Category Airplane Stability and Control, Second Edition

Aerodynamic and Thrust Considerations

It has been known for some time that landing approach path control by elevator or pitch adjustments does not work for low-aspect-ratio (stubby) straight or sweptback wings. This is due to the variation of drag with airspeed when the lift is equal to the gross weight in level flight conditions. We normally expect level-flight drag to increase rapidly with increas­ing airspeed, and so it does at cruising airspeeds. At cruising airspeeds height control by pitch attitude changes using the elevator is stable and effective. The throttle can be left fixed.

However, the level-flight drag for any airplane increases with decreasing airspeed near the stall, as a result of induced drag increases and flow separation at high angles of attack. As airspeed is reduced from cruising values level-flight drag reaches a minimum and then actually increases again as the airspeed is reduced still further. The airspeed at which level – flight drag, and thrust required to hold level flight, reach minimums was given the name “minimum drag speed” by Stefan Neumark in Britain (1953).

The increase in level-flight drag near the stall is accentuated for airplanes with low-aspect – ratio wings, leading to increases in minimum drag speed. The minimum drag speed for an airplane with a low-aspect-ratio wing can be well above the low approach airspeed desired for carrier landings. Thus, if an airplane with a low-aspect-ratio wing is on a stabilized descent at a low landing approach speed typically used for aircraft carriers and the pilot retrims the airplane to a higher angle of attack, reducing airspeed, the airplane will rise at first relative to the original path and then settle even faster. The flight path will become steeper, a counterintuitive result.

For landing approaches below the minimum drag speed, where increasing thrust is re­quired for decreasing airspeed in level flight, sometimes called “the back side of the thrust required curve,” pitch attitude control by the elevator is unsatisfactory, even with the throttle used to control height. Thrust control by the pilot or an automatic system (the Navy’s APCS) to hold constant airspeed or angle of attack has been used to artificially create the normal variation of thrust required for level flight.

“Backside” carrier-based approach problems were first recognized about 1950 (Shields and Phelan, 1953). Pilots needed to use higher approach speeds forthe XF-88A andXF3H-1 airplanes than the standard rules of thumb based on stalling speed. Shields and Phelan proposed a fixed-throttle pitch-up test maneuver that is similar to a popup maneuver later adopted as one criterion for minimum carrier-approach speed. The first large-scale organized set of data on minimum approach airspeed behavior for jet airplanes was taken at the NACA Ames Aeronautical Laboratory (White, Schlaff, and Drinkwater, 1957). Carrier – type landing approaches were made with seven straight – and swept-wing jet airplanes, the FJ3, F7U-3, F9F-6, F4D, F-100A, F-94C, and the F-84F. The objectives of the 1957 Ames tests was to find the minimum “comfortable” approach airspeeds for carrier-type landings for these representative jet airplanes.

The reason most frequently given by the NACA Ames pilots for minimum approach airspeeds was inability to control precisely altitude or flight path at lower speeds. However, there was a surprising lack of correlation between the minimum comfortable approach airspeed and the Neumark minimum drag speed. For example, Ames pilots set the minimum comfortable approach airspeed for the Douglas F4D-1 Skyray at 121 knots, while the minimum drag speed is 152 knots. Similar results appeared with the North American F-100A Super Sabre, where a minimum approach airspeed of 145 knots was selected, as compared with the minimum drag speed of 150 knots (Figure 12.2). Clearly, some other factors than inability of the elevator or stabilizer to control height without reversal were critical.

Another set of carrier-approach tests (Bezanson, 1961) found that flight path control of the Vought F8U and Douglas F4D-1 airplanes at low landing approach speeds required use of the throttle and was not satisfactory by angle of attack or pitch control modulation alone. Bezanson found that with thrust modulation as the primary path controller the dynamic characteristics of the thrust control system became important, including such factors as throttle friction and breakout force, throttle sensitivity (pounds of thrust per inch of throttle movement), and thrust time lag following abrupt throttle movements.

In contrast to pure jet engines, turboprops are operated at high RPMs all the time. Thrust modulation is done by propeller pitch changes, with very small time lags. The poor engine dynamic behavior of pure jet engines, particularly engine thrust time lag at low power levels (Figure 12.3), kept U. S. Navy interest alive in turboprop combat airplanes long after the U. S. Air Force had switched to pure jets. For example, the Douglas/Navy turboprop A2D-1 Skyshark made its first flight in 1950, the same year as the start of production on the Boeing/Air Force B-47A six-jet bomber.

