Category Airplane Stability and Control, Second Edition

Principal Axis Inclination Instability

Lateral-directional dynamic instability due to nose-down inclination of the princi­pal axis is not strictly a high Mach number or compressibility phenomenon. However, this type of instability is linked to high-speed flight, and so it is included in this chapter.

The symmetric principal axis is defined as that airplane body axis in the plane of sym­metry for which the product of inertia Ixz vanishes. Mathematically, Ixz = f xz dm, where x and z are the X – and Z-axis coordinates of each elementary mass particle dm. Weights high on the vertical tail, such as a T-tail, cause the principal axis to be inclined nose-downward with respect to normal body axes.

A nose-down inclination of the principal axis with respect to the flight path desta­bilizes the lateral-directional or Dutch roll oscillation (Sternfield, 1947). Actual lateral – directional dynamic instability due to a nose-down inclination was encountered dramati­cally in May 1951 by the NACA test pilot Bill Bridgeman. This was in a series of flight tests of the Douglas D-558-2 Skyrocket research airplane. In tests reaching a Mach number of 1.79 serious rolling instability occurred during pushovers after rocket-powered steep climbs. The principal axis inclination to the flight path becomes quite nose-down during pushovers.

The test team evidently failed to connect the rolling instability with the principal axis effect and concluded that even higher speeds could be reached safely. Bridgeman was asked to nose over from the climb to a very low factor of 0.25, in an effort to reach a Mach number of 2.0. According to Richard Hallion (1981):

the Skyrocket rolled violently, dipping its wings as much as 75 degrees. He cut power, but the motions, if anything, became even more severe. Finally he hauled back on the control column, for the Skyrocket was in a steep dive and getting farther and farther away from the lakebed. The plane abruptly nosed up and regained its smooth flying characteristics, and he brought it back to Muroc.

However, concerns about Dutch roll instability due to principal axis nose-down inclina­tion have been eliminated by the almost universal use of yaw damping stability augmentation on high-speed airplanes.

1948 and 1966 NACA and NASA Test Series

Robert Gilruth’s codified requirements for satisfactory flying qualities of 1941 opened the way to apply flying qualities technology to the safe airplane problem. Paul A. Hunter made the first NACA flying qualities measurements specifically on personal-owner airplanes in 1948. This was followed by a second test series on light airplane flying qualities (Barber, Jones, Sisk, and Haise, 1966).

The seven light airplanes tested in 1966 were bigger, heavier, and more complex than the group of five looked at in 1948. Four of the seven were twin-engined; the single-engine ships were the straight and vee-tailed Beech Bonanza and a 285 HP Cessna Skylane RG. In keeping with NASA’s practice at that time, data presented are not identified as having come from specific airplanes.

Reported flying qualities problems ranged from rather trivial trim change difficulties to more serious issues. As in the case of the Spitfire and DC-3 (Chapter 3), static lon­gitudinal instability was present for some of these airplanes within their normal loading ranges, especially with flaps down and high power settings. Bobweights and downsprings provided stable force gradients in some cases, without improving stick-fixed stability. Low Dutch roll damping reduced the accuracy of instrument approaches in turbulence (Figure 15.4).

Dangerous stalling characteristics were encountered in the tests. Quoting from the Barber report:

1948 and 1966 NACA and NASA Test Series

Figure 15.3 The 1940 ERCO Ercoupe, as first produced. (From Weick, From the Ground Up, 1988)

Two of the aircraft tested have unacceptable power-on stall characteristics in the landing configuration. The lateral-directional trim changes of one aircraft show that the addition of power introduces a left yawing moment and that the pilot must use full right rudder to maintain heading when near the stall speed. The large yawing moment due to power coupled with the lack of rudder authority causes the aircraft to encounter an uncontrollable left roll/yaw motion at the stall. This motion places the aircraft in a spin that requires 600 to 1200 feet of altitude for recovery. All of the evaluation pilots exceeded the gear and flap placard speeds when recovering from this spin. Another aircraft has a rapid left rolloff in the power-on accelerated stall with landing flaps extended. The rolloff is difficult to stop in less than 60 to 70 degrees of left bank without anticipation and instantaneous recovery control on the part of the pilot. Such a stall may occur when a pilot tightens his final turn in the landing pattern to prevent overshooting the runway. From a left turn, the attendant rolloff, on occasion, proceeded to a nearly inverted attitude that required 200 to 300 feet of altitude to recover.

