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Aviation History
1913
1913 - 0061.PDF
JANUARY 18, 1913. [fiJGHf SOME THOUGHTS ON STABILITY AND CONTROL. By A. E. BERRIMAN. (Continued II. The influence of direction on power of recovery. Still air stability and virtual firs. Reverting to the general problem presented by positive wing lips, the study thereof is obviously incomplete without reference to iheir power of recoverirg balance by oblique movements, which is, in part, the tasis of the security of the modern positive wing-tip machine. A machine of this class, it has already been argued, will not continue to steer a safe circular couise with fixed controls. Con sequently, if it be assumed that the system is nevertheless inherently secure, such security must lie in the quality of automatic recovery of balance, and its existence must depend on the inherent tendency of the system to maintain a straight line flight. We are thus brought back to a realisation of the intimate cornec- tion between directional and lateral stability in a laterally unstable system, and to the fundamental necessity of considering the problem of balance from the point of view of steering control. Directional stability, it has been made clear in the first part of this article, is related to the spin of the machine about its vertical axi«, rather than to its course in the air. Thus, the term weather cock directional stability has been applied to the quality of freedom to spin in sympathy with the veering or the backing of the wind, just as a weathercock spins on its pivot when the air in its vicinity changes its direction of flow. If the wind-vane were jammed, it would exhibit directional stability in another sense. Directional stability of this kind is alao displayed by the axis of a gyroscope and the needle of a compass. The latter sugges's the phrase "compass directional stability" as suitable to be applied to a system that exhibits no tendency to spin in sympathy with a veering wind. A veeiing wind, it has been argued, is in itself a relative spin, and, as such, produces a virtual acceleration of one wing-tip accom panied by a virtual retardation of the other. The problem of absolute lateral stability thus, in principle, resolves itself into eliminating the tendency to cant under these conditions. It has been explained that negative wing tips potentially satisfy the above requirements. Positive lift wing tips, on the contrary, do cant in a relative spin of the wind, and are, therefore, liable to have their lateral balance disturbed under the conditions of practical flight. Positive lift wing lips are thus inherently unstable, but if the system to which they belong possessed such sensitive weathercock directional stability as to prevent a relative spin of the wind by causing the wings to pivot on their vertical axis in complete harmony with a veering or a backing wind, the cause tending to make them lose balance would be neutralised. This latter alternative having been dismissed as impracticable, renders it necessary to assume that any inherent security in a system possessing positive wing tips must of necessity be confined to the quality of automatic recovery of lateral balance, which quality, it has been explained above, must in turn be accompanied by a tendency on the part of the machine to avoid a circular course. In fine, if the machine with positive wing tips is to display the quality of automatic recovery of its lateial balance when disturbed, it must possess inherent " compass " directional stability. Weathercock directional stability implies that the tail of the machine swings to leeward when the wind changes, the axis of the machine remaining always in line with the relative wind. On the contrary, compass directional stability implies that the head and the tail of the machine slide to leeward together when the wind changes. Owing to the inertia of the mass of the machine, a time interval is involved in acquiring this leeward motion. The real wind changes with great rapidity, but the machine as a whole is less mobile. It is even less mobile as a whole than it is as a system revolving about its vertical axis, for if it be assumed that the wind changes with the same rapidity in both cases, then the acceleration required of the entire mass in the one case is that required princi pally of the tail portion in the other case. When the system has accelerated to leeward and has thereby acquired the speed of the lateral component of the real wind, then the only relative wind rcmainirg will have become longitudinal once more. Thus, but for the fact of the inertia above mentioned, the machine would slide laterally with the acceleration of the lateral component of the wind. In such a case, which is, of course, impracticable, compass directional stability would be equivalent to weathercock directional stability in so far as it conferred lateral stability by eliminating the lateral component of the wind. In the above case of sensitive weathercock stability, the spin of from page tf.) the machine is supposed to harmonise with the angular velocity of the wind ; under the o.her hypx thesis the two rectangular compo nents of the wind are supposed to be dealt with separately. Neither case is feasible in a real aeroplane, but it is important to note that there is a general tendency towards directional stability of the weathercock order in any machine with positive symmetrical wing tips. On the general principle of the balance of power to the two wirgs, it is apparent that neither will tend to accelerate in its own level of its own accord. Conversely, if the conditions of relative acceleration is imposed by a veering wind, the balance of power will tend to engender spin about the vertical axis in sympathy with the wind, if canting is prevented. Inettia to rotation will prevent the spin of the machine being as quick as the angular acceleration of the wind, and for this reason inherent lateral stability demands as a primary feature of the system that it should not cant while this relative spin of the wind continues. As there is undoubtedly a canting couple induced on positive wing tips by a relative spin of the wind, it is in negative wing tips, which are not thus affected, that I see at present the only plausible solution to inherent absolute lateral stability. A simple practical test for the possession of that quality is, I have suggested, the ability to fly a complete circular course with fixed controls. Even with inherent lateral stability there still remains the fundamental necessity for high reserve power, in order to avoid descent when turning. Among other things, the above reasoning thus leads me to the thought that the really succcsslul aeroplane of the future will be somewhat like the modern motor car of to day in respect lo its engine being considerably larger than is needed for ordinary flight. Whereas the automobile of the road uses its reserve power for ascending hills at a good rate of speed, however, the voiture of the air will apply it for negotiating turns and for combating high winds in order to prevent leeward drift. In this latter respect high power must ever be a limit to the capacity of the aircraft to keep its course, and inasmuch as leeward drift may involve the alternative of a dangerous landing or being blown out to sea, so will high power become, as I said in the first instance, a primary " factor of safety " in flying. Diagrams published in Part I of this article showed the relation ship of the bank and the turning force. For a bank of 45 degrees, for instance, the centripetal force is equal to the weight supported against gravity. The radius of a given bank increases as the square of the speed needed for the support of the lead due to the centri fugal force and the weight, which speed, other things being equal, depends on the wing loading. Thus, if a bank of 45 degrees is completely supported at 80 ft. per second, the radius of the turning circle is 200 ft. ; if a lower loading permitted the same bank to be maintained at 60 ft. per second the radius would be reduced to about 112 ft. Alternatively, if the speed on the turn is very much above the normal it may suffice to support a very steep bank at a small radius. The question of a small turning circle, therefore, depends on the reserve power that can be converted into extra speed for the purpose of generating extra wing pressure. Other things l>eing equal, tin- lower speed machine will manoeuvre in the least radius and will be able to put about in the least time. Before proceeding to discuss the possible ability of positive wing tips to recover their lateral balance after being disturbed, let us consider for a moment the drift effect of a veering wind. Symmetrical positive wings, it has been pointed out above, tend to spin while the wind is in angular acceleration ; the machine as a whole likewise tends to drift or slide to leeward. When the angular acceleration of the wind ceases, the tendency to spin ceases also. Similarly, the acceleration of the lateral drift on the machine as a whole remains until it has acquired a sideways s'ide equal in velocity to the lateral component of the wind. Actually, these two accelerations of spin and lateral drift commence simultaneously. If the inertia to spin is proportionately small, the spin will be relatively great. On the other hand, if the system has much vertical surface, it is likely to accelerate quickly to leeward, thus reducing the tendency to spin. In a system such as an aeroplane, the significance of the spin lies in its influence on the direction of the propeller thrust. The propeller being axial, the line of its thrust is turned more against the wind by weathercock directional stability, and so the lateral drift component of the wind is thereby opposed. With sensitive weathercock directional stability, the lateral drift would be eliminated, but the existence of absolute sensitiveness 6l D 2
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