My current fort in 34.11 called Geniushammers has been playing with accelerator coils. A number of prototype devices have been built around these since they are compact, easy to build, and have a variety of uses. I also like their quick reaction time to a lever being pulled to open the door - the cart is ready to roll! Downside is that a coil can only hold one cart at a time, so barring a return system it's a one-shot deal.
First use has been as a basic building destroyer trap. Heavy (gold or platinum) minecart in a coil and wait for the door to be attacked. (Optionally just hook the door to a pressure pad a two spaces away where the destroyers prefer to stand.) Cart fires out and you get something's attention at the very least. Large creatures can take the hit, and I've only bruised or stunned forgotten beasts with one so far.
I have also put a coil's door on a lever and fired it down an open space into an oncoming goblin unit during sieges. Results are mixed since I have seen the cart only hit and hurt 1-2 creatures. But I've also seen it pinball 4-5 creatures into each other and also directly hit a Goblin Elite Archer in the head.

Second use has been as a light anti-intruder trap as part of some in-depth defenses. An wide open area has a coil at the north end which will fire the cart south - where a curve turns the cart around to send back into a coil. About 10-16 tiles from north-to-south. A few of these set-ups are augmented with additional accelerators at the south end to help return the cart to speed after collisions. Essentially a "frogger" device using a coil to hold the cart at speed until deployment. Deployed between caravans or just after the ambassadors and liaisons get into the fortress, and during sieges.
Results during sieges have been mixed since hitting a heavy mount like a cave croc can slow or stop the cart on level ground. Have also seen one tear up most of a goblin cavalry squad by itself. The device is stellar against kobolds, snatchers, and ambush squads - you just suddenly see body parts and corpses appear in the back end as they get exploded by the collision effects. However, this device will eat caravan guards and wayward fortress residents. I have an extra door on a lever to cover the return side - it's the "safety" to totally seal the coil from access, or can be used to stop the cart entirely if necessary.
Lastly, I have a working watergun which uses a coil as part of the main firing mechanism. It's a standard design with a cart hitting a wall, firing the ball through a fortification on the level above, and then dropping down a hole into a reservoir to be re-filled and then cycled back to the accelerator level to be fired again.
The coil can hold a water-loaded cart which will then fire the initial water ball 3-4 ticks after the lever is pulled. Cyclic fire rate after that point with a single cart is roughly 92-95 ticks after that point. I have also experimentally had a second cart dropped into the system and which initially fires about 35 ticks after activation. This will double the rate of fire, but I have also seen "cart creep" with a cart eventually catching up to and colliding with the other cart to cause a jam. [Diagrams below]
Water ball trajectories and velocity seem to be variable. On a range that is 30 tiles long and 5 tiles wide wall impacts occur anywhere from 6-7 tiles down range to balls hitting the end of the range with no side deviation. (Experimentation in a freezing biome with a water gun has indicated that trying to "ice" targets is a uncommon occurrence and is more like to result in ice walls blocking the field of fire.)
The gun itself is pretty straightforward. As is dumping the cart into a trench of water that has a reservoir the next level up to keep the trench filled to 7/7 water. (I fill the reservoir from the fort's aquifer, and also installed drains, etc. so that maintenance can be done.)
The tricky and frustrating part has been getting the ramp and track combinations right that will lift a loaded cart out of the trench, out of the reservoir, and then additionally back up a few levels to feed it back into the accelerators. That is the main thing I want to get a diagram or picture out of in order to save others the trial-and-error effort if they want to build one of these.
==== Design pictures forthcoming====