Blind-Flying Demands on Stability and Control

Blind flying is controlled flight without reference to the outside scene, more specif­ically, the horizon. Simply put, there is no way that an airplane can be made suitable for blind flight by aerodynamic design alone. A pilot must rely on some form of gyroscopic device to retain control, either as a panel instrument or as part of an automatic pilot.

The need for instrumentation comes from the effects of spiral instability, or aileron control friction on airplanes that are spirally stable, as discussed in Sec. 5. Even if strong spiral stability were to be built into a design, at the expense of other desirable flying qualities, a pilot could lose control over altitude unless trained to damp the phugoid mode (Chapter 18, Sec. 9) by reference to airspeed alone.

Spatial disorientation due to illusions can be prevented by reference to instruments. The FAA’s Aeronautical Information Manual (1999) lists no fewer than 14 flight illusions that have been identified, such as a Coriolis, graveyard spin, somatogravic, and inversion illusions.

Atmospheric Models

A mathematical model of the earth’s atmosphere is needed for stability and control flight simulation and other computer programs. These programs typically use dimensionless stability derivatives in setting up equations of motion for flight dynamics studies, and stability augmenter and autopilot analyses.

Standard atmospheric mathematical models were published by NACA starting in 1932. A 1955 model covered altitudes up to 65,800 feet (ICAO, 1955). NACA, the U. S. Air Force, and the U. S. Weather Bureau extended that model to an altitude of 400,000 feet (ICAO, 1962). The AIAA publishes a guide to standard atmosphere models (1996). For all its utility, the standard atmospheric model is based on quite simple assumptions: The air is dry, it obeys the perfect gas law, and it is in hydrostatic equilibrium.

Standard atmosphere computer codes for stability and control computer programs nor­mally accept as inputs the airplane’s altitude and true speed at each computing time. A minimum set of outputs at each computing time would include atmospheric density, Mach number, dynamic pressure, and equivalent airspeed. Additional outputs that could be gen­erated are static pressure and calibrated airspeed.

The standard atmosphere FORTRAN computer code shown in Figure 18.10 represents one of the two methods used in stability and control programs. In this example, air den­sity (RHO) is curve-fitted with exponential functions. Four function fits give satisfactory accuracy over the entire range of -4,000 to 400,000 feet. Speed of sound (ASPE), from which the Mach number is calculated, requires eight curve-fitted linear equations. The al­ternate standard atmosphere coding is ordinary interpolation from stored tables of density and speed of sound.

It has become increasingly important to represent wind gusts, shears, downbursts, and vortex encounters in stability and control flight simulation. Early flight simulations relied on a very simplified approach in which an additional gust angle of attack or sideslip is simply added to the values calculated at each instant from the airplane’s motions in an inertial space reference.

The sounder approach, now in common use, is an inertially fixed model for the wind environment, including gusts, shears, downbursts, and vortices. A NASA downburst model uses the conservation of mass principle to calculate wind velocity at all points within a down – burst (Bray, 1984). A central core is surrounded by an annular mixing region and a region of outflow parallel to the ground (Figure 18.11). In the Bray inertially fixed wind environment, an airplane penetrates the wind model as it moves along its path, just as in reality.

Earlier ad hoc wind shear models were proposed by NASA for flight simulation. A boundary layer shear model represents a low-level temperature inversion overlaid by strong winds. Two additional shear models, with the colorful names of the Logan and Kennedy shears, represent meteorologists’ best estimates of conditions existing at those airports during specific airplane wind shear encounters.

In Bernard Etkin’s terminology, the Bray downburst model and the NASA shear models are usually used as point atmospheric models, in which variations of local wind velocity over the airplane’s dimensions are neglected. Otherwise stated, the airplane is assumed to be vanishingly small with respect to the wavelengths of all spectral components in the turbulent atmosphere. This assumption obviously fails for gust alleviation systems that depend on sensing devices that sample air turbulence ahead of the main structure.

Etkin (1972) provides a thorough study of the finite airplane case, in which local wind ve­locities vary over the airplane’s dimensions. The required mathematics are surprisingly com­plex because atmospheric turbulence is a random process, and only a statistical, probabilistic



X(3) = ALT

IF(-X(3)-35.E3) 300,300,310 300 Z1 = 342.5E2 + X(3)*4.3/35.

