Category Airplane Stability and Control, Second Edition

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).

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

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

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.

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

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.

The word “departure” is used for uncontrolled flight following stalls, the first stages of spin entry. Rather violent departures appeared with the advent of swept wings and long, heavily loaded fuselages, the same features that lead to inertial coupling. Pilots reported nose slices, whirling motions, wing rock, and roll reversals and divergences. There was interest almost at once in finding aerodynamic parameters specifically tied to these anomalies.

The initial search led back to stability and control’s early days, a time of high interest in Routh’s criterion and stability boundaries. Lateral stability boundaries are formed from the lateral characteristic equation

X4 + BXi + C Xі + DX + E = 0.

A necessary condition for stability is that the constants B, C, D, and E all be positive in sign. The last two constants, D and E, are associated with real roots, or convergences or divergences, rather than an oscillation.

In the lateral stability boundaries developed by L. W. Bryant in 1932 and by Charles H. Zimmerman in 1937, sign changes in D and E plotted as functions of static lateral and directional stability define the boundaries. Zimmerman specifically associated the constant D with directional divergence.

Two later investigators, Martin T. Moul and John W. Paulson, followed in Bryant’s and Zimmerman’s footsteps, but associated directional divergence with the constant C rather than D. Robert Weissman’s name is also associated with this development (Figure 9.10). Moul and Paulson coined a new term, “dynamic directional stability,” or C„^dyn for an approximation to C. This approximation is

Cnedyn = Cne cos a – (Iz/Ix)Ch sin a.

Together with another factor called “lateral control departure parameter” or LCDP, departures and post-stall gyrations, as well as roll reversals and tendencies to spin, are

correlated with stability derivatives. LCDP in particular, developed by Pinsker (1967), predicts high angle of attack nose slice departures while the pilot attempts to hold the wings level.

The pioneering work of Moul, Paulson, Pinsker, and Weissman in revisiting the Bryant – Zimmerman concept of stability boundaries for departures and post-stall gyrations was followed by several other noted investigators, who developed additional criteria for departure resistance. Figure 9.11 shows another set of departure and roll-reversal boundaries that are based completely on static aerodynamic derivatives (Bihrle and Barnhart, 1978). The advantage of using static derivatives in setting the boundaries is that they can be applied on the spot during conventional low-speed wind-tunnel tests of a complete model.

The Bihrle boundaries are based on digital simulation of a canned full control deflection maneuver involving an initial steep turn followed by full nose-up pitch control, then full opposite roll control. In papers given in 1978 and 1989, JuriKalviste and Bob Eller proposed coupled static and dynamic stability parameters that are based on separation of the full airplane equations of motion into rotary and translatory sets. These parameters amount to generalizations of the Moul-Paulson C„^dyn and LCDP parameters.

The level of sophistication of this work was raised by use of pilot-in-the-loop considera­tions, which are treated more fully in Chapter 21, “Flying Qualities Research Moves with the Times.” In the period 1976 to 1980, David G. Mitchell and Donald E. Johnston correlated

some departure characteristics with airplane frequency-response parameters involved with pilot loop closures. Negative values of the lateral transfer function numerator term NSa causes roll reversal, for example. Mitchell and Johnston found two additional closed-loop departure parameters for either rudder or aileron maneuvering control that correlate with nose-slice departures.

The vexing question of just how far one can go in using departure criteria based on linearized aerodynamics, or the stability derivatives, is addressed in a paper delivered by Donald Johnston at a1978 AGARD Symposium on Dynamic Stability Parameters. Although the linearized parameters clearly have some predictive value, Johnston concludes:

the more common frequency domain linear analysis techniques applied to symmetric, frozen point airframe models may produce totally erroneous answers if the aircraft exhibits significant coupling due to sideslip. These same analytic techniques provide valid predic­tions incases where Cm, Cl, Cn are f (а, в) providing the frozen point model represents asym­metric trim conditions and the analytic results are not applied to в excursions through zero.

