# SL2

A further analysis of SpinLaunch, ca. 8 August 2022

Hi, Tamie,

The new, long video about SpinLaunch is much more detailed than any before.

Yet:

* It is incomplete in critical areas

* The team has done some very good engineering, but, in light of critical oversights, it amounts to boys playing with very big and dangerous toys.

They have launched a solid projectile with a smaller version of their final design. The projectile survived the launch and the huge dynamic pressure and drag heating because it is (1) solid, (2) of a high thermal inertia in the sheddable skin (that’s shed only in the “final” design), and (3) not going nearly as fast as in the final design.

Let’s look at their specs for the final design:

* Tangential speed of the projectile just before release: Mach 6, or v = 2,000 meters per second (4,500 mph).

* The length of the launch arm is 45 meters.

🡪 The centrifugal acceleration is v2/r = 4,000,000 m2s-2/45 m = 90,000 m s-2. That’s 9,000 times the acceleration of gravity!

1. As I’ve noted before, this would twist into junk any delicate plumbing and wiring of a rocket being enclosed in the projectile. There has to be a rocket inside, as SL people acknowledge, since even 2,000 meters per second is far below the 7,000 meters per second to reach low Earth orbit (LEO). This problem doesn’t come up when you’re trying to launch a solid projectile, as they are, but a solid projectile won’t make it to LEO. I note also that a satellite’s structure and electronics will not withstand 9,000 g’s!
1. They show a rocket held inside the final design. The fuel tank has to be kept from slamming through their aeroshell, the outside skin. What kinds of forces are acting on the spherical tank’s steel shell? It’s a very weird stress analysis, with huge stress on the outer side and little on the inner side. Nonetheless, I offer a quick estimate. Across the tank at its widest point it might be 0.5 meters (they show the aeroshell as 1 meter in diameter). So, you have fuel with a density of about 800 kg per cubic meter. That gives a fuel mass per area of 400 kg per square meter. It’s accelerated at 90,000 m s-2. That gives a force of about 36 million newtons per square meter. That’s 360 atmospheres! Can this be withstood safely? I found this nice discussion at https://academic.uprm.edu/pcaceres/Courses/MMII/IMoM-6A.pdf. For ¼” steel (6 mm), the safe pressures are on the order of 50 atmospheres, far lower. That’s not taking into account a buckling stress at the midline.
2. There is a worse problem than high centrifugal acceleration, and it’s called jerk. Jerk is the rate of change of acceleration. It’s what you feel if you suddenly stop and your innards sling forward. It is often the most damaging effect in a car collision. The amount of jerk depends on the details of how the projectile is released. It is huge, in any case, as the release has to be done in a small fraction of a revolution of the throwing arm. If it’s over, say, 3 degrees of rotation, that’s 1/120 of the rotational period, which they show as 45 times per second. That’s (1/120)(1/45 s) or a bit less than one five-thousandth of a second. So, the jerk is 9,000 g *5,000, or 45 million meters per second cubed. That would turn any fine plumbing and wiring into a thin paste, even if the original centrifugal force hadn’t already done so. What is shocking is that the SL team did not imbed a jerk sensor into the projectile – easily done with materials of different densities.

Summary: It’s boys with toys, and no prospects for launching anyone’s real equipment. They’re enjoying the challenges such as making the carbon-fiber launch arm that will be carrying the greatest stress of anything built before. Have fun, but do not, do not, do not ask anyone to invest in this, especially not the taxpayer with no say-so.

Oh, and I still don’t see a safety screen. What happens if the projectile is released (as by breakage of the launch arm) when that projectile is heading, say, horizontally? Remember, they deliberately made the projectile heavy to minimize the heating (small frontal area). It’s going to weigh 10 tonnes, in the final version (see minute 6 in the video). The kinetic energy at release is ½ mv2, or 0.5*10,000 kg * 4,000,000 m2s-2, or 20 billion joules. That’s the energy in 5 tons of TNT! How do you devise shielding for such an accident?!

Oh, and power demand. I didn’t see a figure in the video for how long the spin-up takes. Suppose it’s 10 minutes, 600 seconds. Divide 20 billion joules by 600 seconds and you get a power demand of 33 megawatts, not accounting for any air friction, etc. That’s a big load to deliver out to the boonies! Oh, around minute 24 in the video they admit to as much as 150 MW!  They do discuss this and basically say they’ll make their own power station.

Cheers,

Vince