. Railroad construction. Theory and practice . Fig. 26. Fig. 27. intersects the new tangent. The solution is almost identicalwith that in § 33, a. b. Assume that it is desired to change the forward tangent(as above) but to retain the same radius. In Fig. 27 (7?2~^i) cos J2 =02ny (R2-R,) cosi2 =02V. X = 02n—02n = {R2 — Ri) (cos J2 — <^os J2O• cos J/ = cos J- X (24) R2—R1 The is moved backward along the sharper curve anangular distance of J2 —^2 = ^1 —^/. In case the tangent is moved inward rather than outward,the solution will apply by transposing J2 and Jg- Then weshall have X cos Ji
. Railroad construction. Theory and practice . Fig. 26. Fig. 27. intersects the new tangent. The solution is almost identicalwith that in § 33, a. b. Assume that it is desired to change the forward tangent(as above) but to retain the same radius. In Fig. 27 (7?2~^i) cos J2 =02ny (R2-R,) cosi2 =02V. X = 02n—02n = {R2 — Ri) (cos J2 — <^os J2O• cos J/ = cos J- X (24) R2—R1 The is moved backward along the sharper curve anangular distance of J2 —^2 = ^1 —^/. In case the tangent is moved inward rather than outward,the solution will apply by transposing J2 and Jg- Then weshall have X cos Ji^ = COS ^2 + R2—RI (25) §39. ALIGNMENT. 41 The is then moved forward. c. Assume the same case as (b) except that the larger radiuscomes first and that the tangent adjacent to the smaller radiusis moved. In Fig. 28 (Ro—R{) cos J, =0{n;(R,-R,) cos J/=0,n\ x=0^n^—0{ii= (7^2—^i)(cos i/—cos ii). cos i/ = cos ii R2—-^1 (26). 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,
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