GO TO 500

310 IF(-X(3)-45.E3)320,320,400 320 Z1 = 299.5E2-.285*(-X(3)-35.E3)

GO TO 500

400 IF(-X(3)-60.E3) 405,405,410 405 Z1 =271 .E2-.1 2*(-X(3)-45.E3)

500 RHO = .002377*EXP(X(3)/Z1)

GO TO 490

410 IF(-X(3)-140.E3) 415,415,420

415 RHO = EXP(-4.67263E-5*(-X(3)-6.E4)-8.41 364)

GO TO 490

420 IF(-X(3)-240.E3) 425,425,430

425 RHO = EXP(-3.871 2E-5*(-X(3)-14.E4)-1 2.1 51 584)

GO TO 490

430 RHO = EXP(-5.18378E-5*(-X(3)-24.E4)-16.022785)


IF(-X(3)-362.E2)600,600,700 600 ASPE = 1117.-149.*(-X(3)/362.E2)

GO TO 800

700 IF(-X(3)-66.E3) 710,710,720 710 ASPE = 968.

GO TO 800

720 IF(-X(3)-105.E3) 730,730,740

730 ASPE = 6.71 282E-4*(-X(3)-66.E3) + 968.

GO TO 800

740 IF(-X(3)-1 555.E2) 750,750,760 750 ASPE = 1.73941 E-3*(-X(3)-105.E3) + 994.1 8 GO TO 800

760 IF(-X(3)-1 72.E3) 770,770,775 770 ASPE = 1082.02 GO TO 800

775 IF(-X(3)-200.E3) 780,780,785 780 ASPE = -1.21 5714E-3*(-X(3)-1 72.E3) + 1082.02 GO TO 800

785 IF(-X(3)-2625.E2) 790,790,795 790 ASPE = -2.6 236 8E-3*(-X(3)-200.E3) + 1047.98 GO TO 800 795 ASPE = 884.

800 AMACH =VEL/ASPE DYN = (RHO/2.)*VEL* *2 VEKT = 1 7.1 861 21 6*SQRT(DYN)



Figure 18.10 FORTRAN digital computer subroutine for the NASA/USAF/USWB standard atmo­sphere. Air density (RHO) and speed of sound (ASPE) are curve-fitted in altitude bands from -4,000 to 400,000 feet. The subroutine requires inputs of altitude (ALT) and true speed (VEL). The subroutine outputs density, Mach number (AMACH), dynamic pressure (DYN), and equivalent airspeed (VEKT). (From ACA Systems, Inc. FLIGHT program)

treatment can be made (Ribner, 1956). Local wind velocity is a random function of both space and time. It simplifies things to assume stationarity, homogeneity, isotropy, and Gaussian distributions. Experimental data exist that provide adequate turbulence models for both high altitudes and near the ground, where isotropy does not hold.

More exotic atmospheric disturbances are significant for operation at very high altitudes and at hypersonic speeds. Flight disturbances due to temperature shears experienced by the

Atmospheric Models

Figure 18.11 Vertical cross-section through the Bray model of a down-burst. Arrow lengths are proportional to air flow velocity. (From Bray, NASA TM 85969, 1984)

Lockheed SR-71A and the North American XB-70 are discussed in Chapter 11, “High Mach Number Difficulties.” In anticipation of a National Aerospace Plane (NASP) that would fly hypersonically, NASA laboratories at Dryden, Marshall, and Langley and the McDonnell Douglas Houston operation collaborated on a sophisticated FORTRAN atmospheric model called the NASP Integrated Atmospheric Model (Schilling, Pickett, and Aubertin, 1993).

The model is suitable for real-time simulations as well as batch programs. It provides global coverage, from the ground to orbital altitudes. The NASP model features of partic­ular stability and control interest are the small-scale perturbations that include continuous turbulence and the “thermodynamic” perturbations of density, pressure, and temperature. Gusts and thermodynamic perturbations can be selected either in patches or as discrete upsets.

Isolated mountain ridges that lie at right angles to the direction of strong prevailing winds can generate a so-called mountain wave. Air over the top of such a ridge cascades in huge volumes onto the lower terrain to the leeward. It then seems to bounce off, rising, then falling, and then rising again in a series of diminishing waves, all parallel to the ridge line. A huge rotor, or horizontal vortex, forms to the leeward of the first bounce. The characteristic mountain wave structure is well known to glider pilots, since glider altitude records are set by maneuvering into the rising air of the first bounce. Glider pilots also know to avoid the rotor, whose lower edge generally just brushes ground level. The National Transportation Safety Board (NTSB) concluded that a rotor was a possible cause for at least one airline accident. This was United Airlines Flight 585, a Boeing 737 lost at Colorado Springs in 1991. Various jet aircraft encounters with a rotor are modeled by Spilman and Stengel (1995).