Calculations on the Vought A-7 airplane provide additional evidence of the importance of sideslip coupling on departures (Johnston and Hogge, 1976). Sideslip angles up to 15 degrees have a moderate stabilizing effect on the Dutch roll and longitudinal short-period modes of motion. However, the spiral and roll modes combine to form a new low-frequency or phugoid-type lateral mode, which is unstable at the higher sideslip angles. A pitch attitude numerator factor, or zero, moves to the right half of the s-plane with sideslip, creating a potential instability with pilot loop closure.

The presence of stability augmentation, such as roll rate feedback to the ailerons, clearly affects departures. Extension of the determinant of the equations of motion to include augmentation feedbacks produces modified departure criteria (Lutze, Durham, and Mason, 1996).

Peter Mangold of Dornier reviewed departure again, to account for the trend toward higher usable angles of attack, where forebody vortices from the nose, strakes, or canards dominate lateral-directional stability. From Mangold’s paper (1991):

For the older aircraft the dynamic [rotary] data were of minor influence and the departure characteristics in Weissman’s correlation were dominated by the static derivatives. High angle of attack characteristics of modern aircraft are more dependent on dynamic derivatives which are heavily influenced by forebody geometry.

Mangold goes on to reaffirm the validity of the Bryant-Zimmerman characteristic equa­tion approach in the modern context and offers four rules to follow to avoid departure, as follows:

1. Avoid autorotation tendency (Clp < 0) and maintain yaw damping (C„r < 0) in order to keep the B coefficient [not Zimmerman’s D or Moul’s C] of the characteristic equation greater than zero.

2. C„edyn must be kept larger than zero, since this parameter determines the C coeffi­cient.

3. Close to maximum lift, where Cir is considerably larger than 1.0, it is essential to maintain C„edyn > 0 with negative Cie and only slightly positive C„e.

4. Nonlinearities and hysteresis effects versus sideslip have to be avoided.

The interesting reason for the fourth rule is the inaccuracy of sideslip sensors at high angles of attack, which makes it difficult to schedule control laws to cope with the problems of nonlinearities and hysteresis.

Recognizing the ingenuity and skill of the developers of departure parameters, it is still possible to question the place of these parameters in modern design practice. Departure pa­rameters such as C„edyn and LCDP may remain of interest in preliminary design. However, in a sense, departure parameter research is working behind the curve of modern computer development. Designers responsible for the stability and control of expensive new airplanes will recognize the essential nonlinearity of the departure and spin problems and plan ex­haustive digital simulations to explore the full envelope of flight and loading conditions and control inputs. Automated analysis can stack cases on cases and then winnow out those of no interest by algorithms that scan the results.

There is still the major effort required to build aerodynamic data bases for such enter­prises. Furthermore, such efforts would presumably evaluate candidate stability or control augmentation schemes, as well. Augmentation schemes for fly-by-wire systems, such as

used on the Tornado, can produce care-free airplanes that cannot be made to depart under any pilot action. Departure parameters would be of interest after the fact, to help make sense of the results and as a guide to the future.

The carrier-approach problem for naval aircraft received a great deal of atten­tion from leading aeronautical research organizations, starting in the late 1950s. We note

particularly contributions to the theory by groups at the NACA Ames Aeronautical Labora­tory, the Royal Aeronautical Establishment, and Systems Technology, Inc. Two main lines of investigation were prediction of the minimum acceptable carrier-approach airspeed for any airplane and the physics of optimum vertical path control during approaches.

The NACA Ames group examined some five candidate predictors for minimum ap­proach airspeeds (Drinkwater and Cooper, 1958). As found earlier, minimum drag speed correlated poorly with minimum acceptable carrier-approach airspeed. Other performance – related criteria were no better. Two that failed to correlate were the minimum air­speeds at which a given rate of change of flight path angle or a 50-foot climb could be obtained.

In the end, the Ames researchers concluded that a simple criterion based on stalling speed correlated best with the data. The minimum comfortable carrier-approach airspeed agreed best with 115 percent of the stalling speed in the power approach (PA) configuration, that is, flaps and landing gear down, power for level flight.

