. Railroad construction. Theory and practice . als. An approximate value of R may be rea^dily found from thefollowing simple rule, w^hich should be memorized: R^ 5730 D Although such values are not mathematically correct, since Rdoes not strictly A^ary inversely as D, yet the resulting value iswithin a tenth of one per cent for all commonly used valuesof R, and is sufficiently close for many purposes, as will beshown later. 19. Length of a subchord. Since it is impracticable toi^easure along a curved arc, curves are always measured by laying off lOO-foot chord means that the actua
. Railroad construction. Theory and practice . als. An approximate value of R may be rea^dily found from thefollowing simple rule, w^hich should be memorized: R^ 5730 D Although such values are not mathematically correct, since Rdoes not strictly A^ary inversely as D, yet the resulting value iswithin a tenth of one per cent for all commonly used valuesof R, and is sufficiently close for many purposes, as will beshown later. 19. Length of a subchord. Since it is impracticable toi^easure along a curved arc, curves are always measured by laying off lOO-foot chord means that the actual arc isalways a little longer than thechord. It also means that a sub-chord (a chord shorter than the unitlength) will be a little loiiger thant)ie ratio of the angles subtendedwould call for. The truth of thismay be seen without calculationby noting that two equal sub-chords, each subtending the angleFig. $. ^-D, w^ill evidenth be slightly longer than 50 feet each. If c be the length of a subchord subtend-ing the angle dj then, as in Eq. 2,. sin ^d = 2R § 20. ALIGNMENT. 2i or, by inversion, c=272 sin i^ . (3) The nominal length of a subchord=100^ For example, ca nominal subchord of 40 feet will subtend an angle of y^^^ ofD°; its true length will be slightly more than 40 feet, and maybe computed by Eq. 3. The difference between the nominaland true lengths is maximum when the subchord is about 57feet long, but with the low degrees of curvature ordinarily usedthe difference may be neglected. With a 10° curve and anominal chord length of 60 feet, the true length is ^ery sharp curves should be laid off with 50-foot or even 25-foot chords (nominal length). In such cases especially the truelengths of these sub chords should be computed and used insteadof the nominal lengths. 20. Length of a curve. The length of a curve is alwaysindicated by the quotient of lOOJ-^D. If the quotient ofJ^D is a whole number, the length as thus indicated is thetrue length—measured in 1
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