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Aviation History
1919
1919 - 0310.PDF
1/ P <?££&& MARCH 6, 1919 SOME POINTS IN AEROPLANE DESIGN BY F. S. BARNWELL, CAPTAIN, R.A.F. [Continned from page 280) Plate VII.—I attempt now, from model data, a simple investigation into comparative size of tail plane required to give longitudinal stability to a monoplane, a " square " biplane and a " staggered " biplane. The aerofoil form is the same throughout. On the figures are shown the five different fore and aft positions, and the constant vertical position, of centre of gravity of whole aeroplane considered for each type. The curves below each type give for it values of pitching moment on a base of angle of incidence, for each of the five different positions of centre of gravity. The pitching moment at any one attitude is the product of the ' absolute " coefficient of total reaction on the aerofoil (or aerofoils), multiplied by the vertical distance (expressed as a fraction of chord length) of the line of this reaction from the centre of gravity of the whole aeroplane. The curves indicate diving moment when above the heavy horizontal zero line, and stalling moment when below this line. The small figures in circles attached to each curve give the fore and aft position of centre of gravity for which the parti cular curve is drawn. It is interesting to note how the range of pitching moment decreases as the centre of gravity is moved forwards, also that it is, on the whole, less for the " square " biplane than for the monoplane, and less for the " staggered " than for the " square " biplane. These figures are all obtained directly from experiments made by the N.P.L. on model aerofoils of 18 in. span by 3 in. chord at 40 ft. per sec. ; no attempt has been made to correct for " full size " conditions. The correction required would be almost entirely due to increased lift coefficient values (especially at small angles of incidence), for " full size " condi tions ; the values for centre of pressure position would be practically unaltered. As model figures are also used when considering the tail required for stability, the increase in lift coefficient value due to change from model to " full size " conditions may, I think, be considered to alter by about the same amount for both aerofoils and tail; that is to say, the same proportions of tail should produce about the same results for both model and full-size machines. Pate VIII—On this plate are given the three different forms of tail plane which are investigated. Case I is a " symmetrical section " tail, Case II a " wing form " tail with its convexity downwards, Case III the same " wing form " tail but with its convexity upwards. In the present state of aeronautical nomenclature, Case I would be mis called a "non-lifting" tail; Case II a "depressing" tail (I suppose); Case III a " lifting " tail, and all three terms would be erroneous. You will note that I have assumed a constant position for centre of reaction on the tail, which is accurate enough for our purpose, as the tail chord is small compared to distance of tail from centre of gravity. I have taken that the distance of this assumed fixed centre of reaction on the tail is a distance from centre of gravity of aeroplane of amount equal to two and one-half times the chord length of the aerofoil, or aerofoils. I have also, for simplicity in calculating the tail moment, assumed that the chord of the tail when produced passes through the centre of gravity of the aeroplane. Figures for all three tails are taken directly from N.P.L. figures for models of 18 in. span by 3 in. chord at 40 ft. per sec, and both the " wing form " tails are of the same form as the main aerofoils. I have next proceeded to find the smallest size for each of these three forms of tail, which would make each of these three aeroplanes just stable, for each of its five positions of centre of gravity, assuming the tail to be in undisturbed air. The method used in doing this is as follows :—On tracing cloth I drew out a series of curves of " tail moment " on a base of angle of incidence of tail. As the chord of the tail points at the centre of gravity, it was necessary only to con sider the normal force on it. The " tail moment," therefore, for any particular angle of incidence for the tail, is the product of the " absolute " normal force coefficient for this incidence multiplied by 2.5 x a. a, the area value of tail, is taken as a fraction of the main aerofoil (or aerofoils) area. Of course, the same scales were used in drawing these tail moment curves as were used for the pitching moment carves. For each tail, then, were run a series of curves with values for a, varying from . 