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Vertical Curves
Grading
The Shape Of A Vertical
Curve
Properties Of A Parabola
Highest (Or Lowest Point)
On A Crest Curve
Lengths Of Vertical
Curves
Centrifugal Effects
Sight Distance
Setting Out Vertical
Curves
Example
Sight Distance
In the design of a convex curve (summit) it is required to calculate the minimum length of curve which will give the required sight distance.
Three cases should be considered:
1. The curve is greater than the sight distance (L > S)
| The height of 0 above A = | L | x | p |
| 2 | 100 |
| The height of 0 above B = | L | x | q |
| 2 | 100 |
The height of 0 above N (the mid point) is therefore:
| NO = | 1 | ( | Lp | + | Lq | ) |
| 2 | 200 | 200 |
| = | L | (p + q) |
| 400 |
Let the height of the driver's eye above the road be h and the required sight distance be S, from the property of a parabola
| MC | = | DE2 |
| MN | AB2 |
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2. The curve is less than the required sight distance (L < S)
| MO = MN = | (p + q) | L |
| 800 |
| By similar triangles = | NO | = | AB |
| CO | DE |
|
|
3. The curve is equal to the required sight distance (L = S)
Substituting L = S into the formula for L at (a) above
| L = | L2(p + q) |
| 800h |
| L = | 800h |
| (p + q) |
Note. Height of eye of driver - 1.15m; height of oncoming vehicle - 1.15m.
(National Association of Australian State Road Authorities).