Category Airplane Stability and Control, Second Edition

Remaining Design Problems in Power Control Systems

The remarkable development of fully powered flight control systems to the point where they are trusted with the lives of thousands of air travelers and military crew persons every day took less than 15 years. This is the time between the Northrop B-49 and the Boeing 727 airplanes. However, there are a few remaining mechanical design problems (Graham and McRuer, 1991).

Control valve friction creates a null zone in response to either pilot force or electri­cal commands. Valve friction causes a particular problem in the simple type of mechanical feedback in which the control valve’s body is hard-mounted to the power cylinder. Feedback occurs when power cylinder motion closes the valve. However, any residual valve displace­ment caused by friction calls for actuator velocity. This results in large destabilizing phase lags in the closed loop.

Another design problem has to do with the fully open condition for control valves. This corresponds to maximum control surface angular velocity. That is, the actuator receives the maximum flow rate that the hydraulic system can provide. The resultant maximum available control surface angular velocity must be higher than any demand made by the pilot or an autopilot. If a large upset or maneuver requires control surface angular velocity that exceeds the fully open valve figure, then velocity limiting will occur. Velocity limiting is highly destabilizing. Control surface angles become functions of the velocity limit and the input amplitude and frequency and lag far behind inputs by the human or automatic pilot.

The destabilizing effects of velocity limiting have been experienced during the entire history of fully powered control systems. A North American F86 series jet was lost on landing approach when an air-propeller-driven hydraulic pump took over from a failed engine-driven pump. When airspeed dropped off near the runway, the air-propeller-driven pump slowed, reducing the maximum available hydraulic flow rate. The pilot went into a divergent pitch oscillation, an early pilot-induced oscillation (PIO) event (see Chapter 21). Reported actuator velocity saturation incidents in recent airplanes include the McDonnell Douglas C-17, the SAAB JAS-39, and the Lockheed Martin/Boeing YF-22 (McRuer, 1997).

Design for Spin Recovery

Simple preliminary design rules that would increase the chances for an airplane to have satisfactory recovery characteristics from spins were an important product of the NACA spin tunnel group. Figure 9.4 reproduces the best-known set of preliminary design rules (Neihouse, Lichtenstein, and Pepoon, 1946). Two separate parameters are used. One

Design for Spin Recovery

Figure 9.3 An example of the standardized spin recovery charts produced by the NASA Langley spin tunnel. The box locations correspond to control positions for the developed spin that precedes the recovery attempt. Blanks generally correspond to control positions for which the model would not spin. This particular chart is for the Grumman OV-1 Mohawk Army observation airplane. (From Lee, NASA TN D-1516, 1963)

is called TDR, the tail damping ratio, affecting whether the steady spin is steep or flat. The other is called URVC, the unshielded rudder volume coefficient, based on the rudder areas nominally out of the horizontal tail wake and their moment arms. The product of the two parameters is the tail damping power factor, or TDPF.

The 1946 TDPF design rules are a modification of a Royal Aircraft Establishment (RAE) criterion by E. Finn. Both the RAE and NACA criteria are based on empirical results, grounded in the flight mechanics of spins. For example, the TDR rule specifies a minimum

Design for Spin Recovery

Figure 9.4 Method of applying the 1945 Neihouse/Lichtenstein/Pepoon tail design requirements for satisfactory spin recovery, a controversial standard because it neglects factors otherthan the tail. (From Stough, Patten, and Sliwa, NASA TP 2644, 1987)

fuselage area under the horizontal tail for the spin to be normal, and not the flat, high-rotation – rate variety. At spin attitudes, that is, at high angles of attack and large yawing velocities, that particular area should indeed develop high static pressures and a considerable yawing moment resisting the spin rate, or damping the spin.

The 1946 NACA TDPF design rules were followed one year later by design rules drawn up specifically for personal-owner-type airplanes (Figure 9.5). The 1947 NACA TDPF rules use a 60-airplane subset of the 100 airplanes on which the 1946 rules are based. Both sets of tail design rules are considered to be a useful guide for airplanes with the general layout and weight distribution of that period in aeronautics. This includes propeller-driven general – aviation airplanes of the present day, so it is a source of wonder and alarm that these rules are ignored by many modern designers.

On the other hand, James S. Bowman, Jr., recently retired from NASA, points to cases in which light airplane configurations that satisfy the 1947 TDPF criterion have unsatisfactory spin recovery characteristics, weakening the case for applying the criterion to present-day airplanes. This is further discussed in Section 9.11, “The Break With the Past.”

