Value 



°f|_(A 



A'orA") 

 in the 

 Segmt. 



Railway Curves. 127 



' In the ordinary position of the parts, ) -r, . t, na — B 



as in fig. M, for an S curve } BAD = Su l 3t - of -^ 



In the possible arrangement of parts, ) t, .-r. C( i,a-\~B 



as in fig. NA for an S curve } BAD = Su P*- of ^ 



In the case of a compound curve BAD = 90° + a ~^P 



2 



(The same in effect as in fig. M, but that a in this figure is the conpt. 



of a in fig. M.) 



(As proved on preceding page.) 



The radius A of C = \ chd. cosec. Sl = ^£ Cosec. BAD 



2 2 



Or, if a table of secants is not at hand, say r. a. of c.= 2 _ 



Sin. BAD 



A simplification of common method of setting out curves will be 

 explained hereafter. 



Use of the arc of contact. — It is observable that the prolongation 

 of one of the railway tangents TD intersects the arc of contact at A", 

 (this prolongation may be considered, for uniformity's sake, an arc 

 of infinite radius), but that beyond that point the arc of contact is 

 not available for an S curve, nor short of that point for a compound 

 curve. It is evident, however, that if the absence of obstructions 

 allows the choice of any available point on it, as A or A', the $ or 

 compound curve will have greater freedom than the sharp curve A"B. 



The length DA" of the prolongation of the tangent that of the 

 chord A"B and r, the radius of such simple arc, may be found by 

 calculation ; thus, (values of A", B, D, being given in the investiga- 

 tion below.) 



The DATA are DB or d and a and 8. 



(i.) DA"=cZ sin. A + D cosec. A"; (n.) BA"=<i cos a cosec. A" 



i AB . ~ x 



and r = . cosec. A . (in.) 



Note — That this observation and these three formulae apply to the 

 case where one of the railway tangents produced cuts the arc of 

 contact. At this end of the curve is the |_ designated the a in the 

 second of these formulae. 



Investigation of the above three formuke. 



In the A A'DB, the |_ A"=BAD, the [_ of the segment, (Its value 



already stated.) 

 L D —a — 90° in all cases of one arc curve. 

 LB =supt. (A" + D) 



