. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools, and a hand-book for the use of engineers in field and office . 8137 72 = log = 7) =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 tatigent 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 separate
. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools, and a hand-book for the use of engineers in field and office . 8137 72 = log = 7) =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 tatigent 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 twosirnple curves has special properties which are worth investigat-ing and utilizing. In the following demonstrations R2 alwaysrepresents the longer radius and R^ 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 Ri, 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. Fig. 30. the compoutid curve having radii of R^ and R2 and central anglesof Ji and Jj- Produce the arc ^C to n so that AO{n^A. Thechord Cn produced must intersect B. The line nSj parallel toCO2, will intersect BO^ so that Bs=sn=^0/)^^ = R2—Ri. DrawAm perpendicular to 0{n,. It will be parallel to hk. 78 RAILROAD CONSTRUCTION. § ^8. ; Br=sn vers Bsn =(i?2—^i) vers J2>mn=AOiYeis AO{n ==J?ivers J;Ak=AV sin AVk ^TysinJ;Ak=hm^wn + nh=mn + Tisin J=7?i vers J + (i?2—-^i) vers J2- • • (20)Similarly it may be shown that Tj sin J=R2 vers J -(7?2 -Ri) vers Jj. , . (21) The mutual relations of the elements of compound curvesmay be solved by these two equations. For example, assumethe tangents as fixed (.4 therefore known) and that a curve ofgiven radius Ri shall start from a given point at a distance
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