Fences and Wing Engine Pylons

Wing fences are streamwise panels on the wing’s upper surfaces. They are intended to interrupt and shed the wing’s low-energy boundary layer outflow (toward the wing tips) that would otherwise accumulate and cause flow separation and tip stall. Fences are found

Fences and Wing Engine Pylons

Figure 11.10 Stall patterns on a sweptback wing equipped with slat, leading-edge extension, and drooped-nose leading-edge flap. Initial tip stall is prevented in all three cases. (From Furlong and

McHugh, NACA Rept. 1339, 1957)

on some early swept-wing jets, such as the Comet 1, Sud Caravelle, Tupolev Tu-54M, and Gulfstream II.

The pylons for underwing jet engines can be a substitute for wing fences on high – aspect-ratio-swept wings. This was discovered by the Boeing Company, probably during the wind-tunnel test program for the B-47 airplane. Figure 11.11 shows how bound vorticity of a lifting wing induces sidewash at the nacelle-pylon combination, which in turn causes a sideload. The side-loaded pylon-nacelle combination creates a tip or edge vortex over the top of the wing, opposing the normal outward wing boundary layer flow, which tends to

Fences and Wing Engine Pylons

Figure 11.11 Wing bound vorticity induces sidewash on jet engine pylons. The pylon load creates an upper wing surface vortex that opposes the normal outflow of wing boundary layer, reducing the tendency to flow separation at the wing tips.

follow isobars on the wing and so reduces the tendency toward wing tip stall and airplane pitchup. This same phenomenon is taken advantage of on the B-52 and 707 airplanes, neither of which ever required boundary layer fences on the upper surfaces of their wings.

The Boeing 707 pylon-nacelle arrangement was adopted by the Douglas Aircraft Corpo­ration for the DC-8 airplane. On the DC-8, in addition to reducing spanwise wing boundary layer flow, the pylon-nacelle combination also caused early wing stall at the pylon locations. When fixed slots (opened only with full flaps) were put on the wing near the pylons to inhibit local stall, pilots complained of airplane pitch-up problems (Shevell, 1992). Pitchup was remedied by reducing slot size and later by cutting back the pylons to the location of the wing stagnation point at maximum lift coefficient. Cutting back the pylons also reduced local high-Mach-number “hot spots” on the wing’s upper surface at cruising speeds.

Douglas company aerodynamicists realized what a good thing pylon-nacelle combina­tions were during the wind-tunnel development for the DC-9 airplane, which had none. Fitting two pylon-nacelle combinations from the DC-8 model to the DC-9 model cured its tip stalling problems; removing the nacelles from the pylons worked, too. Finally, the pylons were reduced in size, streamlined, renamed “vortillons,” and patented. The spanwise vortillon location was chosen to produce desirable vortex flow at the tail, which up till then had been insufficient to recover from a deep stall.

The DC-10 airplane has large vortex generators, or strakes, on the sides of its nacelles to alter nacelle and wing stall behavior at high angles of attack. Nacelle strakes also are found on some Boeing airplanes, but on one side of the nacelle only. David A. Lednicer writes:

The story I have heard is that McDonnell Douglas [held] the patent for the use of strakes on both sides of the nacelle, so Boeing circumvented the patent by putting them on only one side.

Lifting Body Stability and Control

A lifting body is a wingless vehicle that depends on lift generated from an elongated body or fuselage. Both lifting bodies and ballistic shapes had been studied as space vehicles by NASA before the choice of the Mercury, Gemini, and Apollo ballistic capsule designs. However, lifting body research continued, first at the NASA Ames and Langley Research Centers, then at the NASA Flight Research Center (Reed, 1997). Figure 14.19 is a general arrangement drawing of a typical lifting body design, the NASA/Northrop HL-10 (Heffley and Jewell, 1972). Configurations such as the HL-10 have evolved into the space shuttle Orbiter and follow-up concepts such as the X-33 research vehicle.

Lifting Body Stability and Control

Figure 14.19 Three-view drawing of the NASA/Northrop HL-10 lifting body. (From Heffley and Jewell, NASA CR-2144, 1972)

Stability and control characteristics of a series of lifting bodies were investigated in wind – tunnel and flight tests starting in the mid-1950s in the United States and later in Russia, Japan, and France. All of the problems associated with swept wings and heavy fuselage loadings appeared in the course of these tests, in addition to a number of instances of control oversensitivity and pilot-induced oscillations. Lifting body configurations typically have high dihedral effect, or rolling moment due to sideslip, in proportion to roll damping. The coupled roll-spiral mode of motion (Chapter 18, Sec. 9) may thus exist.

