I don't know for sure, but I'm under the impression that the Madison is one of the many super-slack fixed gear road bikes, not really designed for velodrome use. That's not to say that it can't be done, but there are probably better options out there, if you're looking for an affordable track bike.
Custom Built Aluminum ATB frame. Vintage Colnago. Have had Eddy Merckx, Colnago, Ciocc, Cannondale, Santana Tandems &++++
Schwinn Madison used to be an entry level track bike. Great for the new rider and a great training bike.
Lots of velodromes used them for training because they are cheap and reliable. Encino velodrome had a small fleet of them for training bikes at one time. (many moons ago)