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Aviation History
1918
1918 - 0126.PDF
nH III II Ift! i _^hapre_ojt ~* 4 1£ur,<i nf each Particle f \ / f i X m = H 7\ \ i \ 2_ \ \ / HI •a— a —i —-r TO | / / \ / \ jCvcle df Gvro'. iftz t •\I -=H 1—4- about AJ 7/ -pr- \ / ?— \ \ \ -v- \/ a' \ riR ( \ )•/•— \ 'V. —1—r—I— 3copic Torque—f r q^—i )f Nutation -22 r \ > T / / / // / / / \ / / y /* \ -A: 1 \ \ \ . .... Gyroscopic Torciue Due to particle 1 H m -, 4... \r T \ \P / V \ 2 / 21 NI— 2 r • / / -25 ('\ ! Cyc| \J* • -i 1 ab ^— \ X yf D—* led )Ut V\ V\ \ / ! Axj X "~*Tyro so // V JANUAR1 sco; f P 1k ^ 3 ic Torque ecessipn \ \ I vA y / 1 , I V r"V ~r 918 -I'4- i >; • ' Fig. 14. F => Smv"/r, Dividing F by the section area now gives the average centrifugal stress. Bending stresses.—The bending moment M, at any section of a straight radial blade, is computed by the formula M — "Zfl, where /, taken normal to the plane of the neutral surface at the section, is the component of the air force on any small block of the outer segment of the blade, / its distance from the section. Dividing M by the section modulus gives the bending stress in the outer fibre at the section. Resultant stress and safety factor.—The bending stress isplus or minus. The centrifugal is plus ; the maximum is the greatest sum of the positive or tensile stresses. Dividingthis sum into the tensile strength of the material gives the factor of safety. Diagram of stresses and of safety factor.—Fig. 5 portraysgraphically the foregoing stresses and factor of safety for all parts of a blade except the tip where they die away, andthe root where they are negligible if the hub be properly designed. Grouping of data and analytic results.—Figs. 1 to 6 presentin systematic order the data and analytic results for an entire aerodynamic and stress analysis of a propeller atboth high and low speeds of steady flight. The basic data are given in Figs. 1 and 2 ; the analytic results are given forlow speed and for high speed in Figs. 3, 4 and 5. The pro- peller map, showing the thrust, power and efficiency atvarious speeds, is reproduced in Fig. 6, and is the aggregate result of a complete aerodynamic analysis for a graded setof speeds of translation and rotation. (b) Load increments due to unsteadiness of flight.—Theadded stresses due to unsteadiness of flight are usually smaller than those just treated, but require pas ing notice. Translatory acceleration loads.—If the screw receives atranslator^ acceleration _;, every particle m opposes this with a force mi, which in practice is negligibly small. Rotatory acceleration loads.—If the screw receives anacceleration oc about its axis, every particle m opposes this with an inertia force mrx, or an axial torque m r* », where r is the radial dif tance of m. Hence the axial torque offered by any blade segment against rotatory acceleration is .. ... ,. - Q = 2m r2 » 12) Fig. 15. integrated throughout the segment and from this value themoment at any blade section, due to the mass of said seg- ment, can be found by elementary statics. 122
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