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Inhaltsangabe
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. 1920 Excerpt: ...2/ra I = 2ra But/a-BI).-. Z = 2BI) (14) That is the transition curve is twice the length of the circular arc BI), C being the middle point of the curve (this is a very close approx.). Therefore for point C putting I /s p A =-2 in equation (13), gives y =--= j. = SC (15) BD2 I1 I3 P ButDF = B2r =,andatB,y = = Gr...BD-HE-DF-£--£-(16) Here BI) is taken equal to the arc instead of the chord. 1 The complete equation giving y in terms of K may bo derivod from (7) by subatituting--t for 0, and is SD, which is called the "shift," is designated by the letter S, and is the minimum distance between the circular curve and the tangent or straight. Note.--In using formula I = as suggested on p. 124, S becomes constant and equal to chains or 2' 9". I2 But SC was shown to be equal to jg-. Therefore SD is bisected by the spiral at C, and C is also the central point of the spiral. Again BE = =4.-= 4S (17) Now take any point P on the transition curve and join it to A by chord PA (Fig. 42), and let the angle PAE be 0. tan 6 = y x but the equation of the curve is of the form--y = nx3.-. = Snx2-tan f.: tan f = 3»x2 = 3y = 3 tan 0.: for small values of f, 0 = lf.: angle APG or 0 = §£ = 20. The error due to making this assumption is imperceptible in all ordinary cases. For a 9-chain curve the spiral angle 8, for the last point on the transition, will have an error of 9 seconds, the error being less for other points on the curve. In the case of a 5-chain curve, which is one of extremely sharp curvature, the error at the end point of a transition curve 2.J chains long is 22 seconds. The true value of 6 derived from the previous equations is given by--tan0 = + f-+ JL +--£-+... 3 105 5997 198700 T Again, by (13) substituting 1 for A at any ...
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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. 1920 Excerpt: ...2/ra I = 2ra But/a-BI).-. Z = 2BI) (14) That is the transition curve is twice the length of the circular arc BI), C being the middle point of the curve (this is a very close approx.). Therefore for point C putting I /s p A =-2 in equation (13), gives y =--= j. = SC (15) BD2 I1 I3 P ButDF = B2r =,andatB,y = = Gr...BD-HE-DF-£--£-(16) Here BI) is taken equal to the arc instead of the chord. 1 The complete equation giving y in terms of K may bo derivod from (7) by subatituting--t for 0, and is SD, which is called the "shift," is designated by the letter S, and is the minimum distance between the circular curve and the tangent or straight. Note.--In using formula I = as suggested on p. 124, S becomes constant and equal to chains or 2' 9". I2 But SC was shown to be equal to jg-. Therefore SD is bisected by the spiral at C, and C is also the central point of the spiral. Again BE = =4.-= 4S (17) Now take any point P on the transition curve and join it to A by chord PA (Fig. 42), and let the angle PAE be 0. tan 6 = y x but the equation of the curve is of the form--y = nx3.-. = Snx2-tan f.: tan f = 3»x2 = 3y = 3 tan 0.: for small values of f, 0 = lf.: angle APG or 0 = §£ = 20. The error due to making this assumption is imperceptible in all ordinary cases. For a 9-chain curve the spiral angle 8, for the last point on the transition, will have an error of 9 seconds, the error being less for other points on the curve. In the case of a 5-chain curve, which is one of extremely sharp curvature, the error at the end point of a transition curve 2.J chains long is 22 seconds. The true value of 6 derived from the previous equations is given by--tan0 = + f-+ JL +--£-+... 3 105 5997 198700 T Again, by (13) substituting 1 for A at any ...
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