Going deeper on lesson 7. The sheet draws one circle: a fixed budget of grip that braking, cornering and accelerating share. That is the right picture to drive with. This page is the three ways it is wrong, each of which shows up on the g-g diagram the data logger will draw, and each of which the lap model gets wrong in a way you can see in its own numbers.
Synthetic data. The traces on this page are not measurements. They come from a lap model (our lap model) built from our kart's real numbers - 360 lb, 72/20 gearing, 10.9 in tires, a 6100 rpm limiter, a 0.69 mi track, and the real 58.33 s best lap, which is the only thing the model was tuned to match. The layout is an approximation of Buttonwillow from the track map. When the data logger goes on the kart, the difference between these curves and the real ones becomes the lesson.
1. It is an ellipse: the limits are not the same in every direction
Lesson 7 uses 1.5 g for cornering and 1.0 g for braking (both typical). Those are not the same number, so the boundary of the budget is not a circle: it is wider than it is tall. Three reasons, in order of size for our kart:
- The brakes are on one axle. Braking at 1.0 g with all four tires would be easy for rubber that corners at 1.5 g. But the front tires do none of the braking (rear-brake-only, lesson 5), so the longitudinal limit is set by two tires carrying a third of the weight at that moment (lesson 3 Q7). Cornering uses all four.
- Accelerating is engine-limited, not grip-limited. The model's biggest forward g is 0.145 (out of the hairpins). The tire could give ten times that; the LO206 can't. So the top of the "circle" is a flat lid at 0.15 g that has nothing to do with grip. Below the lid, the rear tires never run out of traction under power. That is why wheelspin is not a thing in this class and throttle is on/off.
- Tread construction. A tire's carcass is stiffer one way than the other; kart slicks are built to be stiff laterally. The pure-rubber limit is a little higher sideways than fore-aft even with brakes on all four wheels.
So the honest shape for our kart is: 1.5 g left and right, 1.0 g at the bottom (braking), 0.15 g at the top (power). An ellipse with the lid cut off.
2. It moves: the budget is per tire, and it follows the weight
The circle in lesson 7 is for the whole kart. The real thing is four circles, one per tire, each with a radius set by that tire's load at that instant (lesson 4: grip ~ load^0.9). In a corner, weight moves outward (lesson 3), so the outside tires' circles grow and the inside tires' shrink. Under braking, weight moves forward: the rear circles shrink exactly when the rear tires are being asked to do all the braking. The kart's total budget is the sum, and because of the 0.9 exponent the sum is always less than it would be with the weight spread evenly.
Which is the physics of the driver's 9/19 report in one sentence: on entry, the rear circles are smallest (weight forward), the rear tires are spending part of what is left on braking, and the remainder for cornering is less than the front is generating. The rear steps out. The lesson 7 circle can't show this because it has no front and rear.
3. Combined slip: spending in two directions at once
A tire generates grip by slipping a little: a few degrees of slip angle sideways (the angle between where the tire points and where it is actually going), a few percent of slip ratio fore-aft (the tread turning slightly faster or slower than the road passing under it). When you ask for both, the rubber in the patch is sliding along a diagonal, and the force it gives back points along that diagonal too. That is the real reason the budget is shared: not that there are two accounts, but that there is one force vector and you choose its direction.
Trail braking is the name for choosing a direction that is not straight back. Brake hard in a straight line (force vector straight down on the g-g diagram, the plot section 4 describes), then as you turn in, ease the brake as the cornering builds, so the vector swings around the edge of the ellipse from "down" to "sideways" without ever leaving the edge. Every instant the vector is inside the edge, grip is going unused.
4. What the g-g diagram shows
The logger's accelerometer records lateral g and longitudinal g at every sample. Plot one against the other, every sample a dot, and you get the g-g diagram: the region the driver actually used. Read it like this:
- The outer edge is the kart's real budget: the ellipse, as driven.
- A cross shape (dots only on the axes, none in the corners of the plot) means the driver brakes, THEN turns, THEN accelerates. Straight- line braking. Time is being left on the table in the transition.
- A filled ellipse means the driver is trail braking into corners and feeding throttle out of them: the vector is sweeping around the edge instead of jumping between axes.
- The top being flat is the engine (section 1). No driving fixes it.
- Asymmetry left vs right means the kart, the track (more left turns than right), or the driver prefers one direction. On a left-dominant layout the right-hand lobe is smaller because there are fewer right turns to fill it.
5. The model's g-g diagram is a cross, and that is the point
From the 72T trace (the model's own columns):
max lateral g: 1.50 (every corner, exactly)
max braking g: -1.10 (1.0 g of brake plus drag)
max accelerating g: 0.145 (hairpin exits, engine-limited)
samples with lateral > 0.3 g AND braking > 0.2 g: noneNone. The model brakes in a straight line to the corner speed, holds exactly 1.5 g at exactly that speed through the whole arc, and only then accelerates. Its g-g diagram is a cross with a flat top: dots on the axes, nothing in between. It is the picture of a driver who has never trail braked, drawn by a model that has no idea trail braking exists, and its lap time is still 58.27 s because the model was tuned to that number and it compensated by cornering a fraction faster than a real kart can.
That is the disagreement to look for first when the real trace arrives. A real driver's g-g plot has dots in the lower-left and lower-right quadrants, and how many there are is a direct measurement of how much of the entry budget he is using. The lesson 7 sheet said trail braking is spending the budget well; the diagram is the receipt.
6. What to measure
The logger's g-g diagram from one clean session, plotted with the same scale both axes. Two numbers off it: the largest resultant g (sqrt of lateral^2 + longitudinal^2) anywhere on the plot, which is the kart's real budget and replaces the model's 1.5; and the fraction of braking samples that also carry more than 0.3 g of lateral, which is how much of the entry the driver is trail braking. The first number goes into the lap model. The second one goes to the driver.