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Aviation History
1939
1939 - 0848.PDF
SUPPLEMENT TO FLIGHT 3046 10 THE AIRCRAFT ENGINEER MARCH 23, 1939 When wind-tunnel tests of a lateral control are carried out in this country, the tunnel measurements are' made about wind axes, but the results are converted to body axes for comparison with other data, and although there has been much talk recently of '' favourable '' and '' un-, favourable " yaw, this talk has been of a loose nature, and nobody seems to have made up his mind how much "favourable" yaw is favourable. In short, the A.R.C. have made no real attempt to enquire into the soundness of the basis on which control comparisons are being made, or to find a fixed anchorage for the vague talk about yawing moments. It seems certain that the axes question is retard ing the search for better lateral control, and it is in the hope of provoking a fresh consideration of this important matter that these notes have been written. American Views It is encouraging to find that, in some of the more recent N.A.C.A. reports, the Americans (who at the beginning of a long series of tunnel and flight tests of lateral controls were quite adamant about the body axes being the only valid ones) have later slipped quietly into the use of wind axes " in order to correspond to the pilot's reactions to the motion of the airplane." Surely pilots' reactions alone are not sufficient ground for changing the basis of a scientific in vestigation without sound reasons as well! So if they became convinced that body axes were unsound, why not say so frankly and give the reasons, instead of glossing over the change of front? The Problem, Simply If anyone doubts the soundness of rolling the aeroplane about the wind axis, let him mount a wing near the stall in a tunnel so that it is free to roll about its chord axis, and he will see how strenuously it resists any attempt to roll it. If left to itself, however, it will start oscillations of increas ing violence as soon as any stalling takes place; this behaviour seems to be similar to that of the full-scale aeroplane when ailerons are used to roll a machine near the stall. It begins to roll, but then reverses the roll and spins the other way. The effect can also be observed with a small dynamic flying model. Consider now the influence of inertia on lateral control. Apart from the obvious factors of rolling power of the con trol, damping in roll of the wing, and inertia of the wing, there are three other main factors which govern lateral control at high incidence, namely, the line of action of the control force applied, the line of action of the altered air forces on the wing due to the rolling, and the inertia of the other parts of the aeroplane, especially the body; these three factors govern the generation of yaw, which is so potent at high incidence. The importance of body inertia can be seen if a very simple case is taken, and the air forces are for the moment ignored. Suppose an aeroplane is flying level at 150 incidence and its fuselage is very light and its wing very heavy, then, if a vertical controlling force is applied to one wing tip, that tip will move almost vertically, and the machine will roll about the wind axis. If, however, the wing should be very light and the fuselage heavy, then the machine will roll almost about its body axis. (If anyone doubts this it is easy to verify with a crude model.) It will thus be seen that, even though the air forces of control and damping may act only about the wind axis, yet the fuselage can, by its inertia, have a bad effect on the motion of the machine in roll. This is the point that it is particularly desired should be brought out, and this is why the N.A.C.A., in changing from body to wind axis, has still not reached a sound basis on which to compare lateral controls. It may perhaps be argued that the rudder is always available for the pilot to counteract the unwanted yawing effect of the ailerons, but three separate controls are quite enough already without having two of them inextricably mixed as well, and it is unfair to the pilot to inflict this on him. An aeroplane can, of course, be controlled in roll at the stall by the rudder alone, through the rolling moment due to yaw, but anyone who has tried it will agree that it is a precarious and unsatisfactory method. Let us now consider the body inertia effect more care fully with reference to Fig. 1, in which the aeroplane is flying level at a high incidence. Ignoring the air reactions for the moment, we see that if a controlling force OA is applied to one wing tip, and at right angles to the body axis OE, the machine will roll about this axis, and the wing tip will move along OA. But if the control force is about the wind axis, as denoted by OC, then the body inertia comes into play. Were it not for this, the wing tip would move along OC (as it might in a tailless design)° Now, since the fuselage inertia and the wing inertia are both of the same order of magnitude in the average machine, let us take the case where they are equal. Resolving OC into OA and OE (its components about inertia axes) we see that, while OA is overcoming the wing inertia, OE has to cope with the fuselage inertia as well, so that the angular acceleration in yaw will be halved in consequence, and the wing tip will move along OB instead of along OC. Thus the application of a wind-axis force OC does not produce a wind-axis motion in roll. To secure this, the applied con trol force would have to be along OD, where AC = CD. It follows that the angle X is nearly equal to the incidence if this is small, but is somewhat less than equal at large incidences. We thus see that, so far as the inertia effects are con cerned, we must push a wing back as well as down, or forward as well as up, even with reference to the wind axes, if we wish to roll the machine about the wind axis or to check such a roll. The angle at which the control force must act depends on the ratio of body-to-wing inertia, as we have seen; the greater the body inertia the greater the angle X. Damping in Roll Let us now see just how the aeroplane resists our attempts to roll it about the wind axis as regards air re actions. It is obvious that at large incidences the fin, rudder and fuselage surfaces will exert a damping force, as well as that due to the wing. . All these are allowed for in Fig. 2, which has been plotted from data in R. & M. 1743, giving rolling and yawing moments due to roll, on a wind- axis basis, for a complete model Puss Moth. The curves are for three rates of roll (for the ratios of tip speed to forward speed of .05, .10 and .15) and are plotted vectorially. It will be seen that if a wing is pushed down while at 12.1 deg. incidence it resists, and also tries to move forward, at each of the three speeds. The size and direction of the damping force is represented by a vector from the origin to the 12.1 deg. point on the curve in question- Below the stall, it will be seen, the inclinations of these vectors to the wind axes are not very far removed from their incidence values, especially at the lower rates of roll. This is very fortunate, for it means that the control force needed to overcome the damping must be inclined at about the same angle(X) to the wind axis as we have already seen is required by inertia considerations; that is if yawing with regard to the wind axis is to be avoided. What is also fortunate is that if a roll about the wind axis is allowed to damp itself out, or if it is checked and reversed by the lateral control, the inclination is appropriate in all these circumstances too—that is if the wing and body inertias are about equal, or if the body inertia is somewhat the smaller, and if, of course, a lateral control can be found to supply the desired effect! If a rapid roll is performed near the stall the case is rather altered. It will be seen that if a wing is depressed so quickly that it begins to stall it drags back. If the incidence is 160 and the rate of roll .10 or .15 autorotation sets in, and the falling wing needs even more yawing moment to hold it forward than it does rolling moment to hold it up (vectors from 16 deg. to origin). It is difficult to see how this change-over in behaviour almost at the stall can be catered for in a lateral control, so that it is perhaps fortunate that one does not usually try to
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