==Edit==
I think I've got the Cheetah race covered. All the physics of the go-kart are thoroughly explained here, and all that's left is for me to apply the ideal inputs in such a way that no walls or grass are touched. Old GMV here:
GMV:
link
Savestate:
link
Watchlist:
link
The rest of the post is more or less a research paper for my own reference, but presented in a way that future runners can use.
Kart directions ("Target Angle" value)
Each angle is calculated relative to the four major directions (i.e. the 0° angle means due north, due east, due south, or due west.) Borderline cases are somewhat difficult to test, so the specific numbers may be off.
0° = -32 to 31
22.5° = 32 to 96
45° = 97 to -96
67.5° = -95 to -31
Typically the kart can switch angles within 8-9 frames, though it's possible and recommended to do the first 7-8 frames ahead of time. With preparation, a 90° turn can be completed in about 25 frames, and 180° in about 57.
Top speeds per angle ("Slide" value)
0° = 768, 0
22.5° = 709(-710), 293(-294)
45° = 543, 543
67.5° = 293(-294), 709(-710)
Speed effects ("Slide" value)
The best way to explain speed is to imagine a "bank" of 96 frames. The accelerator (A) adds 1 frame to the bank, and letting go takes 1 away. The brake (B) by itself takes away 3, and A+B takes away 1. When you reach 96 frames, the slide speeds should be at their cap. On a straightaway, A will raise your speed by 8 per frame; even on other angles you will reach top speed in the same time, though floating points seem truncated in RAM Watch.
If you turn, both Slide values will change by 12 (up or down) until they meet the value they should be at. The B button changes the values by 20, but remember that holding B will take away frames. Basic technique is to turn while holding A+B until it stops changing by 20, then keep going, but that brings down your cap speed by a lot. A better technique is to brake for a while, then let off early, so that you continue turning with the 12 increase right up until your 96-frame bank is filled again.
This has been tested exhaustively. If you do a rapid 180° while letting go of A, you can see your slide value swing from 768 to -144 in intervals of 12, and then back to 0 in intervals of 8. Also, driving in grass immediately cuts your bank down to 48.
What this means
The objective is to reach top speed quickest after exiting a turn. This is done by maximizing the number of frames the brake is used (for the 20 boost) without hitting the lowered cap too early and forcing Slide to increase by 8 instead of 12. Consider a 90° turn from full, while assuming each step takes 8 frames of turning action, and remembering the top speeds per angle.
23°, 8 A+B frames:
Slide = 20*8 = 160
Cap = 293 * 88/96 = 268
45°, 8 A+B frames:
Slide = 160 + 20*8 = 320
Cap = 543 * 80/96 = 452
68°, 8 A+B frames:
Slide = 320 + 20*8 = 480
Cap = 709 * 72/96 = 531
90°, 24 A frames:
Slide = 480 + 12*24 = 768
Cap = 768 * 96/96 = 768
Ideal use of the brake can be calculated in this manner for any situation as long as you know your starting slide and cap speed. This only solves the problem of optimal brake use, but the fact that it can be predicted at all is a blessing. I still have to determine optimal starting positions/angles for the hairpin turns. I will apply my findings to the run soon.
==Edit==
First hairpin officially dealt with for good: I began as close to the wall as possible, with barely enough Slide.y to clear the grass, and then, before Slide.y could reach 0, I did a full 90° turn with 24 A+B frames and came out hugging the border. Literally no speed was lost unnecessarily. This is good progress.