2 to . 5. I assumed that the aeroplane is to trim at j 20 incidence for main aerofoils.. So a tail moment family of curves was slid in turn over each of the pitching moment curves, and thence, by interpolation if necessary, was found the particular tail curve which, when intersecting the pitching moment curve at +20, would just he altogether above the pitching moment curve to left-hand side of intersection and altogether below piching moment curve to right-hand side of intersection. Reverting again to Plate VII, I have not shown the series of tail moment curves employed, but on the monoplane pitching moment diagram are shown a few selected curves of tail moment. Intersecting the .30 centre of gravity pitching moment curve at + 2° is shown, in dotted line, the moment for a symmetrical tail of area ^ .035 main aerofoil area. This curve cuts the base line at + 8.90. Therefore we see that with this tail set at — 8.90 to the aerofoil chord the aeroplane will just be stable ; you will note that there is a neutral spot at 4- 6.50. Also in tersecting the .30 centre of gravity pitching moment curve at + 20 is shown, in dot and dash line, the moment for a " wing form " tail " con vex-down " of area = ,025 main aerofoil area. This curve also cuts the base line at about + 8.90. Therefore we see that with the chord of this tail at — 6.50 (its zero lift is at + 2.4°) to the aerofoil chord the aeroplane will just be stable ; you will note that again there is a neutral spot at 4- 6.50, and that with this " convex- down " tail the stabilising moment is greater for nose diving and less for stalling than it is with the symmetrical tail of same area. On the .36 centre of gravity pitching moment curve is drawn, in dotted line, the moment curve for a symmetrical tail of area = . 038 main aerofoil area, set at — 3.20 to chord of main aerofoil. This gives stability with a neutral point at -f- 14°. On the .42 centre of gravity pitching moment curve is drawn, in dotted fine, the moment curve for a symmetrical tail of area = . 064 main aerofoil area, set at — 1.40 to chord of main aerofoil. This gives stability with a neutral spot at about -f 13J0. Also on the .42 centre of gravity pitching moment curve is drawn, in dot and dash line, the moment curve for a " convex-up " tail of .064 main aerofoil area, set at — 3.50 (its zero lift is at —2.4°) to main aerofoil chord. This gives stability with a neutral spot at — 4.50. You will note that with the " convex-up " tail the stabilising moment is greater for stalling and smaller for nose-diving than with the symmetrical tail. We cannot give more time to considera tion of the method employed, and I hope this brief explana tion is sufficient. Returning agiin to Pla*e VIII, we have then values for size of tail plane required, and required setting for chord of tail relatively to chord of main aerofoil, considering the tail as in undisturbed air. These values are given in jthe curves at the bottom of Plate VIII. We must proceed to the consideration of what will be the added drag due to tail. I have made a very rough assumption as a start, namely, that due to the downwash from the main aerofoils we must employ a tail of twice the area found necessary in undis turbed air. As a matter of fact, this is pretty nearly correct, and at any rate is quite a fair assumption for a comparative investigation, which is what this is intended for. I have taken the " absolute " drag coefficients for tail fromha curves at the top of Fig. 8. For any one case, then, the tail drag is taken as area of tail (expressed as a fraction of main aerofoil area) multiplied by " absolute " drag coefficient proper to tail, and divided by " absolute " drag coefficient proper to main aerofoil. This gives us a value for tail drag expressed as a fraction of the main aerofoil drag. But this is not the total drag due to tail, for if the tail has to exert a downward force for stabilising, the wings must exert a lift, over and abcve total weight of aeroplane, of amount equal to down load on tail, and this added lift must be paid for by added drag. Similarly if the tail has to exert an upward force for stabilising, the lift of the wings will be less than the total weight of the aeroplane by an amount equal to lift of tail, and this decrease of wing lift gives decrease of drag. The amount of the necessary addition to, or sub traction from, lift of wings, for any one condition, is given by—value for pitching moment divided by tail lever ; so it is worthy of note that a long-tailed machine will, at high speeds at any rate, have a smaller increment of wing drag due to tail down load, than will a short-tailed machine. 3IO
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