A Simple Way to Measure Understeer Gradient Direct measurement without the use of a skid pad

Albert Loh - 21 August, 2015

IntroductionMeasurement of understeer gradient usually involves the use of a skid pad. The

method outlined here is simple, repeatable and easy to do. All it requires is a straight road with a constant side slope or camber.

MethodWhen a vehicle moves along a straight path with a cross-slope,

there is a side thrust due to the component of the vehicle weight acting down the slope. Slip angles will be

generated front and rear to counter the side thrust due to the slope.

At a steady state, there will be a constant steering angle required to maintain a straight course. This steering angle divided by the cross slope is the understeer gradient.

Theory

Definition of Understeer Gradient

Steering angle = Ackerman steering angle + USG * Ay

Since the vehicle is travelling straight, Ackerman steering angle is = 0.Lateral Acceleration Ay = FYV / W (in g’s) = cross slope (for small angles)

Therefore, Understeer Gradient USG = Steering angle / cross slope.

A SIMPLE WAY TO MEASURE UNDERSTEER GRADIENT - ALBERT LOH �1

FYV

W

A SIMPLE WAY TO MEASURE UNDERSTEER GRADIENT - ALBERT LOH �2

Direction  of  travelß

ß

∂  =  αF  -­‐  αRFYV

αFαR

Fig 1 - Understeer Gradient Measurement - ∂ > 0 — Steer into Slope (Understeer)

Sideslip  angle  ß  =  rear  slip  angle  αR  Steering  angle  ∂  =  αF  -­‐  αR    >  0  

Understeer  Gradient  USG  =  ∂  /(FYV/W)

αRαF

αR

Direction  of  travelß

ß

∂  =  αF  -­‐  αR

FYV

αR

Fig 2 - Understeer Gradient Measurement - ∂ < 0 — Steer Away from Slope (Oversteer)

αF

Sideslip  angle  ß  =  rear  slip  angle  αR  Steering  angle  ∂  =  αF  -­‐  αR    <  0  

Understeer  Gradient  USG  =  ∂  /(FYV/W)

αR αF

αR

∂  

∂