Transactions

LIPETZ—PLOTTING TIME-SPEED-DISTANCE CURVES FOR RAILWAY TRAINS 607F ig . 4L i p e tz ’ M e t h o d f o b S p e e d -T im e C u r v ewhich is the acceleration curve of Fig. 3 redrawn somewhat differently.The time needed for covering e distance of an elementaryincrement will bewhere Va is the average speed for the distance increment. Thissuggests a simple method for construction of the time curve.Divide the speed-versus-distance curve into elements. Theeasiest way is to take the elements already drawn in Fig. 3through the same steps of speeds. Mark the middle points of theelements o, 6, c, d, e, f, etc., (Fig. 4); drop perpendiculars fromthese points to the distance axis OS — 1, 2, 3, 4, etc.; measureup a constant parameter b equal 2 in. from each foot of the perpendicularsto points a1, bl, c1, d1, etc.; draw radii vectors a’a,6*6, c‘c, d'd, e'e, /*/, etc., to the middle points, and direct 0a2perpendicularly to a‘a through the length of the first interval;o262 perpendicularly to b'b through the second interval; b2c2perpendicularly to c'c through the third interval and so on.All these constructions are identical with the construction shownin Fig. 4 for the fifth interval, as an example, from which it isevident thatscale. The broken line Oa^c^th, etc., is the desired time curve.The total time is equal to the height of the last construction. Forconvenience, the broken line can be divided into branches A, B,etc., and their heights, measured to a certain scale, added together,will represent the total time.As to the scales by which the distance and time should bemeasured and read, the procedure is the same as the one usedbefore, namely, the distance was based on the construction shownin Fig. 3 and determined by Equation [4], orif v is in miles per hour, s in miles, t — r in lb per ton of weight,f is the coefficient equal 37.5, for y = 0.0528. If we should usefor the variables the scales given previously, namelyv = 10 mph = 1 in.