Question #251512

A vertical parabolic curve is designed to pass through three points on the profile of an existing unimproved road with the stationing and corresponding elevations as follows:

POINTS | STATIONING | ELEVATION

A | 5+432 | 45.00 m

B | 5+592 | 48.00 m

C | 5+682 | 43.30 m

a) Determine the stationing of the summit.

b) Determine the elevation of the summit.

c) Determine the grade of the back tangent.

POINTS | STATIONING | ELEVATION

A | 5+432 | 45.00 m

B | 5+592 | 48.00 m

C | 5+682 | 43.30 m

a) Determine the stationing of the summit.

b) Determine the elevation of the summit.

c) Determine the grade of the back tangent.

Expert's answer

“Symmetrical Parabolic Curve”

In highway practice, abrupt change in the vertical direction of moving vehicles should be avoided. In order to provide gradual change in its vertical direction, a parabolic vertical curve is adopted on account of its slope which varies at constant rate with respect to horizontal distances.

(b)

“PropertiesofVertical ParabolicCurve”

For a symmetrical parabolic curve, the number of stations to the left must be equal to the number of stations to the right, of the intersection of the slopes or forward and back tangent.

The slope of the parabola varies uniformly along the curve, Therefore the rate of change of slope is constant and equal to:

r = (g2 – g1) / L

(c)

The maximum offset H = 1/8 the product of the algebraic difference between the two rates of grade and the length of curve:

H = (1/8)(L)(g1 – g2)

9. Location of the highest or lowest point of the curve.

From the P.C. S1 = (g1L)/(g1-g2)

From the P.T. S2 = (g2L)/(g2-g1)

and S1 +S2 =L

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