The Ames result is valid for airplanes of the general type tested, but one might be concerned at applying the 115-percent stalling speed prediction result to airplanes that differ radically from those tested. It seemed logical to try to develop a carrier-approach flight path model based on the fundamental flight and control dynamics and human factors of the problem. That was the motivation behind the work at Systems Technology, Inc., sponsored by the U. S. Navy. The STI engineers, including Tulvio S. Durand, Irving L. Ashkenas, Robert F. Ringland, C. H. Cromwell, Samuel J. Craig, Richard J. Wasiko, and Gary L. Teper, brought to the carrier-approach problem their well-known systems analysis techniques.

An interesting result, due to Ashkenas and Durand, identifies the transfer function pa­rameter associated with minimum drag speed, the point at which height control by elevator becomes reversed from the normal sense. This is a numerator factor in the elevator to height transfer function called 1/Th1. Negative values of this factor put a zero in the right half of the s-plane. Closing the height to elevator loop results in an aperiodic divergence corresponding to the reversal of normal height control below the minimum drag speed.

Around 1962, Ashkenas came up with the first systems analysis basis for minimum carrier-approach airspeed prediction. That is, his prediction for minimum approach airspeed was based on assumed pilot loop closures with an airframe defined by arbitrary mass, aerodynamic, and thrust characteristics (Ashkenas and Durand, 1963). Since the systems analysis approach does not merely correlate the behavior of existing airplanes, the results should apply to airplanes not yet built whose characteristics are beyond the range of those tested so far.

The Ashkenas-Durand systems analysis prediction for minimum carrier approach air­speeds can be explained as follows:

1. The approach is assumed to be made in gusty air.

2. In gusty air the pilot attempts to close the pitch attitude loop at a higher frequency than the gust bandwidth, or as high a frequency as possible.

3. The highest possible pitch attitude loop bandwidth occurs when the pilot’s gain is so high that the closed-loop system is just neutrally stable.

4. By excluding pilot model leads and lags, or treating the pilot as a pure gain, a definite gain value is associated with the neutrally stable closed pitch loop.

5. Similarly, an outer altitude control loop is closed by the pilot using pure gain, or thrust proportional to altitude error.

6. With both pitch and altitude control loops closed by the pilot, the sensitivity of the pitch control loop break frequency to pilot pitch control gain is calculated, as a partial derivative.

7. The sign of this partial derivative of pitch loop bandwidth to pilot pitch control gain, called the reversal parameter, is taken as an indication of carrier-approach performance. Positive reversal parameter values mean that increasing pilot gain improves bandwidth and performance.

8. The lowest airspeed at which the reversal parameter is positive is taken as a pre­diction of minimum carrier-approach airspeed.

The reversal parameter was refined in subsequent studies by Ashkenas and Durand in 1963 and by Wasicko in 1966. An interesting consideration was the finding in 1964 by Durand and Teper that the carrier-approach piloting technique as the airplane nears the carrier ramp changes from that assumed in the reversal parameter model. However, the approach airspeed would have already been set in the early part of the approach.

A later (1967) study of the carrier-approach problem by Durand and Wasicko went into the problem in greater detail, including the dynamics of the optical projection device that pilots use as a glide slope beam. The 1 /Te2 zero in the pitch attitude to elevator transfer function turned up as a primary factor, both in simulation and in landing accident rates. Unfortunately, this zero is dominated by airplane lift curve slope and airplane wing loading. Lift curve slope in turn is fixed by wing aspect ratio and sweep.

Wing loading, aspect ratio, and sweep are among the most fundamental of all design parameters for an airplane, affecting its flight performance. When a new carrier-based airplane is being laid out and wing loading, aspect ratio, and sweep are being selected to maximize such vital factors as range and flight speed, it is hard to imagine that a statistical connection with landing accident rate will be prominent in the trade-off.

Systems analysis methods were applied again to the carrier-approach problem in 1990 by Robert K. Heffley of Los Altos, California. Heffley studied the factors that control the carrier-approach outer loop involving flight path angle and airspeed. The higher-frequency pitch attitude inner loop was suppressed in the analysis, assumed to be tightly regulated by the pilot.

