Bikes don't have to apex every corner in a velodrome because they're simply not going fast enough to overcome available grip. Motorcycles and cars are absolutely going fast enough. If they had unlimited grip, they would drive the shortest inside line because it covers less overall distance.
I have a roughly square lap I ride inside the parking lots at our defunct airport. Because mine is square, I am apexing every corner, but choosing the entrance and exit angles is where the fun is. I've tried sticking to the inside as close as possible, but I can feel and see the speed losses due to wheel scrub from taking the corners too sharply. If I enter or exit a corner too wide, I can feel the extra time required to cover the added distance. Getting it just right feels amazing.
So going in a circle, you want the tightest line on which you can pedal continually, without scrubbing speed off of the tires.
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