Static wheel loads
Before the car moves, its weight \(W = mg\) is shared between the axles according to where the center of gravity (CG) sits along the wheelbase \(L\). Taking moments about each axle (a statics problem you have solved many times):
where \(a\) is the distance from the front axle to the CG and \(b\) the distance from the CG to the rear axle. The ratio \(b/L\) is the front weight distribution, usually quoted as a percentage. For a left–right symmetric car, each wheel on an axle carries half that axle's load.
Longitudinal load transfer
When the car brakes, the tires push backward on it at ground level, but the car's mass is concentrated at the CG, a height \(h\) above the ground. The braking forces therefore produce a nose-down pitching moment about the CG of \((\Sigma F_x)\,h = m a_x h\). The only thing that can balance it is a change in the vertical tire loads: the front gains load and the rear loses the same amount. Taking moments:
Under braking this load moves from the rear axle to the front axle; under acceleration it moves the other way. That is why most race cars have more braking capacity at the front, and why rear-wheel-drive cars put power down better than front-wheel-drive cars.
Lateral load transfer
In a corner the same thing happens sideways. The tires push the car toward the turn center at ground level, while the mass sits at height \(h\). The resulting roll moment \(m a_y h\) is balanced by the outside wheels gaining load and the inside wheels losing it. If each wheel's load changes by \(\Delta F_{z,f}\) at the front and \(\Delta F_{z,r}\) at the rear, and both axles have track width \(t\):
The total lateral load transfer depends only on mass, lateral acceleration, CG height and track width. Springs and anti-roll bars cannot change it. What they can change is how it is distributed between the front and rear axles.
“Stiffer springs reduce weight transfer.” Stiffer springs reduce body roll, but in steady cornering the total lateral load transfer is fixed by \(m a_y h / t\). To reduce it you must lower the CG, widen the track, or lose mass.
Front/rear distribution: roll stiffness
When the body rolls through an angle \(\phi\), the front suspension (springs plus anti-roll bar) resists with a moment \(K_{\phi f}\,\phi\) and the rear with \(K_{\phi r}\,\phi\). Each axle transmits its share of the moment as a change in wheel loads, so with a simplified model in which the car rolls about an axis at ground level:
The right-hand side is the front roll stiffness distribution. Make the front stiffer — for example with a thicker front anti-roll bar — and more of the load transfer happens at the front.
This is a deliberate simplification. Real cars also transfer load through the suspension links (roll-center effects) and through the unsprung mass. Lesson 3.2 and Module 8 refine the model; the conclusions below still hold.
Why load transfer changes grip and balance
If tires were perfectly linear in load, load transfer would not matter: what the inside tire lost, the outside tire would gain. But in Lesson 2.1 you saw that tires are load-sensitive, so a pair of unequally loaded tires produces less total force than an equally loaded pair, with a loss proportional to \(\Delta F^2\).
That gives two powerful conclusions:
- Less total load transfer means more grip. This is why race cars are low and wide.
- The axle with the larger share of load transfer loses more grip and will reach its limit first. If that is the front axle, the car understeers at the limit; if it is the rear, it oversteers.
| Set-up change | Effect on load transfer | Typical balance change at the limit |
|---|---|---|
| Stiffer front anti-roll bar / springs | More of the transfer at the front | More understeer |
| Stiffer rear anti-roll bar / springs | More of the transfer at the rear | More oversteer |
| Lower CG | Less total transfer at both ends | More grip overall |
| Wider front track only | Less transfer at the front | Less understeer |
This is one of the main tools a race engineer uses to adjust a car's handling at the track — and it rests entirely on tire load sensitivity.
- With the Club racer preset at 1.0 g, check the readout for total lateral load transfer against \(m a_y h / t\).
- Move the front roll stiffness slider from 40% to 70%. Watch the balance plot: which curve moves, and when does the limiting axle switch?
- Find the front roll stiffness that gives the highest maximum lateral acceleration. How does it compare with the front weight percentage?
- Set the load sensitivity \(s\) to zero. Does roll stiffness distribution still affect the balance? Explain why using Lesson 2.1.
- Push the lateral acceleration past the limit and watch the tire insets. Which axle's dot sits on the peak? Change the front roll stiffness until the other axle saturates first.
- Raise the CG by 0.1 m. How much maximum lateral acceleration do you lose?
- Set \(a_y = 0\) and brake at 1.0 g. Which wheels gain load, and by how much?
The club racer (750 kg, \(h = 0.40\) m, \(t = 1.50\) m, 52% front weight, 58% front roll stiffness) corners at 1.2 g. Find the four wheel loads.