Heffley closed the outer loop under three different strategies, depending on whether the airplane was on the front side or back side of the drag required curve. The results give interesting insights into factors affecting the approach (Heffley, 1990). Another study in this series is an application of the Hess Structural Pilot Model (discussed in Chapter 21) to the carrier-approach problem, using a highly simplified pilot-airframe dynamic model.

The current U. S. Navy criterion for minimum carrier-approach speed, as exemplified by the system specification for the F/A-18 Hornet, gives no fewer than six possible limiting airspeeds, such as the lowest speed at which a 5-foot per second squared longitudinal acceleration can be attained 2.5 seconds after throttle movement and speed brake retraction. Heffley concludes that two additional criteria might be needed. One is a refinement of existing lag metrics to one that combines coordinated pitch attitude and thrust inputs. The other is an extension of the popup maneuver dealing with the end game, when the airplane is quite near the carrier’s ramp.

Canard aircraft are characteristically difficult to stall at all. The canard surface is generally designed to stall before the main, or aft, wing does, when the angle of attack is increased at a normal, gradual rate. When the canard does stall, with the main wing still unstalled, the airplane tends to pitch down, recovering normal flight. However, William H. Phillips comments that in the airplane pitch-down following canard stall, the canard surface’s angle of attack is increased again by the airplane’s angular velocity. This could delay recovery from an unstalled condition until the airplane has reached a steep nose-down attitude. It can be argued that an aft-tailed airplane also tends to recover automatically from a stall. On aft-tailed airplanes the horizontal tail, operating in the wing’s downwash, experiences a relative upload when the wing stalls. This is because the wing downwash drops off when the wing stalls.

The main concern in canard airplane stalls is the dynamic stall, entered at a high rate of angle of attack increase. Pitching momentum could carry the angle of attack up to the point where the main wing stalls, as well as the canard. In combination with unstable pitching moments from the fuselage, this could produce a total nose-up pitching moment that cannot be overcome by available canard loads. Wing trailing-edge surfaces that augment canard pitching moment control would be ineffective with the main wing stalled. Thus, a canard airplane’s main wing stall could produce deep stall conditions, in which a recovery to unstalled flight cannot be made by any forward controller motion (see Chapter 14). Deep stall at aft center-of-gravity positions and high power settings was identified in NASA tests of a tractor propeller canard configuration (Chambers, 1948).

The possibility of dynamic stalling on canard airplanes is minimized if the configuration is actually a three-surface case: main wing, canard, and aft horizontal tail. Examples of three – surface configurations are the Piaggio P180, the Sukhoi Su-27K, the DARPA/Grumman X-29A forward-swept research airplane, and the many three-surface airplanes designed by G. Lozino-Lozinsky, of MiG-25 fame. Even at extreme angles of attack that stall the main wing, the aft horizontal tail may be in a strong enough downwash field to remain unstalled, or it may be unstalled by nose-down incidence. With an unstalled aft horizontal tail, longitudinal control can be maintained.

Another way to minimize the possibility of dynamic stalling of canard airplanes is to operate them at centers of gravity far forward enough so that elevator power cannot produce high nose-up rotation rates. This amounts to restriction of the available center-of-gravity range and a reduction in the airplane’s utility.

The World War II Japanese Zero fighter airplane had very low roll performance at high airspeeds, due to wing twist. U. S. combat pilots took advantage of this weakness. They avoided circling combat and established high-speed, single-pass techniques. At high airspeeds, the roll rates of the U. S. airplanes could not be followed by the Zeros, which were operating near their aileron-reversal speeds.

The role of aileron reversal due to torsional flexibility on missions of the Boeing B-47 Stratojet is mentioned in Chapter 3, “Flying Qualities Become a Science.” Boeing engineers attempted to deal with the roll reversal problem when designing the B-47 (Perkins, 1970). They knew there was a potential roll reversal problem since the B-47’s wing tips deflected some 35 feet between maximum positive and negative loads. Using the best approach known at the time, strip integration, torsional airloads were matched to stiffness along the wing span. This method predicted an aileron-reversal speed well above the design limit speed. Unfortu­nately, this approach didn’t take into account wing bending due to aileron loads. Wing bend­ing on long swept wings results in additional twist. The actual aileron-reversal speed turned out to be too low for low-altitude missions. Quoting from Perkins’ von Karman lecture:

