My freshman year was the inauguration of chariot races. We learned how to make them quick and easy, and (reasonably) safe.
You need:
2 bicycles the same size, with fenders.
1 crate - about the size of your chariot
3/4 inch plywood
3 foot piece of 1 inch steel pipe
2 angle brackets
2x4 lumber
lots of pipe or conduit hangers
Cut the crate like this:
http://mssscrafts.com/crafts/chariot/index.htm
Cut the bikes, such that the rear wheel still has the triangular frame, where the seat mounts, and the pedals are installed. Remove all components - seat, pedals, crank, chain, gears and sprockets, etc. Grind sharp edges smooth and coat cut parts with a glue gun, and a few layers of duct tape. Keep the fenders on.
Put a layer of 3/4 inch plywood on the inside and outside of the chariot body, on the sides where the wheels attach.
Put an angle bracket on each axle, and rest the body on the bracket. Put the pipe through the hole where the pedal crank came out, and rest the front edge of the body on the pipe. Clamp the bike frames to the sides of the body - drill holes in the 3/4 plywood and attach in at least eight places. Use grade 5 bolts and nylon insert nuts. You may have to drill out the pipe clamps - use 3/8 bolts or bigger.
For a tow bar, use a 2x4 and bolt it to the bottom. Bolt cross pieces for the "horses". (Don't try to race with three or four abreast - too many accidents) Varnish the cross pieces, and the rim of the body heavily, to keep splinters from poking your driver and team.
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