Torque Steer

Torque Steer is a yawing effect caused by unequal stiffness driveshafts, most frequently due to unequal length. A stiffer shaft will turn the wheel further than a softer shaft for the same input torque.

Example Calculation

Using ballpark values, we can calculate an approximate torque steer value for a generalized FSAE car.

Step 1: Polar Moment of Inertia

The moment of inertia (J) for a hollow shaft is calculated as follows:

π/32 * (D⁴-d⁴)

Using values from an RCV axle below, we can find J.

Shaft OD (D)	0.8"
Shaft ID (d)	0.5"

Shaft Area of Inertia: 0.034076in²

Step 2: Calculate Torsional Stiffness

We will use 4130 chromoly steel as our half-shaft material, most steels have a very similar shear modulus (G) so this choice is not a driving factor in the result. The torsional stiffness (k) of the shaft will be found using the following formula and values:

k = G*J / L

Shaft Material	4130 Steel
4130 Shear Modulus	1.16e+7 psi
Left Shaft Length (LL)	15 in
Right Shaft Length (LR)	19 in

Left Torsional Stiffness (k_L): 38.3379023 lb-ft / degree

Right Torsional Stiffness (k_R): 30.26401 lb-ft / degree

Step 3: Find Torque

Our last input value that we need to find is the torque experience by the driveshafts. This is the torque output by the motor and transmitted through the final drive ratio. The maximum torque applied to the driveshafts by the engine will be during launch, when the wheels are still and we can assume a perfect launch by the driver, applying the maximal engine torque for the split second we are examining.

Max Torque from Engine: 40 lb-ft

Final Drive Ratio: 3.55

Torque Seen by Driveshaft: 142 lb-ft

Step 4: Find Shaft Twist

phi = T / k

Left Shaft Twist (phi_L): 3.704 degrees

Right Shaft Twist (phi_R): 4.692 degrees

Step 5: Find Vehicle Yaw

Tire travel (T) = Shaft twist/360 * Tire Circumference

Yaw = arcsin(T_max-T_min / Track Width)

Circumference of Tire: 56.52 in

Left Tire Travel: 0.582 in

Right Tire Travel: 0.737 in

Rear Track: 36 in

Yaw: 0.247 degrees