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Aviation History
1929
1929 - 0846.PDF
SUPPLEMENT TO FLIGHT 28 APRIL 26, 1929 THE AIRCRAFT ENGINEER angles were measured from the vertical axis oy. If the values of the spar " constants " about the vertical axis oy are required, or if angles are measured from the horizontal axis, a length in replacing I, expression for integration is : f*3 re r (m + r sin2 6) dQ = r (m* + 2 mr sin 0 + r3 sin*0) dQ J a a = r m2 + 2 mr sin 0 H (1 — cos 2 0) \dQ Giving r | | m2 + — )6 — 2 mr cos 0 sin 2 0 = rj ( w»* -f — J(p — a) — 2 mr (cos 3 — cos a) r5 1(sin 2 (3 — sin 2a) When a = 0 m = 0 P = 3 the expression reduces to sin 2 S\ The distance of the centre of gravity from oy is (TO -f r sin 0) rf0 m((3 — a) — r (cos [3—cos a) 3" when »i = 0 a = 0 a; = r (1— cos !3) P Then vertical * sin 2 2(1—cos P~~ ... (6) From expressions (5) and (6) a set of graphs showing corre- sponding values of I^, r and f) can be plotted. With such a set of charts at hand, the determining of the necessary con- stants for complicated sections made up of circular arcs and straight lines is easily and quickly carried out. THE THEORY OF LONG-DISTANCE FLIGHT. By ROBEBT J. NEBESAR In this theoretical discussion of the factors of long-distance flight the following nomenclature will be employed. The theoretical parts are based on the metric system. The coefficients are in the absolute and not the engineering values. American unite are used in all charts for practical use in conjunction with metric units. A = area of wings in square metres b — span of wings in metres Bo = engine brake horse-power at sea level BA = engine brake horse-power at altitude h metres above sea level B, = engine brake horse-power at moment t c8 = specific fuel consumption in kilograms per horse- power/hour C = coefficient of total drag n prof LD = coefficient of induced drag coefficient of profile drag coefficient of structural drag (parasite drag) in the polar diagram (recalculated on the unity of the area of wings) coefficient of lift total drag in kilograms D/, = total drag at altitude h metres above sea level, in kilograms T)im, = induced drag in kilograms IVw = profile drag in kilograms structural drag in kilograms efficiency of the propeller cD vro/ +_cD,,™ unuseful to H X VD ,W/profile drag acceleration of gravity in metres per second per second a certain altitude during the flight, in metres absolute ceiling of the aeroplane, in metres theoretical ceiling of the aeroplane, in metres — = aspect ratio of wingA power loading at the beginning of flight, in kilo- grams per horse-power* Lw = wing loading at the beginning of flight, in kilo- grams per square metre p0 = specific weight of the air at sea level Pi, = specific weight of the air at altitude h metres above sea level R = maximum cruising radius of an aeroplane at the variable speed, in kilometres Rnml,t = maximum cruising radius at the constant speed, in kilometres t = a certain moment during the flight T = duration of the flight for the distance R, in hours T(. = duration of the flight for the distance R^u^t in hours V = speed in metres per second Vo = speed at sea level, in metres per second V/, = speed at altitude h metres above sea level, in metres per second V( = speed at moment t, in metres per second W/ w = — = ratio of the fuel weight to the total weight of an aeroplane at the beginning of flight Wy = weight of fuel in kilograms W = total weight of an aeroplane in kilograms W( = total weight of an aeroplane at the moment /, in kilograms 1. Speed at Minimum Drag. The primary factor for a successful long-distance flight is the minimum consumption of fuel for a given distance. We shall assume a monoplane flying at a constant altitude at sea level, also that the engine has surplus power which will enable the plane to climb. The total drag of an aeroplane consists of three parts, which are the induced, the profile, and the parasite drag. The profile and parasite drags are unuseful. 2a W*The induced drag D,, ld = = ——p T. • V* • tr The profile drag Dw = The parasite drag D,,,,,, = £ • C D „,.„, A • V2 A • V1 The foregoing formula for the induced drag is correct for the elliptical lift distribution. For any other distribution ol the lift we shall include the increase of the induced drag in • The power loading is taken at the start of the flight, after the desired altitude hM been reached and aeroplane has started for its objective. 33&2
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