Explanation Given: The grade of tangent at higher elevation is, + 2.5 % . The grade of tangent at lower elevation is − 3.5 % . The separation between two tangents is, 1150 ft . The design speed is 50 mi / h . Formula used: The formula to calculate the absolute value of difference in grades of crest vertical curve is given by, A c = | G con − G 2c | ...... (I) Here, G 2c is the final grade of sag vertical curve in percentage, G con is the constant grade connection in percentage, and A c is the absolute value of difference in grades of crest vertical curve. The formula to calculate the absolute value of difference in grades of sag vertical curve is given by, A s = | G con − G 1s | ...... (II) Here, G 1s is the initial grade of crest vertical curve in percentage, G con is the constant grade connection in percentage, and A s is the absolute value of difference in grades of sag vertical curve. The formula to determine the length of sag vertical curve is given by, L s = K s A s ...... (III) Here, L s is the length of sag vertical curve, K s is the horizontal distance required to effect 1 % change in slope of the sag curve. The formula to determine the length of crest vertical curve is given by, L c = K c A c ...... (IV) Here, L c is the length of crest vertical curve, K c is the horizontal distance required to effect 1 % change in slope of the crest curve. The formula to calculate the total length of curve is given by, L total = K s A s + K c A c ...... (V) Here, L total is the total length of the curve. The formula for total elevation over the alignment is given by, Elevation Diff = [ A s L s 200 + ( G 1s × L s 100 ) ] + [ A c L c 200 + ( G 2c × L c 100 ) ] ...... (VI) Here, Elevation Diff is the total elevation over the alignment. Calculation: Substitute + 2.5 % for G 2c and in equation (I). A c = | G con − ( + 2.5 % ) | = | G con − 2.5 % | ...... (VII) Substitute − 3.5 % for G 1c and in equation (II). A s = | G con − ( − 3.5 % ) | = | G con + 3.5 % | ...... (VIII) The value of rate of vertical crest curvature and sag curvature from "table 3.2" and table "table 3.3" book "Principles of highway engineering and traffic analysis" for the design speed of 65 mi / h is k c = 84 , and k s = 96

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ISBN: 9781119688372

Author: Mannering

Publisher: WILEY

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Chapter 3, Problem 38P

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The common grade between sag and crest curves and the elevation difference between PVCs, and PVTc.

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Chapter 3, Problem 37P

Chapter 3, Problem 39P

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The common grade between sag and crest curves and the elevation difference between P V C s , and P V T c .

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The common grade between sag and crest curves and the elevation difference between PVCs, and PVTc.

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