Going deeper on lesson 5. The sheet says braking moves weight forward, off the only axle that has a brake. This is what that costs, in numbers, and why the class is built that way anyway. Nothing here is a fact about our kart until the logger's longitudinal g trace exists; the split, the height and the grip number are all marked (typical).
1. The rule, and the norm
Sprint karts in this class run a single brake on the rear axle. The club rulebook requires a working brake system with a safety tether on the rod, and checks the caliper and master-cylinder fasteners; it does not require front brakes, and Senior LO206 karts run without them (typical: front brakes appear on shifter karts, where the speeds and the rules are different). So our kart stops with two tires, and those two tires are the ones the physics is about to unload.
2. Braking takes weight off the braked axle
Lesson 3: braking at g moves weight forward by
transfer = g x W x h / LW = 360 lb, h = 10 in (typical), L = 41 in. The rear axle starts with 57% of the weight (typical), 205 lb, and loses 88 lb per g of braking.
Now the catch. The braking force the rear tires can make is their grip coefficient mu times the load on them, and that load is falling as the braking gets harder:
braking force = mu x (0.57 W - g W h / L)and braking force is also what produces g:
braking force = g x WSet them equal and solve for g:
g = mu x 0.57 / (1 + mu x h / L)The h / L term is the transfer eating its own grip. The harder you brake, the less rear load there is to brake with.
3. The numbers
mu = 1.2 (typical for a kart slick in braking): g = 0.53. Rear load at that point: 159 lb, down from 205.
mu = 1.5 (the lateral number from lesson 7): g = 0.63.
Compare: a kart that could brake with all four tires would stop at g = mu, 1.2 or more. So rear-only braking gives you roughly half the stopping power the tires could deliver. From 55 mph: 191 ft to stop at 0.53 g, 84 ft at 1.2 g. A hundred feet of straight, every lap, spent on the brake because the front tires aren't helping.
A car for comparison, rear brakes only: 50/50 split, h = 20 in, L = 108 in, mu = 1.0: g = 0.42. Worse than the kart, and it's why no car does it. The kart gets away with rear-only because it is low (h / L small) and rear-heavy (the 0.57 in the formula is the rear's share of the weight).
4. What the lap model assumed
The lap model (our lap model) brakes at 1.0 g (typical). By this derivation that is optimistic by almost half. Either the real mu under braking is higher than 1.2-1.5, the center of mass is lower than 10 in, the weight split is more rearward, or the model over-brakes and under-predicts the braking zones. The logger's longitudinal g trace settles it in one lap: read the flattest part of the trace under braking, and that number is g. (Lesson 3 Q10 - the corner weights and CG height - is how you find out which term was wrong.)
5. What it means for the driver
- Lock-up is easy. Above the limit the rear tires slide, and a sliding rear axle on a kart with no differential is the "rear steps out on the brakes" from 9/19. The limit isn't a fixed pedal pressure; it drops as the kart pitches forward, so the pedal has to come off as the braking builds, not stay planted.
- Straight-line braking is cheap, trail braking is expensive. Lesson 7: braking and cornering share one budget. With only two tires braking and those two also carrying all the cornering load at the rear, turning in with the brake still on takes grip from an axle that is already short of it. Do the heavy braking straight, and release most of it before turning in.
- Rear track and seat height show up here. Lower h means less transfer, which means more rear load under braking, which means a higher braking limit. The seat is a braking adjustment, not just a cornering one.
One thing to measure: braking g on the main straight, from the logger, alone, brakes only, no steering. One number ends the argument between 0.53 and 1.0, and the lap model's braking zones get corrected the same day.