-density, pressure, viscosity, and speed of sound---and of airflow parameters—Mach number and Reynolds number—on the aerodynamic forces and moments are discussed. Methods used to simplify the calculations are presented and special methods applicable to rolling airframes are described.
Chapter 6 briefly describes various types of missile propulsion systems and gives the detailed methodology for determining these force and moment vectors at each computational time step for solid propellant rocket motors. Consideration is given to the effects of initial propellant grain temperature, ambient atmospheric pressure, changes in mass and moments of inertia, and tube launch.
Chapter 7 describes mathematical techniques employed in missile flight simulations to calculate the motion of both the missile and the airborne target. Methods of combining the gravitational, aerodynamic, and propulsive forces (described in Chapters 4, 5, and 6) with the vehicle equations of motion (described in Chapter 4) are presented. Variations in the methodology for treating different numbers of degrees-of-freedom are described; and the equations for simulating simple target evasive maneuvers are given. A method of calculating the closest approach vector and the time of closest approach is provided.
Methods of simulating the guidance and control functions of a missile are described in Chapter 8. Since simulation methodology depends on the type of missile guidance system being simulated and on the objectives of the simulation itself, specific computational methods are given to meet different modeling requirements. The guidance and control functions considered are seekers, guidance processors, autopilots, and control systems.
Methods of modeling optical and radio frequency (RF) seekers are given for a wide range of fidelity levels. Lower levels of seeker fidelity are represented by perfect tracking and by accurate tracking but with a time lag. An intermediate fidelity seeker model—useful for analyzing the effects of multiple track points within the seeker field of view—is described. And for simulations that require the highest seeker fidelity, employment of actual missile seeker hardware in the simulation loop is described.
Equations are presented for modeling the guidance system processor at various levels of fidelity for both missile borne and ground-based target trackers. The types of guidance laws considered are proportional navigation, command, and command to line-of-sight. A method of employing a transfer function to simulate the control system response to guidance commands is described.
Missile hardware-in-the-loop simulations are discussed for two basic approaches to hardware substitution—missile seeker in the loop and missile electronics in the loop. Also employment of actual missile autopilot and control system hardware in the simulation loop is described. A checklist of special considerations of laboratory procedures for using hardware in the simulation loop is provided.
Requirements for simulating target scenes are described in Chapter 9. Three types are addressed: mathematical scenes for purely mathematical flight simulations, physical scenes for simulations that use seeker hardware in the simulation loop, and electronic scenes for simulations that use seeker electronic hardware in the simulation loop. Methods and equipment used to simulate the scene elements —target, background, and countermeasures—are described for both optical and radio frequency (RF) sensors.
Chapter 10 addresses (1) selection of a computer system suitable for implementing the equations and algorithms, (2) selection of a computer language to develop the simulation, (3) application of numerical techniques required for digital solutions, and (4) special instructions to operate missile flight simulations that contain missile hardware in the simulation loop.
Chapter 11 gives an overview of the processes required to ensure that a simulation represents actual missile performance to an acceptable level of confidence. Usage of the terms associated with verification and validation within the simulation community are discussed; and the need to tailor the validation effort to meet simulation objectives is emphasized, A range of possible methods of validating simulations is presented.
Chapter 12 employs an example to illustrate how the level of detail in a simulation is selected to satisfy simulation objectives, and to show how to synthesize a complete flight simulation by combining the subsystem models. MATLAB® and SimulinkTM are used to implement the model and execute the necessary simulation runs. Simulation results are presented and analyzed.