One is left to wonder how those two airplanes ever got to be certified as airworthy by the Federal Aviation Administration.

Wind, Body, Stability, and Principal Axes

One of the most distressing experiences for beginning stability and control en­gineers is to be faced with at least four alternate sets of reference axes for the equations of airplane motion. The original Bryan set, called body axes, is perhaps the most easily

Wind, Body, Stability, and Principal Axes

Figure 18.6 Representative lateral-directional stability boundaries. Spiral and directional divergence boundaries are given, along with approximations for Dutch Roll period and damping. The airplane relative density і is used in the chart coordinates. (From Zimmerman, NACA Rept. 589, 1937)

grasped. Orthogonal reference axes are fixed in the airframe as if they were painted on, remaining in place through all subsequent motions. To be fair, even body axes can migrate with respect to the airframe, since the most common form has its origin at the airplane’s center of gravity, which shifts about with different loadings.

Body axes have the practical virtue that the variables of motion that are calculated, such as the linear and angular velocities, are easily related to the readings of flight instruments, which are, after all, also fixed to the body. However, in the early days of stability and control analysis, there were advantages to wind axes (Zimmerman, 1935).

In wind axes, the forward or X-axis points into the wind during the entire motion, rotating about the center of gravity with respect to the airframe. The independence of translatory and rotational motions allows this to happen without affecting the calculation of pitching motions. An advantage of wind axes is that the X and Z forces are the exact negatives of the familiar drag and lift forces presented in wind-tunnel test reports and used in airplane performance calculations.

Stability axes came into the picture in the 1940s, as a device to simplify calculation of small-perturbation airplane motions. Stability axes are a special set of body axes. The X stability axis points into the relative wind in the equilibrium flight that precedes the disturbed motion, but remains fixed in the body during the calculated motions around equilibrium. All that is accomplished by stability axes is the elimination of a few terms in the equations that include initial angle of attack. With the advent of powerful new digital computers stability axes have become mostly a curiosity, except for the fact that the primed derivatives mentioned in Sec. 2 have their basis in stability axes. Duane McRuer notes that

Primed derivatives based on stability axes often have a remarkably simple connection with the basic motions of the aircraft…. [For example] the square of the Dutch roll undamped natural frequency is usually given to a high degree of accuracy by N^…. stability axes are appropriate for determining the characteristic modes [of motion] and their predominant constituents.

To complicate things, the term stability axes sometimes has quite another meaning than that of a special set of body axes for flight dynamics studies. Wind-tunnel data are quite often produced in what are called stability axes, but for clarity should be named wind-tunnel stability axes. The Z-axis is in the plane of symmetry and normal to the relative wind; the X-axis is in the plane of symmetry and is normal to the Z-axis; the Y-axis is normal to both X – and Z-axes.

Principal axes are another curiosity in present-day practice, since they are used only to eliminate the product of inertia terms in the equations of motion. As with stability axes, principal axes have been obsoleted by powerful digital computers. A few added terms in the equations seem to add nothing to computing time.

The hybrid case in which wind axes are used for the three force equations and body axes for the three moment equations can be found in some simulations. The first hybrid application the authors are aware of was made by Robert W. Bratt at the Douglas Aircraft Company’s El Segundo Division, about 1955, in connection with inertial coupling studies. A more recent example of hybrid axes is NASA’s SIM2, which actually uses three sets of axes, wind, wind-tunnel stability, and body (Figure 18.7). SIM2 was first put to use at the NASA Dryden Flight Research Center for real-time digital simulation of the McDonnell Douglas F-15. The aerodynamic data base was filled in to an angle of attack of 90 degrees, to allow simulation of stalls and spins. Later SIM2 applications were to the space shuttle Orbiter and to the Northrop B-2 stealth bomber.

With three axes systems carried along simultaneously in the solution, the angular rela­tionships among the SIM2 axes sets must also be continuously computed. The fundamen­tal force vector equation on moving axes used in SIM2 uses the vector cross-product of angular velocity of wind axes and the velocity vector. A key vector equation solves for the angular velocity of wind axes as the angular velocity of body axes minus two terms, the angular velocity of wind-tunnel stability axes with respect to wind axes and the angular velocity of body axes with respect to wind-tunnel stability axes.

