Understeer gradient and the skidpad

One number describes a car's steady-state balance: how much extra steering it needs as lateral acceleration rises. And a car can be perfectly neutral at 0.3 g while oversteering at the limit — which is the setup in this app.

Everything in this module has been about mechanisms. This chapter is about the single number that summarizes the result — the one a vehicle dynamicist quotes when asked what a car does.

Defining it

Drive a constant-radius circle and slowly increase speed. As lateral acceleration builds, the tires need more slip angle, so you need more steering lock to hold the same radius. How much more, per g, is the understeer gradient.

Start from the geometry. To follow a circle of radius $R$ with wheelbase $L$, the pure-rolling steer angle — the Ackermann angle from chapter 11 — is:

Real tires need slip angle on top of that, and the extra is proportional to lateral acceleration:

$K$ is the understeer gradient, in degrees per g. That’s the whole definition: the slope of steering angle against lateral acceleration on a constant-radius circle.

• K > 0 — understeer. More lock as you go faster. The front is working harder.
• K = 0 — neutral. Same lock at any speed.
• K < 0 — oversteer. Less lock as you go faster, and past a critical speed the car is unstable.

Why oversteer is a stability problem, not a taste

Positive K is self-correcting. Go faster, need more lock than you’re giving it, and the car runs wide — which slows it and reduces the demand. It converges.

Negative K does the opposite. Go faster, need less lock than you’re giving, so the car turns in more, which raises lateral acceleration, which needs even less lock. It diverges. Above a critical speed the car will not hold a line without continuous correction.

That asymmetry is why essentially every production car leaves the factory with K > 0, and why chapter 19’s rule — front roll stiffness share above weight share — is the default choice rather than a tuning preference. It’s a safety decision.

The setup in this app is a good bad example

The layout in the app measures:

Negative gradient, rear-limited. This car oversteers, and chapter 19 already told us why: its roll stiffness split is 61% front against a 64% front weight distribution, so the rear is carrying more transfer than its share and gives up first.

But look at what it does below the limit:

Neutral everywhere you’d normally drive, and oversteering at the limit.

That combination is genuinely dangerous, and it’s the most useful thing in this chapter. A driver learns the car at 0.3–0.6 g, where it feels balanced and trustworthy, and gets no warning at all that the last 10% behaves differently. The transition arrives with no build-up.

This is why a single gradient number, quoted from linear-range testing, is not enough — and why the app reports linear balance and limit balance separately. A car that changes character between them is worse than one that’s mildly wrong throughout.

Notice also the roll rate: 0.88° at 0.3 g, 2.63° at 0.9 g — about 2.9 deg/g, near enough linear. Roll angle behaves itself while balance does not, which is a good reminder that the thing you can see from the driver’s seat isn’t the thing that bites.

Measuring it for real

The standard test is a skidpad: a constant-radius circle, usually 30 m or 200 ft, driven at increasing steady speeds while recording steering angle and lateral acceleration. The slope of that line is K.

For this car at 1.01 g on a 30 m circle, the limit speed works out at 62 km/h — which is the number a skidpad session would produce, and a useful sanity check on any simulation.

The test is simple enough to do in a car park with a phone-based accelerometer and some cones, and it’s the most informative hour you can spend with a car you’re developing.

Go look at it

Open the strut layout and go to the Handling tab.

1. Find Understeer grad — about −0.37 deg/g — and Limit speed, with the balance read-out beside it.
2. Step the Corner severity up from low to the limit, watching Balance at each step. Note where it stops saying neutral. That gap between linear and limit behavior is this chapter.
3. Now fix it with chapter 19’s tool. Increase the front sway bar until Understeer grad goes positive. The car now runs wide at the limit instead of rotating.
4. Check what it cost: look at Max grip before and after. Safety usually costs a little peak grip, and knowing the size of that trade is the point of measuring.
5. Try to make the car neutral in the linear range and at the limit. Harder than it sounds — and it’s the actual job of a chassis engineer.
6. Then raise the CG height and watch both the gradient and max grip degrade together, tying this back to chapter 18.

What it costs you

Understeer is the safe default and it is not free. A car tuned to understeer at the limit is slower, because the front tires reach their peak while the rears still have grip in hand — you’re leaving rear capability unused. Every road car does this deliberately, trading lap time for predictability, and it’s the single biggest difference between how a road car and a race car are set up.

There’s also a real limitation in the number itself. K describes steady-state, constant-radius behavior. Most of what a car actually does is transient: turn-in, mid-corner corrections, lift-off, braking into a corner. A car can have an excellent steady-state gradient and horrible transient behavior, and the skidpad will not tell you. Rear-engined cars are the classic case — respectable steady-state numbers, and a transient response that made them famous.

So treat K as a necessary summary, not a sufficient one. It tells you what the car does when everything has settled. It says nothing about the half-second in which most accidents happen.

Rules of thumb

• Road car: K between +1 and +4 deg/g. Family cars sit at the higher end.
• Sports car: +0.5 to +2 deg/g — closer to neutral, still stable.
• Race car: near zero to slightly positive, tuned per circuit, and driven by someone who can catch the difference.
• Never ship negative K on anything a normal driver will use.
• Check linear and limit balance separately. Agreement between them matters more than either value.
• Rally-raid and desert: steady-state gradient is close to irrelevant. These cars spend their lives in transient states on surfaces whose grip changes meter to meter, and drivers use throttle and weight transfer to rotate the car deliberately. Mild limit oversteer that would be unacceptable on a road car is often exactly what’s wanted — the driver is steering with the rear axle on purpose. The safety argument for positive K assumes a driver who will not correct; that assumption does not hold here.

Try this

1. Get this car to K ≈ +2 deg/g. What did you change, and what happened to max grip?
2. Find a setup that is neutral in the linear range and mildly understeering at the limit. Which adjustment did the work?
3. Compute the critical speed for the car as it ships — the speed at which negative K makes it directionally unstable. Is it a speed anyone would reach?

That’s Module 3 complete. You know that total load transfer is fixed by mass, CG height and track; that springs and bars only move the split; that the split decides which axle gives up first; that the mechanism is a tire whose μ falls with load; and that one gradient number summarizes the result — provided you check the linear and limit answers separately.

Module 4 is braking: the multiplication chain from your foot to the pad, and why the front usually locks first.

Preset values are illustrative starting points, not a measured setup for any particular car.