Does some have am answer for this? When they open the doors, (I was told they are using door and not a membrane as shown in the promo video) won't atmospheric air replace the vacuum? Seems to me that sudden blast of air is going to 1 - Greatly slow the projectile down, 2 - Cause a sudden and rapid change in temperature for projectile, 3 - As the projectile travels through earth's atmosphere it's going to get very hot like when satellites/space shuttle re-enters earth's atmosphere, and 4 - Cause a sonic bomb.
The other question I have is once released, how to they intend on "steering" the projectile to get it in the correct orbit? Once the projectile is released I would think differences in atmospheric air pressure/winds aloft would alter the trajectory.
I still think the force difference across the skin of the project is going to cause the skin of the projectile to buckle.
This is not my area of expertise, but I did take a physics calls and understand forces and what happens to materials at high forces and temperatures.
1. They actually have a series of doors. All but the last are open until the projectile goes by. They shut extremely fast. They showed it happening in the video. I didn't count frames, but it was substantially closed in a second or less and bouncing ended within three. These doors are intended to limit the amount of air getting into the spin chamber, so a a couple of seconds of leakage isn't super critical. By the way, the pressure in the spin chamber is held to 0.01 Torr, which I believe is equivalent to well over 200,000 ft. The Concorde example is not applicable. The purpose of the doors is twofold. It keeps the spin tank in high vacuum for two reasons. To avoid drag, heating and aerodynamic problems with the spinning tether. And to avoid the time and cost of pumping back down to the moderately low pressure they need.
2. The air coming into the last door is at one atmosphere. Hence the fastest it can come in is Mach 1. Which doesn't make a huge difference in the relative projectile velocity. The extra heating that comes from this just lasts for the transit time of the exit tube, which at their project velocities is on the order of 10 mSec.
3. Their test video shows pretty massive pitch and yaw rates due to conservation of angular momentum and details of the release process, and possible some wind effects from the in rushing air. But the center of pressure of the projectile is far aft of the center of mass so their are massive restoring forces. The large area of the tail fins provides high damping. The upshot is these issues seem manageable.
3. They spend quite a bit of time in the video on their thermal management approach. Basically the tip is made of copper and is followed by a massive aluminum heat sink. The tip does heat to red heat temperatures with somewhat lower temperatures in the aluminum heat sink. The heating drops rapidly during flight due to the projectile slowing and atmosphere thinning. About the time all of this heat is starting to encroach on the second stage the whole outer assembly is discarded, taking all of the heat with it. Proof will be in the pudding but the models look correct.
4. Orbit is achieved with a conventional second stage rocket. The guidance package in this will take out any errors in the ballistic trajectory. One can only guess if they have budgeted the right amount of propellant for this, but again no laws of physics are broken.
5. They have built a centrifuge which achieves the expected g loadings. And have tested many representative components and claim to have successfully hardened them for survival. Photos imply that they have tested components that worried me, such a batteries and they spent a few minutes describing a credible approach to hardening the momentum wheels used for pointing. This includes the skins you are concerned about.
6. Their approach to sonic boom is to put their launcher out in some desert where no one cares. This is in conflict with their need to have access to quite a few megawatts of electrical power to spin up their launcher.
They were very coy about some of the hard parts of the design, claiming proprietary interests but overall they seem to be approaching the problems properly and have solve many. And they are very cavalier about the unbalance on release problem, with just outline sketches of solutions. For those interested in spending 45 minutes here is the link to the video I watched.
I totally agree with Rick Law that economic viability is in real question and it is hard to tell whether they have solved half of their tough problems or 90%.
For Doug Spindler, you don't really understand physics until you put actual numbers against a problem. And an appropriate model. In the airline cases, people were not sucked out of a window, but blown out due to the higher internal pressure. You can actually estimate pressure differences knowing that cabins are usually pressurized to 8000 ft altitude and using either window area or body area to compute force. Of course in the pilots case once his torso was outside there are also drag forces involved.