Category Airplane Stability and Control, Second Edition

Layout Principles

6.1.1 Subsonic Airplane Balance

Subsonic tail-last (not canard) airplanes are generally balanced to bring their cen­ters of gravity near the wing-alone aerodynamic center. This is the point at which the wing’s pitching moment coefficient is invariant with angle of attack. For reasonably high wing aspect ratios, the wing-alone aerodynamic center is near the 25-percent point behind the leading edge of chord line passing through the wing’s center of area. This chord line is called the wing’s mean aerodynamic chord or mac. Figure 6.1 shows the simple geometric construction defining the mac for straight-tapered and elliptical wings.

Tailless airplanes must have their centers of gravity ahead of the wing aerodynamic center or 25-percent mac point to be inherently statically stable. If the wing is swept back, it can be trimmed at a reasonably high lift coefficient with trailing-edge-up deflections of its elevons. The degree of static stability desired and the maximum lift coefficient ob­tained are interrelated. Tailless airplanes can have their centers of gravity behind the wing

Layout Principles

Figure 6.1 Geometrical constructions for the mean aerodynamic chord (mac) on straight-tapered and elliptical wings.

aerodynamic center if static stability is provided by artificial means or stability augmentation (see Chapter 20). Longitudinal trim then requires trailing-edge-down elevon. This increases effective wing camber, with beneficial effects on performance (Ashkenas and Klyde, 1989).

The canard configuration, abandoned after 1910 by its inventors, the Wright brothers, has been revived in recent years, notably by Burt Rutan, in the belief that the arrangement provides natural stall prevention (see Chapter 17, Sec. 2). Also, trimming with an upload is thought to reduce induced drag, although this has been disputed. The neutral point, or center of gravity for neutral stability, of canard airplanes is considerably ahead of the 25-percent point of the wing mac. On the Rutan machines, fuel tanks are fitted in triangular leading-edge extensions to keep the fuel near the airplane’s center of gravity.

Rotary Balances and the Steady Spin

Rotary balances are designed to extract rotary derivatives from wind-tunnel tests. The model is typically held at some fixed angles of attack and sideslip to the relative wind and rotated by an electric motor at a fixed rate (Figure 9.6). Combined aerodynamic, gravity, and inertial forces and moments are measured by a six-component balance internal to the model. The desired aerodynamic forces and moments are obtained by subtracting the other components, as tares. Rotary balance tests in which angles of attack and sideslip remain constant are called “coning tests.” The spinning axis is aligned with the tunnel flow direction for coning tests.

Rotary balance testing actually predates the free-spinning tunnel, with E. F. Relf and T. Lavender’s 1922 and 1925 measurements in Britain. An earlier paper (Relf and Lavender,

Rotary Balances and the Steady Spin

Figure 9.6 The NASA Langley Research Center’s current spin tunnel rotary balance rig. The electric motor that spins the model is outside the tunnel. At the left, a model in a flat-spinning orientation; a normal spin orientation is at the right. This is believed to be the only rotary balance in current (early 1990s) use at Langley. (From Bihrle and Chambers, AGARD AR 265, 1990)

1918) described some of the first tests on autorotating wings. Autorotation is wing negative damping in roll, at angles of attack beyond the stall. Autorotation provides a driving or propelling moment in spins.

Until the coming ofthe jet airplane and the oscillatory spin, the chiefuse of rotary balance testing was in finding the steady spin modes of an airplane. That is, would spins be steep, or easily recoverable, or fast and flat, with problematic recoveries? The pioneering rotary bal­ance work of thistype wasdone by P. H. Allwork using the NPL 7-foot wind tunnel in Britain, and Millard Bamber and Charles Zimmerman in the NACA 5-foot vertical wind tunnel.

With simplifying assumptions, the three force equations of the ordinary 6-degree – of-freedom equations of airplane motion reduce to only two equations, which are not simultaneous with the three moment equations. Under steady conditions, angular accel­erations drop out. With aerodynamic data from rotary balance coning tests, the remaining three simultaneous moment equations are fairly readily solved for the equilibrium spin.

The groundwork for equilibrium spin analysis was laid in a remarkable 1926 report by Sidney B. Gates and L. W. Bryant. The Gates and Bryant report was far ahead of its time, and quite comprehensive. A modern explanation of the mechanics of the equilibrium spin solution is given in William Bihrle, Jr.’s paper in Sec. 9.1 of AGARD Advisory Report No.265, dated 1990.