A complete theoretical solution to the problem was undertaken at the same time [as the strip method application] and due to its complexity and the lack of computational help, arrived at the right answer two years after the B-47 first flew. A third approach to the problem was undertaken by a few Boeing experimentalists who put together a crude test involving a makeshift wind tunnel and a steel sparred balsa wood model that was set on a spindle in the tunnel with ailerons deflected and permitted freedom in roll. The tunnel speed was increased until the model’s rate of roll started to fall off and then actually reverse. This was the model’s aileron reversal speed and came quite close to predicting the full-scale experience. The test was too crude to be taken seriously and again results came too late to influence the design of the B-47.

According to William H. Cook, the B-47 not only had excessive wing torsional deflection due to aileron forces, but also slippage in the torsion box bolted joints. The wings would take a small permanent shape change after every turn. These problems led to a test of spoiler aileronsona B-47, although the production airplane wasbuilt with normal flap-type ailerons.

Airplane stability augmentation must be rethought when designers choose to add direct normal and side force control surfaces. For example, with direct lift control through a fast-acting wing flap, pitch attitude can be controlled independently of the airplane’s flight path, and vice versa. The utility of such decoupled controls for tracking, defensive maneuvers, and for landing approaches is reviewed by David J. Moorhouse (1993).

20.4 Integrated Thrust Modulation and Vectoring

An airplane’s propulsion system can be integrated into a stability augmentation system that uses aerodynamic control surfaces. The total system would operate while the airplane remains under the control of the human pilot, qualifying as a stability-augmentation system rather than as an automatic flight control system.

For comparison, the previous coverage of propulsion systems in this book included:

Chapter 4 the effects of conventional, or fixed-configuration, propeller-, jet-, and rocket-propulsion systems on stability and control;

Chapter 10, Sec. 8 thrust vector control to augment aerodynamic surfaces in supermaneuvering;

Chapter 11, Secs. 14 and 15 propulsion effects on modes of motion and at hypersonic speeds;

Chapter 12, Sec. 1 carrier approach power compensation systems, for constant angle of attack approaches;

Chapter 20, Sec. 11 Propulsion-controlled aircraft, designed to be able to return for landing after complete failure of normal (aerodynamically implemented) control systems.

Depending on the number of engines under control, thrust modulation and vectoring systems can supply yawing, pitching, and rolling moments, as well as modulated direct forces along all three axes. Thus, thrust modulation and vectoring integrated into a stability – augmentation system can augment or replace the aerodynamic yawing, pitching, and rolling moments provided by aerodynamic surfaces. The situation is similar to aircraft like the Space Shuttle Orbiter, which carries both aerodynamic and thruster controls. However, in the context of stability augmentation, thrust modulation and vectoring would be used normally at the low airspeeds of approach and landing, rather than in space.

While in principle thrust modulation and vectoring can take the place of aerodynamic control surfaces at the low airspeed where the aerodynamic surfaces are least effective, it is reasonable to ask whether thrust stability-augmentation systems could satisfy flying qualities requirements. In a simulation program at DERA, Bedford (Steer, 2000), integrated thrust vector control was evaluated at low airspeeds on the baseline European Supersonic Commercial Transport (ESCT) design. The nozzles of all four wing-mounted jet engines were given both independent pitch and yaw deflections, providing yawing, pitching and rolling moments. Nozzle deflections were modeled as first-order lags. Conventional pitch rate, pitch attitude, velocity vector roll rate and sideslip command control structures were programmed.

Pitch control by thrust vectoring at approach airspeeds was as good as aerodynamic or elevon control, for a reason peculiar to the very low wing-aspect-ratio ESCT configuration. That is, the airplane has high induced drag at approach angles of attack, requiring large levels of thrust to maintain the glide path, thus making available large pitching moments with thrust deflection. Low airspeed roll and sideslip thrust vector control were positive and suitably damped but did not satisfy MIL-STD-1797A criteria.

