. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . The is moved forward along the easier curve an angular distance of i/ —il = i2~^2•In case the tangent is moved inward, transpose as before and we have Fig. 33. cos J/ = cos JI X (27) R2—R1The 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. 34. For the diagrammatic solutionassume that R2 is to be increasedby O2S. Then, since /?/ mustpass through 0^ and extend be-yond Oj a dista
. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . The is moved forward along the easier curve an angular distance of i/ —il = i2~^2•In case the tangent is moved inward, transpose as before and we have Fig. 33. cos J/ = cos JI X (27) R2—R1The 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. 34. For the diagrammatic solutionassume that R2 is to be increasedby O2S. Then, since /?/ mustpass through 0^ and extend be-yond Oj a distance OiS, thelocus of the new center must lieon the arc drawn about 0^ ascenter and* with OS as locus of O2 is also givenby a line 02p parallel to BVand at a distance of i?2 (equalto S ,,. ) from it. Thenew center is therefore at theintersection O2. An arc with ra-dius 7^2 will therefore be tangentat B^ and tangent to the oldDraw OjTi^ perpendicular to O2B,. Fig. 34. curve produced at new § 70. ALINEMENT. 81 With O2 as center draw the arc 0{m, and with O2 as center drawthe arc O^m, mB=YnB=R^. .\ mn= m^n = {R2 — Ri) vers J-/ = (R2—Ri) vers Jg- .-. versJ/ = ^^^|^versJ2 (28) OiU = (R2—Ri) sin J2) Oy = (^2--Ki) sin {n - 0{n = (R/ - 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 R2, sl given change BB^ is to be made. Jjand J?2 ^re required. Eliminate i^z 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 §§ 62 and 63, the above^problems are but a few, althoughperhaps the most common, of the problems the engineer maymeet with in compound curves. All of t
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