CHALLENGE: launch a creature at least 15 z-levels into the air and have it land safely (unharmed, uninjured). Landing on a platform in midair is acceptable (and recommended).
I'll see your 15 and raise you another 11! But we'll get to that...
To get around having to "raise the sky" I decided to dig a 90-tile long, 30-z deep trench, and have the accelerator underground.
When accelerated by 51 impulse ramps and hitting the ramp, the path of the cart was as follows, with each x representing 1 tick:
x xx
xx x x x x x x x x x x x
x x x
x x
x x
x x
x x
x
x x
x
x x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
___▲█
The trench I built ran out of space around this point, but the rest of the arc can be more or less extrapolated. The peak here is 26-z up and about 74 tiles along from takeoff, and reached after 40 ticks.
Crucially, the only accelation is vertical and not horizontal. This means
another ramp can be built at a higher level and the minecart can be launched on another arc, raising the prospect of a system of launches from the depths. In order for a cart be relaunched it must first "make contact" with a surface, which it can only do when travelling downwards, so any extra ramps have to be placed at least after the highest point reached. I did manage to achieve this, although my minecart quickly ran into the hitting-the-sky problem highlighted earlier. It also accidentally ran into something else:
You may have noticed the red x in the chart above, 13-z above takeoff. This was the initial point of impact. The cart lost some of its momentum here and failed to reach its normal height. The eagle, however, was propelled along the cart's initial arc and hit the ramp I had constructed at the peak. (It was then quickly collected and dismembered by my butcher.)
As for dwarven flight, well I removed the top ramp and replaced it with a straight section of track and a stretch of track stops. Six was enough to stop an unmanned cart, and when I then tried a live test it worked out just the same: