Whips and Chains

As a kid, I played around with launching paper clips or folded bits of paper by placing the projectile in the middle of a piece of string, then quickly pulling on the ends of the string. With some practice, you can get some respectable velocity. Inevitably, I started to fantasize about using the same principal at a large scale to launch spacecraft. The figure below shows one possible configuration. Imagine two subsonic transports each trailing a tether that is attached to a projectile vehicle. At the beginning of the sequence, the transports begin to turn in opposite directions. A wave propagates down the tether, resulting in a whipping action that accelerates the projectile to a speed that is much larger than the original transport speed. As the tether pulls taught, the projectile reaches a maximum velocity and releases. At the same time, the two tethers disconnect from each other so that the transports do not yank themselves out of the sky. Pretty wild, and probably impractical, but the whole point of this blog and website is to numerically examine the possibilities. If I can prove it doesn’t work, then I don’t have to waste any more brain time imagining whipping payloads into space.

I now have some tools for simulating the process. The chain model discussed in the last posting works beautifully for setting up the problem (and thus my overly clever post title).  I didn’t spend a lot of time trying to optimize all the parameters. There is a study on the main website that goes into the details. Briefly, I assumed the initial speed of the transports was 300 m/sec (high subsonic speed), and the transports make a 2g turn (4.6 km turning radius). The tethers are graphite fiber, 14 km long, and 3.5 cm in diameter. The mass of a tether is 25,000 kg, which should be manageable for a 747 class transport. For a 1000 kg projectile, the simulation gave a 2.2 km/sec launch velocity. Pretty respectable. Note that I have not included aerodynamic drag. Drag will go up dramatically at supersonic speeds and that could well kill the whole idea. An animation of the tether trajectory is shown at the bottom of the post (visible if you have the Wolfram CDF add-on installed on your browser). In the animation, the red dot represents the payload. A velocity function is applied to the opposite end of the chain to simulate the path of the transports. In the simulation, the projectile is not actually released. We run the model a bit past the point of maximum velocity.

The trouble with the 2.2 km/sec launch is that just before the peak velocity, the stress in the tether is well above the possible strength of current materials. One trick is to release everything a bit before the peak. Releasing 2 seconds before the peak reduces the launch velocity to 1.1 km/sec, while keeping the tensile stress down to the range of possible. Thus, the whipping action can be used to magnify the transport speed by about a factor of three. Just before release, the acceleration of the projectile is around 15g’s; too high for people and delicate payloads. For the same tether and stress level, you can accelerate a 10,000 kg projectile to 870 m/sec.

In the end I failed to disprove the idea would work and thus exorcise the fantasy. At this level of simulation, it sort-of works, but there are lots of problems. As I mentioned, aerodynamic drag would be significant. Also, the simulation is two-dimensional. Even with aerodynamic lift, the tethers will drop below the altitude of the transports. And in the end, it is not clear whether flying multiple transports and dealing with long cables could be justified to gain a 800 m/sec kick-start on the way to orbit.

I did find one reference to a vaguely similar concept posted by Dmytry Lavrovon the web. He mentions a student competition paper, but I was not able to find the original paper. His study involved propagating waves on a tether as an accelerator, but in a space vacuum. Another distant relative is called the Kinetics Interchange TEther (KITE) Launcher which has a patent application by Dana Johansen. As the Kite name implies, it uses a combination of aerodynamic forces and a tether connected to a large transport to build up a projectile velocity larger than the transport initial velocity.

 


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