The largest ammo I ever sent flying fast with a homemade contraption was 20 mm steel ammo, and that required fairly stout bands:
Hypothetically (I've never shot with XXX-L ammo) what works for fairly standard 9 mm (38 cal.) steel ammo in terms of a straight trajectory over, say, 10 yards could be used as a viable basis to calculate the draw weight required for a tennis ball by multiplying the draw weight used for the 9 mm ammo according to the actual weight of the tennis ball. You will of course need to take into account the thickness and length of the rubber flat bands, bearing in mind that more band thickness (layers) will require more band length for the specific draw length required to optimize ballistics. Unknown territory...
Your pouch would of course have to be of a material and thickness to resist the somewhat high draw weight, and the overall design of the XL-sized slingshot for the job will need to be structurally sound to avoid catastrophic failure :hmm: . Trial and error is fine of you have a basic understanding of what wood and metal does when subjected to stress: basically, you want to make something that is stronger than it needs to be, unless of course you can get some relevant advice from an engineer. If not, maybe hide behind a tree when you try out your future device for the first time
anic:.
If ever, this is what it takes to shoot 80 mm diameter steel balls (oh, don't do this at home):
Last, but certainly not least, you may find that achieving a range of 200 yards will be challenging in view of the projectile weight (tennis balls are relatively light) and aerodynamic considerations: round ammo does not do very well here, and "hop-up" (backspin or "Magnus effect) might be difficult to achieve. A look at a top notch player like Roger Federer with his tennis racket in full swing should give you a rough idea whether a 200 yard range is feasible.
Intrigued by that last aspect, I had a look at how far tennis balls had ever been sent flying with a tennis racket:
https://www.menstennisforums.com/threads/how-high-how-far-can-you-hit-a-tennis-ball-with-a-racquet.953520/
(Quote) "the fastest official shot was 157mph by Isner. Assuming a tennis ball weight of 57 grams, a 1G drag function, a 0.56 Newton of G force, and normal atmospheric and altitude conditions, that ball would have travelled 134 yards horizontally and 91 yards vertically."
Ouch, my physics is a bit rusty these days...but OK, 134 yards. Not bad.
My 2 cents worth...but by all means, give it a try, and let us know what you come up with. Good fun...