. Railroad construction. Theory and practice . Fig. °30 with QV, or cmF = l°30. Qcm = cmV-cQm. Thevalue of cQm is known from previous work. The deflectionfrom c to Q then becomes known. ac7n = cmV— cap = cmV — caq — qap. caq is the deflection an-gle to c from the tangent at a and will have been previouslycomputed numerically, gap = 15. acm therefore becomesknown. 6cm = iof 45=2230; dcn = i of GO=30. §49. ALIGNMENT. 51 ecn=ecd —ncd^, ncd^=^cmV, tan ecd = {ee—dd)-^cej allof which are known from the previous work By this method the deflections from the tangent at any point. Fig. 33. of the cu
. Railroad construction. Theory and practice . Fig. °30 with QV, or cmF = l°30. Qcm = cmV-cQm. Thevalue of cQm is known from previous work. The deflectionfrom c to Q then becomes known. ac7n = cmV— cap = cmV — caq — qap. caq is the deflection an-gle to c from the tangent at a and will have been previouslycomputed numerically, gap = 15. acm therefore becomesknown. 6cm = iof 45=2230; dcn = i of GO=30. §49. ALIGNMENT. 51 ecn=ecd —ncd^, ncd^=^cmV, tan ecd = {ee—dd)-^cej allof which are known from the previous work By this method the deflections from the tangent at any point. Fig. 33. of the curve to any other point are determinable. These valuesare compiled in Table IV The corresponding values of theseangles when the increase in the degree of curvature per chordlength is 30, and when it is 2°, are also given in Table IV. 49. Connection of spiral with circular curve and with Fig. 33.* Let AV and BV be the tangents to be connected * The student should at once appreciate the fact of the necessary distor-tion of the figure. The distance MM in Fig. 33 is perhaps 100 time^ its realproportional value. 52 RAILROAD CONSTRUCTION. § 49. by a D° curve, having a suitable spiral at each end. If nospirals were to be used, the problem would be solved as in simplecurves giving the curve AMB Introducing the spiral has theeffect of throwing the curve away from the vertex a distanceMM and reducing the central angle of the D° curve by the curve beyond Z and Z to .4 and B, we willhave AA^ = BB =^MM\ ZK = the x ordinate and is thereforeknown. Call
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