. Field-book for railroad engineers. Containing formulas for laying out curves, determining frog angles, levelling, calculating earth-work, etc., etc., together with tables of radii, ordinates deflections, long chords, magnetic variation, logarithms, logarithmic and natural sines, tangents, etc., etc . 0 : B E^ BC: :hBC=E C: CD. Hence 7? = BC^2 CD MISCELLANEOUS PROBLEMS. 59 This problem serves to find the radius of a curve on a track alreadylaid. For if from any point C on tlie curve we measure two .1 Cand B C, and also the perpendicular CD from Cu2)on thewhole chord A B, we
. Field-book for railroad engineers. Containing formulas for laying out curves, determining frog angles, levelling, calculating earth-work, etc., etc., together with tables of radii, ordinates deflections, long chords, magnetic variation, logarithms, logarithmic and natural sines, tangents, etc., etc . 0 : B E^ BC: :hBC=E C: CD. Hence 7? = BC^2 CD MISCELLANEOUS PROBLEMS. 59 This problem serves to find the radius of a curve on a track alreadylaid. For if from any point C on tlie curve we measure two .1 Cand B C, and also the perpendicular CD from Cu2)on thewhole chord A B, we have the data of this problem. 80. Prot>l.(3lll. To draw a tangent F G {Ji<j. 30) to a given curvefrom a given point F. Solution. On any straight line F/1, ichich cuts the curve in two points,measure F C arid FA, the distances to the curve. Then, by Gcometrv, FG =yFCx FA. This length being measured from F, will give the point G. WhenFG exceeds the length of the chain, the direction in which to measureit, so that it will just touch the curve, may be found by one or two trials. 8\. Problem. Having found the radius A 0 ^ E of a curve(fg. 31), to substitute for it tico radii A E = R^ and D F = Ao, (he,ongcr of vhich A E or B E is to be used for a certain distance only aimrh end of the >Jolution. Assume the longer radius of any length ivhich mat/ be thought 60 CIRCULAR CURVES. proper, and find (§ 9) the corresponding deflection angle D^. Supposethat each of the curves A D and B D is 100 feet long. Then drawingCO, we have, in the triangle FOE,OE:FE = : sin. the side OE = AE—AO = Ri —R, FE = DE — DF ==Z?i — /?<., the angle FOE = \S0° — A 0 C ^ 180° — i /, and theangle 0FE=A0F— 0EF=^I-2Di, since 0 E F = 2 D,(§ 7). Substituting these values, and recollecting that sin. (180° — ^7)= sin. ^ /, we have R^ — R\R^ — R. = sin. (i / — 2 Z),) : sin. ^ 1Hence sin.(i7-2Z)J ^2 is then easily found, and this will be the radius from D to D
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