The idea of launching objects into space using a catapult interests me if only because my physics profs in high school and university all have at one point or another shot down the idea of space catapults. Since I don't remember exactly what their beef with space catapults was about, I figured I'd have a go and see if I could get an estimation of feasibility myself.

I am also not an aeronautical engineer (or even close to being one), but I do have some free time and I have a notepad.

According to Wiki[1], ∆V to LEO is ~8km/s plus 1.5km/s to account for drag (so a total of 9.5km/s total). The article claims that the craft exits the launch device at ~1.3km/s which leaves 8.2km/s to be accounted for. For the purposes of our math, let us assume that the craft has an alternate way to get up to speed. We'll note that SpinLaunch is not throwing their spacecraft into space at all; in fact, they're barely getting their spacecraft off the ground (relative to LEO).

Even with the significantly reduced launch speed, getting the craft spun up to speed is no small task. The equation for relating linear speed to angular speed is:

[Linear Speed] = [Rotational Speed]*[Radius]

Since we have a linear speed in mind, we can make assumptions for rotational speed or for the radius of the launching arm and solve for the other. I think revolutions per second is easier to imagine, so we'll just Fermi this out.

If your maximum angular speed is one revolution per second (~6.3rad/s), then your launching arm will need to be ~213m long. To put that in perspective, the centrifuge would need to be about four football fields in diameter. Not only that, but it would be hurling a spacecraft around the circumference once every second! Because the relationship is linear, if you want to halve the angular speed, then you'd have to double the radius. Just building a structure that can not only support the weight of a spacecraft at the tip, have a diameter of 450m, and complete full revolution every second seems like a challenge already.

Additionally, unlike a regular centrifuge, this launch structure would likely not be parallel to the ground either; you want to launch your craft into space after all. Which means that you'll have to deal with unequal forces and accelerations as you spin.

To really put things into perspective, the largest centrifuge in the world is the TsF-18 in Russia and it has a radius of 18m and can only manage 0.65 rotations per second at maximum speed[2].

But hey, I'm no mechanical engineer either, so maybe that's no big deal. Maybe introducing a vacuum in the launch structure makes such a huge difference that getting up to speed is easy enough.

How does one exactly create such a big vacuum chamber though? Even if the height of the chamber is only 5m tall, the total volume is ~710,000m3. The largest vacuum chamber is the Space Power Center and it has a maximum volume of 22,653 m3[3].

You'll need to build something that outspins the largest centrifuge in the world (by more than an order of magnitude) and outsucks the largest vacuum in the world (by more than an order of magnitude). If somehow SpinLaunch can build the most spinniest and suckiest structure ever built, you're still only 13% of the way into space.

Really puts into perspective how outrageous SpinLaunch's claims are.

1: https://en.wikipedia.org/wiki/Delta-v_budget

2: http://www.rusadventures.com/tour35.shtml

3: https://www1.grc.nasa.gov/facilities/spf/