P. Si to the foot of the spiral offset. Consequently, the spiral offset and the spiral very nearly bisect each other; the point M at which the spiral cuts the offset is almost exactly half way between the P. C. and the original tangent. Tangent Distance.-The tangent distance of a transition spiral is the distance of the P. Si from the point of intersection of the tangents at the points of spirals. When the lengths of the two spirals are equal (Fig. 3), TC= length of spiral-t cor. + (R+F) tan }I in which R is the radius of the circular curve and F the spiral offset EV. When the lengths of the spirals are unequal (Fig. 4), the tangent distance of the shorter spiral is TC= length of spiral-t cor.+(R+F) tan }I+ F'-F sin I and the tangent distance of the longer spiral is TC' = length of spiral-t cor.+(R+F) tan } I− (F' — F) cot I F' and F denote, respectively, the spiral offsets of the longer and shorter spirals. TABLES FOR TRANSITION SPIRALS The following tables contain the data required for the laying out of eleven different spirals. The unit degree of spiral is marked at the top of each table. The column headed contains the length, in feet, between the P. Si and the points on the spiral, and the one headed d gives the degrees of curve of spiral at these points. The third column gives the corresponding deviation angles; the fourth the deflection angle; and the remaining columns give the values of the spiral offset F, the coordinate y, and the corrections x and t, all in feet. As an illustration of the use of these tables, let the preceding example be solved by means of them. Since a = 0, reference is made to the table for a=0° 30′, where it is found that for 1=400 ft., the corresponding value of F=2.33, and that of t cor.=.03. Then, as before, EV=2.33 ft. and CV 199.97 ft. = LAYING OUT A SPIRAL IN THE FIELD Let RT and R'T, in the accompanying illustration, be the two tangents that are to be connected with the circular curve AB by the two spirals CA and C'B. It will be assumed that the two spirals are of equal length. Compute the unit degree of curve of spiral, the spiral offset VE=V'E', and the distance CV = C'V', or obtain these quantities with the help of the tabies and compute the distance |