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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
Comfort Criteria (Centrifugal Effects)
The rate of change of gradient is
| d2y | = 2K = | (p + q) | (this is change per unit distance) |
| d2x | 100L |
To determine comfort criteria a rate of change of gradient per unit time must be calculated. Consider travel at a velocity v m/sec for time t sec.
| y | = kx2 = K(vt)2 | (m) |
| = Kv2t2 | ||
| dy | = 2Kv2t | (m/sec) |
| dt |
| d2y | = 2Kv2 = | (p + q) | v2 | (m/sec2) | |
| dt2 | 100L | ||||
| but | d2y | = a | (m/sec2) | ||
| dt2 | |||||
For comfort: a < 0.1g (1m/sec2)
| i.e. | (p + q) | v2 < 1 | or | L > | (p + q) | v2 |
| 100L | 100 |