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Aviation History
1920
1920 - 0105.PDF
JANUARY 22, 1920 however, the approximation suggested is sufficiently accurate,and has the advantage of being extremely easy. Oleo Gear In its simplest form the oleo gear consists of a piston (A) of circular cross section which can move in a cylinder (B) against a resistance. This resistance is provided by oil, which as the piston advances is forced through some small orifices (C) in the piston head with a very high velocity. If A = effective area of piston head, i.e., total area less area of orifices. • .; , a = effective area of orifices. . ' . I =• length of orifice. m = hydraulic mean depth of orifice = area of orifice/ perimeter. V = velocity of piston. , .- - . . v = 'velocity of liquid through the orifices. F = frictional coefficient due chiefly to the surface ' - of the orifices. _._'... •' p — density of liquid. • - p = excess pressure behind the orifices in lbs. We have p ^_ v2 ( Fl\To * + m) . P 2£\ (See Gibson on " Hydraulics and its Applications.")For continuity of liquid flow AV= av and therefore p = V* A» / Fl\ P 2g a* \ "•" m J Total resistance (I) Tg F/ r; I I + — kV* If W is the weight of an aeroplane with oleo gear on either wheel of a two-wheeled undercarriage, it follows that dV For a movement x of the piston head with a fall off in velocity from V,,to V! we have, integrating the last equation. w or * = log< Vi 2k - (2) This equation gives the velocity at any time in terms of the original velocity and the piston travel. The pressure p may, however, rise to a value considerably higher than is convenient. In the case of a simple oleo a valve may be provided, set so that whatever the vertical velocity the load on the piston will not be sufficient to break the aeroplane, though, of course, there is no guarantee that with high velocity all the kinetic energy of the machine will be absorbed. If no valve is fitted there is a definite limiting velocity above which the forces set up on the gear can no longer be sustained by the aeroplane. A valve (D) is, there- fore, set in the piston head, which opens as soon as p rises above a value previously determined upon. By this arrange- ment the maximum pressure on the sides of the cylinder and on the piston head is known, and the gear can be made just strong enough to stand this pressure. Until the valve closes the retardation is constant and given by dV •'•••• . 2irA = — WV 3— _ • dx where T is the pressure at which the valve opens. * • The value of V when the valve closes is given by *A=AV2 (3) and when the valve closes the equation (2) holds providing Vo has the value determined in equation (3). The next stage in the development of the oleo gear is that the free movement of the piston, besides being retarded by the oil, is further retarded by some spring device shown diagrammatically at (E). In an aeroplane this resistance is generally provided by the extension of elastic. If Tt is the tension in the elastic at any stage, the rate of retardation is given by - . T, + 2*V* = - W -^ = - WV^j- In practice this equation is not, as a rule, amenable to mathematical treatment, and the slowing up of the aeroplane is best done by step by step integration. When, however, the oleo gear is fitted with a valve to keep the pressure in the cylinder below a certain value, an approxi- S-OI ,.* < z 0-8 Ob 0* 0 Z n \ O \ \ 1 GR PPH OF - .. -• . " '• . I , -- - •• \ \ PI&TOM ,.9*_/C*0 FIC, - TR <WE\_ ( INC> 24 - ~ - • i -> 6 mate value for the total distance travelled by the piston before the energy of the aeroplane is absorbed can be obtained in the manner shown in the following example. (No further extension of the general case can be given.) For a particular design of oleo gear4 =io8 A = 3.98 sq. in. F — 0.005 see Gibson on " Hydraulics ") m = ~o384 VI — = 0.16 mp = 62.4 . vWith these values/) = 91 V2 k - 362 The weight of the aeroplane is 7,500 lbs. and so V = Vo x io-°-1126* where x is now in inches,, * = 91 V,« where Vj is downward velocity of the aeroplane when the valve closes. The pressure after a distance of travel x inches after the valve closes is given by £=91 Vs -91 Vi2X IO "0.225* and the total pressure = pK = 362 V,a x 10 - °-226 *• The work done in travelling this distance x inches "XT Jo 362V,2 x = 3.98 ir 1.93 (1-10-°-225:r) inch pounds (4) The function 1-93 (1 - 10 -0.226 x) has been plotted against x, and with the help of the graph it is simple to find the work done for any distance of travel a- up to 8 ins. after the valve closes (Fig. 24). The work done in the oleo with constant total pressure 3 • 98 7r over a distance of travel of y inches with constant ^-Tis 3.98 vy inch lbs. (Fig. 25.) If Ey represents the work done in extending the elastic y inches beyond its original extension, the tota1 work done, for each leg, is Ey + 3 -98 wy inch lbs. 10a
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