satisfies the rules?

Volvo’s 2004 extreme gravity racer does have 4 wheels, but as the race director notes in the comments, the headfirst driving position is illegal in the Canary Derby. Too bad.

Portland Adult Soap Box Derby (Mt Tabor)

link to official site

mayhem

Red Bull Ljubljana

Even more fun (lots more Red Bull race videos on YouTube)

Red Bull Race 2006

Fun stuff

some British cars

A couple of pics from cars entered in a race held at the Goodwood Festival of Speed a few years ago. Note that the cars in those races had to negotiate a slalom portion of the course, as a pack, at speed. That explains the side rails (to prevent wheels interlocking, the wheel spats might be a rule requirement too, to reduced wheel to wheel unpleasantness) and the sophisticated suspension and steering. Also their rules dictated a minimum car height. Click on image for full size.