Summit Curve

Finding The Length Of Parabolic Curve Given Change In Grade Per Station

Problem
A +0.8% grade meets a -0.4% grade at km 12 + 850 with elevation 35 m. The maximum allowable change in grade per station is 0.2%. Determine the length of the curve.

A.   300 m C.   80 m
B.   240 m D.   120 m

 

Problem 04 - Symmetrical Parabolic Curve

Problem
A highway engineer must stake a symmetrical vertical curve where an entering grade of +0.80% meets an existing grade of -0.40% at station 10 + 100 which has an elevation of 140.36 m. If the maximum allowable change in grade per 20 m station is -0.20%, what is the length of the vertical curve?
A.   150 m
B.   130 m
C.   120 m
D.   140 m
 

Problem 03 - Symmetrical Parabolic Curve

Board Problem
A grade line AB having a slope of +5% intersect another grade line BC having a slope of –3% at B. The elevations of points A, B and C are 95 m, 100 m and 97 m respectively. Determine the elevation of the summit of the 100 m parabolic vertical curve to connect the grade lines.
 

01-006-elevation-of-summit-parabolic-curve.gif

 

Parabolic Curve

Vertical Parabolic Curve
Vertical curves are used to provide gradual change between two adjacent vertical grade lines. The curve used to connect the two adjacent grades is parabola. Parabola offers smooth transition because its second derivative is constant. For a downward parabola with vertex at the origin, the standard equation is
 

$x^2 = -4ay$   or   $y = -\dfrac{x^2}{4a}$.

 

004-verical-symmetrical-parabolic-curve.gif

 

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