. Railroad construction. Theory and practice . The is moved forwardalong the easier curve an angulardistance of i/ —Ji = i2~^2 Fig. 28. In case the tangent is moved inwardj transpose as before andwe have cos J/ = cos JI X (27) R2—R1 The is moved backward. d. Assume that the radius of one curve is to be altered with-out changing either tangent. Assume conditions as in Fig. 29. For the diagrammatic solutionassume that i?2 is to be increasedby 02^,. Then, since R-/ mustpass through 0^ and extend be-yond Oi a distance O^S, thelocus of the new center must lieon the arc drawn about 0^
. Railroad construction. Theory and practice . The is moved forwardalong the easier curve an angulardistance of i/ —Ji = i2~^2 Fig. 28. In case the tangent is moved inwardj transpose as before andwe have cos J/ = cos JI X (27) R2—R1 The is moved backward. d. Assume that the radius of one curve is to be altered with-out changing either tangent. Assume conditions as in Fig. 29. For the diagrammatic solutionassume that i?2 is to be increasedby 02^,. Then, since R-/ mustpass through 0^ and extend be-yond Oi a distance O^S, thelocus of the new center must lieon the arc drawn about 0^ ascenter and with OS as locus of O2 is also gJA-enby a line O2P parallel to BVand at a distance of R2 (equalto S . . ) from it. Thenew center is therefore at theintersection O2 . An arc with ra-dius R2 will therefore be tangentat B and tangent to the oldDraw O^n perpendicular to O2B,. FjG. 29. curve produced at new 42 RAILROAD CONSTRUCTION. § 40. With O2 as center draw the arc OiW, and with O2 as center drawthe arc O^m^ viB=mB =R^. .. mn=mn = (R2 —Ri) vers J2=(i?2 —^1) ^^rs J2- .-. versJ/ = ^^fc||^^ versJ, (28) 0{n = {R2 — R)) sin A2,0,n = (R2-R,) sin J/.BB = 0{n - 0,n = {R2 - R,) sin J2 ~ (^2 - ^1) sin J2. (29 This problem may be further modified by assuming that theradius of the curve is decreased rather than increased, or thatthe smaller radius follows the larger. The solution is similarand is suggested as a profitable exercise. It might also be assumed that, instead of making a givenchange in the radius Ro, a given change BB^ is to be made, ijand R2 are required. Eliminate R2 from Eqs. 28 and 29and solve the resulting equation for ^2- Then determine 7?2by a suitable inversion of either Eq. 28 or 29. As in §§32 and 33, the above problems are but a few, althoughperhaps the most common, of the problems the engineer maymeet with in coiTipound curves
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