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Aviation History
1913
1913 - 0036.PDF
1/yGHTj also make it more difficult to analyse the disturbing forces on the wings while flying. In as much as a centrifugal couple of some magnitude is certainly in operation against the bank, it is apparent that there must be an equal pressure couple opposing it, if the balance and the bank of the machine are both to be maintained. Evidently then, if the wings are warped, their relative angles must not entirely neutralise the difference in the relative velocities of the wings. Apart from other considerations, therefore, it seems to me as if the conditions of lateral balance on a banked turn could not*be satisfied by a helical warp of the kind that simultaneously increases the angle of the inner wing in proportion to the decrease of the outer wing. Such warping might be made to satisfy the requirements of a turn made on level rings, but this manoeuvre supposes the machine to be fitted with a vertical fin about the e.g., which it is the object of banking to avoid by the use of the projected area of the canted wings. In short, it would seem desirable to be able to warp each wing independently. Ruddering outwards, it has been shown above, may be necessary while turning, in order to counteract the centrifugal couple of the tail ; so long as that force is balanced, the warp may be considered as a unit apart. Clearly, the wings will always tend to divide the engine power equally between them. If the resistance of one wing is less than that of the other, the wing having the lesser resistance will accelerate, and vice versa until the balance is established. While flying on a circular course, a difference of velocities is essential; consequently the resistance of the outer wing must be less than the inner wing. If the wings have similar angles, the resistance of the faster wing will certainly exceed that of the inner wing, consequently a turn with unwarped wings will not continue. If, however, angular momentum is generated about the vertical axis by a preliminary spin, engendered by ruddering inwards in order to increase a turn, then a curved path with banked but unwarped wings may continue while the energy lasts. If the wings are independently warped, then, from previous considerations, it is apparent that the resistance of the lower wing must be proportionally greater for the load supported than is the resistance of the upper wing. From experimental evidence, it is well known that the aerody namic efficiency of a cambered wing varies with the angle of incidence, and this suggests that a pair of independently warped wings might satisfy the conditions of equilibrium while turning. The inner wing would, of course, have the greater angle of incidence. It remains to be seen how far they might tend to confer the stability on the system. If a positive lift wing is warped so as to increase the angle, the momentary reaction is obliquely upwards and backwards, being in part added resistance and in part added lift. Of these compo nents the former tends to reduce the velocity in a sense appropriate to the conditions of turning with the warped wing inwards, but the latter tends to cant the wings the wrong way. Conversely, if the other positive wing is warped to reduce the angle, its resistance and its lift are momentarily decreased. On the one part, therefore, it tends to accelerate and on the other part to descend. A tendency simultaneously to accelerate and to ascend is, however, what is required of the outer wing when initiating a turn. Clearly, therefore, warping by itself is an unsatisfactory method of steering an ordinary aeroplane, and seems a dangerous operation rather than otherwise. As the cant introduces a steering force quite irrespective of whether it is or is not accompanied by a spin, it is the cant that governs the situation. It is, therefore, apparent that the rudder must be used against the warp resistance when initiating a turn. The machine will then steer in sympathy with the initial rudder move ment, and the wing with the greater angle will ascend. But so soon as the bank appropriate to the desired turn has been established the machine enters upon its curved course and the warp must immediately be reversed, because the relative angles of the wings are opposite to the real requirements. Further consideration of this matter shows, moreover, that the manoeuvre calls for precision and skill, if danger from overbanking is to be avoided. While rising, a positive angle of incidence is virtually diminished. Opposed by the rudder in its line of retreat, it is thus evident that the line of least resistance for the warped wing with the greater angles, which is rising, is to rise still more. The balance of power will not support its superior angle, and the only way in which the angle can become less under the circum stances is by continued ascent. In fine, warped positive wing tips appear to me to be inherently unstable. JANUARY n, 1913. From the foregoing considerations, however, it is clear that the inner wing should be warped to a greater angle while turning, in order to provide the increase in the resistance requisite to the maintenance of a circular course. But it has just been shown above that the warp itself works the wrong way for initiating a turn, con sequently nothing is left for the pilot but to " fish about," as it were, after banking until he finds a warp suitable for maintaining the turn. Unsatisfactory at its best, \ the procedure is evidently also fraught with considerable risk. If the warp of the inner wing is made excessive, its oblique pressure will, as usual, have two components, one tending to lift the wing the other tending to make it retreat. If the wing rises the other wing must descend, which would virtually increase its angle and its load. If not opposed by the rudder, the line of least resistance, it appears to me, is one of retreat, for the outer wing will be very willing to decrease its angle by ascending in sympathy with the spin. If this happens, the bank and the spin are increased simulta neously, and the turn culminates in a spiral nose dive or side slip according as to whether the bank or the spin predominates. If the preceding remarks are logical, sufficient has been said to show that the warping of positive wing tips is no aid to practical stability while turning, whatever advantage they may have as a means of restoring lateral balance after a disturbance on a straight line flight. Wherever the warp is used, it is essential to be ready with the rudder, and one way and another this organ assumes a position of vital importance to the safe control of the modern machine. More may have to be said later, and of a less favourable character, as to its significance when regarded as a neutral fin. For the time being I will endeavour to advance the argument on the problem of turning, by drawing especial attention to that fundamental aspect of the case for which I have used the expression " balance of power." From what has been said, it seems evident that a stability analogous in principle to the stability of a table on the floor is required to satisfy the conditions. A table is stable, because, when it is tilted, the e.g. of the system is raised. In short, because work is done on the system. If a wing were unable to move either way from its relative position without doing work on the system, it would be stable. Symmetrical positive wing tips would be stable if they could not spin about the vertical axis, for if one wing ascends it decreases its virtual angle, and if the other descends in harmony it increases its virtual angle. The different relative angles represent different relative resist ances, and therefore tend to produce different relative speeds: in short they tend to initiate a spin. If a spin is impossible, they tend to destroy the balance of power, which is stable. If, when one wing rises, the other does not descend, the e.g. of the system is raised, which is also stable. To the above I mainly attribute the natural lateral steadiness of a modern aeroplane in the hands of the average pilot. In principle it seems to me analogous to the steadying effect of the keel of a yacht. Normally neutral, the keel assumes an angle of incidence while the boat rolls under a puff of wind on the sail. The spin of an aeroplane is ordinarily resisted by the rudder, and the rudder is thus the chief organ controlling the equilibrium of the modern machine. But the wind may spin relatively to the machine by veering or backing. To still be stable, the rudder must auto matically spin the machine in sympathy with the wind; i.e., there must be sensitive directional weathercock stability in order to obtain lateral stability with positive wing tips. Clearly, a machine so large as an aeroplane has too much inertia to spin in complete harmony with the wind. Sensitive weathercock directional stability is, therefore, not feasible in a practical aero plane and positive wing tips are, therefore, unstable, although they may be reasonably steady. From preceding remarks about veering winds and spinning, a clue to a possible principle of lateral stability suggests itself in the reflection that if a pair of wings experienced no tendency to cant when spinning, neither would they be disturbed by veering winds. Other than a flat plate of zero incidence, the only form satisfying in this condition is one in which the wings have permanently negative (down pressure) tips. When angular acceleration of such wings takes place about the vertical axis, the negative tip is supposed to neutralise the increasing lift of the positive part of the wing. It is, of course, a matter of experiment to show how far this condition can be satisfied with practical wings. In forward motion, the combined positive parts of the wings would have to support the negative pressure of the tips as an extra load on the machine. Part of the price to be paid for this form of stability would, therefore, be relative inefficiency—but one might well pay more than that for safety, seeing that the efficiency itself already costs so much.
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