Early Numerical Work

Useful solutions to Bryan’s equations of airplane motion for scientific or engi­neering uses are either roots or eigenvalues or actual time histories, which give airplane responses to specific control or disturbance inputs. Either type of solution was essentially out of the question with the means available in 1911. However, by 1920 Bairstow had found useful approximations that served as starting points for developing eigenvalues from the Bryan equations.

When, later on, research engineers in both the United States and in Britain generated time history solutions to the linearized Bryan equations, it was only with great labor. Early step-by-step numerical solutions were published for the S. E.-5 airplane of World War I fame by F. Workman in 1924. A year later, B. Melvill Jones and A. Trevelyan (1925) published step-by-step solutions for the lateral or asymmetrical motions.

As an advance over step-by-step methods, B. Melvill Jones (1934) applied the for­mal mathematical theory of differential equations to the linearized Bryan equations, pro­ducing a marvelously complete set of time histories for the B. F.2b Bristol Fighter at an altitude of 6,000 feet (Figure 18.5). A generation of pre-electronic-computer engineers struggled through those formal solutions. The complementary function is found first. In addition to using a considerable amount of algebra, one has to find the real and complex roots of a fourth-degree polynomial. The complementary function gives the time histories of the variables of motion under no applied forces and moments, but with arbitrary initial conditions.

The last step in the formal solution is finding a particular integral of the equations. This adds to the complementary function the effects of constant applied moments, such as are produced by deflections of the airplane’s control surfaces. In Jones’ own words, “The numerical computations involved… are heavy, they involve amongst other things, the solution of four simultaneous equations with four variables.” It is little wonder that numerical time history calculations languished for years, until electronic analog computers were commercially available, about the year 1950.

Control System Coupling with Elastic Modes

Coupling of the B-47’s yaw damper system with the airplane’s fuselage side­bending mode was resolved simply when the yaw damper’s rate gyro was relocated. That is, the rudder’s yaw damping action cut off at a low enough bandwidth that the side-bending mode itself was not reinforced.

The coupling of stability augmentation systems and airplane elastic modes takes on a new dimension for high-bandwidth control systems. If the flight control system is capable of interacting with the airplane’s structural modes, the stability of the combination must be assured. A conventional approach is gain stabilization, in which control system response at structural mode frequencies is attenuated by notch filters. The notch filters reduce rate gyro and accelerometer outputs in a narrow band around modal frequencies.

While effective, notch filtering invariably introduces lag at lower frequencies, which can adversely affect flying qualities. Phase stabilization (Ashkenas, Magdaleno, and McRuer, 1983) attempts to replace or supplement notch filtering by creating dipoles out of the

Control System Coupling with Elastic Modes

Figure 19.10 The first six normal modes at the centerline of a Boeing supersonic transport proposal, typical of the data used in the normal-mode method for the effect of aeroelasticity on stability and control. The modes are normalized in amplitude. Modes 1 and 2 are rigid-body plunge and pitch.

(From Ashkenas, Magdaleno, and McRuer, NASA CR-172201, Aug. 1983)

structural bending poles. The dipoles are the stable type referred to in the “Transfer Function Dipoles” section of Chapter 20, with the zero below the pole in the s-plane. Zero location for particular modes can be controlled by sensor location, but locations that produce stable dipoles for some modes will be wrong for others.

Bandwidth-Phase Delay Criteria

The insights furnished by the crossover model for compensatory operation lead to criteria that can be used in control system design, as in the Neal-Smith approach. An important example is the Hoh-Mitchell-Ashkenas bandwidth and phase delay criteria (Hoh, 1988), a combination of two individual metrics, illustrated in Figure 21.6.

The first metric is aircraft bandwidth, defined as the frequency at which the phase angle of attitude response to stick force input is -135 degrees. The aircraft bandwidth measures the frequency over which the pilot can control without the need for lead compensation. The second metric is phase delay, defined as the difference in response phase angle at twice the frequency for a -180-degree phase angle and 180 degrees, divided by twice the frequency for a -180-degree phase angle. The phase delay metric approximates the phase character­istics of the effective airplane dynamics, from the region of crossover to that for potential pilot-induced oscillations. Systems with large phase delays are prone to such oscillations.

