. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . 18 then reduces to VP AF = -r^.(l +COS Ji) =VP cot iJ, sm JJ^ as might have been immediately derived from Eq. 8. In case the point P is given by the offset PK and by thedistance VK^ the triangle PKV may be readily solved, giving thedistance VP and the angle /?, and the remainder of the solutionwill be as above. 65. Determination of the curvature of existing track, (a) Usinga transit. Set up the transit at any point in the center of thetrack. Measure in eech direction 100 feet t
. Railroad construction, theory and practice; a text-book for the use of students in colleges and technical schools . 18 then reduces to VP AF = -r^.(l +COS Ji) =VP cot iJ, sm JJ^ as might have been immediately derived from Eq. 8. In case the point P is given by the offset PK and by thedistance VK^ the triangle PKV may be readily solved, giving thedistance VP and the angle /?, and the remainder of the solutionwill be as above. 65. Determination of the curvature of existing track, (a) Usinga transit. Set up the transit at any point in the center of thetrack. Measure in eech direction 100 feet to points also in thecenter of the track. Sight on one point with the plates at 0°.Plunge the telescope and sight at the other point. The anglebetween the chords equals the degree of curvature. (b) Using a tape and string. Stretch a string (say 50 feetlong) between two points on the inside of the head of the outerrail. Measure the ordinate (x) between the middle of the stringand the head of the rail. Then ^=^-|^(very nearly) (19) For, in Fig. 29, since the triangles AOE and ADC are similar, §66. ALINEMENT. 75. AO : AE :: AD : DC or R = ^AD-^x. When, as is usual,the arc is very short compared with theradius, AD = iAB, very nearly. Makingthis substitution we have Eq. 19. With achord of 50 feet and a 10° curve, the result-ing difference in x is .0025 of an inch—farwithin the possible accuracy of such amethod. The above method gives theradius of the y inner head of the outer should be diminished by ^g for the radiusof the center of the track. With easy curvature, however, thiswill not affect the result by more than one or two tenths of oneper cent. The inversion of this formula gives the required middle or-dinate for a rail on a given curve. For example, the middleordinate of a 30-foot rail, bent for a 6° curve, is a: = 900 -- (8 X 955) =.118 foot = inches. Fig. 29. Another much used rule is to require the foreman to have astring, knotted at the center, of such len
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