Spinlaunch with Basic Physics [pdf]

OP here: I saw the spinlaunch video and got really excited that this was completely tractable in simplified form with basic physics. So I did the math expecting to see a huge savings in fuel mass and....it was basically negligible. I'm curious if anyone on HN (maybe even from Spinlaunch!) could explain where I go wrong. Otherwise you might find it interesting to read. Thanks!

The last story I looked at said they're planning for 10,000G launches of 200kg payloads.

I want one; to fire iron slugs at small game. damned coyotes.

Other than that (probably very small market); I think the main purpose here is to separate investors from their money.