Static: \(W = 750 \times 9.81 = 7358\) N. Front wheels \(7358 \times 0.52 / 2 = 1913\) N; rear wheels \(7358 \times 0.48/2 = 1766\) N.
Total lateral transfer: \(\dfrac{m a_y h}{t} = \dfrac{750 \times 9.81 \times 1.2 \times 0.40}{1.50} = 2354\) N.
Front share: \(0.58 \times 2354 = 1366\) N; rear share: \(0.42 \times 2354 = 989\) N.
Front outside \(= 1913 + 1366 = 3279\) N, front inside \(= 1913 - 1366 = 547\) N.
Rear outside \(= 1766 + 989 = 2755\) N, rear inside \(= 1766 - 989 = 777\) N.
The front axle's loads are much more unequal than the rear's, so with load-sensitive tires the front will run out of grip first: this set-up understeers at the limit.
Check your understanding
A 750 kg car with a CG height of 0.35 m and a wheelbase of 2.5 m brakes at 1.2 g. How much load transfers from the rear axle to the front axle?
\(\Delta F_z = m a_x h / L\) — remember to convert g to m/s².
\(\Delta F_z = 750 \times (1.2 \times 9.81) \times 0.35 / 2.5 = 1236\) N.
A Formula SAE car (300 kg with driver, CG height 0.30 m, track 1.20 m) corners at 1.5 g. What is the total lateral load transfer (front plus rear, per-wheel)?
\(\Delta F_{z,f} + \Delta F_{z,r} = m a_y h / t\).
\(300 \times (1.5 \times 9.81) \times 0.30 / 1.20 = 1104\) N.
The same car has 48% front weight and 55% front roll stiffness distribution. What is the load on the inside front wheel at 1.5 g?
Find the static front wheel load, then subtract the front axle's share of the lateral load transfer from the previous question.
Static front wheel: \(300 \times 9.81 \times 0.48 / 2 = 706.3\) N.
Front transfer: \(0.55 \times 1103.6 = 607.0\) N.
Inside front: \(706.3 - 607.0 = 99.3\) N — the wheel is close to lifting off the ground.
An engineer fits a stiffer front anti-roll bar. In steady-state cornering at the same lateral acceleration, what happens to the total lateral load transfer?
- It decreases, because the car rolls less.Less roll, yes — but total transfer is \(m a_y h / t\), which does not involve roll stiffness.
- It stays the same, but a larger share happens at the front axle.Roll stiffness distribution changes where the transfer happens, not how much there is.
- It increases, because a stiffer bar transmits more force.The bar redistributes the roll moment between axles; the total moment \(m a_y h\) is unchanged.
A driver reports that the car understeers in long, steady corners. Using only roll stiffness, which change is most likely to help?
- Stiffen the front anti-roll bar.That moves more load transfer to the front, reducing front grip further — more understeer.
- Soften the front anti-roll bar or stiffen the rear.Shifting load transfer toward the rear gives the front tires more equal loads and more grip relative to the rear.
- Stiffen both bars by the same amount.If the distribution stays the same, the balance hardly changes.
Why does lowering the center of gravity increase a car's maximum lateral acceleration?
- It increases the normal force on the tires.The total normal force is still \(mg\); CG height does not change it.
- It reduces load transfer, so the tires are more evenly loaded and lose less grip to load sensitivity.Less \(\Delta F\) means a smaller \(\Delta F^2\) loss at each axle.
- It reduces the car's mass.Moving mass lower does not remove any of it.
Going further with Milliken
Read: RCVD Chapter 18, Wheel Loads. For how roll stiffness is built up from springs and anti-roll bars, look ahead to Chapter 16, Ride and Roll Rates.
As you read, look for answers to these questions:
- How does the full treatment split lateral load transfer into components, and which of them can an engineer adjust?
- What assumptions in this lesson's simplified model does the chapter remove?
- How do aerodynamic loads change the static and dynamic wheel loads at speed?
Summary
| Idea | Key relation |
|---|---|
| Static axle loads | \(W_f = W b/L,\quad W_r = W a/L\) |
| Longitudinal transfer | \(\Delta F_z = m a_x h / L\) |
| Total lateral transfer | \(\Delta F_{z,f} + \Delta F_{z,r} = m a_y h / t\) |
| Front share (simplified) | \(K_{\phi f} / (K_{\phi f} + K_{\phi r})\) |
| Balance rule of thumb | The axle with more load transfer saturates first |