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Aviation History
1913
1913 - 0035.PDF
apparent, for the same reasons, that any improvement in the safety of this manoeuvre would be of the very greatest service to the progress of flying, especially at the present time. One advantage of discussing at once the subject of stability on a curved course is that it brings to the fore the primary essentials required for initiating and maintaining the machine in its turning circle. It is essential to realise that the e.g. of any system such as is, in this case, represented by an aeroplane, will not change its straight line course unless a force be applied from without directly upon the e.g., and along the path in which the e.g. is required to accelerate. A particle moving in a circle is accelerating towards the centre, and the acceleration is constant when the velocity of the particle on the periphery is uniform. The acceleration increases with an increase of velocity and also with a decrease in radius. From the fact that the acceleration is along a radius, it is evident that the initial direction of the steering force should originate at right-angles to the straight line path formerly pursued by the aero plane. This at once draws attention to the potential advantage of banking the wings in order to initiate a steering movement, for the pressure on the wings remains at right-angles to the wing spars, and when canted it thus automatically provides a centripetal component. A rudder, as ordinarily understood, is not, it seems to me, fundamentally necessary for steering if the wings can be banked properly by other means. Consider for a moment the accompanying diagrams which are supposed to represent the forces as seen in an end on view of an approaching aeroplane. Fig. I shows the lift, P, equal to the weight, W, the wings being level. In Fig. 2 the wings are canted to 450. As the pressure remains at right angles to the wing spar, its direction is tilted in sympathy with the bank. Assuming the relative air speed to be unchanged, the magnitude of the pressure will be the same as before. In it's new direction it is unable to support the entire load of the weight, a fraction of which thus initiates downward acceleration. But, there is now a horizontal component of the pressure causing acceleration to the left (supposing the machine to be advancing out of the plane of the paper towards the spectator) and this centripetal force is opposed by the equal centrifugal force as the machine proceeds along its appropriate circular path. For the particular speed, there is a particular radius that will provide the proper centrifugal force to balance the centripetal force due to the bank, and the circular pa'h corresponding to this radius the machine automatically pursues without any aid from the rudder. While the bank, represented in Fig. 2, is being established, the radius of the turning circle is diminishing, when the bank is fixed, the centre of the turning circle is also fixed. The conditions of Fig. 2 may thus represent the beginning of the turn, or any instantaneous position during the turn. It will be understood, therefore, that Fig. 2 represents a state of turning on a circular path, accompanied by an accelerated descent due to the weight being insufficiently supported. This latter is, of course, a possible source of danger at low altitudes when the ground may intervene to prevent the proper completion of the turn. If the lift should be reduced for any reasin, the unsupported fraction of the weight is increased at the same time that the radius of turning increases, as khown in Fig. 3. In order to turn on the same level, it is necessary to increase the speed, which means increasing the power output. Reserve power is thus a primary " factor of safety " for turning. In Fig. 4 is shown the case of a 15° bank, and increased speed giving sufficient wing pressure to support the load and maintain a rather wide turning circle. In Fig. 5 the increase in the wing pressure needed to support a 30° bank is indicated, and in Fig. 6 the bank is again 450, as in Figs. 2 and 3. The pressure, it will be observed, is nearly one-third greater than normal. If P :o V'2, then the velocity required represents an increase of about 15 percent. Beyond the angle of 45° the wing pressure needed to support the load plus the centrifugal force increases very rapidly as is shown in Fig. 7. For a bank of 60° the wing pressure is about twice the normal, for 700 it is about three times the normal, and for 8o° it is about six times the normal value ; the corresponding increments in speed are about i'4, I'74, and 2 "45 times the normal velocity. From the limited reserve power of modern engines, it is apparent that steep banks must, of necessity, be accompanied by rapid descents while turning. It is necessary to emphasize that extra power must be provided because the angle of incidence remains constant under longitudinal weathercock stability. Variable speed by variable resistance accompanied by variable angle of incidence will not meet the conditions of the diagrams. The energy of a steep dive during which abnormally high velocity has been acquired under gravitational acceleration may suffice for, although it certainly does