Wind axes differ from wind-tunnel stability axes only by a positive sideslip angle rotation about the Z stability axis, so that the second of the three terms in the vector equation for wind axes angular velocity has only one nonzero element, the sideslip angle rate. Likewise, wind-tunnel stability axes are derived from body axes by a single angle of attack rotation

along the negative Y-body axis. The required vector transformations are made in component form, always taking care to add components in the same axis systems.

The sideslip and angle of attack variables that define the difference among the three axis sets in SIM2 have one of the two possible definitions. The SIM2 convention happens to agree with the most common definition, in which wind axes are derived from body axes by an initial negative angle of attack – a rotation followed by a positive sideslip angle rotation в (Figure 18.8). The reverse convention is rare but not unknown.

Extended airplane axes sets that allow for flight at extreme speeds and altitudes, taking into account the earth’s actual shape, are treated in Sec. 15.

Automatic Pilots in History

Stability augmentation goes back only to about 1945, while the history of airplane and missile automatic pilots, or autopilots (that word happens to be a trademark of a par­ticular manufacturer), actually begins before the Wright brothers, with Sir Hiram Maxim’s 1891 designs. That history has been told by several authors, including Bollay (1951) and the scholarly but very readable account of automatic pilot development in the first chapter of Aircraft Dynamics and Automatic Control by McRuer, Ashkenas, and Graham, dated 1973.

An additional historical account of airplane automatic pilots is that ofW. Hewitt Phillips, in his Dryden Lecture in Research (1989). All of these authors refer to the remarkable 1913— 1914 demonstration of the Sperry “stabilizer,” which provided full automatic control of a Curtiss Flying Boat. However, the present chapter deals only with stability augmentation.

Gust-alleviation systems are a specialized form of airplane automatic pilots, designed to reduce structural loads and to improve ride quality in rough air. These systems are of less interest now than formerly because modern airplanes can fly above turbulence or use weather radar to avoid storms. A complete historical review of gust-alleviation systems is available in a NASA Monograph (Phillips, 1998).

Faceted Airframe Issues

The Lockheed F-117A’s faceted airframe flies in the face of conventional aero­dynamic wisdom, which requires smooth surfaces to maintain attached flow under the widest possible ranges of angles of attack, sideslip, and angular velocities (Figure 22.1). On the other hand, the aerodynamic forces and moments of faceted airframes are reasonably linear functions of these variables for sufficiently small ranges.

Large-wing sweepback, 67 1/2 degrees in the case of the F-117A, extends the linear ranges somewhat, making facet edges into side edges instead of breaks normal to the flow direction. Still, the stability and control engineer who is faced with a faceted airframe such as the F-117A must expect to restrict flight parameters in order to avoid nonlinear and unstable aerodynamic moments that exceed available control power. The F-117A was originally called “The Hopeless Diamond” by Lockheed aerodynamicists.

Faceted Airframe Issues

Figure 22.1 Faceted structure of the Lockheed F-117A Stealth Fighter. (From Lockheed Advanced Development Company, J. W. Ragsdale)

On the F-117A, the angle of attack is hard-limited, but sideslip angles are unlimited with the landing gear down for cross-wind landings. With landing gear up, the sideslip angle is nulled by closed-loop control, a normal loop closure. F-117A longitudinal static margins are low or negative within the angle-of-attack limit range, but air combat maneuvers can be made within that range. Severe pitchups and pitchdowns occur outside of the angle-of-attack limit range (Farley and Abrams, 1990). Without augmentation, the airplane is directionally unstable over large parts of its operational envelope.

The four F-117A elevons have relatively large travels of 60 degrees up and down, which are necessary to deal with nonlinear and unstable moments within the angle-of-attack limit range. The two vertical tails are all-moving, for the same reason. The F-117A has quadruple fail-safe fly-by-wire controls, using F-16 technology. An 18-foot-diameter brak­ing parachute doubles as a spin chute, an unusual feature for a service airplane. Nominal landing speed is 160 knots, at an angle of attack of 9 1/2 degrees.