Boundaries in aircraft bandwidth-phase delay space have been developed using flight and simulator pilot ratings and commentary. Similar boundaries have been especially useful for rotorcraft and special (translatory) modes of control. With these boundaries, designers are able to account for closed-loop pilot-airplane dynamics, using effective airplane dynamics alone. A related airplane-alone criterion based on the crossover model is the Smith-Geddes (1979) criterion frequency. Still another criterion based on airplane-alone dynamics places boundaries in the Nichols plane of the attitude frequency response (Gibson, 1995). The idea is to confine the attitude frequency response within boundaries defined by the best piloted closed-loop flying qualities. All of these boundary methods depend on simple correlation. They should be effective to the extent that new cases resemble those on which the boundaries are based.

Bandwidth-Phase Delay Criteria

Figure 21.6 Definitions of the bandwidth and phase delay criteria. (From MIL-STD-1797A, 1990)

Good design practice suggests using all of these criteria to examine airplane dynamics at issue.

Modern Stability and Control Teaching Methods

The digital computer has revolutionized the teaching of airplane stability and control, just as it has its practice. In precomputer times, flight dynamics students had to learn numerical techniques for factoring high-degree polynomials and producing linearized transient responses. Eigenvalues or roots of the equations of airplane motion were extracted by factorization, and the flight modes of motion were found.

Computer programs for root extraction and a great deal more are at the modern engineer’s fingertips, and present-day teachers of flight dynamics have found ways to use the digital computer to improve their courses. A few instances follow. Stanford University Professor Arthur Bryson’s book Control of Aircraft and Spacecraft uses Matlab® computer routines in many examples and problem assignments. For example, pages 199-201 show a student how to synthesize an optimal climb-rate/airspeed stability augmentation system using Matlab. As with other mathematics computer packages, Matlab is available in a low-cost student edition.

The State University of New York at Buffalo Professor William J. Rae assigns exercises that use a 6-degree-of-freedom computer program called SIXDOF to explore in detail the solutions of the nonlinear equations of airplane motion. This supplements normal instruction in the modes of motion and control theory using linearized equations. Still another approach has beenpursuedby University ofFlorida Professor Peter H. Zipfel. He makes available to his students a CADAC CD-ROM disk, with which to build modular aerodynamics, propulsion, and guidance and control computer models. As in the previous cases, students are able to solve realistic stability and control problems without getting lost in routine mathematical detail.

In France, Professor Jean-Claude Wanner, on the staffs of several universities, is devel­oping an advanced flight mechanics teaching tool, in the form of a CD-ROM. A stability volume computes the time response of an airplane specified by the user to control and throt­tle inputs, presenting results in the form of conventional strip charts, but also in real time as viewed from the cockpit or the ground. There are preliminary interactive chapters, including text and exercises, on subjects such as phugoid motion and accelerometer instruments.

The only cautions that might be applied to these modern approaches are the same ones that must be observed in the practice of engineering, using powerful digital computers. Both student and working engineer must keep in mind the assumptions that lie behind flight dynamics computer programs, their limitations as well as their capabilities. Good practice also requires reasonableness checks on computer output using independent simple methods.

Background to Aerodynamically Balanced Control Surfaces

When airplanes and their control surfaces became large and airplane speeds rose to several hundred miles per hour, control forces grew to the point where even the Gough – Beard-McAvoy force limits were exceeded. Pilots needed assistance to move control surfaces to their full travels against the pressure of the air moving past the surfaces. An obvious expedient was to use those same pressures on extensions of the control surface forward of the hinges, to balance the pressure forces that tried to keep the control surfaces faired with the wing.

The actual developmental history of aerodynamically balanced control surfaces did not proceed in a logical manner. But a logical first step would have been to establish a background for design of the balances by developing design charts for the forces and hinge moments for unbalanced control surfaces. That step took place first in Great Britain (Glauert, 1927). Glauert’s calculations were based on thin airfoil theory. W. G. Perrin followed in the next year with the theoretical basis for control tab design (Perrin, 1928).

Background to Aerodynamically Balanced Control Surfaces

Figure 5.1 Pitching moment and control effectiveness parameters for plain flaps on the NACA 0009 airfoil, derived from pressure distributions. The dashed lines are Glauert’s thin airfoil theory. (From Ames and Sears, NACA Rept. 721, 1941)

The next significant step in the background for forces and hinge moments for unbalanced control surfaces was NACA pressure distribution tests on a NACA 0009 airfoil, an airfoil particularly suited to tail surfaces (Ames, Street, and Sears, 1941). Figures 5.1 and 5.2 compare those results with Glauert’s theory. The trends with control surface hinge position along the airfoil chord match Glauert’s thin airfoil theory exactly, but with lower flap effec­tiveness and hinge moment than the theoretical values. Ames and his associates developed

