The Field Practice of Laying Out Circular Curves for Rail-roads |
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Page 16 - ... sto, of the curve tio; making at the same time the chord to, equal to 100 feet. NB — If running the curve by eye, use the tangential distances, instead of the angles. ARTICLE XV. — RADII. To find the radius corresponding to any given angle of deflexion, and to equal chords of any given length. Rule 1. Subtract the angle of deflexion from 180°, then say as nat. sine of angle of deflexion, is to nat. sine of half the remainder, so is the given chord to the radius required. Example. — Let...
Page 18 - To find the deflexion distance with chord of 100 feet and any radius. — Divide the constant number 10000 by the radius in feet ; the quotient will be the deflexion distance : — for the deflexion distance with a radius of 10000 feet is 1 foot, and the deflexion distances for other radii increase inversely as the radii. Example. — What is the deflexion distance for a 5° curve, the chord being 100 feet ? Here ^^ = 8-72 feet, the deflexion distance. To find the deflexion...
Page 20 - ... the remainder will be ec; then from the square of the radius ci, subtract the square of the distance oi, which the required ordinate i n, is from the middle ordinate de, and extract the square root of the remainder. This square root will be o c. From this square root oc, subtract ec; the remainder will be oe, which is equal to in, the required ordinate. Example. — The middle ordinate de, of a 100 feet chord ba, to a radius of 819 being 1-528 feet, it is required to find the length of the ordinate...
Page 2 - M, sight back to u, and lay off first the exterior angle pvw, double the tangential angle, and afterwards continue the tangential angles wvx, xvy, &c., as before, to the end of the curve. Finally, in order to pass from the end of the curve at y, on to a tangent yz, place the instrument at y, and sighting...
Page 7 - ARTICLE V. Ordinates for Entire Chords. It would be both tedious, and liable to inaccuracy, to attempt to fix all the necessary points in railroad curves by the foregoing means, which are employed only for entire chords, or for such sub-chords as may be required at the ends of curves. The best method is to stretch a piece of twine ab, fig. 6, 100 feet long, between two adjacent chord-stakes...
Page 1 - B s, st, tu,uv, &c., equal to each other, then the points B, s, t, u, v, &c., will be situated in the circumference of a circle, which is tangential to the line AD at the point B. The first of these angles DB...
Page 9 - Having given the radius ac,fig. 7, of a curve, and the angle abd, it is required to find the number of chords of 100 feet that will constitute the curve. Rule. — Subtract the angle abd from 180°, and divide the remainder by the angle of curvature, or deflexion of the curve. The quotient will be the required number of chords.
Page 12 - Butif greater, we must either re-measure the angle a ef correctly, and go over the whole work again, or resort to some other mode of obviating the difficulty. The angle ae/may be difficult of access; or the curve may be so long that to retrace it would be a work of much labor. We may then adopt the method of compound curves, by which much trouble will be avoided, and a considerable portion of the first part of the curve be allowed to remain as it is. Thus, whether the curve abc fall beyond the true...
Page 10 - ... ends tangentially to a line parallel to said tangent, either within it as at c; or beyond it as at b. Being first certain that no error has occurred in tracing out the curve, ascertain with the compass the bearing of the line ad, and removing the compass to the end of the curve at c or b, (as the case may be,) run the line bo or co, in the same course as...
Page 10 - ... ad, and, removing the compass to the end of the curve at c or b, (as the case may be,) run the line bo or co, in the same course as ad, until it strikes the tangent dom; which may be ascertained by ranging two stakes placed on the tangent. Then measure bo or co, (as the case may be,) and if the curve fall within the tangent om, as at c, measure forwards from t towards d the distance ta, equal to co; or if the curve fall beyond the tangent, as at b, measure backwards from * the distance sa, equal...