. Railroad construction : theory and practice : a textbook for the use of students in colleges and technical schools . Fig. 26. Fig. 27. intersects the new tangent. The solution is almost identicalwith that in § 38, n. b. Assume that it is desired to change the forward tangent(as above) but to retain the same radius. In Fig. 27 {R2 — R1) cos J2 =02n; (R2-R1) cos J/ =02V. X=02 -O2V =(i?2-^l)(C0S J2-COS J/).X COS Jo= COS Jo (24) J2—^ua^2 —^ ^ II2 —/ti The , is moved backward along the sharper curve anangular distance of J2~^2 = ^i~^/- In case the tangent is moved inward rather than outward,
. Railroad construction : theory and practice : a textbook for the use of students in colleges and technical schools . Fig. 26. Fig. 27. intersects the new tangent. The solution is almost identicalwith that in § 38, n. b. Assume that it is desired to change the forward tangent(as above) but to retain the same radius. In Fig. 27 {R2 — R1) cos J2 =02n; (R2-R1) cos J/ =02V. X=02 -O2V =(i?2-^l)(C0S J2-COS J/).X COS Jo= COS Jo (24) J2—^ua^2 —^ ^ II2 —/ti The , is moved backward along the sharper curve anangular distance of J2~^2 = ^i~^/- In case the tangent is moved inward rather than outward,the solution will apply by transposing J2 ^^^ ^i - Then weshall have X cos Jo= cos ^9 + 7?2 ~-^l (26) §30. 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 (R2—R1) cos J^ =0{n;{R2-R1) cosii=OiV. x=0,n-0,n cos i/ = COS ii + R2 — RI -COS Jj). (26). The is moved forwardalong the easier curve an angulardistance of J/ —ii = J2 —^2- In case the tangent is moved inwardj transpose as before andwe have X Fig. 28. cos J/=cos J I — j (27) 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 O2S. Then, since /?2 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 givenby a line Oi^p 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 ^^ill therefore be tangentat B^ and tangent to the oldDraw 0^n^ perpendicular to O2B, \syi
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