Dynamic longitudinal stability

The free longitudinal motions of any airplane fall into two modes. The first of these is a short-period oscillation. It is highly damped for conventional airplanes and also for all-wing airplanes in spite of the relatively low pitch-damping, Cmq. This somewhat surprising result is due to a coupled motion such that the vertical damping . . . comes into play absorbing the energy from the oscillation. Also, low moment of inertia in pitch makes the small existing Cmq more effective than a similar value would be in conventional types. In tests on the N-9M airplane this short-period oscillation was too rapidly damped to obtain a quantitative check. The combination of low static stability in pitch, as previously described, and low moment of inertia in pitch results in periods of oscillation for all-wing airplanes that are comparable to those of conventional types.

The second mode of longitudinal motion is a long-period oscillation commonly called the phugoid. This is a lightly damped motion even for conventional airplanes, and seems slightly less damped for all-wing airplanes, because of the fact that they have relatively low drag, and drag is the chief means of energy absorption in this mode. N-9M tests indicate that calculation is slightly optimistic in this matter, but still this phugoid motion is sufficiently damped so as to give no serious difficulties. Being a slow motion, it is easily controlled. . . .

Dynamic longitudinal response

The criterion of response is probably the only category in which the flying wing is importantly different from the conventional airplane for longitudinal motion. The action of the two types in an abrupt vertical gust is especially interesting, two factors combining to reduce the accelerations experienced by all-wing airplanes. These factors are the relatively larger wing chord and shorter effective tail length of the all-wing type. The first characteristic increases the time for the transient lift to build up and is the more important in reducing accelerations. The second decreases the time interval between the disturbing impulse at the lift surface and the correcting impulse at the effective tail, so that the airplane tends to pitch into the gust. This latter characteristic is a matter of concern to pilots, since a disturbance in the air is likely to leave them farther from trim attitude, consequently requiring more active pilot control in rough air. It is believed, however, that automatic control will effectively eliminate this difficulty.

The response of the all-wing airplane to elevator deflection seems entirely adequate. It errs, if at all, on the side of over-sensitivity because of low Cmq and low moment of inertia in pitch. An abrupt control movement giving the same final change in trim speed for a conventional and a comparable all-wing airplane results in a larger initial swing in pitch for the all-wing.

Dynamic lateral stability

As with longitudinal motion, there are two characteristic modes that are of interest laterally. the first of these is the spiral motion which is usually divergent on modern airplanes, thus uncontrolled flight results in a tightening spiral. This slight instability seems favored by pilots. All-wing airplanes have readily acceptable characteristics in this mode requiring from 15 to 20 seconds to double amplitude. In general, any time greater than five seconds to double amplitude is considered acceptable.

The second mode, the "Dutch Roll" oscillation, is more critical for all-wing airplanes, particularly at low speed, high weight and high altitude. All-wing airplanes seem comparatively bad in this respect because of the combination of relatively large effective dihedral and low weathercock stability and, for the conditions noted above as critical, are likely to approach neutral damping in the Dutch Roll mode. However, analytical determinations of this motion, using calculated damping derivatives, indicated less satisfactory characteristics than were obtained in actual flight tests. Because of a relatively low weathercock stability, the Dutch Roll is of a rather long period, in the order of ten seconds for the XB-35. It is usually assumed that for periods of such length, it is not important to have a high rate of damping since control would seem easily "inside" the motion. However, there may be particular instances where this is not true. For instance, in an all-wing airplane in which the rudder is particularly weak, the time of response to rudder control may be of the same order as the period of Dutch Roll motion. This would make directional control extremely difficult in a condition, such as landing, where the roll controls are not usable for changing heading. It is notable that for the very low weathercock stability commonly encountered in all-wing airplanes, the conventional solution of increasing weathercock stability to offset increased dihedral does not hold. . . .

