Subsystem Models

The equations of motions are the most important part of a simulation, but by no means the most complicated ones. Their models are already in mathematical form and easily programmed. However, an aerospace vehicle consists of many more subsystems encompassing numerous technical disciplines.

The aerodynamicist provides the mathematical model of the aerodynamic forces and moments that act on the vehicle; thrust tables are generated by the propulsion expert; the control engineer designs the flight control system; and INS, sensors, and seekers are modeled by the appropriate experts.

We first discuss the modeling of the aerodynamics of aircraft, hypersonic vehi­cles, and missiles. The approach differs from the five-DoF implementation because now the aerodynamic forces and moments are untrimmed and depend on the con­trol surface deflections. I shall acquaint you with the aerodynamic models of a typical aircraft, like the Fighting Falcon, a NASA hypersonic vehicle, and an air- to-air missile. Each model represents a different approach. The first two, with their planar airframes, use the Cartesian incidence angles of angle of attack and sideslip angle. The missile is modeled with the polar incidence angles of total angle of attack and aerodynamic roll angle.

For propulsion you can reach back to Secs. 8.2.4 and 9.2.2, where I discussed rocket motors, subsonic turbojets, ramjets, and scramjets. Those models can also be used in six-DoF simulations. If you want to build a detailed engine model however, you need to consult with propulsion experts and the references that they suggest.

In six-DoF simulations autopilots and flight control systems are represented by their full-up designs. No simplifications are required as in the pseudo-five-DoF simulations. When introducing you to six-DoF autopilots, I provide fairly simple
structures. They are based on pole placement techniques that have the advantage of adapting to varying flight regimes.

The actuators execute the autopilot commands and turn them into control surface deflections. For aircraft we deal with aileron, elevator, and rudder actuators and in some cases with elevons and rudder. Missiles most likely have four control surfaces with four actuators. Their autopilot commands roll, pitch, and yaw, and the signals are divided up for the four surface actuators. Besides aerodynamic control, I also give you a model of thrust vector control for agile missiles.

Then we take on the subsystems of navigation and guidance. The INS is an inte­gral part of any modern aerospace vehicle. I derive the equations of space stabilized and local-level systems and provide you with a nine-state error formulation.

Earlier you were introduced to proportional navigation. I expand on that discus­sion and derive the compensated PN and advanced guidance law (AGL). Whereas PN was formulated in inertial LOS rates, AGL uses differential velocity and dis­placement, expressed in inertial coordinates, as navigation input.

Finally, I augment the seeker discussion of Sec. 9.2.5 with an imaging IR seeker. We will investigate the intricate modeling of focal plane arrays, and mechanical and virtual gimbals. We also address noise and biases that corrupt the signals.

These subsystems are intended to serve as examples for modeling important components of aerospace vehicles. Although complete in themselves, they do not represent the most sophisticated models that you will encounter in six-DoF simulations. Regard them as instructional material that will get you started, guiding you from concepts to mathematical models and code implementation. You will find most of the subsystems, discussed in this section, coded up in the six-DoF simulations FALCON6, GHAME6, and SRAAM6, available on the CADAC CD.