Principal Axis Inclination Instability

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

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

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

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

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

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

1948 and 1966 NACA and NASA Test Series

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

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

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

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

1948 and 1966 NACA and NASA Test Series

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

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

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

Wind, Body, Stability, and Principal Axes

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

Wind, Body, Stability, and Principal Axes

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Automatic Pilots in History

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

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

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

Faceted Airframe Issues

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

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

Faceted Airframe Issues

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

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

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

The First Flying Qualities Specification

Edward P Warner, acting as a consultant to the Douglas Aircraft Company in the design of the DC-4E transport, has the distinction of having first embodied flying qualities research into a specification that could be applied to a new airplane design, much as characteristics such as strength and performance had been specified previously. Warner’s 1935 requirements were based on interviews with airline pilots, industrial and research test pilots, and NACA staff engineers. Warner also recognized the need to put flying qualities requirements on a sounder basis by instrumented flight tests correlated with pilot opinions.

3.2 Hartley Soule and Floyd Thompson at Langley

Warner’s ideas were picked up by the NACA (Warner was, after all, a member of the main committee; his ideas counted), and the grand comprehensive attack on airplane flying qualities started. The authorizing document was NACA Research Authorization number 509, “Preliminary Study of Control Requirements for Large Transport Aircraft” (Hansen, 1987). Hartley A. Soule (Figure 3.3), a portly, worldly-wise staff member at the NACA Langley Aeronautical Laboratories in Hampton, Virginia, ran tests the following year (1936) that attempted to correlate the long-period longitudinal or phugoid mode of motion with pilots’ opinions on handling qualities. The phugoid motion involves large pitch attitude and height changes at essentially constant angles of attack. Eight single-engine airplanes were tested by Soule and his group. This pioneering attempt showed that neither period nor damping of the phugoid motion had any correlation with pilot opinion.

However, the NACA was fairly launched on the idea of correlating flying qualities mea­surements with pilots’ opinions. Soule and his associate, Floyd L. Thompson, outlined the practical steps needed to carry out Warner’s ideas. Flying qualities had to be defined “in terms of factors known to be susceptible of measurement by existing NACA instruments or by instruments that could be readily designed or developed.”

Thompson and Soule started with what we would now call a set of “straw man” require­ments based on Warner’s work, but modified to be measurable by NACA’s instruments. They used a Stinson Reliant SR-8E single-engined high-wing cabin airplane (Figure 3.4) for the tests. It turned out that the only instruments that needed to be specially developed for the Stinson tests were force-measuring control wheel and rudder pedals. These used hydraulic cells developed by the Bendix Corporation as automobile brake pedal force indicators.

The “straw man” NACA requirements seemed to ignore Soule’s previous findings of the unimportance of the longitudinal phugoid motion, and a reasonably well-damped oscillation of period not less than 40 seconds was specified. Even more curiously, F. W. Lanchester’s research on the phugoid period was quite overlooked in the straw man requirements, although Lanchester’s results were given in the well-known 1934 “Dynamics of the Airplane,” by B. Melvill Jones, which was included in Volume V of W. F. Durand’s Aerodynamic Theory. Lanchester had shown that the phugoid period for all aircraft was linearly proportional to airspeed and would invariably fall below the required 40 seconds at airspeeds under about 150 miles per hour.

The First Flying Qualities Specification

Figure 3.3 Hartley A. Soule (1905- ), a pioneer in flying qualities research. (From Hansen,

Engineer in Charge, NASA SP-4305, 1987)

Aside from this cavil, Soule’s research followed reasonable lines. Each straw man re­quirement was stated, test procedures to check each requirement were spelled out, and the test results were presented and discussed. Some of Soule’s 1940 test procedures have come down to our day virtually unchanged except for the increased sophistication of data recording. For example, there were measurements of elevator angle and stick force for equi­librium flight at various airspeeds, measurements of time to bank to a specified angle, and, most advanced of all, measurements of the period and damping of the phugoid oscillation

The First Flying Qualities Specification

Figure 3.4 The Stinson SR-8E airplane used in Hartley Soule’s pioneering stability and control flight

test measurements. (FromNACA Rept. 700, 1940)

as a function of airspeed (Figure 3.5). The Lanchester approximation for phugoid period is shown as a dashed line in Figure 3.5(a).

