Expedition - ex·pe·di·tion

A) A journey undertaken by a group of people with a definite objective: an expedition against the enemy stronghold; a scientific expedition to the South Pole.

B) The group undertaking such a journey.


Exhibition - ex·hi·bi·tion

A) The act or an instance of exhibiting.

B) Something exhibited; an exhibit.

C) A large-scale public showing


I believe the word you're looking for is Exhibition (unless of course, you're TEAM LEWIS AND CLARK!). Exhibitions usually aren't competitions. Who will be doing the judging? What are the judging parameters?

PS: Also, there usually isn't a whole lot of seat time involved in an Exhibition...so how many people are going to get to drive and for how long?