I had a slingshot when I was a kid but it didn’t look like this!
Potential applications of this family of machines include ground-to-space or intercontinental launch, for which large L/D projectiles would be required as shown in some images. The machine would also be of interest in providing a very high impact power source for physics experiments, including possibly impact fusion using magnetized fuel targets for which shorter L/D projectiles would be used.
It looks like Ed Schmidt and Mark Bundy of the Army Research Lab are looking at ways of firing projectiles into orbit.