In his published report Soule (1940) provides the variations with airspeed for equilibrium flight of both the elevator angle and the control column position from the dashboard. These data would give exactly the same trends were it not for stretch of the control cables that connect the two, under load. Vincenti’s book tells the interesting story of the discovery of the effects of cable stretch on the Stinson data.

Soule’s report was reviewed in preliminary form by engineers at the Chance Vought Aircraft plant in Connecticut, who noticed that different incidence settings of the horizontal tail affected the variations in elevator angle for equilibrium flight, an unexpected outcome. C. J. McCarthy of Chance Vought wrote to Soule suggesting that the discrepancy might be explained by control cable stretch if the elevator angle had been deduced from the control column position, rather than having been measured directly at the surface itself. According to Vincenti:

Robert R. Gilruth, a young engineer who had recently taken over the flying quality program when Soule moved to wind tunnel duties, measured the stretch under applied loads and found that Chance Vought’s supposition was in fact correct… In tests of later airplanes, elevator angles were measured directly at the elevator. Such matters seem obvious in retrospect, but they have to become known somehow.

The First Flying Qualities Specification

Figure 3.5 Dynamic stability measurements for the Stinson SR-8E, made around 1937 by Hartley Soule. (FromNACA Rept. 700, 1940)

Some Stinson measurements called for by the straw man requirements are definitely archaic and not a part of modern flying qualities. Very specific requirements were put on the time needed to change pitch attitude by 5 degrees; these were checked. Likewise, the need to limit adverse yaw in aileron rolls was dealt with by measuring maximum yawing acceleration and comparing it with rolling acceleration. The yaw value was supposed to be less than 20 percent of the roll value. However, all of the pieces were in place now and ready for the next major step.

After the Stinson tests the NACA had the opportunity to test a large airplane, the Martin B-10B bomber. Those results went to the Air Corps in a confidential report of 1938. According to Vincenti, Edward Warner was able to feed back both the Stinson SR-8E and Martin B-10B results to his flying qualities requirements for the Douglas DC-4E, which was just beginning flight tests.

3.3 Robert Gilruth’s Breakthrough

Robert R. Gilruth (Figure 3.6) came to NACA’s Langley Laboratory in 1937 from the University of Minnesota. His slow, direct speech reflected his midwestern origins. He is remembered for a remarkable ability to penetrate to the heart of problems and to convince and inspire other people to follow his lead. When Gilruth fixed one with a penetrating stare and, with a few nods, explained some point, there was not much argument. Many

The First Flying Qualities Specification

Figure 3.6 Robert R. Gilruth (1913-2000). An early expert in airplane flying qualities and design methods. He played a leading role later on in NASA’s space program. (From Hansen, Engineer in Charge, NASA SP-4305, 1987)

years later, when NACA became NASA, Gilruth was tapped by the government to head the NASA Manned Spacecraft Center.

Gilruth’s seminal achievement was to rationalize flying qualities by separating airplanes into satisfactory and unsatisfactory categories for some characteristic, such as lateral control power, by pilot opinion. He then identified some numerical parameter that could make the separation. That is, for parameter values above some number, all aircraft were satisfactory, and vice versa. The final step was to develop simplified methods to evaluate this criterion parameter, methods that could be applied in preliminary design.

The great importance of this three-part method is that engineers now could design sat­isfactory flying qualities into their airplanes on the drawing board. Although proof of good flying qualities still required flight testing, engineers were much less in the dark. The old way of doing business is illustrated by an NACA report (W-81, ACR May 1942) on the de­velopment of satisfactory flying qualities on the Douglas SBD-1 dive bomber. Discussing a Phase III series of tests in September 1939, the report said, “The best configuration from this phase was submitted to a pilot representative from the [Navy] Bureau [of Aeronautics], who considered that insufficient improvements [in control force characteristics] had been made.”

Two applications of this new method were published (1941) by Gilruth and co-authors Maurice D. White and W. N. Turner to static longitudinal stability and to lateral control power, respectively. White had joined Gilruth at Langley in 1938. Fifteen airplanes ranging in size from the Aeronca K to the Boeing B-15 were tested in the first series, on longitudinal stability. Gilruth and White suggested a design value of 0.5 for the gradient of elevator angle with angle of attack, for the propeller-idling condition, to ensure power-on stability and adequate stick movement in maneuvers.

