One of the most sophisticated and feared siege weapons of the Middle Ages has been the trebuchet. Thanks to a relatively simple system of counterweights, which impressed by its sheer size, whole boulders could be fired at enemy positions and ramparts. Fortunately there are a lot of medieval-enthusiastic people these days, who are not afraid to build and test siege weapons on a grand scale.... Like this one here:
Finally, it was the task of our programmer to calculate and implement the ballistic trajectory of the projectile. Actually not such a difficult task, but since we had to start from a perfect trajectory to a fixed target, among other things for the AI, the whole thing became a little more difficult. Wikipedia could only help us with this rather less revealing formula:
Yes, this was not exactly what we were looking for. Some hours in mathematical forums and a lot of trial and error attempts later the trajectories now had the desired shape, so our trebuchet is finally ready for use.