Theoretically, How far would it take for a rocket vehicle on a straight-line track to break the sound barrier?

For my history final at school, we have to pick a topic or time period in American history and make a theme park out of it, drawing the park on poster board and writing a paper which explains each attraction. I chose the history of American aviation and I wanted to include a ride themed after the Bell X-1 (1st plane to break the sound barrier) which works like a rocket sled and actually breaks the sound barrier. I was going to say in the paper that the track was one mile, but just so I don't sound like an idiot I figured i'd get a more professional opinion.

Public Comments

1. This one doesn't quite break the sound barrier and is 12,000 feet long. I also doubt that any community would put up with sonic booms all day long http://www.afa.org/magazine/Aug1956/0856rocket.asp
2. Without government approval it is illegal to break the sound barrier in the United States or its territories. Your best bet would be to make a ride that actually uses a centrifuge and a simulator screen. The centrifuge will create G forces while the electronics will make the noise and visual experience. It'll be significantly cheaper and less dangerous. The rocket sled breaking the sound barrier would blow out ear drums of everyone in the area (likely shattering glass with it). Remember those rides where you spin around in a circle and are held outwards? Same idea. All you need to do is make 4 or 5 cars, equally spaced in a circle (possibly shaped like the X-1A for theme) seating 4 people. They climb in and strap seat belts on. Put blinking lights and some flat panel screens for the windows. Create radio chatter that somehow narrates it ("Ok X-1, go for release" as the car shakes and the plane is dropped from the B-52). Once the rocket motors fire the centrifuge speeds up, steadily increasing Gs, but no more than 3gs, which the average person has never experienced and will feel pretty crazy. Some rocket noise through speakers and airflow hissing getting rougher until "breaking the barrier" when the airflow gets smooth again. Engine burns out, centrifuge slows down and everyone claps and celebrates over the radio. Just an idea. Hope it works out for you! Good luck.