not warrant, the manoeuvre. From the above considerations it is apparent that it is dangerous for the bank to tend to increase of its own accord while turning ; it remains, therefore, to consider the tendencies in this direction. This phase of the problem is evidently related to the organs of control, and before entering into a discussion thereon, it is helpful to fix in the mind a picture of an aeroplane flying along a circular course. As an artifice to this end, it is convenient, I find, to imagine that the machine is swinging around a sort of maypole and to place one self mentally at the top thereof. In order to complete the picture, imagine oneself to be holding a fine thread leading straight down to the button «n the top of the pilot's cap. The idea of a thread lends emphasis to the fact that it does not help to support the weight of the machine, while at the same time it assists in mentally fixing the desired conditions. The thread is in line with the wing pressure, P, of the diagram. Thus, the steeper the bank the lower is the height of the maypole on which one is sitting. For a bank of 90% one would be on the same level as the pilot ; for no bank at all, the height of the pole would be infinite. It is also self evident from the mental picture that the inside wing tip might be attached by another imaginary thread to a point lower down the pole. As the aeroplane pursues its circular course, these threads, which may be supposed attached at their lower ends to rings, maintain an angular velocity about the pole, and the spectator, who may be supposed to be on a revolving chair, looks down always on the same perfect plan view of the machine. The conditions that have established the spectator's position are the speed and the initial bank, both under the pilot's control. Assuming, therefore, that the pilot temporarily fixes his controls in those positions, the e.g. of the aeroplane should continue its circular course unchanged, and we may say, therefore, that anything tending to stretch or slacken our imaginary threads is a sign of the instability in the system. It is apparent, by the way of a preliminary investigation, that sucli disturbances may be due either to an alteration in the angle of bank which will affect both threads, or to the machine beginning to spin about its own vertical axis, which will twist the upper thread and stretch the lower. Let us ascertain, therefore, what occurs when either of these things happens, so that we may be better in a position to realise what qualities are required of a stabilising system that is intended to prevent the disturbance. Firstly, however, let us be clear as to what peculiarities, if any, distinguish a proper circular flight. One thing at least will be apparent to our spectator on the top of the maypole, namely, that the inner wing is travelling through the air at a lower speed than the outer wing. Notwithstanding its lower speed, it is evidently supporting its proper share of the load, otherwise there would be an unbalanced couple about the longitudinal axis tending to increase or diminish the bank. Again, from the fact that there is no spin about the vertical axis of the machine, it is apparent that there is no unbalanced torque due to the relative resistances of the two wings at their respective speeds. When an aeroplane is flying on a straight line course, its balance is procured by similar considerations, namely, each wing lifts its share of the load, and each wing experiences the same resistance at the same speed while so doing, and thereby avoids any tendency to create a spin about the vertical axis. Knowing that the two wings are geometrically similar in respect to effective angle when flying on a straight course, it may reasonably be argued that they must be dissimilar in this respect while flying a curved course, unless it can be shown that a proportionately heavier load on the outer wing due to the curvature of the path and the bank. The equivalent of such a load might be provided by the centri fugal couple, but it requires to be investigated whether this couple varies with the conditions in such a way as to preserve the balance. If a stick has a string attached to the centre of its length and is whirled at the end of the string, it has two positions of equilibrium, only one of which is stable. The position of unstable equilibrium is when this stick is perpendicular to the string ; if tilted, the increased radius of the outer half of the stick now produces an increased velocity, and therefore an increased centrilugal force, which, being cumulative, causes the tilt to increase uneil the stick lies in line with the string. It is then in stable equilibrium. This centrifugal couple must, it seems to me, be an important factor in the stability of an aeroplane while flying on a curved course owing to the span and weight of the wings. Also, it is present as a disturbing influence on the tail owing to the overall length of the machine. This latter may cause pilots to feel the necessity of ruddering outwards while turning inwards, in order to prevent the machine turning inwards too much of its own accord. The centrifugal couple on the tail of modern aeroplanes would 35
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