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Aviation History
1932
1932 - 0984.PDF
SUPPLEMENT TO FLIGHT SEPTEMBER 30, 1932 THE AIRCRAFT ENGINEER Now, if 6 = proportion of profile drag in the slipstream k^0 X 0-00237p SV2 = 0-00237p 8 [b kw Vs2 -f(l - 6) hm V2] kn0 = 6 kv +' 1 - *) *i uting (3 == &DO b I (4) Substitutin (3) in (4) 4 (fcao fo,) X 0-00237 S 1+1 This reduces to 46 x O-00237Si-1,„ i DO 1 - NZ = k i Dot 1 46 x 0-00237S fcD,\ NZ fci NZ-+46 X 0-00237S-/fci>, S • K])o J NZ-46 X 0-00237S Now, induced drag coefficient kv, = C KL2 where 0 is a constant depending on the wing arrangement "NZ + 46 x 0-00237 SC KL . •. kno = kn This gives kvu = where 6 = kn NZ - 46 x 0-00237 S fcD0 = e + (!> KL» (5) (6) NZ <1> = &n f \NZ - 46 x 0-00237S k, ( 46 X 0-00237SC (NZ - 46 X 0-00237S km\ If sufficient machine data is known, the constants are easily calculated, but in the absence of more accurate data, the following values may be taken 6 = 1-1 kD0 for all machines. 4> = 0-5 kD0 for multi-engined aircraft with engines mounted on the wings. <j> = 0,8&i)o to 1*2 kD0 for single-engined aircraft with tractor airscrew mounted in the nose. <J> is more susceptible to the aircraft and airscrew dimen sions and, if possible, should be calculated for the particular case under consideration. Values of C in the equation for induced drag coefficient are obtained by the usual Prandtl methods, and are plotted for quick reference in Figs. 1 and 2 for rectangular monoplanes and equal span-chord biplanes. Now, in the light of the above assumptions, consider a machine cruising at a speed of V ft. per sec. at any altitude. Let p = the specific consumption in lbs. per B.H.P. per hour. P = actual consumption in lbs. per hr. . •. P = pH where H = Brake horse power. Now at any speed V Thrust HP = Dras x is; = (* V 550 *D() X 0-00237 p SV 2 x ~ 560 022 0-20 018 , 016 a 014 o uo-12 & 0-10 0-08 0'06 004 FIG.I. I 1 1 1 1 1 1 | INDUCED DRAG OF RECTANGULAR MONOPLANES VALUES OF"C" IN THE EQUATION INDUCED DXA0 COEFFT k0l«.CkL4 •4(ltS)KJ dki/i 15 TAKEN AS 3per RADIAN IN " TWO DIMENSIONAL FLOW 6 7 ASPECT RATIO A •34 32 30 •28 •26 •24 b'22 g 20 § 18 u- '16 14 12 •10 08 00 fv 1 *^^ , FIG.2 1 EDUCED DRAG OF tUUAL 5PAN.RtCTAN6ULAK BIPLANE k*r, < *s < <c * VALUES OF'C" IN THE EQUATION INDUCED DRAG C0EFF1 - kDi -C V A -ASPECT RATIO ft^ dKL 16 TAKEN AS 3 PER RADIAN IN aoc 1WU DIMENSIONAL FLOW _Z~~f ~" •05 10 15 -20 25 GAP MEAN SPAf- • • 1—T—:—k- _ i —' 1 1 1 1 •50 -35 -40 45 -50 FENTON CW2 and since £D, = CK L 2 = - 0-002372p2SaV4 where W = weight of aircraft in lbs. Thrust HP ='^X 0-00237 pSV* 550 Now from assumption (3) kZ = e + 4 KL2 = e + .-. Thrust 6x 0-00237 p SV3 HP = TTT h CW: 550 X 0-00237 pSV <f>W2 0-002372p2S2V W2(<|> + C) 550 ' 550 X 0-00237 p SV . •. If 7] = aircrew efficiency brake horse power taken from engine J_J0-—=™fi , W2(i+_C)J (-) p = 550rj ( /' •00237 p SV36 + 0-00237 pSVj W2((j> + C) ) «O^\°-O0ajn«'SV,e' 0-00237 pSVj (8) Let m = lbs. of petrol used per foot travelled = 3600V p f W2(<f> + C) i .-. m = - \ 0-00237 PSV26 -] ' H9) 3600 X 5507)\ H T 0-00237 p SV2/V ; Now at the most economical cruising speed, m is a minimum i.e., dm/dV = O Difierentiating (9) with respect to V, and equating to O, we get '$ + C\ / W V4 = 0 0-00237 pS i.e., most economical cruising speed 4 Vc *-v x 8 0-00237 p ft. per sec. (10) w where w = wing loading = — lb. per sq. ft. FORMULA FOR RANGE Two cases will be considered. (a) Range at constant speed, neglecting the variation in gross weight of the aircraft during the flight. This case should only be used when the weight of petrol carried is a small proportion of the total weight. If Gross wt. of aircraft — W lb. Weight of petrol = WP lb. WP Then Range R feet = ro and from equation (9) 918*
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