. The steam-engine and other heat-motors . 06). Case I.—Infinite Connecting-red. Let F= constant velocity of the crank-pin in feet per second;v=variable velocity of the piston in feet per second;r = radius of crank in feet; 0=length of the arc, measured from the dead-center, swept through by a point on the crank-arm at unit distance from center of the shaft in t seconds; IF=weight of the reciprocating parts. Then rO = length of arc swept through by crank-pin in t seconds = Vt. rdd^vdt, hence -j-=— dt r J distance the piston moves in t seconds from aI dead-center whilst the crank-pin moves rd.
. The steam-engine and other heat-motors . 06). Case I.—Infinite Connecting-red. Let F= constant velocity of the crank-pin in feet per second;v=variable velocity of the piston in feet per second;r = radius of crank in feet; 0=length of the arc, measured from the dead-center, swept through by a point on the crank-arm at unit distance from center of the shaft in t seconds; IF=weight of the reciprocating parts. Then rO = length of arc swept through by crank-pin in t seconds = Vt. rdd^vdt, hence -j-=— dt r J distance the piston moves in t seconds from aI dead-center whilst the crank-pin moves rd. ds d(r — r cos 6) r sin Odd TT . n . rdd TT dt=—dt—=^r~=Vsmd QmceTt=v , A. dv d2s d(Vsind) V cos Odd F2cos# But acceleration =-77 =—^ = t. = -j.— = . dt dt2 dt dt r The product of the acceleration and the mass that has been accele-rated gives the force required to produce the acceleration; or W V2 cos 6p = . =the total force required to produce the necessary acceleration of the reciprocating parts at the piston position cor-. SPEED VARIATION CONTROL. 377 responding to a crank-angle, 6, if the crank-pin revolves uni-formly. As the indicator-cards show pressures in pounds per squareinch it is advisable to divide the totalpressure F by the area of the piston in M w v2 cos e. , square inches. Hence / =—r is the loss or gain of pressure in pounds persquare inch of piston area arising from thenecessary acceleration, positive or negative,of the reciprocating parts (at a piston posi-tion corresponding to the crank-angle 0). Mass of Reciprocating Parts Considered as Concentrated at theCenter of the Crank-pin.—If the weight of all the reciprocatingparts could be concentrated at the center of the crank-pin the cen- WV2 tripetal force of such a weight would be . The horizontal 6 gr WV2 cos 0projection of this radial force would be or the above force, F. In the above equation for /, the only variables are / and cos the equation is of the first degree, it is therefore
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