Background to Aerodynamically Balanced Control Surfaces

Figure 5.2 Hinge moment parameters for plain flaps on the NACA 0009 airfoil, derived from pressure distributions. The dashed lines are Glauert’s thin airfoil theory. (From Ames and Sears, NACA Rept. 721, 1941)

a fairly complex scheme to derive three-dimensional wing and tail surface data from the two-dimensional design charts. That NACA work was complemented for horizontal tails by a collection of actual horizontal tail data for 17 tail surfaces, 8 Russian and 3 each Polish, British, and U. S. (Silverstein and Katzoff, 1940). Full control surface design charts came later, with the publication of stability and control handbooks in several countries (see Chapter 6, Sec. 2.6).

5.2 Horn Balances

The first aerodynamic balances to have been used were horn balances, in which area ahead of the hinge line is used only at the control surface tips. In fact, rudder horn balances appear in photos of the Moisant and Bleriot XI monoplanes of the year 1910. It is doubtful that the Moisant and Bleriot horn balances were meant to reduce control forces on those tiny, slow airplanes. However, the rudder and aileron horn balances of the large Curtiss F-5L flying boat of 1918 almost certainly had that purpose.

Wind-tunnel measurements of the hinge moment reductions provided by horn balances show an interesting characteristic. Control surface hinge moments arise from two sources: control deflection with respect to the fixed surface (5) and angle of attack of the fixed or

Background to Aerodynamically Balanced Control Surfaces

Figure 5.3 Typical hinge moment parameter variations with size for unshielded horn aerodynamic balances. The hinge moment due to angle of attack Cha is affected more strongly by the horn balance than by the hinge moment due to surface deflection Ch5. (From Phillips, NACA Rept. 927, 1948)

main surface (a). The relationship is given in linearized dimensionless form by the equation Ch = ChsS + Chaa, where the hinge moment coefficient Ch is the hinge moment divided by the surface area and mean chord aft of the hinge line and by the dynamic pressure. Chs and Cha are derivatives of Ch with respect to 8 and a, respectively. Both derivatives are normally negative in sign. Negative Ch8 means that when deflected the control tends to return to the faired position. Negative Cha means that when the fixed surface takes a positive angle of attack the control floats upward, or trailing edge high.

Upfloating control surfaces reduce the stabilizing effect of the tail surfaces. It was discov­ered that horn balances produce positive changes in Cha, reducing the upfloating tendency and increasing stability with the pilot’s controls free and the control surfaces free to float (Figure 5.3). This horn balance advantage has to be weighed against two disadvantages. The aerodynamic balancing moments applied at control surface tips twist the control sur­face. Likewise, flutter balance weights placed at the tips of the horn, where they have a good moment arm with respect to the hinge line, lose effectiveness with control surface twist.

A horn balance variation is the shielded horn balance, in which the horn leading edge is set behind the fixed structure of a wing or tail surface. Shielded horn balances are thought to be less susceptible to accumulating leading-edge ice. Shielded horn balances are also thought to be less susceptible to snagging a pilot’s parachute lines during bailout. Vortex Lattice Methods

When the vortex lattice method is applied to wings, the surface is arbitrarily di­vided in the chordwise and spanwise directions into panels or boxes. Each panel contains a horseshoe vortex. The vortex-induced flow field for each panel is derived by the Biot-Savart Vortex Lattice Methods

Figure 6.3 Example formula and charts from the USAF DATCOM. This covers only a small part of the material for calculation of the derivative C^ for straight-tapered wings. RAeS data sheets have similar functions and appearance.

law. While this implies incompressible flow, the Prandtl-Glauert rule can extend the results to subcritical Mach numbers. The boundary condition of no flow across panels is fulfilled at just one control point per panel. Angle of attack and load distributions for the panels are found from a system of simultaneous linear equations that are easily solved on a digital computer. Distortions in data due to Reynolds’ number mismatches, jet boundary correc­tions, and model attachment problems in real wind tunnels are replaced with the necessary approximations of computational fluid dynamics.

When the panels lie in a flat plane and occupy constant percentage chord lines on an idealized straight-tapered wing at more or less arbitrary spanwise locations, and when each panel contains a line vortex across its local quarter chord point and trailing vortices along its side edges, whose collective vorticity provides tangential flow at every panel local three – quarter-chord point, the bound vorticity in each panel can be found by desktop methods, as in the Weissinger method. However, when panels or a mesh cover a complete airplane configuration, automatic machine computation methods become necessary. Depending on the method used, the computer defines the vortex strength for each panel.