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Aviation History
1931
1931 - 0660.PDF
FLIGHT, JUNE 26, 1931 By the aid of equations 6, 7, 8 and 9, and Figs. 3 and 4,the characteristics of any wing of approximately rectangular or elliptical plan form (without twist) can be obtained.Having now our wing characteristics, we can proceed to examine how they are utilised to find the speeds, glidingangles, and rates of descent of a full-scale craft. Reference to Fig. 2 will show that for steady flight con-ditions the weight of the glider must be balanced by com- ponents of lift and drag.Since the lift and the drag act at right angles to one another, their resultant is given by ,/R2 + Ls, but for glides not Steeper than 1 in 11 or 12 this quantity is very nearly the same as L, and will be taken as such. So that from equation 2 we can write ; w = *S<r <12) for ground level conditions.From considerations of elementary trigonometry, it is obvious from Fig. 2 that the angle of glide is given by :— RTan <p = |- (13) or the glide is on a gradient of LGliding angle = 1 in R (14) Substituting for L and R from equations 2 and 3 gives :— KGliding angle = 1 in „ (15) where KK is the wing drag coefficient plus the coefficient ofbody drag ; in other words, K R is the overall drag coefficientand R the overall drag. The rate at which the glider would descend in free air isgiven by the speed divided by the gradient of the glide, i.e., if u = downward speed in f.p.s.— V f.p.s. or if V is in m.p.h. 1-467 V m.p.h. v f.p.s. = KL/KJT^ (16) At some speed the rate of descent becomes a minimum,and when flying at tlu's air speed the greatest advantage is taken of any upward current in the atmosphere.The presence of an upward current of air of any speed does not affect the speed at which this minimum rate of descentoccurs. Where it is necessary to go from one point in the air toanother with the least loss of height, flight is made on the smallest angle of glide or the speed corresponding to maxi-mum value of KL/KR.If flight is to be made from some point in the atmosphere to some distant point on the ground, the conditions aredifferent and changeable, depending on the direction and strength of the wind. For flights from one cloud to another, the best resultswould be obtained at the minimum gliding angle ; that is, at the speed where KI./KR is a maximum.Perhaps a numerical example will clear up any little points of doubt in the reader's mind. Take the case of a glider having the following particulars :— Span : 50 ft. Wing area : 250 sq. ft. Plan form : Elliptical. Wing section : Gbttingen 549. Weight fully loaded : 500 lb. Assume that the drag of the fuselage and tail unit is 40 lbs.at 100 m.p.h. 1. The Wing Characteristics. From equation 1 :— Ss 508_'• Aspect ratio = A = g- = ss = 10. from equation 8 0-636AK D = —jQ- KL8 = 0-0636 KL8 K. - KDp (from Fig. 3) + 0-0636 KL« 240 GLIDING GRACENT__ 1 IN — Gliding flight in still air. From equation 9 36-5 36-5Aa = - A- KL = -]ft- KL = 3-65 KL .-. a = a,, (from Fig. 3) + 3-65 KL. 2. Body Drag Coefficient. Equation similar to that for drag is :— Body drag = KB. fc^75 = 40 lb. at 100 m.p.h. S7,,V2.-. K B = Body drag -^ 195T5 250 x 1002= 40 -r —, 195-5 = 0-00313 KR = KD/, + 0-00313 + 0-0636 KL2. Gliding Flight at Ground Level. A = 10-0. Choose KL Knp (Fig. 3) + 0-00313 AKD = 0-0636 K,2 0-1 0-00813 0-00064 0-2 0-3 0-J, etc. 0-00778 0-00254 0-00773 0-00572 0-00786 0-01018 Sum Gilding gradient 1 in KL/KR Kate of descent VK R1-467. 0•00907 62-5 11-0 8-33 0-01032 ! 0-01345 ' 0-01S04 44 2 19-4 3-34 3fi-l 22-3 2-37 31-3 220 2-07 The complete results are plotted in Fig. 5. The points of minimum rates of descent and minimumgliding angle are marked. The correspondiiig curves for a similar glider, but havi;gan aspect ratio of wing of 5 is also given for comparison. The difference in the gliding angle and the speed of desce >tclearly shows why the sail plane has to have such a lar,;e aspect ratio. The differences noted in Fig. 5 are due solely to the efft tof aspect ratio, the wing area, the weight and the body dr g are the same in both cases.
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