Another factor contributing to the relative lack of damping of all-wing airplanes in Dutch Roll motion is the low value of the damping coefficient in yaw. . . . This appears to be inherent in all-wing designs, particularly if the use of fins is abandoned. For special occasions, when particular airplane steadiness is required (such as a bombing run), it is probable that the equivalence of such damping in yaw may be supplied by an automatic pilot, or by temporarily increasing the drag at the wing tips. This latter effect can be accomplished on the XB-35 by simultaneously opening both rudders and gives deadbeat damping in yaw.

Dynamic lateral response

As in the longitudinal motions, the amplitudes of response of an airplane in lateral motion are probably as important as the damping rates in determining free-flight characteristics. All-wing airplanes seem slightly rougher in turbulent air than conventional aircraft of similar weight. This is due chiefly to the reduced wing loading, but high effective dihedral and low weathercock stability may have an added effect. This is a matter of interest in fixing upon analytical criteria for the description of free-flight qualities. As mentioned above, increasing the weathercock stability for all-wing airplanes has a slight effect on the damping rates; however, it affects the amplitudes of response to gusts materially.

Some data from the free-flight tunnel of the National Advisory Committee for Aeronautics indicate that increasing weathercock stability, even for all-wing airplanes, materially helps the "flyability" of the airplane. Another bit of evidence that is of interest in this connection has to do with the magnitude of the side force derivative, Cy.B. Increase of this parameter improves Dutch Roll damping very materially but has virtually no effect on amplitude of response to gusts, according to calculations. Free-flight wind tunnel data again give tentative support to the investigations of response as a criterion by showing little improvement of flight qualities of models with increase of Cy'B.

Flight tests of the all-wing glider in which the vertical fin, located aft on the ship's center line, was varied in size from approximately 2 to 7 percent of the wing area, left the pilot somewhat undecided as to fin requirements except that the larger fin seemed somewhat easier to fly. Presumably, this was, in the light of the foregoing discussion, primarily because of the increased CnD, the coincidental increase in Cy'0 not being effective.

Automatic pilot control

The application of automatic pilot control to an all-wing airplane has certain difficulties which are associated primarily with the low value of C ,B. In conventional applications the fact that the airplane is side slipping is detected by either a lateral acceleration or an angle of bank. In an all-wing airplane neither of these indications exists except in an almost undetectable amount. Accordingly, it is necessary, in order to fly the airplane at zero sideslip, and therefore in the direction of its center line, to provide a yaw-vane signal to which the pilot or automatic pilot will respond. This introduces some difficulty in automatic pilot design because for small disturbances the sideslip angle with respect to the wind, and the yaw angle with respect to a set of fixed axes, are nearly equal and opposite for a flying wing. The customary automatic pilot control on azimuth angle therefore tends to oppose the necessary control on sideslip. To avoid this difficulty it is necessary only to reduce the rate of control on sideslip to approximately one-third that on azimuth. This modification to a conventional automatic pilot was flown on the N-9M with complete success.

Problems of configuration--swept vs.non-swept wings

Let us now turn to a consideration of the practical limitations in arrangement of the tailless airplane. They may be summarized briefly as sweepforward, sweepback, and a non-swept wing configuration. The sweepforward arrangement requires the use of a large fixed load forward of the leading edge at the center section for proper balancing of the airplane. Therefore, a fuselage with some substantial part of the weight empty of the airplane disposed therein is required. The swept-forward wing itself is unstable directionally and requires some type of fin for weathercock stability. To this must be added more fin area to stabilize the fuselage. In addition, it may be noted that the moment arm of the fin about the C.G. of the airplane is necessarily comparatively small, still further increasing the size of the required fin. If we add to the airfoil a protruding fuselage and an unusually large vertical tail surface, we have departed from our basic all-wing concept. We have incorporated virtually all the elements of drag found in the conventional aircraft and have not accomplished our intent of improving efficiency.. For the above reasons, which could be argued pro and con for hours, our company has done no active design and development work on airplanes with swept-forward wings.

Click here for next page