. Railroad construction : theory and practice : a textbook for the use of students in colleges and technical schools . hord lengths. What is the true length of the subchords? (d) Given two tangents making a central angle of 15° is desired to connect these tangents by a curve which shallpass feet from their intersection. How far down thetangent will the curve begin and what will be its radius? (UseEq. 8 and then use Eq 4 inverted.) 25. Curve location by deflections. The angle between asecant and a tangent (or between two secants intersecting on anarc) is measured by one half of the i
. Railroad construction : theory and practice : a textbook for the use of students in colleges and technical schools . hord lengths. What is the true length of the subchords? (d) Given two tangents making a central angle of 15° is desired to connect these tangents by a curve which shallpass feet from their intersection. How far down thetangent will the curve begin and what will be its radius? (UseEq. 8 and then use Eq 4 inverted.) 25. Curve location by deflections. The angle between asecant and a tangent (or between two secants intersecting on anarc) is measured by one half of the intercepted arc. Beginningat the PC (A in Fig. 10), if thefirst chord is to be a full chordwe may deflect an angle VAa(=^D), and the point a, which is100 feet from .4, is a point on thecurve. For the next .station, h,deflect an additional angle bAa(=^D) and, with one end of thetape at a, swing the other enduntil the 100-foot point is on theline Ab. The point b is then onthe curve. If the final chord cBis a subchord, its additional deflec- Fig. 10. tion (^d) is something less than JD. The last deflection (BA V) is. 24 RAILROAD CONSTRUCTION. § 26. of course JJ. It is particularly important, when a curve beginsor ends with a subchord and the deflections are odd quantities,that the last additional deflection should be carefully com-puted and added to the previous deflection, to check the mathe-matical work by the agreement of this last computed deflec-tion with JJ. Example. Given a 3° 24 curve having a central angle of18° 22 and beginning at sta. 47 + 32, to compute the deflec-tions. The nominal length of curve is 18° 22^3° 24= ^ = stations or feet. The curve therefore endsat sta. 52 + The deflection for sta. 48 is iVoXi(3°24)=°.7 = l°.156 = 1° 09 nearly. For each additional 100feet it is 1° 42 additional. The final additional deflection forthe final subchord of feet is ^X i(3° 24) = 1°.2274 = 1° 14 nearly. The deflections are P.
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