questions of crank ratio physics

I play unicycle football on a fifty yard field. Wheels up to 29" are allowed, and that’s the size I use. My only smaller option is a 20" and I want more speed than that. My friend who has a 24" with 140mm cranks keeps even with me in 100 yard races whether I use 125 or 145 cranks. It shocked me. I want more speed than him within 30 yards. The equivalent ratio for a 29" would be almost exactly 150mm cranks. I could use more practice with acceleration and startup, but these vary with crank length also. With my 125mm, I spend most of the race catching up, so I am faster, but with these short distances, it doesn’t matter.

How should I maximize acceleration within these parameters of distance?

That is, should I ideally have even longer cranks than the equal ratio of his crank/wheel simply because my unicycle is bigger?

How could I calculate something like this?

Also, if anyone has experience racing, and has used a 29, or just if you have tried this stuff, what is the fastest way to mount (and by ‘fastest’ I mean most conducive to immediate acceleration)?

The equivalent ratio for a 29" is actually obtained with 170 mm cranks as you can see here: Gain ratios

Fastest mount is a rolling mount (look it up). For quicker acceleration, you can keep tweaking the equipment, or actually practice the technique of explosive acceleration. I learned how to do that back in my days of Track racing, and can still do the acceleration part (not so much the top speed part). The more time & effort you put into practicing technique, the less your crank length will matter.

Obviously 125 puts you at a short distance disadvantage over a 24" with 140s. All other things being equal, he’s going to out-maneuver you no matter what. I’d try some 140s on there, to give you more power for the starts, but still an ability to spin pretty fast once you get going.