Curve resistance and grade compensation

Curve resistance

Curve resistance is the additional tractive resistance a vehicle has to overcome when it moves along a horizontal curve. When the front wheels are turned through an angle $\alpha$, only the component $T\cos\alpha$ of the tractive force $T$ acts along the direction of motion, so the loss is $T(1-\cos\alpha)$. The sideways slip of the tyres, the lateral friction needed to resist the centrifugal force and the off-tracking of the rear wheels add to it. It increases as the radius becomes smaller, so a gradient and a sharp curve at the same place can overload the vehicle.

Grade compensation

Grade compensation (grade reduction) is the reduction of the design gradient on a horizontal curve, so that the total resistance (grade + curve) on the curve is not more than the resistance on the straight section.

IRC formula (R in metres):

$$\text{Grade compensation} = \frac{30 + R}{R}\ \%\ \ \text{(max } \frac{75}{R}\%)$$

• It is not needed when the gradient is flatter than 4%, and in practice it matters mainly for sharp curves (small $R$).
• Example: $R = 60$ m: $(30+60)/60 = 1.5\%$, maximum $75/60 = 1.25\%$, so adopt 1.25%. If the ruling gradient is 6%, use $6 - 1.25 = 4.75\%$ on the curve.
• Used chiefly on hill roads.