Converting everything to metric and working out the centripetal acceleration, a radius of 1 mile yields a centripetal acceleration of 232g, to an arbitrary 3 si

Converting everything to metric and working out the centripetal acceleration, a radius of 1 mile yields a centripetal acceleration of 232g, to an arbitrary 3 significant figures. A radius of 2 miles yields 116g. The acceleration would drop linearly along the length of the "arm" as you move toward the center, so you could calculate (with calculus, over which I can't be bothered at the moment) the optimal way to taper the arm from root to tip for a given end load. Drag losses on the arm at a 1 or 2 mile radius would dominate, and ridiculously so. Frankly, roughly 100-230g is not severe at all for a properly engineered vehicle at the payload ratio you could expect to achieve if you get the first 2.2 km/sec "free", as you would in this scheme. That's the majority of a factor of exhaust velocity for a kerosene/lox engine, and all of a factor of the exhaust velocity for a solid rocket motor. Multiples of exhaust velocities are factors of e, so you're probably better than doubling the payload ratio. Perhaps counterintuitively, going from 3 percent mass fraction to 6 percent brings your vehicle size down by half. You go from ~33 times the payload to ~16 times the payload. And, while others are talking a good game about drag, this saves you loads in gravity losses, as the rocket is spending far less time fighting gravity with this initial boost. (1g for two minutes is 1.2 km/s, give or take centripetal effects from your curved launch trajectory. Not negligible, at all.) The other commenters seem also to be mostly neglecting that the motor/engine will very quickly reach near-vacuum conditions, not immodestly increasing its ISP. Much better than a mile-long tether would be, in my not-so-humble initial opinion, to reduce the tether length by a factor of 10 or 100 from "a mile", to give a centripetal g load of 2k-20k g. Again, calculus tells you how to taper your (probably carbon fiber, possibly consumable, most definitely streamlined) attachment rod. And don't bother with the complexity of a vacuum. The Nike program launched vehicles at Mach 10 in the lower atmosphere. That's 3.4 km/s, 1.2 km/s faster than SpinLaunch's proposal. Given that heating goes something like the 4th power of velocity, Mach 6 or so is going to be much, much less severe than the Mach 10 environment encountered by Nike. Why, SpinLaunch vehicles won't even get to glow white hot!