@wendinoakland

How big a trebuchet is required to fling a typical manned capsule in the ISS' orbit ?

It can't be done!

But why not?

A typical trebuchet is 100% gravity powered. You have a heavy weight at one end of the throwing arm, which is mounted to the frame on an axle. The projectile to be launched is secured in a sling attached to the sling end of the arm, opposite the weight. The weight is hoisted up high by the trebuchet operators, where it has greater gravitational potential energy. When the weight is released it begins to fall, forcing the throwing arm to rotate about its axle. By the time the weight finishes falling, all of the gravitational potential energy imparted by the hoisting has been converted to kinetic energy, some – but not all – of which was transferred to the projectile as the sling swung about the throwing arm.

In order to launch something into space, you have to overcome the force of gravity. You need to supply enough net force over a period of time to reach escape velocity. At this velocity, you'll have enough kinetic energy to make it into space before gravity can stop you and pull you back.

"What's this got to do with trebuchets," you're wondering? Well let's say you have a space capsule loaded in your giant trebuchet sling. For the sake of illustration, pretend our counterweight is the same mass as the capsule. You hoist up the counterweight, increasing its stored gravitational potential energy. If we could raise the counterweight all the way into orbit, and then instantly impart all of its gravitational potential to the capsule as kinetic energy, we'd just barely get into orbit. Obviously we can't raise the weight that high. If we could, why not just hoist the capsule into space instead? And we can't instantly convert potential energy into kinetic energy, let alone transfer it from one object to another in the process.

Instead, we have to start with more potential energy. That means the counterweight must be many times more massive than the capsule. How many times? That depends on the ratio of the weight arm length to the sling arm length. In other words, how much longer is the sling side of the arm than the weight side?

We need the weight to drop fast, so the weight side of the arm needs to be relatively short. We'll say 10ft. Now let's say our weight drops in 1 second. To reach low earth orbit, we need to accelerate the capsule to about 17,000mph = 7600m/s. To reach that velocity during the 1s fall, we'll need to accelerate at 7600m/s². That's nearly 800 times the acceleration imparted by the force of gravity!

Our weight falls under the normal force of gravity, or 1G. To impart 800G to the capsule, we need the sling side of the arm to be 800G/1G = 800x longer than the weight side. The weight side is 10ft, so the sling side is 8000ft. That's over 1.5 miles long!

Let's say our crew capsule is about 5,000kg and it's a one way trip for the poor souls on board (they'll be dead long before they get to space, after all, as humans can't survive an even a fraction of our 800G acceleration). Since the sling side of the arm is 800x longer than the weight side, and we need the weight falling around 1G, it should be in the ballpark of 800x more massive than the capsule. 800 * 5,000kg = 40,000,000kg. That's ¾ of the mass of the Titanic. And it needs to fit on the end of the 10ft weight arm! The strength of the throwing arm would need to be impossibly high, seeing as it's nearly 2 miles long with a space capsule at one end and an ocean liner at the other.

Even if you could build this thing, your capsule would surely be incinerated by atmospheric drag, likely before even making it out of the sling!

Goal: launch astronauts into space with a trebuchet. Result: astronauts torn limb from limb by tremendous G forces and then everything explodes violently into flame, all within a fraction of a second. Mission accomplished.

https://www.reddit.com/r/theydidthemath/comments/4q86cj/request_how_big_a_trebuchet_is_required_to_fling/

it is easier just to send them to the titanic.

https://en.wikipedia.org/wiki/Titan_submersible_implosion

#oceangate

@missbullitt @TidalFlats @glasspusher @Kierkegaanks