Vortex wakes left in the atmosphere by airplanes flying ahead can be a severe hazard, although the principles for avoiding vortex wakes are known. Vortex wake fields can be modeled for flight simulation (Johnson, Teper, and Rediess, 1974).

Transfer-Function Numerators

Airplane transfer-function denominator factors, or roots, govern airplane motions following initial disturbances. Stable roots, having negative real parts, lead to subsidence of oscillatory or aperiodic motions. The same is true for the denominators of closed-loop transfer functions, and early root locus work, such as the material in Dr. William Bollay’s 1950 Wright Brothers Lecture, dealt with roots, or poles, of the closed-loop denominator. Transfer function numerator factors are called zeros. A response survey to step inputs for a systematic variation in pole-zero combinations (Elgerd and Stephens, 1959) gives striking results, particularly for the case of two real poles and one real zero. Depending on whether the zero is between the poles or to the right, the step response appears either deadbeat or with a large overshoot.

Transfer-function zeros play an important role in the closed-loop responses of stability – augmentation systems. The details are too involved to go into here, but some examples can be touched upon. In the altitude or glide path loop in which errors are corrected by elevator or stabilizer control, a zero called 1 /Th1 can be in the right half of the root locus plane. This occurs on the back side of the power required curve, or at airspeeds below the minimum drag point. Loop closure drives a closed-loop real root into the right half-plane, with consequent divergence. An inner stability augmentation loop can correct this.

Another example is the complex zero associated with bank angle control by the ailerons. The Systems Technology, Inc., symbol for the undamped natural frequency associated with this zero is Шф. For values of Шф that exceed the Dutch roll undamped natural frequency rnd, loop closure excites the Dutch roll and closed-loop stability is degraded. A complete tutorial discussion of this problem, as well as the altitude control zero problem, is given by Duane T McRuer and Donald E. Johnston (1975).

Altitude Response During Landing Approach

An early pilot-induced oscillation experience with the Space Shuttle Orbiter ALT – FF5 landing approach tests (Powers, 1986) led to some concern about the shuttle’s com­bination of large airplane size and distance of the pilot ahead of the center of gravity, and initially reversed altitude response with elevon control deflections. On the shuttle, more than 2 seconds elapses before altitude starts to increase following a step nose-up elevon deflection (Phillips, 1979). F. A. Cleveland (1970) gives a value of 0.8 second for this de­lay parameter on the C-5A Galaxy and speculates that glide path control during landing approach would be unsatisfactory for time delays above 2 seconds.

Cleveland’s analysis of the effects of airplane size gives a linear growth in the altitude delay parameter with size. Time delay would reach 2 seconds on a C-5A scaled up about

2.4 times, requiring direct lift control or canard surfaces. Digital sampling delays in the pitch control circuit and elevon rate limiting are known to contribute to the Space Shuttle’s pilot-induced oscillation tendency. According to Robert J. Woodcock (1988)

extensive, continual training [for the Space Shuttle Orbiter] has resulted in very good landing performance (smooth landings with small dispersion, mostly on long runways, in smooth air).

The conclusion is that large airplane sizes might indeed lead to landing approach prob­lems related to delayed altitude responses following pitch control inputs and special design features to correct the problem.

An alternate criterion for the control response of very large airplanes is the generic re­sponse to abrupt control inputs, as shown in Figure 10.5. Grantham, Smith, Person, Meyer, and Tingas (1987) compared large airplane flying qualities with the generic pitch response requirements of MIL-F-8785C. Maximum effective time delays of 0.10 to 0.12 second are specified in MIL-F-8785C, based on tests of relatively small tactical airplanes. These requirements may be much too stringent for large airplanes in all but very high-gain oper­ations. Satisfactory, or Level 1, flying qualities are obtained in simulation of a Lockheed 1011-class transport for effective time delays of 0.15 second, suggesting even larger accept­able values for superjumbo jets. On the other hand, the effective longitudinal axis dynamics of the Boeing 777 compares with some fighters.

John Gibson (1995) suggests that the observed sluggish response of the Space Shuttle Orbiter is caused by poor control laws as much as airplane size. Increasing pitch rate overshoot in a pullup would improve the observed sluggish flight path angle response. This further suggests that the flexibility of fly-by-wire technology can provide the necessary quickness of response in large airplanes without requiring special features such as direct lift control or canards.