But after a quick search, I found that a titanium alloy has an ultimate tensile strength of 900 MPa. With that, I can calculate the width of a beam with a square cross section that can support this force. Actually, as you can see above, it isn’t bad–just 15 centimeters. That’s doable.
What about the power? Power is the rate that you do work (with respect to time). In this case, the work done is the increase in kinetic energy of the spacecraft, where kinetic energy is defined as:
With this change in kinetic energy and a time of 1.5 hours, I get an average power of 103 kilowatts. That’s pretty high, but not crazy high for something like this.
Can It Reach Orbit?
So far everything seems legit. I mean, you shouldn’t build this in your backyard or anything, but from an engineering standpoint it looks possible. But can a system like this actually put a payload in orbit? For that we need to review orbital motion. (This older post also gives a pretty good overview on the topic.)
Let’s say you want to get this payload to low Earth orbit (LEO), like where the International Space Station orbits. You have to do two things: First, you need to get up to orbital height, about 400 kilometers above the surface of the Earth. Second, you have to go fast–real fast. Otherwise you just fall back down.
For LEO, that means the spacecraft needs a final speed of 7,666 meters per second (17,148 mph). Clearly, this spinning launch isn’t going to get the thing all the way into orbit, but it will give it a nice boost.
But wait. There’s another issue–air drag. As soon as this vehicle is launched from the spinner thing, It enters the atmosphere. As it moves through the air, the air pushes back on the craft with a force that depends on its speed (v). We call this the air drag force. It’s the thing you feel when you put your hand out of a moving car window. This force also depends on the density of the air (?), the shape of the object (C), and its cross-sectional area as viewed from the front (A). The magnitude of this force can be modeled (in many but not all) cases as the following: