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Aviation History
1918
1918 - 0100.PDF
JANUARY 24, 1918. AIRSCREW ANALYSIS. Introduction. By A. F. *"" Scope.—In a mathematical estimate of the merits of anairscrew it is customary to make, (1) an aerodynamic analysis ; 2) a stress analysis ; the first to determine the performance,the second the structural safety. Basic Data for Airscrew Analysis.—Most airscrews consistof one or more blades secured to, or integral with, a central hub designed to be carried by a shaft rotating about an axisand moving along it. From hub to tip the blade varies in cross- sectional form, size and incidence. These three elementsare usually planned to ensure the greatest efficiency consistent "4zr 1333 3333 0.663 onot 6.90 .520 Fig. 1. Basic data forwith structural safety and adequate thrust.a typical airscrew are given in Figs. 1 and 2. Aerodynamic Analysis. Velocity and Air Force at Any Blade Section.—Each point of an airscrew blade describes a helical path whose pitch is constant when the speeds of rotation and translation bear a fixed ratio. The path is usually referred not to fixed space but to the general mass of approaching air, since this itself may be in translation. Fig. 3 shows how to find graphically the helix^angle A, the incidence i, and resultant velocity V, at any point of a blade Whose peripheral and forward velocities, referred to the general air mass, are given.f Analytically A, i, and V are computed by the formulas : tan ,4 = V/zvrN (1) V = V* + 47TMW1)1/1 (2) i =, B ~ Awhere V is the translational, N the rotational speed, r the radial distance of the moving point, and B the blade angle at r.The unit air force at any section with speed V, maybe found in magnitude very approximately by theformula E = KPV* (3) in Which p is the density, K is the air force per unit surface at unit speed for an aerofoil having the form and inci- dence of said section and moving in air of unit density 4 The direction of R in terms of the incidence is commonly known from aerofoil experiments. Other- wise the unit lift and drift are computed, and thence the resultant force. The unit lift is LpV* ; the drift is DpV-; their ratio, D/L - tan -1 G, gives the " gliding angle," or direc- ZAHM.* tion of R referred to the lift.f If V be in miles per hour the lift and drift per square foot are .0051IF2, and .oo5iDV*, respectively. , „ — ™, Thrust and Torque, Thrust Power and Torque Power.—The forward component Rr of the air force in Fig 3 w the unit thrust • the peripheral component i?*, multiplied by the section radius is the unit torque. Multiplying these units by the blade width gives the thrust and torque per unit length of blade, as tabulated and plotted in Fig. 4 ; and integrating obviously gives the whole thrust and Whole torque for the blade From these are derived the thrust power and torque OBD - ate etc 010 noo • r~rt • s J A, eu.t / s OF 'AKh y y / y y * / / / y/ ' J 11 A AU 1 wo*. / rt/ •Of •NCI "7 If s* DMA 1^—-- en — - l | t -4 -Z -O Z 4 •** -£ O Z •+. 4 Afi&Le OF ATTACH POO* OS mar TO CAT/0. t 1 \ 3 [; -6' - - ao3 - — •4' IOII srs 2-9 I*S — -3' -£' I7CI UTS S3) 6.1 -'• » -cr 23 IJ95 111 BZ as S.0 r 201.3 zjoe 96 //./ lit 3' *' 333S 3O5 2J5S5 /az' IIS IS.B £' 3.91 33t 339 9.7 IC9 «•/ /c (f 7 6 5 9 a ig- 2. 1500 /400 1300 /ZOO power, on multiplying respectively by the forward and therotational speed.|| For use with a propeller computer, to be described presently,the unit thrust is written Ry = .oo5iF.L.FsecGcos(^ +G) (4) when .0051V is called the "velocity factor"; FsecGcos (A+G) the "thrust factor." Fig. 3 shows that this thrust factor times the lift on an element equals the unit thrust there. • From Aviation (N.S.) t It is here assumed that the air approaches the screw plane normally withuniform velocity V. A slight correction for this assumption must be made. No perfectly adequate formula is available for this correction. Riach proposesa theoretical formula assuming V normal to the screw plane and increasing in velocity.—Joum. Aeron. Soc. Gr. Brit., March 21st, 1917. t The effects of air viscosity and compressibility are here ignored. No materialerror thereby ensues. See J. C. Hunsaker, Theory of Similitude of Aerial Pro- pellers ; also Edgar Buckingham, Physical Similarity.§ L and D are the absolute lift and drift coefficients, or the components of K taken respectively with and across the relative wind.II The method of this paragraph is usually attributed to S. Drzewiecki; see his Des Helices Aeriennes, Paris, F. Louis Vivien, 1909. eo 96 Fig. 6.
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