Momentum grade explained

Momentum grade is a gradient steeper than the ruling gradient that can be used when it is preceded by a long downgrade or a level section, because the vehicle gains speed (kinetic energy) on the approach and uses that momentum to climb the steeper slope without losing much speed.

Conditions of use

• The approach must be a downgrade or level section long enough for vehicles to gain speed.
• The steep grade must be short (not long enough to stop heavy vehicles), and the vehicles must not be required to stop before it (no junction, no sharp curve).
• Used in rolling and hilly terrain to reduce the cost of earthwork.
• The sight distance should be adequate and the grade should not be used on a long upgrade.

Length of momentum grade

For a vehicle entering at speed $v_1$ and leaving at $v_2$ on a grade $G$ (as ratio):

$$L = \frac{\gamma\,(v_1^2 - v_2^2)}{2g\,(G + f)}$$

where $f$ is the rolling/friction resistance coefficient and $\gamma$ the coefficient of inertia of the vehicle's rotating parts.

 \                 ____ steep grade (momentum)
  \  gain speed   /
   \_____________/