Ad Astra Per Ballista?

Problems To Ponder Whilst Puffing A Perdomo

Got an interesting email from a buddy of mine this week:

Is It Possible?

How big would a trebuchet have to be to place an Apollo sized space
craft in low Earth orbit? Arm length? counter weight mass?

I had to think about that one for a couple of days...

My email reply:

Been thinking about this for a while now…

Couldn’t find any of my old physics textbooks, so I’m gonna wing it.

Is it possible?

The short answer is, probably not. Unless Materials Science gets to the point where we can dump raw material into a hopper, and let nanobots construct the entire thing from the molecular level over the space of years, it would be cost-prohibitive. Much cheaper to build booster rockets.

The Saturn V rocket could boost 262,000 lbs into low earth orbit. To do that it had to burn a metric assload of fuel to hit escape velocity.

According to Wikipedia: On the surface of the Earth, the escape velocity is about 11.2 kilometers per second (~6.96 mi/s), which is approximately 34 times the speed of sound (Mach 34).

That’s pretty fargin’ fast. To get that kind of force out of a trebuchet, you’d have to have one seriously long swingarm.

Using the usual swinging-bucket trebuchet, that long whippy arm would snap under the load. On the version that uses a thick pole with a fixed counterweight at the base, the total weight would probably be too great for the axle bearings. There’s a top-end limit on how large you can forge or machine parts, and the axle would have to be thicker than a sequoia trunk. We’d be talking about a kilometer-long arm, and a 2km high frame with a base area the size of the I-610 loop.

The counter weight would have to allow for not only the mass of the payload, but the weight of the entire arm. I can’t see the swinging-bucket type being usable. Even if you went with a floating-arm trebuchet, the the torsion and flex of that whole thing moving would be unmanageable. No welds or rivets could take the load. It would have to be a monolithic frame, which brings me back the nanobot construction scheme.

Add to that the insane g-forces inflicted on the payload during the fling, and I just don’t see it as feasible.

Probably cheaper to build a Beanstalk!

If there's any physics gurus out there, please feel free to chime in!