In either case, whether airplane flying qualities are specified by a standardized specification such as MIL-F-8785 or by negotiations involving a Military Standard, there is still the matter of getting new airplanes to meet flying qualities requirements. In other words, the science of flying qualities is useless unless airplanes are held to the standards developed by that science.

In recent years, new airplanes are being bought by the U. S. armed services in a way that seems designed for poor flying qualities. Program officers are given sums of money sufficient to produce a fixed number of airplanes on a schedule. Military careers rest on meeting costs and schedules. These are customarily optimistic to begin with, having gotten that way in order to sell the program against competing concepts or airplanes.

The combination of military career pressures and optimistic cost and schedule goals usually leads to the dreaded (by engineers) “concurrency” program. Production tooling and some manufacturing proceed concurrently with airplane design and testing, rather than after these have been completed. When flying quality deficiencies crop up late in a concurrent program, requiring modifications to tooling and manufactured parts, it is natural for program officers and their counterparts in industry to resist.

Three notable recent concurrent programs were the Lockheed S-3 Viking anti-submarine airplane, the Northrop B-2 stealth bomber, and the U. S. naval version (T-45A) of the British Aerospace Hawk trainer, being built by McDonnell Douglas/Boeing. The Lockheed S-3 and McDonnell Douglas/Boeing T-45A concurrency stories are involved with the special flying qualities requirements of carrier-based airplanes and are discussed in Chapter 12, on that subject.

Another control surface balance type that appeared about the same time as beveled controls was the internally balanced control. This control is called the Westland-Irving internal balance in Great Britain. Internally balanced controls are intended to replace the external aerodynamic balance, a source of wing drag because of the break in the wing contour. In the internally balanced control the surface area ahead of the hinge line is a shelf contained completely within the wing contour (Figure 5.12). Unless the wing is quite thick and has its maximum thickness far aft, mechanical clearance requires either that the shelf be made small, restricting the available amount of aerodynamic balance, or control surface throws be made small, restricting effectiveness.

By coincidence, internally balanced controls appeared about the same time as the NACA 65-, 66-, and 67-series airfoil sections. These are the laminar flow airfoils of the 1940s and 1950s. Internally balanced ailerons are natural partners of laminar flow airfoil sections, since aerodynamic balance is obtained without large drag-producing surface cutouts for the overhang. Not only that, but the 66 and 67 series have far aft locations of wing maximum thickness. This helps with the clearance problem of the shelf inside of the wing contour.

An internal balance modification that gets around the mechanical clearance problem on thin airfoils is the compound internal balance. The compound shelf is made in two, or even three, hinged sections. The forward edge of the forward shelf section is hinged to fixed airplane structure, such as the tail or wing rear spar (Figure 5.13). The first application of the compound internal balance appears to have been made by William H. Cook, on the Boeing B-47 Stratojet. Internally balanced elevators and the rudder of the Boeing B-52 have compound shelves on the inner sections of the control surfaces and simple shelves on the outer sections.

Compound internal balances continue to be used on Boeing jets, including the 707, 727, and 737 series. The 707 elevator is completely dependent on its internal aerodynamic balance; there is no hydraulic boost. According to Cook, in an early Pan American 707, an inexperienced co-pilot became disoriented over Gander, Newfoundland, and put the airplane into a steep dive. The pilot, Waldo Lynch, had been aft chatting with passengers. He made it back to the cockpit and recovered the airplane, putting permanent set into the wings. In effect, this near-supersonic pullout proved out the 707’s manual elevator control. The 707’s internally balanced ailerons are supplemented by spoilers, as described in Chapter 19, “The Elastic Airplane.”

The later Boeing 727 used dual hydraulic control on all control surfaces, but internal aerodynamic balance lightens control forces in a manual reversion mode. An electrically driven adjustable stabilizer helps in manual reversion. At least one 727 lost all hydraulic power and made it back using manual reversion.

Internally balanced controls were used on a number of airplanes of the 1940s and 1950s. The famous North American P-51 Mustang had internally balanced ailerons, but they were unsealed, relying on small clearances at the front of the shelf to maintain a pressure

differential across the shelf. The Curtiss XP-60 and Republic XF-12 both used internally balanced controls, not without operational problems on the part of the XP-60. Water col­lected on the seal, sometimes turning to ice.

