Category Airplane Stability and Control, Second Edition

Nonelectronic Stability Augmentation

Really ingenious nonelectronic stability augmentation systems came out of the jet’s awkward age, as designers tried to have artificial damping without the heavy, costly, and, above all, unreliable electronics of the period. A mechanical yaw damper, invented by Roland J. White and installed on early Boeing B-52 Stratofortresses, is a good example of the genre.

Imagine a rudder tab that is free to rotate on low friction bearings. Instead of being connected to an electric actuator, or to cables leading to the cockpit, the free tab is driven by

Nonelectronic Stability Augmentation

Figure 7.1 Boeing B-52 rudder control linkages. R. J. White’s magnetically phased bobweight yaw damper operates the stability tab. (From B-52 Training Manual, 1956)

inertia forces acting on a small bobweight located ahead of the hinge line (Figure 7.1). Tab position is further modified dynamically by an eddy current damper, providing damping hinge moments proportional to tab rotational velocity.

As the airplane goes through a typical lateral or Dutch roll oscillation, the vertical tail assembly swings from side to side, accelerating the tab bobweight. Without the eddy current damper it is clear that the tab will take up deflections in phase with the lateral accelera­tion at the vertical tail. However, ideally, tab positions should be phased with respect to yawing velocity in such a way as to drive the rudder in opposition. This is the classic yaw damping action, right rudder in opposition to left yawing velocity. The function of the eddy current damper is to “tune” tab deflections to create exactly that phasing. In 1952, a similar approach was taken by M. J. Abzug and Hans C. Vetter of the A3D Skywarrior design team at Douglas Aircraft, to provide nonelectronic yaw damping for that airplane. The design method was cut and try on the analog computer, to find the proper combina­tion of bobweight mass and damper size that would phase the tab, creating effective yaw damping.

The obvious practical problem with the B-52 and A3D yaw dampers is one that is faced with any purely mechanical system, as compared with a modern electromechanical control system. In the mechanical system, the result or output depends critically on the condition of each component. If the free tab’s bearings deteriorate over time or are invaded by grit, or if the eddy current damper’s effectiveness is changed, tab phasing will be thrown off.

In the extreme case, tab action could actually add to the airplane’s lateral oscillation, instead of damping it.

In a July 1994 letter Roland White describes such a situation that actually occurred on a B-52, as follows:

A rudder tail shake on a test airplane caused the magnetic damper to lose its damping. A serious accident would have occurred if the bobweight did not jam due to a mechanical failure. After that I found when going to work the next day your friends will ask if you still work here.

A modern, electromechanical yaw damper drives the rudder in opposition to the measured rate of yaw. It does so by comparing the current rudder position with the desired value and continuing to exert torque on the rudder until that value is reached, overriding mechanical obstacles such as sticky bearings or even losses in performance of the motor that drives the rudder.

The practical shortcomings of purely mechanical yaw damping were not unknown to the Boeing and Douglas design staffs. When a chance appeared to get a yaw damper function electronically, that option was taken instead. In the case of the B-52, the spring-tab – controlled rudders were replaced by powered rudders, allowing Boeing to use the electro­mechanical yaw damper design developed successfully for the B-47.

In the Douglas case, electromechanical yaw damping was installed using components of the airplane’s well-proved Sperry A-12 automatic pilot. The Sperry Gyroscope Company’s DC-3 “dogship” proved the concept in test flights at the Sperry plant in Long Island, New York. Signals from the outer, or yaw, gimbal of the A-12’s free directional gyro were elec­tronically differentiated through a lead network and sent to the rudder servo. Differentiated yaw angle is of course yaw rate.

This worked well when the system was transferred to the A3D and flown routinely at Edwards Air Force Base. Then one day a test pilot bringing an A3D back for landing dove at the runway and pulled up into a chandelle, a natural thing to do for a high-spirited test pilot with an airplane he likes. The A3D, with yaw damper on, responded by applying bottom rudder during the nearly vertical bank, diving the ship back toward the ground.

The pilot regained control and an investigation started at once. The A-12 and yaw damper function were found to be in perfect order. The culprit turned out to be what had been called for years “gimbal error.” The A-12 directional gyro is a conventional two-gimbal free gyro, with yaw measured on the outer gimbal. The rotor, spinning in the inner gimbal, is slaved to magnetic north and the inner gimbal itself is erected to gravity by a bubble level system. The angle between the outer gimbal and the instrument’s case is true yaw or heading angle as long as the outer and inner gimbals are at right angles to each other. This holds only for zero bank angle. At the sharp bank angles of the chandelle, or in any steep turn, the yaw reading picks up errors that depend on the heading angle (Figure 7.2).

During turns, differentiation with respect to time of the erroneous yaw angle exagger­ates the ordinary gimbal errors. The A3D experience proves dramatically that one cannot in general differentiate free gyro signals to produce damping signals for stability augmen­tation, at least for airplanes that maneuver radically. After the all-mechanical and free-gyro A3D yaw damper designs were proved faulty the airplane was finally fitted with what is now the standard design, a single-degree-of-freedom yaw rate gyro driving the rudder servo.

