. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . ping lines joined by a curve. When a curve is on a:grade, the center line is realh^ a spiral, a curve of double curva-ture, although its horizontal projection is a circle. The centerline therefore consists of straight lines and curves of singleand double curvature. The simplest method of treating themis to consider their horizontal and vertical projections treating simple, compound, and transition curves, only thehorizontal projections of those curves will be cons
. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . ping lines joined by a curve. When a curve is on a:grade, the center line is realh^ a spiral, a curve of double curva-ture, although its horizontal projection is a circle. The centerline therefore consists of straight lines and curves of singleand double curvature. The simplest method of treating themis to consider their horizontal and vertical projections treating simple, compound, and transition curves, only thehorizontal projections of those curves will be considered. SIMPLE CURVES. 46. Designation of curves. A curve may be designated eitherby its radius or by the angle subtended by a chord of unitlength. Such an angle is knownas the degree of curve and isindicated by D. Since the curvesthat are practically used have verylong radii, it is generally impracti-cable to make any use of the actualcenter, and the curve is locatedwithout reference to it. If AB inFig. 11 represents a unit chord (C)of a curve of radius Rj then by theabove definition the angle AOBequals D. Then. AO sin iD = iAB = iC. R = Wsin JD (1) 55 56 RAILROAD CONSTRUCTION. §47. or, by inversion, i^-M (2) The unit chord is variously taken throughout the world as100 feet, 66 feet, and 20 meters. In the United States 100feet is invariably used as the unit chord length, and throughoutthis work it will be so considered. Table I has been computedon this basis. It gives the radius, with its logarithm, of allcurves from a 0° 01 curve up to a 10° curve, varying by singleminutes. The sharper curves, which are seldom used, are givenwith larger intervals. An approximate value of R may be readily found from thefollowing simple rule, which should be memorized: r> 5730 Although such values are not mathematically correct, since Rdoes not strictly vary inversely as D, yet the resulting value iswithin a tenth of one per cent for all commonly used valuesof R, and is sufficiently close
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