Field engineering; a handbook of the theory and practice of railway surveying, location and construction

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1901 Excerpt: ...be the value of the angle i. When R, = Ri, cot t = 0 and i--90 and the tangent point J will be on a perpendicular to BA drawn through the middle point K; and a = /. On the contrary, as (R3--Ri1 increases, i becomes less, and the foot, H, of the perpendicular HI moves toward B, the tangent point of the curve of smaller radius Bi. The distance HK = p cot i. The connecting curve is farthest from the tangent BA at /. To find the ordinate from BA to the curve' at any other point, subtract from p the tangent offset for the length of curve from I to the ordinate in question. §115, eq. (39) may be used on flat curves with tolerable accuracy, even when the distance equals several hundred feet. IV. It is evident that in this problem R, must be greater than either R, or R3. As the centre 0, is taken nearer the line Oi03i i?a grows less, and is a minimum when 0a falls on the line 0,03. In this case we have Aa = 180, and B, = i(Ba + R, +Oi03); a minimum. (183) This limit must be regarded in assuming the value of Ra. Since 0,0,-0,03-(i?,-R,1-(R2-iis) = (R,-i?,) a constant value, independent of Ri, we infer that the centre 0a is always on a hyperbola of which Oi and Oa are the foci; (B3--i?i) equals the diameter on the axis joining the foci; and I equals the diameter at right angles to it, for in the triangle 0,00,, ia = 'OTO?-(R,-R,1 (184) 178. Given1 a three-centred compound curve to replace the middle arc by an arc of different radius. I. When the radius of the middle arc is the greatest. Fig. 57. First find the length and direction of the common tangent AB. Let A a = central angle of the middle arc, Bt = its radius, and Bi and B3 the radii of the other arcs. From eq. (179). I = V2(fia-fi,) (i?a-R.,1 vers Aa (185) Then find i by eq. (170), a and f t by eqs. (181) ...