I took this video in Dublin during a visit to see a Demo of the Bramor UAV manufactured by C-Astral, the thing I like the most was their catapult. It is made from box alluminium and uses a winch to tension the bungees which are doubled up. A carriage runs on the track, with hooks that cup around the leading edges of the Delta wing.
The carriage is locked, then the bungees tensioned by pulling a steel wire rope, which is attahced to the bungee block and then pulls this block to the back underneath the track. The winch is the same that you see on small boat trailers or car recovery trailers.
Note the hook each side of the cradle, these cup around the wing to stop the plane sliding off the carriage. Here is a video of the catapult launching the Bramor UAV Chocks Away!