I have a 26" Schwinn Typhoon. It is a massive single-speed bike that my parents got me about 40 years ago. My younger brother got a nearly identical bike at the same time, but in 24". Don't know if his was a "Typhoon" or not, but it was black while mine is red. His bike was given away decades ago, but I was curious about what tires it would have taken. My 26" bike takes an odd size tire that is difficult to find, but even Harris Cyclery does not have tires for a 24" Schwinn. Did Schwinn use a standard-sized tire on this bike, or are the tires simply not available?
On this site, he shows two different 24" Schwinn tires, plus a couple of others. I don't know what the "normal" 24" tire was (or is!): http://www.sheldonbrown.com/tire-sizing.html
24 x 1-1/4 "Schwinn Juvenile"
24 x 1-3/8 "Schwinn Juvenile lightweights"
If I remember correctly, Schwinn made 26" bikes that used an oddball Schwinn tire and also bikes that used normal 26" tires, so there's no guarantee that a Schwinn bike used a special size.