Electronic digital computerswere still yearsaway when Phillipsdid hisinertial cou­pling research. For numerical solutions that would attack the problem Phillips was obliged to simplify the equations with a series of ingenious mathematical steps. His successive transfor­mations led to inertial coupling stability boundaries derived by a simple quadratic equation.

For generality, Phillips nondimensionalized aircraft static stability parameters in terms of rolling frequency, or number of complete roll cycles per second. That is, the levels of both longitudinal and directional static stability or stiffness are characterized by their respective nonrolling natural frequencies, in short-period longitudinal and Dutch roll modes. These frequencies, expressed as cycles per second, are divided by the rolling frequency, as defined above, for the Phillips charts (Figure 8.2).

The remarkable but strong mathematical transformations added to the academic flavor of the charted results obscured the work’s significance to the hard-pressed stability and control engineers working in aircraft plants in the late 1940s, who should have paid more attention to Phillips’ results. Had a 1980s type digital computer been available to Phillips in 1947, permitting a few time histories of forthcoming fighter aircraft full-aileron rolls to

be calculated and presented, the airplane stability and control community would have taken notice.

Interesting background on Phillips’ inertial coupling work was contained in a 1994 letter from him. An excerpt from the letter reads:

In thinking about the subject lately, I have concluded that my approach was based on my training at MIT. In the courses that I took, particularly by Prof. Koppen, the derivations did not start with the complete equations of motion. The equations had already been divided into lateral and longitudinal groups and linearized. In Prof. Draper’s courses on instrumentation, much emphasis was placed on nondimensionalizing the results in terms of natural frequency. I did not read Bryan’s report, which starts from basic principles, for many years after that. If I had known the complete equations of motion, I might have been discouraged from attempting a solution.

While W. H. Phillips gave the first account of inertial coupling in the open literature, there seems to have been at least three other independent discoveries of inertial coupling. While working at the Boeing Company on the then-classified Bomarc missile, Roland J. White, Dunstan Graham, D. Murray, and R. C. Uddenberg found the problem and reported it in a Boeing Company document dated February 1948. At the Douglas Company’s El Segundo Division about the same time, Robert W. Bratt found inertial coupling in drop tests of a dummy Mark 7 bomb shape. A small amount of fin twist made the bomb spin. When the spin rate agreed with the bomb’s natural pitch frequency the spin went flat, or broadside to the wind.

Additional early work involving inertial coupling took place at the Cornell Aeronautical Laboratory in Buffalo, New York, by Donald W. Rhoads, John M. Schuler, and J. C. O’Hara. This was sponsored by the Structures Branch of the U. S. Air Force Wright Aircraft Laboratory, starting in 1949. Rhoads, Schuler, and O’Hara studied rolling pullouts, ma­neuvers that combine rolls and pullups. During the latter part of World War II vertical tail failures had occurred during rolling pullouts, as a result of large side-slip angles (Rhoads and Schuler, 1957).

Rhoads, Schuler, and O’Hara included inertial coupling terms in their study, among other refinements. Calculations of the critical peak side-slip angles agreed well with flight tests. However, their early numerical work, done at about the same time as the Phillips discovery, was for the Lockheed P-80 Shooting Star, whose inertial parameters are not much different than those of World War II airplanes. The P-80 has straight wings of moderately high aspect ratio and a fairly small value of the important inertial coupling parameter (Ix — Iy )/Iz. Inertial coupling was not prominent in the early stages of the Cornell Laboratory rolling pullout work, which actually extended over a period of five years. The stability and control community was not alerted.

The Phillips inertial coupling work, followed by flight occurrences of the phenomenon, led to a series of studies in Great Britain. W. J. G. Pinsker (1955, 1957, 1958) and H. H. B. M. Thomas (1960) were especially active.

Thus, the inertial coupling phenomenon, having been discovered in the late 1940s, was ignored by airplane designers until it was rediscovered in flight in the early 1950s. By 1956, the U. S. industry was roused enough to turn out for a conference on the subject held at Wright Field.