This is the most important advice I can offer. If you break one of your derby's rules and your car is disqualified, it doesn't matter how fast it is. Some of the suggestions that follow are illegal in many derbies, including derbies that I have helped organize. Ignore any speed tips that violate the rules for your derby. If its wheels pinch the center guide rail, or if its bottom drags on the center guide rail, then your car may not even reach the finish line.
Unusual designs can encounter other track-fit problems.
As a rule, if the basic shape of your design is unusual, check with whoever sponsors the race to see if it will work with the track's starting gate, finish gate, guide rail, etc. Your Enemy Yes, aerodynamics can make a difference. Yes, getting your car as close as possible to the weight limit can make a difference. Yes, other things can make a difference too. But friction is the most significant force slowing your car down, so reducing friction is the most important thing you can do if you want a faster car.