Simulation of Aerospace Vehicles

Having mastered the skills of modeling, you are prepared to face the challenge of simulation. The venture is not of a theoretical nature but one of encyclopedic knowledge of the subsystems that compose a flight vehicle. Who can claim to be an expert in aerodynamics, propulsion, navigation, guidance, and control all together? To be a good simulation engineer, however, you must be at least acquainted with all of these disciplines. In Part 2,1 will expose you to these topics at increasing levels of sophistication. As we proceed from three – to six-DoF simulations, the prerequisites increase. You may have to do some background reading to keep up with the pace. Yet, let me also caution you that my treatment of subsystems is incomplete and that you must foster good relationships with experts in these fields to gain access to more detailed models.

Seldom will you be called to develop a simulation ex nihilo. Somebody has trodden that path before, and you should not hesitate to follow in his footsteps. At least pick up the outer shell, consisting of executive and input/output handling. A good graphics and postprocessing capability is also important. Then you can fill in the subsystem models and build your own vehicle simulation. But scrutinize the borrowed code carefully. Once you deliver your product, then you will be responsible for the entire simulation.

There are quit a few simulation environments you can choose from. They are categorized by programming language. Most mature simulations are based on FORTRAN with many years of verification and validation behind them. A new crop of symbolic simulations has emerged, e. g., VisSim™, MATLAB®, and Simulink®, which use interactive graphics for modeling and code generation for executable C programs. That development has spawned another trend, namely pro­gramming simulations in C++ directly, the language of choice for most developers today.

I seized on the enormous flexibility of C++ and created a new aerospace sim­ulation environment called CADAC++ (Computer Aided Design of Aerospace Concepts in C++). Over the years it grew from simple three-DoF simulations to sophisticated six-DoF hypersonic vehicle models. Appendix C details the source code that is available in my three AIAA Self Study CD-ROMs.

However, CADAC in its original FORTRAN makeup is still the favored simu­lation environment for this book because of its straightforward implementation. It consists of three-, five-, and six-DoF aerospace simulations. They are provided on the CADAC CD-ROM, which also includes plotting and analysis programs. For a quick start, follow the CADAC Primer in Appendix В.

Table 1.1 lists the prototype simulations. They encompass a broad selection of models from three to six DoF, from flat to elliptical Earth, from drag polars to full aerodynamic tables, from rocket to ramjet propulsion, and from simple to complex flight control systems. The number of lines of code gives you an idea of the size of the subroutines that model the subsystems of the vehicles.

Because practice makes perfect, you should attempt to carry out the projects at the end of Chapters 8-10. The required data are on the CADAC CD. As you exercise your modeling skills, you add to you repertoire the simulations listed in Table 1.2: SST03 highlights the importance of trajectory shaping; AGM5 is an adaptation of the AIM5 simulation for the air-to-ground role; FALCON5 combines trimmed FALCON6 aerodynamics with the navigation aids of CRUISE5; and AGM6 is a detailed air-to-ground missile.

Table 1.1 Prototype simulations based on the CADAC architecture

DoF

Name

Type

Earth model

Lines of code

Three

GHAME3

NASA hypersonic vehicle

Spherical and rotating

1153

ROCKET3

Three-stage-to-orbit rocket

Spherical and rotating

1048

Five

AIM5

Air intercept missile

Flat

1598

SRAAM5

Short range air-to-air missile

Flat

5029

CRUISE5

Subsonic cruise missile

Flat

5367

Six

SRAAM6

Short range air-to-air missile

Flat

5812

FALCON6

F-16 aircraft

Rat

1339

GHAME6

NASA hypersonic vehicle

Elliptical and rotating

4726

All of these simulations support the discussion of subsystem modeling, although the derivations in Chapters 8-10 are self-contained and apply to any simulation environment. We shall revisit the equations of motion, cover many aerodynamic modeling schemes, discuss all types of propulsion, design autopilots, and pro­vide navigation and guidance aids where needed. Each chapter is devoted to one particular type of simulation.