A rather more successful nonelectronic stability augmentation system was developed at the Naval Weapons Center, China Lake, for the AIM-9 Sidewinder missile. The Sidewinder

Nonelectronic Stability Augmentation

Figure 7.2 Gimbal angles of the outer gimbal of the Sperry A-12 directional gyro, as a function of bank and yaw angles. The outer gimbal rate fluctuates strongly in turns at steep bank angles. Differentiating outer gimbal angle to obtain yaw rate caused a near-crash of a Douglas A3D-1 Sky Warrior. (From Abzug, Jour. of the Aero. Sciences, July 1956)

derives roll damping from nonelectronic, air-driven flywheels mounted at the tips of the missile’s ailerons, producing gyroscopic torques that drive the ailerons to oppose roll rate. The flywheel torques are evidently high enough to override variations in aileron bearing friction. There seems to have been no application of this all-mechanical damping system to airplanes.

Air-to-Air Missile-Armed Fighters

A price has to be paid for extreme rolling performance in terms of demands on hydraulic system size and flow rate and on structural weight required for strength and stiffness. This led to a new controversy. As in the days of P-40s versus Zeros, high roll rates were important in dogfight gun-versus-gun battles.

But what about fighters that merely fired air-to-air missiles? Sparrow I and Sidewinder air-to-air missiles both went into service in 1956. Clearly, the missiles themselves can do the end-game maneuvering, to veer left and right, climb and dive, following any feints by the airplane being attacked. Penalizing missile-armed fighters so that they could carry out dogfight tactics might be as foolish as it would have been to require Army tank crews to wear cavalry spurs.

The drive to reduce fighter airplane rolling requirements because of the advent of missile­armed fighters was led on the technical side by a former NACA stability and control engineer who had risen to a high administrative level. The then USAF Director of Requirements weighed in with a letter stating flatly that the F-103 would be the last USAF manned fighter airplane.

The need for high levels of fighter airplane rolling performance was argued back and forth at Wright Field and the Naval Air Systems Command until the issue was settled by the Vietnam War of 1964-1973. U. S. fighters went into that conflict armed with both Sparrow and Sidewinder air-to-air missiles. Nevertheless, they found themselves dogfighting with Russian-built fighters. The reason that aerial combat was carried out at dogfighting ranges was that visual target identification and missile lock-before-launch doctrines were found to be needed, to avoid missile firings at friendly targets. Ranges for positive visual identification were so small that engagements quickly became dogfights. High roll rates were once more in favor. Of course, dogfighting capability meant that guns could still be used effectively on missile-carrying fighters.

Ultralight and Human-Powered Airplanes

The category of ultralight airplanes ranges from hang gliders to light versions of general-aviation airplanes. They fill a need for experimenters and for pilots who want to fly inexpensively and with little regulation. Ultralight airplanes evolved as did the early flying machines, by much cut-and-try and flight testing. Although these designs have been useful, indications are that many commercial ultralights are deficient in stability and control.

Human-powered airplanes are extreme ultralights, designed not for practicality but to push the engineering and human limits of aviation. Early efforts at human-powered flight were discouraging because of the poor performance and extreme fragility of the machines that were constructed before the first successful one, the Gossamer Condor.

13.1 Apparent Mass Effects

For very light airplanes, not much heavier than the air in which they fly, apparent mass effects must be considered. These effects were first noticed in 1836 by George Green, who found that pendulum masses in a fluid medium were apparently greater than in a vacuum. The apparent mass effect can be described as follows (Gracey, 1941):

The apparent increase in mass can be attributed to the additional energy required to establish the field of flow about the moving body. Inasmuch as the motion of the body may be defined by considering its mass as equal to the actual mass of the body plus a fictitious mass, the effect of the inertia forces of the fluid may be represented as an apparent additional mass; this additional mass, in turn, may be considered as the product of an imaginary volume and the density of the fluid. The effect of the surrounding fluid has accordingly been called the additional mass effect. The magnitude of this effect depends on the density of the fluid and the size and shape of the body normal to the direction of motion.

The primary motivation for Gracey’s work was to be able to correct airplane and wind – tunnel model moments of inertia measured by suspending the airplanes or models and swinging them aslarge pendulums. To the extent that the NACA wasinvolved with equations of motion for the airships of those days, this would have given Gracey yet another motivation to study apparent mass.

The 1941, the NACA apparent mass tests were made by swinging covered frameworks of various shapes as compound pendulums. The test specimens were swung both in air and in a vacuum tank. It is interesting that Gracey started out with balsa wood shapes, but found that their weights varied with air pressure and humidity. Gracey’s training in this exacting experimental work must have helped him to appear later on as NASA’s expert in airspeed and altitude measurement methods.

