This section deals with a topic that does not belong to the theory of flight dynamics, but is of transcendent importance, overshadowing all else, when it comes to application of the theory. That topic is the use of computing machines for the solution of equations and the simulation of systems. Without them modern aerospace vehicles and missions could probably not be designed and analyzed at all within practical limitations; with them there is virtually no practical problem in flight dynamics that cannot be solved.

Except when the most extreme simplifications are employed, the equations of flight dynamics are quite complicated, and considerable labor must be expended in their solution. The labor is especially heavy during the design and development of a new vehicle, for then the solutions must be repeated many times, with different values of the parameters that define the vehicle and the flight condition. The process is more or less continuous, in that, as the design progresses, changes are constantly made, improved estimates of the aerodynamic parameters become available from wind-tunnel testing, aeroelastic calculations are refined, and testing of control-system and guidance components provides accurate data on their performance. Recalculation is required at many stages to include these improvements in the data. The number of computing man-hours involved in this procedure for a modern

t For example, when applied to flight through turbulence, q corresponds to the total distance flown, and t* corresponds to the “scale” of the turbulence.

aerospace vehicle would be astronomical if all the computations had to be performed by hand (i. e. with slide rule or desk computer).

In addition to merely making it possible to carry out the minimum amount of analysis that is essential to the achievement of a successful design, the great speed and flexibility of computing machines have led to other important advantages. With them it is feasible to conduct elaborate design studies in which many parameters are varied in order to optimize the design, i. e. to find the best compromise between various conflicting requirements. Another advantage is that the analysis can be much more accurate, in that fewer simplifications and approximations need be made (e. g. more degrees of freedom can be retained).

Among the most important points in this connection is the possibility of retaining nonlinearities in the equations. Adequate analytical methods of dealing with nonlinear systems either do not exist or are too cumbersome for routine application. By contrast, computing machines permit the intro­duction of squares and products of variables, transcendental functions, backlash (dead space), dry friction (stick-slip), experimental curves, and other nonlinear features with comparative ease. They go even further, in making possible the introduction into the computer setup of actual physical components, such as hydraulic or electric servos, control surfaces, human pilots, and autopilots. This technique is, of course, superior in accuracy to any analytical representation of the dynamic characteristics of these elements. The ultimate in this type of “computing” involves the use of the whole airplane in a ground test, with only the airframe aerodynamics simulated by the computer. A human pilot can be incorporated in such tests for maximum realism. A related development is the flight simulator as used for pilot training and research on handling qualities (see Chapter 12). It is basically a computer simulation of a given airplane, incorporating a replica of the cockpit and all the controls and instruments. The pilot “flying” the simulator experiences in a more or less realistic fashion the characteristic responses of the simulated vehicle. Such simulators or trainers have been used to great advantage in reducing the flight time required for pilot training on new vehicle types.

Digital machine computation is, of course, part of the training of all engineering students, and we assume the necessary background in that sub­ject. Analog computation however is not so universally taught, and many students who come to the study of flight dynamics have had no prior ex­perience with it. These we refer to refs. 2.6, 2.7, and 2.12. As a further aid, one example of analog computation is presented rather fully in Sec. 10.2.

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