It's fairly simple; let me see if I can simplify it enough for CoasterBuzz even though I've never seen the system in person. :)
The train is really heavy...let's say a half-ton per car, plus another half-ton of passengers per car, for a total of about 7 tons (14,000 lbs.) for a 7-car train. Say we want to accelerate that train to 60 mph, that would be 88 ft/sec. Let's say we want to accelerate to full speed in 4 seconds. That means we need to accelerate 14,000 pounds to 88 feet/sec in 4 seconds. Let's see...that's 88 ft/sec / 4 sec = 22 ft/sec/sec. * 14,000 lbs = 308,000 ft-lbs/sec for 4 sec. If I did the math right, that would be about 560 HP for four seconds...at high efficiency, that would require about 418 kW of power to operate.
Now, there ought to be a more efficient way to do this than to use a 560-HP motor to pull the train. Particularly since that kind of energy is only needed for a few seconds. Why not store energy over a longer period of time when the train isn't moving, and let it all loose at once when it comes time to launch the train?
That's what the launch system on Montezooma does. A multi-ton flywheel is rotated to high speed. The flywheel is heavy so that it can hold lots of mechanical energy. A wire rope is connected to a pulley which is attached to the flywheel by means of a pneumatic clutch. The wire rope is attached to a pusher mechanism that comes up behind the train. The flywheel spins up to full speed, driven by a small electric motor (it takes longer than it takes to launch the train, but that's OK so long as it reaches full speed before launchtime) and the clutch is engaged. This puts the full rotating inertia of the flywheel into pulling the wire rope and thus pushing the train out of the station.
The train flies out of the station, the clutch releases, and the flywheel is brought back up to speed for the next launch.
Make sense, I hope?
--Dave Althoff, Jr.