The eighth chapter, “Three-Degrees-of-Freedom Simulation,” models point – mass trajectories. The three translational degrees of freedom of the c. m. of the vehicle are derived from Newton’s second law for spherical rotating Earth and expressed in two formats. The Cartesian equations use the inertial position and velocity components as state variables, whereas the polar equations employ geo­graphic speed, azimuth, and flight-path angles.

Here I introduce the environmental conditions, which are applicable to all sim­ulations. The three most important standard atmospheres, ARDC 1959, ISO 1962, and US 1976, are compared. The analytical ISO 1962 model wins the popularity contest for simple endo-atmospheric simulations. Newton’s law of attraction pro­vides the gravitational acceleration. The term gravity acceleration is introduced for the apparent acceleration that objects are subjected near the Earth.

Aerodynamics is kept simple. Parabolic drag polars combined with linear lift slopes describe the lift and drag forces of aircraft and missile airframes. They

Table 1.2 Simulations you can build

DoF

Name

Type

Earth model

Project

Three

SST03

Single-stage-to-orbit

Spherical and

Chapter 8

vehicle

rotating

Five

AGM5

Air-to-ground missile

Flat

Chapter 9

FALCON5

F-16 aircraft

Flat

Six

AGM6

Air-to-ground missile

Flat

Chapter 10

are expressed in coordinates of the load factor plane. We touch on all types of propulsion systems: rocket, turbojet, ramjet, scramjet, and combined cycle engines. Although simple in nature, the propulsion models are used in many simulations, from three to six degrees of freedom.

The ninth chapter, “Five-Degrees-of-Freedom Simulation,” combines the three translational degrees of freedom with two attitude motions, either pitch/yaw or pitch/bank. We make use of a simplification that uses the autopilot transfer func­tions to model the attitude angles. This feature, i. e., supplementing nonlinear trans­lational equations with linearized attitude equations, is called a pseudo-five-DoF simulation. As the examples show, it finds wide applications with aircraft and missiles.

These pseudo-five-DoF equations of motion are derived for spherical Earth and specialized for flat Earth. Because the Euler equations are not solved, the body rates are derived from the incidence rates of the autopilot and the flight-path angle rates of the translational equations. They are needed for the rate gyros of the inertial navigation systems (INS) and the rate feedback of gimbaled seekers.

Subsystems are the building blocks of simulations. I cover them at various lev­els of detail, either in Chapter 8, here, or in Chapter 10. Some of the treatment, especially aerodynamics and autopilots, is tailored to the type of simulation. How­ever, the sections on propulsion, guidance, and sensors are universally applicable. Table 1.3 lists the features available to you.

A detailed description of the AIM5 simulation concludes the chapter. It ex­emplifies a typical pseudo-five-DoF simulation. As you follow my presentation, you will discover how the angle of attack, as output of the autopilot, is used in the aerodynamic table look-up. The guidance loop, wrapped around the control loop, exhibits the key elements: a kinematic seeker, proportional navigation, and miss distance calculations. If you want to work a simple, but complete missile simulation, the AIM5 model is the place to start.

The tenth chapter, “Six-Degrees-of-Freedom Simulation,” explores the sophisti­cated realm of complete dynamic modeling. The three attitude degrees of freedom,

Table 1.3 Subsystem features discussed in Chapter 9

Subsystem

Features

Section

Aerodynamics

Trimmed tables for aircraft and missiles

9.2.1

Propulsion

Turbojet, Mach hold controller

9.2.2

Autopilot

Acceleration controller, pitch/yaw and pitch/bank Altitude hold autopilot

9.2.3

Guidance

Proportional navigation Line guidance

9.2.4

Sensor

Kinematic seeker Dynamic seeker Radars

Imaging infrared sensors

9.2.5

Table 1.4 Subsystem features discussed in Chapter 10

Subsystem

Features

Section

Aerodynamics

Models for aircraft, hyper­sonic vehicles and missiles

10.2.1

Autopilot

Rate damping loop Roll position tracker Heading controller Acceleration autopilot Altitude hold autopilot Flight-path angle controller

10.2.2

Actuator

Aerodynamic control Thrust vector control

10.2.3

Inertial navigation

Space stabilized error model Local level error model

10.2.4

Guidance

Compensated proportional navigation

Advanced guidance law

10.2.5

Sensor

HR gimbaled seeker

10.2.6

governed by Euler’s law, join Newton’s translational equations. Creating a six-DoF simulation is the ambition of every virtual engineer.

