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Aviation History
1912
1912 - 0017.PDF
If Zahm's expression for skin friction is accepted, we may pass on to consider the resistance due to load. It is more convenient, as an intermediate step, first to find an expression for the lifting power itself. On the hypothesis that an aeroplane is supported in flight by the inertia of the air, it becomes possible to apply the fundamental equation P = tnf (where P = lifting force and tn is the mass under acceleration /). In order to apply this fundamental formula, it is necessary to find plausible expressions for the mass of air simultaneously disturbed by the wing in flight, and also an expression for the acceleration induced in that mass. As to the mass itself, it is obviously limited in two dimen sions by the span and chord of the wing (Fig. 5). Its third dimension, which corresponds to the depth of the stratum disturbed, is supposed to be a function of the chord (Fig. 6), and to have a coefficient in the order of unity. Whence we may write mass in the form (pLll = pAl), (where p = density, A = wing area, L = span, and / = chord). Next comes the question of acceleration, which, from the very nature of the function of a wing, is determined by flight velocity and angle. What is the effective angle of a wing ? Some say 8, the angle of incidence, some believe in the angle of trail a, but I submit that the angle of deflection B is the most plausible measurement (Fig. 7). It is immaterial, however, what angle is taken if the assumption be that the air stratum itself is deflected to the assumed degree. Assuming that the angle of deflection as defined in Fig. 7 correctly represents the actual deflection of the air stratum, and that the camber of the wing is such as to produce uniform downward acceleration in each air molecule, then the final downward velocity with which a molecule leaves the trailing edge is represented by the expression (V tan B) and the rate of acceleration itself by the expression j (V tan £ -f- l I = V- tan B/l) (where V = feet per second). Thus, we have established plausible expressions for mass and acceleration, and their product should give a value for the lift or upward force of the wing in flight. Combining these expressions in multiplication, it will first be observed that the chord factor (I) cancels out of the expression, and since the area factor (A) may be removed by working in units of a square foot, or other convenient measure, we are left with an expression in the order of (p V2 tan B). This, put into practical units for ( - ~ .or, ) and (V = miles per evolves the following definite formula for the lift of aY z tan fl 200 The graph of this expression is given in Fig. 8. The next step is to find an expression for the resistance due to load, which involves the assumption that this resistance is confined to the apparent energy in the deflected air stratum. Energy is represented by the fundamental expression imv2), and we have already evolved expressions for mass (m) and downward velocity (v). o ' A/ Of these : m= - A/ = —, and v — V tan 0 whence g 400 , - V2 tan2 $1 , . ., , , , . i mv = —_ foot lbs. per square foot of wing area. per second ; hence the power expended on load may be hour), an aeroplane wing in flight P/3 - Now this energy per square foot is dissipated I ) times Airships Over Paris. WITH a crew of thirteen passengers on board, the dirigible "Adjutant Reau " was cruising for some time over Paris on the last day of the old year. This made the third successive day on which an airship had been seen over the Grand Palais. On the previous day the " Capitaine Ferber" had passed over, while on the 29th the " Adjutant Vinceneau " passed over Paris during a four-hour run starting from and finishing at Toul. "Cipitaine Ferber " Out Aeain. PILOTED by Count de la Vaulx, the Zodiac dirigible " Capitaine Ferber " was out on the 27th ult., and, after making a long excur- expressed V s tan3 Bl Soul foot lbs. per second per square foot which may be converted to resistance by dividing by (V), 'V2 tan2 B\ whence, resistance due to load is 400 lbs. per square foot. (V is in miles per hour.) The other part of the resistance to the flight of the wing is skin friction R = -000018V-', whence the total resistance = \^ooopi8 + tan 2/8) 400 Having evolved expressions for lift and resistance, their ratio gives the coefficient of flight for the wings alone. Thus V-' tan-' B 400 + -000018 \ - tan B /tan- B + '0072 "I 2 tan 0 The graph of this expression is given in Fig. 9. Now, what do these graphs show ? That illustrating the coefficient of flight is particularly interesting, for it indicates that coefficient varies with the angle of the plane, is in dependent of velocity, and has a minimum value in the order of -085 for an angle of deflection of 50. These numerical values result from the assumed coefficient for skin friction and the density of the air ; the principle of an angle of least resistance to flight is unaffected by their variation. That the coefficient is independent of velocity is due to the absolute resistance and the absolute lift of a wing both being proportional to V-. If the speed is doubled, the lift is quadrupled, and so is the resistance ; their ratio is unchanged. It follows, therefore, that the most efficient variable speed machine is one having a variable area lather than a variable angle. Also, that for a fixed area and weight there is a natural flight speed. Since speed does not affect the coefficient, it follows that, from the point of view of the wings alone, the speed should be suited to the use of an angle of least resistance. In the graph, a very flat camber is indicated, which implies a very high flight velocity to attain the loading of the wings that is common practice to-day. It is in respect to the very heavy loading (weight supported per unit of area) of their wings that aeroplanes differ from birds, which have proportionately far larger wings than have flying machines. In the construction of monoplane wings, larger areas imply greater spans and, consequently, involve the use of a greater weight of material per unit of area in order to retain the same strength. Thus, the net lift of the wings per unit of area diminishes in large sizes, whence there are good grounds for the general principle that a heavy monoplane must fly fast in order to use efficient wings. From the point of view of body resistance, a very high flight velocity is wasteful of power, but the magnitude of the loss depends on the efficacy of streamline bodies to reduce resistance. In practice, cambers representing far higher angles than that indicated as possessing least resistance are used, in order that machines of small area may rise at moderate speeds. So the significance of efficiency as a governing factor in long distance flights has been discussed, and a method of mathematical analysis has been suggested. This latter, I wish to say, is intended primarily as an elementary line of thought for students, analogous to presenting the problem of the steam engine in the time-worn formula (PLAN/33000). It does not pretend to be either scientifically complete, nor is it based on practice. It is just a skeleton framework of theory intended to help those who have the concrete bricks of fact to make most use of them in building the houses of experience wherein a practical science can only abide. ® ® ® ® sion to the west of Paris, circled over the Grand Palais bffore returning to its headquarters at St. Cyr. "Parseval XI" Taken Home by Road. As there seemed no possibility of better weather being obtained to enable " Parseval XI " to get home from her enforced resting- place at Trebbin, it was decided on the 26th ult. to deflate the airship and send it back to Bitterfeld by road. Mere Capital for Zeppelins. IN view of the further orders to be given out by the Army Authorities, it is announced that the Zeppelin Construction Co. will shortly increase its capital from one to four million marks. >;
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