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. Despite it's relevance to the discussion of torque steer, the calculation shown here is only an example and should not be copied for use in the design event. There are many points not covered here, and the assumptions are not justified.

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 experienced 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

This step is the meat of the calculation. We can find how far each shaft has twisted using our previous results according to the equation below:

φ = T / k

Left Shaft Twist (φ_L): 3.704 degrees

Right Shaft Twist (φ_R): 4.692 degrees

It is important to note that shaft twist indicates how far each wheel has not rotated compared to the engine.

Step 5: Find Vehicle Yaw

If both shafts were perfectly stiff, one rotation of the driven sprocket would equal one rotation of the wheels, driving the car forward the distance equal to 2 * π * the tire's dynamic radius. Because the shafts twist, the wheels/tires will move less than one full rotation. Because the shafts have different stiffnesses, they will travel different distances under the same load. We will find the distance not rotated to compute vehicle yaw, as we are looking for magnitude, not direction.

Tire travel (T) = φ_shaft/360 * Tire Circumference

Yaw = sin^-1(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

Result

According to our calculations, the vehicle will yaw less than one quarter of one degree, which if even perceptible by the driver will be unlikely to force corrective action. please see further below for discussion of assumptions used and real world relevance.

Assumptions

The following assumptions were used in the example calculation:

• The rear wheels are the driven wheels
• The engine can output a constant torque
• The tire will not break traction with the ground
• The loading of the shaft is quasi-static
• The rear suspension (particularly toe) is infinitely stiff
• The tire contact patch is considered to be a point
• The tire's rolling radius does not change under loading
• Tire circumference is equivalent to 2 * dynamic radius * π
• Shaft hardening does not impact stiffness