In the lateral control application of the new method, 28 different wing-aileron combi­nations were tested, including alterations to the wings and ailerons of two of the airplanes tested (Figure 3.7). The famous lateral control criterion function pb/2V came into being as a result of this work. pb/2V is the helix angle described by a wing tip during a full-aileron

The First Flying Qualities Specification

Figure 3.7 The 15 airplanes tested by Gilruth and White to get data for their longitudinal stability estimation method. (From NACA Rept. 711, 1941)

The First Flying Qualities Specification

Turner. At the minimum allowable pb/2V value of 0.07 radian, the roll helix angle creates a complete roll in a forward distance traveled of 44.8 wing spans, regardless of the airspeed.

roll. Gilruth and Turner fixed the minimum satisfactory value of the full-aileron pb/2V as 0.07, expressed in radian measure (Figure 3.8). A remarkably simple preliminary design estimation technique for pb/2V was presented, based on a single-degree-of-freedom model for aileron rolls (Figure 3.9).

Robert Gilruth’s early flying qualities work was closed out with publication (1943) of “Requirements for Satisfactory Flying Qualities of Airplanes.” This work had appeared in classified form in April 1941. A three-part format was used. First, the requirement was stated. Then there were reasons for the requirement, generally based on flight tests. Finally, there were “Design Considerations” related to the requirement, the all-important methods that would permit engineers to comply with the requirements for ships still on the drawing board.

Gilruth’s 1943 work introduced the concept of the pilot’s stick deflection and force in maneuvers and the criteria of control deflection per g and stick force per g. Vincenti points out that the control deflection and stick force per g criteria may have been independently conceived in Britain by S. B. Gates (Figure 3.10). Prior to the Gilruth/Gates criteria, stability and control dealt with equilibrium or straight flight conditions. W. H. Phillips calls this quantization of maneuverability one of Gilruth’s most important contributions to airplane flying qualities.

The First Flying Qualities Specification

Figure 3.9 The control surface effectiveness derivative к, back-figured from flight tests of 28 different airplane configurations. Wing twist, control system stretch, and nonlinearities at large control angles all account for the markedly lower values than the Glauert thin airfoil theory, shown dotted. (From Gilruth and White, NACA Rept. 715, 1941)

Balancing or Geared Tabs

Control surface tabs affect the pressure distribution at the rear of control surfaces, where there is a large moment arm about the hinge line. A trailing-edge-up tab creates relative positive pressure on the control’s upper surface and a relative negative pressure peak over the tab-surface hinge line. Both pressure changes drive the control surface in the opposite direction to the tab, or trailing-edge-down.

When a tab is linked to the main wing so as to drive the tab in opposition to control surface motion, it is called a balancing or geared tab. Balancing tabs are used widely to reduce control forces due to control surface deflection. They have no effect on the hinge moments due to wing or tail surface angle of attack. Airplanes with balancing tabs include the Lockheed Jetstar rudder, the Bell P-39 ailerons (augmenting Frise ailerons), and the Convair 880M.

Partial Power Control

Another control system compromise made during the jet’s awkward age was to try to get by with direct manual control for one or more surfaces. The Douglas F4D Skyray’s rudder was a good example. The F4D was a small, single-engine jet whose demands for rud­der controllability seemed minimal. Of course, there were no asymmetric power conditions to consider. Rudder control in cross-wind landings and takeoffs and to make coordinated turn entries and recoveries was shown to require only modest amounts of rudder deflection and pedal force.

The F4D could be spun, and was required to have good spin recovery characteristics. Ordinarily, this would require full rudder in opposition to the spin, and the corresponding pedal force for a manually controlled rudder would be high. However, the F4D’s inertia distribution made the elevons the primary spin recovery control. The rudder, in any case fully shielded from the airflow by the wing at spin attitudes, could be in any position without affecting spin recovery

All was fine until F4D test pilot Robert O. Rahn inadvertently entered an inverted spin. The rudder was now unshielded. The air flow direction in the spin drove the rudder in the pro-spin direction. Not only that, but the unshielded rudder’s effectiveness in the inverted spin was high enough to require that it be deflected in the opposite, or anti-spin, direction for a satisfactory recovery. With no hydraulic power assistance, the best Rahn could do with an estimated 300 pounds of pedal force was to neutralize the rudder (and then use the emergency spin chute for recovery). This unanticipated demand for rudder deflection meant that the original decision to save the cost and complexity of hydraulic power for the rudder was not justified.