Interest in apparent mass effects returned with the advent of the plastic and fiber materials that could be used to build very light airplanes, such as the human-powered Gossamer Condor and the high-altitude, long-duration pilotless airplanes Pathfinder and Helios, all built by Aero Vironment, Inc., of Monrovia, California. Apparent mass effects are important as well for lighter-than-air and for underwater vehicles. Mathematical models of these craft for dynamic stability analysis include apparent mass terms, as a matter of course. In the series expansions for aerodynamic forces and moments originated by G. H. Bryan, apparent mass terms appear as derivatives with respect to linear and angular accelerations.

Lacking the vacuum swinging apparatus of Green and Gracey, one can approximate apparent mass terms in the equations of airplane motion by adding cylindrical air masses to the lifting surfaces, with diameter equal to the surface chord for motions normal to the chord and equal to the surface thickness for motions in the chord plane. This approximation yields the following astonishing results for the Gossamer Condor. The apparent masses in lateral and vertical motions are 21 and 170 percent of the actual airplane mass. The apparent moments of inertia in pitch and roll are 140 and 440 percent of the actual moments of inertia.

In addition to measurements on swinging models and the approximations mentioned above, panel computer codes can be used for apparent mass estimation. David A. Lednicer reports that the VSAERO code is used routinely for apparent mass calculations on under­water vehicles.

The Rotation-Only Breakthrough

The rotation-only concept for variable sweep was pioneered by Dr. Barnes Wallis at Vickers-Armstrongs, Weybridge, around 1954. Starting in 1959, brilliant work by a NASA Langley Laboratory team, including Dr. Wallis, made variably swept wings a practical design option. Team members William J. Alford, Jr., Edward C. Polhamus, and Wallis found a practical way to eliminate the translation, or fore-and-aft motion of the wing inboard ends, drastically simplifying the variable-sweep rotation/translation mechanism to rotation alone.

The clue was to pivot the wings well out from the airplane centerline and to bring the wing trailing edges when fully swept parallel and close to the horizontal tail leading edges. In the Alford-Polhamus-Wallis design, the wing pivots are on the outboard ends of a glove, a diamond-shaped, highly swept inboard fixed-wing section. Wing spanwise loads are carried primarily on the outboard or unswept panels when the wings are in the forward position. The wing’s spanwise load shifts relatively inboard, to the glove, when the wings are in the aft position. This relative load shift is exactly what one wants in order to minimize movement of the total wing aerodynamic center when the wings go through its sweeping routine (Loftin, 1985). Alford and Polhamus jointly hold the U. S. patent on this design.

An additional benefit of the Alford-Polhamus-Wallis arrangement arises from downwash changes with wing sweep. Bringing the wing trailing edge close to the horizontal tail drastically increases the downwash rate of change with angle of attack, reducing the tail’s stabilizing effect. That is, the tail’s increasing up-load with increasing angles of attack is reduced. In effect, the wing acts as a huge turning vane, aligning with itself the airflow into the horizontal tail. Reduced stability from the horizontal tail is just what is needed when the wing is swept back by rotation alone.

Another way of thinking of the Alford-Polhamus-Wallis arrangement is to consider the horizontal tail as an extension of the wing when the latter is fully swept back. Surface area at the rear of a lifting surface carries a smaller airload than does the same amount of area as an independent lifting surface. The lower airloads on the horizontal tail result in reduced static longitudinal stability, again just what is needed.

Additional Special Forms of the Equations of Motion

Trajectory or point-mass equations of airplane motion, lacking the torque or mo­ment equations, have been found useful for flight performance studies. In these applications, angles of attack and sideslip are assumed functions of time or are found in simple closed loops, instead of being the result of attitude adjustments influenced by control surface an­gles. Trajectory equations of motion have only 6 nonlinear state equations, as compared with 12 for the complete rigid-body equations. The savings in computer time are unimpor­tant with modern digital computers, but there is a conceptual advantage for performance studies in needing to specify only lift, drag, and thrust parameters.

Another special form of the equations of airplane motion puts the origin of body axes at an arbitrary location, not necessarily the center of gravity. The first use of such equations seems to have been for fully submerged marine vehicles, such as torpedoes and submarines. With the center of body axes at the center of buoyancy, there are no buoyancy moment changes due to changes in attitude (Strumpf, 1979). An equivalent set for airplanes came later (Abzug and Rodden, 1993).

Apparent mass and buoyancy terms in the equations of airplane motion are discussed in Chapter 13, “Ultralight and Human-Powered Airplanes.” The various special forms of the equations of airplane motion for representing aeroelastic effects are discussed in the next chapter, “The Elastic Airplane.”

Equationsof motion for an airplane with an internal moving load that isthen dropped were developed by Bernstein (1998). The motivation is the parachute extraction and dropping of loads from military transport airplanes. A control strategy using feedback from disturbance variables to the elevator was able to minimize perturbations in airplane path and airspeed during the extraction and dropping process.