Load transfer

When a car accelerates, brakes, or corners, load moves between the tires. The total is unchanged, but because peak friction per unit load falls as load rises (load sensitivity), the loaded tire gains less than the unloaded tire loses. Net grip falls, and the axle that lost the most grip decides the balance.

Longitudinal transfer is m · a_x · h / L: mass, acceleration, centre-of-mass height over wheelbase. Braking loads the front; the front axle therefore tolerates more brake torque, which is what brake bias is about.

Lateral transfer is m · a_y · h / t across the track, and the four-wheel model splits it between the axles in proportion to their roll stiffness (springs plus anti-roll bars, see suspension). The axle that takes the larger share loses more grip to load sensitivity, so a stiff front bar adds understeer and a stiff rear bar removes it. The single-track model has longitudinal transfer only, which is why it sits closer to the linear theory below.

Understeer gradient

The steer angle a car needs to hold a circle grows with lateral acceleration. That slope is the understeer gradient. Linear theory gives

K_us = (m / L) · (b / C_f − a / C_r)

with C_f, C_r the axle cornering stiffnesses. A nose-heavy car with equal tires understeers because stiffness per unit load falls with load. The validation page compares the four-wheel and single-track gradients against this formula, corrected for pneumatic trail; the four-wheel value is a few tenths of a degree per g higher because of the lateral transfer.