We ease into the topic with the derivation of the equations of motion for flat Earth and its expansions to spinning missiles and Magnus rotors. Afterward, we accept the challenge and consider the Earth to be an ellipsoid. An excursion to geodesy will expose you to the geodetic coordinate system and the second-order model of gravitational attraction. All will culminate with the six-DoF equations of motion for elliptical rotating Earth, complemented by the methods of quaternion and direction cosine for attitude determination.

The description of subsystems is continued from Chapter 9 and summarized in Table 1.4. Whereas aerodynamics, autopilots, and actuators are partial to six-DoF simulations, the remaining three topics of inertial navigation guidance and seeker apply also to five-DoF models. The best way to master these diverse subjects is by experimenting with simulations. You will find all features modeled at least in one of the simulations SRAAM6, FALCON6, or GHAME6.

Monte Carlo analysis is the prerogative of six-DoF simulations. Their high fi­delity, including nonlinearities and random effects, can only be exploited by a large number of sample runs, followed by statistical postprocessing. The methodology of accuracy analysis is discussed for univariate and bivariate distributions, with particular emphasis on miss-distance calculations.

Wind and turbulence is another field reserved for six-DoF models. With the stan­dard NASA wind profile over Wallops Islands and the classic Dryden turbulence model, you can investigate environmental effects on your vehicle design. Because of the stochastic nature of the phenomena, the Monte Carlo approach will yield the most realistic assessment.

The eleventh chapter, “Real-Time Applications,” gives you a taste of exploring the higher levels of the pyramid of Fig. 1.1. After having spent 10 chapters building the solid foundation of engineering simulations, you can lift your head and strive for piloted engagement simulations, hardware-in-the-loop facilities (HIL), or even participate in war games.

Flight simulators model the dynamic behavior of aerospace vehicles with human involvement. I discuss simple workstation and sophisticated cockpit simulators with their motion, vision, and acoustic environments. They find many uses, from control law development, flight-test analysis to pilot training.

When flight simulators are linked together, role playing can be staged. Blue fighters engage red aircraft, and blue and red missiles fly through the air. I will survey close-in air-to-air combat with its tactics and standardized maneuvers. Par­ticularly, I will discuss the need for high-fidelity missile models and the proper use of five – and six-DoF simulations. To simplify the validation process, a real-time conversion process is described that prepares a complete CADAC model for the flight simulator.

A HIL facility combines hardware with software and executes in real time without humans-in-the-loop. Although expensive to build, it is indispensable for flight hardware integration and checkout. Our discussion will be brief, highlighting the main elements of flight table, target simulator, and main processor. Some of the elements of HIL simulators like aerodynamics, propulsion, and the equations of motion have to be implemented on the processor. Yet seekers, guidance and control systems can be hardware or software based; it just depends on the maturity of the development program.

Finally, let the games begin! Wargaming is an old art that has experienced a renaissance of unprecedented scope. The U. S. Armed Forces try to outdo each other at their annual games: Army After Next, Global (Navy), and Global Engagement (Air Force). You will kibitz a typical scenario and see how war games are built, conducted, and evaluated. But it will hardly make you a commanding general.

We will be content building the foundational engineering simulations on which engagement, mission, and campaign models rest. This book is intended to be your guide for modeling flight dynamics and simulating aerospace vehicles, providing you with virtually everything you need to become a better virtual engineer.

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