I'm not sure what it's called, but I remember an amusement ride when I was a kid. You get strapped in a harness like a parachute, but you jump off a tower that has a couple cables running from it. You get the sensation of being in a parachute and bouncing around, but there's no real danger. Unfortunately, the closest picture I've found is this, but it's not like I remember...
http://www.cs.utk.ed...r/activities.html
Cheers,
Scott.