. American engineer and railroad journal . elerationceases. The latter is either positive or negative. By a nega-tive acceleration is meant the effect of a force that would causea body to move in the opposite direction if it was at Let r = radius of the I = length of connecting-rod. _Let i ■= the time the center of the driving-wheel has movedfrom a fixed point oa the line of railway. Let u = the distance of this fixed point from the piston. Let c = the distance of the piston from the cross-head, whichis [Let V =^ velocity of the engine, which is supposed constant
. American engineer and railroad journal . elerationceases. The latter is either positive or negative. By a nega-tive acceleration is meant the effect of a force that would causea body to move in the opposite direction if it was at Let r = radius of the I = length of connecting-rod. _Let i ■= the time the center of the driving-wheel has movedfrom a fixed point oa the line of railway. Let u = the distance of this fixed point from the piston. Let c = the distance of the piston from the cross-head, whichis [Let V =^ velocity of the engine, which is supposed constant. Let » = velocity of the crank-pin about the center of thedriving-wheel. This, of course, is constant, since Fis con-stant. Let S be the angle made with the horizontal by the radius V> be the angle made with the horizontal by the connect-ing-rod. The angle 0 is measured in the usual manner, butthe angle i» is measured in the opposite way. It follows thatCOS. (p is always;positive,|but^s2/i. ^s^has the same sign as itin. ( For simplicity, the axisof the piston is supposed to he in ahorizjntal plane with the center of the these definitions u = V t -{- r COS. (J -j- I COS. V + c, and differentiating d u , . (18 d (P -r-T = velocity of piston = V — r sin. ff - — I sin. li -~at .-1 ^i f (it Now —7— — — V. The negative sign shows that the driv-ing-wheel turns in such a direction as to decrease sin. i ■= I sin. (j>, , , (IH , , d^ whence r cos. 0 ~— = — v cos. 0 = I cos. o —^ d t ^ d t I d ^ _ V COS. 0 IT COS. 0 and therefored V - V-\-v\ sin. B -\- cos. 0 sin. ^ I t ( ^ COS. (I> \ = 7^ j,»«-(M-i). (I) Tlie force causing acceleration is proportional to (weight) (I ^ ft X -7-77, and the velocity is a maximum or minimum when ac- celeralion ceases, and. therefon, when = 0 d V Hence, differentiating again, aw. ^ _\ («M. (fl-H) <»s. *-f-«in.(9-H) «-*)34+«*. co».(9x*i^, / WAP. iP* *■ dt^^* ^* + dl }, (cince COS.
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Keywords: ., bookcentury1800, bookdecade1890, booksubjectrailroadengineering
