A parabola is preferred for vertical curves because :
- AThe slope is constant throughout.
- BThe rate of change of grade is constant throughout.Correct
- CThe rate of change of radial acceleration is constant throughout.
- DThe rate of change of radial acceleration is zero.
Solution
Concept
Why parabolas are used for vertical curves
Formula
y = a x²; d²y/dx² = constant
Step-by-step solution
1. For a parabola y = a x², the second derivative d²y/dx² = 2a is constant. 2. So the rate of change of grade is constant along the curve.
Explanation
The constant rate of change of grade gives a smooth, comfortable variation of vertical acceleration for a vehicle moving at constant speed and is easy to set out.
Why the other options are wrong
The slope of a parabola changes continuously, so it is not constant. The rate of change of radial acceleration is constant for a transition (spiral) curve in plan, not for the vertical parabola.
Shortcut
Parabola: constant dG/dx. Spiral: constant rate of change of radial acceleration.
Common mistake
Mixing up the transition curve property.
Correct answer: B) The rate of change of grade is constant throughout.