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Aviation History
1919
1919 - 0372.PDF
1/I* <%gggD Lettering of Coefficients. As to the actual lettering of absolute coefficients, it appears impossible to avoid a compound of two letters, one large •and one as a suffix. We have the choice between K/, Krf, K,„, etc., and L,, T)c, Mc, etc. Now the most important letters are of course the 1, d, m, etc., denoting what the coefficient stands for, and not the K or c, which merely stands for coefficient. This presents a very strong case for Lc, &C) Mr, etc. Further, it has been found in actual practice that the suffix letters of K/, etc., being so small are much more liable in printing or typing to get left out, leaving the bare K, whereas if the c is left out of ~LC the consequences of such a mistake are not nearly so disastrous. Times out of number has the K/ been mistaken for K„ and misprinted as such, thereby entailing considerable confusion. It must be admitted by all clear- minded people that anything tending to add to confusion should be avoided at all cost. The complete scheme of absolute coefficients in use in the practical application of aerodynamic research is appended below:— lift.. .. Coeff. L, = _=_.- PAV 2 PAV 2 D -pCfV* R pAV2 »AW L = lift English Metric in lbs. or kgrms. 'Common drag («) Airship En velope drag (b) Resultant force Longitudinal force D,' = R X = D = drag C = vol. of cu. ft envelope R = result, lbs. force m.3 kgms P-' pAV* = ?_ pAV* Rolling moment „ L£ = L Lateral force ^Normal Y = Z X = longit. force Y = lat. force T,«. T Pitching ,, ,, VLC Yawing „ ,, N,• = Pressure .. „ Pr Airscrew thrust (a) Airscrew ,, T/ = thrust(ft) Airscrew ,, T/'= thrust (c) Airscrew Torque (a) Airscrew torque (ft) Airscrew torque (c) Airscrew ,, H : power (a) Airscrew „ H,' •• power (ft) Airscrew „ H" power (c) pAV*i = M pAWi N pAV*i P pV» pV^D1 T pn»D* Tn» Z = nor. „ L = roll. lbs. ft. kgm. mom. metres. M = pitching ,, N = yawing P = pressure lbs./ kgm./ sq. ft sq. m. T = thrust lbs. kgms. T = PD«V J Q = torque lbs, ft. kgm. metres. ..&--M-. Q/'= ¥k Q pD»»« Qn» pV* H PV*D* H pUTD* HO' pV« H=power ft. lbs. metre /sec. kgs./sec. ,, horsepower metrich.p. 55o 75 Drag = D,paV» If He represents the engine power coefficient and r\ the airscrew efficiency then IJH, represents the airscrew power coefficiency. It will be noticed that L occurs twice. The letters, LMN for moments were, it is believed, first used by Euler, and have long been in use in rigid dynamics. L has also been in use to denote lift since very early days of aerodynamics. It is therefore necessary to use different forms of L. In printing the selection of heavy type for Lift presents no difficulty. In typing the following suggestion is made:— If a small " 1 " be superposed directly on capital ** L " on a typewriter it will be found that an L is made with a double upright stroke. This is particularly easy to write or type, and is recommended as the easiest solution of the difficulty. How such a distinction could be made in the K system is difficult to imagine. MARCH 20, 1919 The Representation of Drag. In Aerodynamic calculations the objects or bodies sub jected to air reaction separate out into two diEtinct classes : — 1. Those whose function is to provide a lifting force. 2. Those whose function is to contain some necessary part of the aeroplane such as an engine or a pilot. It is desirable that both kinds carry out their allotted functions with the least possible resistance. Taking the second class of object. These are those which contribute to " parasitic " resistance. The best method of establishing the drag coefficients is based on that of M. Eiffel, viz., that in which the drag is referred to the projected area normal to the relative wind when the object or body is in normal symmetrical aspect. For example :— D<- = abs. drag coeff. p = density *' mass units "/unit vol. a = projected area normal to relative wind direction. V = speed. Once determined " a " of course remains the same what ever attitude the body may ultimately adopt, e.g., it does not take on a new value for any variation in angle of incidence. In estimating up the total drag in calculating the perform ance of an aeroplane, it will be found most convenient to sum up first in tabular form all the products of DH» of the individual parts such as wheels, struts, etc., contributing to the parasitic resistance. For a single seater high-powered machine of clean design DH* may have a value of the order of 3 • 5 or thereabouts. It is approximately proportional to the square of the linear dimensions of machines and inversely as the cleanness of design. This latter quality might be defined in terms oi Dffl and the size of the machine. The actual "parasitic drag " can then be found by multiplying the sum of all the products T>ca by pV». This method is better and quicker than computing each drag separately at some arbitrary speed, as is sometimes done. Similar treatment applies to wings and control surfaces where drags are referred to superficial areas " A " instead of projected area " a." These drag coefficients will in general be lower in actual value than those described above. Plotting Out Coefficients from Laboratory Results. Owing to the effect of viscosity it is known that the drag of models at slow speed does not vary exactly as the square of the speed. Anyone engaged on computing the perform, ance of an aeroplane naturally requires full scale values only- If " v " be the kinematic coefficient of viscosity = '000159 at 15° C, " V " the speed, and if " /" be a linear dimension, it may be deduced from the work of Reynolds, Rayleigh, VI Buckingham and others that for every value of - there is a certain definite " shape " of air flow round the body peculiar to that value, and that further the drag coefficient as defined above has a definite corresponding value. A large number of laboratory experiments have been devoted to finding the variation of the value of the drag VI coefficient with different values of — . In most ordinary work the value of v is taken as constant, and it is sufficient and more convenient to plot the drag coefficient on a base VI as in Fig. 2, which indicates three common lonns of such curves. Low resistance forms usually show no kink in the curve, whereas some high resistance forms may show even two. In any case it seems that where a kink occurs it is almost certainly due to the amalgamation of two entirely different functions representing two entirely different types VI at flow. The value of — where the amalgamation occurs is called the critical value. If / and v be fixed in any series of experiments, then there will be a critical value of V. Con versely, if V and v be fixed and the size of object varied, then there will be a critical size of object. At low values of VI the drag coefficient approaches in finity, since it is referred to V», whereas the actual drag is nearly all due to viscosity and varies almost directly as V. It is found that the curve ultimately becomes horizontal with an increase in values of VI, indicating that the effect of viscosity becomes ultimately negligible and that the resist ance now varying as VJ is due almost entirely to the momen tum effect of shifting the air bodily. It is the object in aero dynamic research to obtain as high values of VI for each object or body investigated and to obtain the value of the drag coefficient at full scale and high speed, by extrapolation if necessary. Abs. drag coefficients range in value from about -035 for the best shape of fusiform body to aboat -77 for a long rectangular plate. 372
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