The tallest and fastest roller coasters on Earth, Top Thrill Dragster, Kingda Ka, and Formula Rossa, all use a hydraulic launch system to get enough energy for recording breaking launches. There are several cylinders with a piston in each. Hydraulic oil pumps from a reservoir into storage cylinders filled with nitrogen. The nitrogen can compress and acts like a spring. On the other side is hydraulic oil that cannot be compressed. The piston slides to compress the gas and the hydraulic fluid fills the other side of the cylinder, building potential energy. The ride operator gets a signal when pressure has built up and the train is ready to launch. Pushing the start button opens high-speed valves at the storage cylinders, the piston is released, the gas expands forcing the liquid out at a very fast speed and sends the oil flowing to 32 hydraulic motors.

Gears on each end of the motors turn a large planetary gearbox. Planetary gearboxes sit on either side of a cable-winding drum that turns at 500 rpm. The drum works like a big fishing reel, taking up cable as it turns. The launch cable attaches to a locking device called a catchcar that, in turn, attaches to the coaster train. The catchcar runs in the track and propels the train forward. Reaching the target speed of 120+ mph disengages the cable from the train, closes the hydraulic valves, and restarts the process.

Kingda Ka’s hydraulic motor can produce a peak power of up to 20,800 hp (15.5 MW) for each launch. One thing to keep in mind is that although hydraulic launches have a lower peak load requirement since the electricity is drawn at a constant rate all day long to continuously pressurize the accumulators, they still use more energy overall because it is a less efficient system due to all the moving parts and mechanical losses.

- https://www.coaster101.com/2016/07/20/coasters-101-launch-co...

--------------------------------------------------
Note added at 1 day 3 hrs (2022-10-27 11:26:12 GMT)
--------------------------------------------------

The heart of the launch system is a large winch, around which the launch cables are wound. This winch is driven by hydraulic turbines. The two launch cables are attached to the winch on its ends, and run through two grooves on top of the launch track. The cables are attached to the sides of the catch-car, which runs in a trough between the grooves. A third, single retractor cable is attached to the rear of the catch-car, it runs around a pulley wheel at the rear end of the launch track and returns to the hydraulic building along the bottom of the launch track, where it is wound in the opposing direction on the winch's drum.

The train connects to the catch-car with a solid piece of metal known as a "launch dog" that drops down from the center car. The launch dog is normally retracted and is held in place by a small magnet, but the launch area has electrical contacts that demagnetize the magnet and cause the launch dog to drop down. The launch dog drops down at an angle, similar to the chain dog that a lifted coaster uses to connect to the lift chain.

Once the train and catch-car are in position and all is clear, the operator presses the "Launch" button and the launch sequence begins

- https://rollercoaster.fandom.com/wiki/Accelerator_Coaster