Going deeper on lesson 4's one idea. The sheet hands you grip = k x load^0.9 as a fact and uses it. This page is about why the exponent is under 1: what rubber is actually doing on asphalt, and why the physics-class friction rule (friction = mu x load, mu constant) is the one rule of thumb that fails worst on a race tire. Numbers use lesson 3's corner loads; the exponent 0.9 is (typical), a published range for kart slicks, until a skidpad or a logger measures ours.
1. The friction you learned is for blocks, not rubber
School friction: force = mu x normal load, with mu a constant for the pair of materials. Double the load, double the friction. It works for a steel block on a steel table because the real contact between two hard surfaces is a few high spots, and the area of those spots grows in proportion to the load pressing them together. Grip proportional to area of true contact, area proportional to load: mu comes out constant.
Rubber is not a hard block. It is soft enough to drape into the texture of the asphalt, and two extra things happen that a block never does:
- Adhesion. Rubber molecules bond, weakly and briefly, to the road surface; sliding has to keep breaking those bonds. This part of grip scales with the area of real molecular contact.
- Hysteresis (energy lost in squashing and unsquashing). Rubber is a lossy spring: push it into the asphalt texture and let it recover, and it gives back less energy than it took. Every bump in the road surface that the tread flows over costs energy, and that lost energy shows up as a force resisting the slide. This part of grip comes from the rubber deforming, not touching.
Both mechanisms grow with load, but neither grows in proportion to it.
2. Why the coefficient falls as load rises
Lesson 1's addendum says the contact patch is roughly force / pressure: more load, bigger patch, in proportion. But the pressure inside the patch is not uniform, and the rubber under the high-pressure center is already draped as far into the asphalt as it can go. Adding load squeezes the center harder without much more real contact, and pushes the extra area out to the edges of the patch where the pressure is low and the rubber is barely working. Real contact area grows slower than load. Adhesion grows slower than load. The coefficient falls.
That is the whole content of the exponent. Grip = k x L^0.9 means the effective coefficient is mu = k x L^(-0.1): it drops slowly as load climbs. Lesson 3's corner loads make it concrete (k = 1, units arbitrary):
| Load, lb | grip (L^0.9) | effective mu (grip / L) |
|---|---|---|
| 45.6 (inside rear, cornering) | 31.1 | 0.683 |
| 102.6 (rear tire at rest) | 64.6 | 0.629 |
| 159.6 (outside rear, cornering) | 96.1 | 0.602 |
The lightly loaded inside tire has 13% more grip per pound than the heavily loaded outside one. It just has a third of the pounds. That asymmetry is what lesson 3 Q6 was measuring when it found that transferring 57 lb costs about 1.5% of the axle's total grip, and it is why the exponent matters more than any single mu value: it sets the price of weight transfer.
One more consequence: put the whole rear-axle load on one tire (205.2 lb, the inside rear lifted clean off) and grip is 120.5; split it 102.6 / 102.6 and it is 129.1. Lifting the inside rear costs 7% of rear grip. The kart pays it because otherwise it cannot turn (lesson 3), and the price is set by the exponent.
3. The temperature window
Both mechanisms depend on how soft the rubber is, and softness depends on temperature. Too cold: the rubber is stiff, cannot flow into the texture, hysteresis is small, adhesion is small. Too hot: the rubber gets greasy, the surface layer shears instead of gripping, and it wears fast. Between them is a window, maybe 30-40 F wide (typical), where a given compound gives its best mu. Evinco Blue is a hard compound with a high, wide window; that is why the class runs it (lasts a weekend) and why the pressures on lesson 4 are about getting it INTO the window fast, not keeping it out of the top.
The pyrometer's inside / middle / outside reads (lesson 4) are three samples of where the tread is in that window. The pressure gauge's growth number is the average of the whole tire's air. Both are measuring the same thing, temperature, and the exponent tells you why it matters: a tire 20 F below its window is running at a lower k, and no amount of load makes that up.
4. Heat cycles: why a tire goes off
Each time a tire is heated to working temperature and cooled, some of the oils in the compound migrate out and some cross-links form that did not exist when it was new. The rubber gets harder. Harder rubber drapes less, hysteresis drops, adhesion drops: k falls, permanently. After a handful of cycles (typical: 3-6 for a race set) the tire looks fine, has tread, holds air, and is a second slower. It has not worn out; it has cured.
This is why "fresh tires" was worth 0.5-0.8 s on 9/19 even though the old set had rubber left. It is also why the one-set-per-weekend rule is a competitive rule and not just a cost rule: everyone is on the same number of cycles.
5. What to measure
Lesson 4 asks for the pyrometer's three reads across each tire. Add one thing: read the same tire twice, once straight off the track and again two minutes later. The drop tells you how fast the surface cools, which is how much of what the pressure gauge saw was the surface and how much was the air. And on the day there is a spare set with a known cycle count, run the same session on the fresh set and the cycled set and take the lap-time difference. That is k, measured, before and after curing, and it is the number that decides whether a practice day on the race tires is worth what it costs.