. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . .48437 E = log= 2) =3° 44 §67. ALINEMENT, 77 COMPOUND CURVES. 67. Nature and use. Compound curves are formed by asuccession of two or more simple curves of different curves must have a common tangent at the point of com-pound curvature (), In mountainous regions there isfrequently a necessity for compound curves having severalchanges of curvature. Such curves may be located separatelyas a succession of simple curves, but a combination of twosi
. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . .48437 E = log= 2) =3° 44 §67. ALINEMENT, 77 COMPOUND CURVES. 67. Nature and use. Compound curves are formed by asuccession of two or more simple curves of different curves must have a common tangent at the point of com-pound curvature (), In mountainous regions there isfrequently a necessity for compound curves having severalchanges of curvature. Such curves may be located separatelyas a succession of simple curves, but a combination of twosimple curves has special properties w^hich are worth investigat-ing and utilizing. In the following demonstrations R2 alwaysrepresents the longer radius and Ri the shorter, no matter whichsucceeds the other. T^ is the tangent adjacent to the curve ofshorter radius (Ri), and is invariably the shorter tangent. J^ isthe central angle of the curve of radius R^, but it may be greateror less than Jj 68. Mutual relations of the parts of a compound curve havingtwo branches. In Fig. 30, AC and CB are the two branches of. 1- Fig. 30. the compound curve having radii of Ri and R2 and central anglesof JI and J 2 Produce the arc AC to n so that AO{n = J. Thechord Cn produced must intersect B. The line ns, parallel toCO2, will intersect BO2 so that Bs=sn=020i=R2—Ri, DrawAm perpendicular to Oiti. It will be parallel to hk. 78 RAILROAD CONSTRUCTION. § 68. Br = sn vers Bsn = (R2 —Ri) vers J2 >inn=AOi veis AO{n —R^ vers J;^A;=^FsmAF/c- =TisinJ;ylit = Am =mn+ n/i =mn + Ti sin J =Ei vers A + (Eg -^1) vers d^. . (20)Similarly it may be shown that T2 sin A =i?2 vers J - {R^ -R^) vers Jj. . (21) The mutual relations of the elements of compound curvesmay be solved by these two equations. For example, assumethe tangents as fixed {A therefore known) and that a curve ofgiven radius R^ shall start from a given point at a distance T^from the vertex, and that the curve shall continue throug
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