Category Airplane Stability and Control, Second Edition

P-51 and P-39 Dive Difficulties

North American P-51 Mustang compressibility dive tests were made at Wright Field in July 1944 in response to fighter pilot reports from combat theaters. Captains Emil L. Sorenson and Wallace A. Lien and Major Fred Borsodi were the pilots in these tests (Chilstrom and Leary, 1993). The P-51 was climbed to an altitude of 35,000 feet, then power-dived to reach Mach numbers where compressibility effects on stability and control were found. Using a newly developed Mach number meter, the onset was found to be at a Mach number of 0.75. The tests were carried out to a Mach number of 0.83.

Longitudinal trim changes and heavy stick forces were encountered, but for the P-51 Mach number increases beyond 0.83 were limited by heavy buffeting. So many rivets were shaken loose from the structure that the airplane was declared unsafe, and the tests were concluded. It was on this series of dive tests that Major Borsodi saw the normal shock wave as a shimmering line of light and shadow extending spanwise from the root on the upper

surface of the wing. Skeptics were silenced only when photos taken by a gun sight camera on later flights showed the same thing.

The Bell P-39 Airacobra was dive tested a few years later at the NACA Ames Laboratory L. A. Clousing was the pilot, a flyer who had a strong interest in stability and control theory. The P-39 had a fairly thick wing; the NACA 0015 at the root, tapering to the NACA 23009 at the tip. Nose-down trim changes and increased stability were encountered in dives up to a Mach number of 0.78. Compressibility effects were a bit obscured by fabric distortion on the airplane’s elevator.

Flight Vehicle System Identification from Flight Test

There are 21 stability and control derivatives that are fairly important in the equa­tions of airplane motion. Model testing in wind tunnels provides good measurements of the important derivatives, values that serve the practical purposes of preliminary stud­ies and control system design. Stability derivative predictions from drawings do almost as well.

In spite of these well-established sources, there has been a long-time fascination with the idea of extracting stability and control derivatives as well as nonlinear and unsteady effects from flight test data on full-scale airplanes or large flying models. One argument is that automatic control system design would be on a firmer basis if it dealt with equations of motion using actual flight-measured aerodynamic forces and moments.

14.8.1 Early Attempts at Identification

Of the 21 important derivatives, one and one only can be extracted in flight tests with simple measurements and with a high degree of accuracy. This is the longitudinal control derivative Cms. Longitudinal control surface angles to trim at various airspeeds at two different center of gravity locations provide the necessary data for this extraction, the aerodynamic pitching moment balanced by a well-defined weight moment. This procedure was used to measure Cms on cargo gliders.

Obtaining Cms using a weight moment inevitably led to somewhat ill-considered plans and even attempts to do the same for the lateral and directional control derivatives. The lateral case would require dropping ballast from one wing; the directional case would require dropping wing ballast while the airplane is diving straight down.

The Special Case of the Voyager

The 1986 nonstop round-the-world flight of Burt Rutan’s Voyager brought deserved high praise for its designer and courageous flight crew. However, the account of that historic flight shows that the pilots were handicapped by the instability of the airplane at high gross weights. The Voyager is a canard configuration whose tips were joined to the main wing by parallel fuselages (Yeager, Rutan, and Patton, 1987). The statement is made, “Hand-flying Voyager required almost all our concentration, and flying it on autopilot still required most of our concentration.”

A note from Brent W. Silver, a consulting member of the Voyager design team, points to a likely cause of this problem. Apparently, bending of the Voyager’s main wing in turbulence coupled into the canard tips through the parallel fuselages. This caused canard twisting in phase with main wing bending and considerable pitch changes. The same main wing flexibility in a conventional tail-last arrangement should have not caused such a pitch reaction.

Aeroelastically Corrected Stability Derivatives

An important by-product of both the early and modern quasi-static aeroelastic methods is a set of aeroelastically corrected stability and control derivatives, such as Cma and Cms, which can be used in the ordinary equations of rigid-body motion. For example, Etkin (1972) derives the quasi-static aeroelastic contributions of symmetrical first-mode wing bending to tail and wing lift, which become ingredients in stability derivatives.

The wind tunnel provides a complete set of rigid-body aerodynamic stability and con­trol data for most new airplane projects. These data are usually corrected for quasi-static aeroelastic effects using the concept of elastic-to-rigid ratios (Collar and Grinsted, 1942). Elastic-to-rigid ratios preserve in the aeroelastically corrected data all of the nonlinearities and other specific detail of the rigid data. Finite-element methods provide a modern source of elastic-to-rigid ratios for this purpose.

Wind-tunnel tests of elastic models have also been used to obtain aeroelastically corrected stability derivatives. Still another approach is the wind-tunnel test of a rigid model that has been distorted to represent a particular set of airloads, such as those caused by a high load factor. A distorted model of the Tornado was tested in a wind tunnel, to determine aeroelastic effect on stability derivatives.

Algorithmic (Linear Optimal Control) Model

The algorithmic or linear optimal control model is partially a structural pilot model in that elements of the optimal controller can be identified with the neuromuscular lag. However, the basic distinction between the algorithmic and structural pilot models is that, except for simple problems, the pilot cannot be represented with a simple transfer function in the algorithmic case. When very simple airplane dynamics (a pure integrator) are postulated in order to be able to generate a pilot transfer function, the linear optimal control pilot

Algorithmic (Linear Optimal Control) Model

Figure 21.3 Degradations (increases) in pilot rating for tracking tasks associated with degree of pilot lead required. (FromMcRuer, AGARDograph 188, 1974)

model is found to be of high order, but with characteristics similar to the crossover model (Thompson and McRuer, 1988).

The linear optimal pilot model hasbeen used to advantage in the generation of pilot ratings (Hess, 1976; Anderson and Schmidt, 1987), the analysis of multiaxis problems (McRuer and Schmidt, 1990), and the stability of the pilot-airplane combination in maneuvers (Stengel and Broussard, 1978).