This month, the Evil Engineer examines whether a machine that was outdated by 1500 could be repurposed for a very modern industry.
Dear Evil Engineer,
After several years working for a reusable rocket start-up in the US, I feel ready to take a risk and start my own business. I am interested in stylish, sustainable alternatives to rocket launches – something to set my offering apart from all of those the other private space companies jostling for contracts. My big idea is to revive and reimagine an iconic bit of engineering history: the trebuchet.
We have access to materials and techniques today that would allow for trebuchets of unprecedented size to be constructed, if there is a business case for it, and I know from my years in the industry that there is demand for cheaper, lower-carbon launches. But is it possible to launch a satellite into orbit with a trebuchet?
Not quite a villain
Dear Not quite a villain,
It’s always encouraging to hear that a bright young engineer is examining all sorts of exciting possibilities for a start-up of their own. I hope you will consider joining the Institution of Evil & Treachery, where you can access a wealth of resources to help you develop the skills you need to move to the next stage of your career. Unfortunately, there is little that I or the Institution can do to help with this particular venture – a gravity-powered machine like a trebuchet is just not going to pack enough of a punch to put a satellite into orbit.
A trebuchet is a kind of catapult. It flings a projectile from a sling attached to the end of a beam, which rotates around an axle suspended high above the ground. When we think of trebuchets, we tend to think of counterweight trebuchets rather than manual trebuchets – counterweight trebuchets call for a heavy weight to be raised and released, the force of which causes rotational acceleration of the beam around the axle.
In the simplest terms, a trebuchet converts the gravitational potential energy of the counterweight into kinetic energy of the payload. In theory, we can write this as: mcgh = ½mpv2. In reality, the transfer of energy is not perfectly efficient. Some is lost to friction within the mechanism, some to the rotating beam, and some remains in the counterweight as kinetic energy as it swings to a halt after launch.
The mechanics of such a system are far from trivial and cannot be unpacked within the confines of this correspondence. However, a helpful paper by Donald B Siano, Trebuchet mechanics (2001), can guide us. It proposed that the optimal configuration for a trebuchet is as follows: the beam angled at 45°; the projectile side of the beam four times longer than the counterweight side; the length of the sling equal to the length of the projectile side of the beam; and the counterweight around 100 times the mass of the projectile. Like this, Siano calculated, a trebuchet could reach energy efficiency of 0.73. Using this figure, we can make a rough estimate for the specs a trebuchet would require to send a payload into orbit. To make this as easy as possible, let’s say our payload is a typical CubeSat weighing 1.5kg, and let’s not worry about what happens after launch (e.g. surviving under those extreme conditions and maintaining a stable orbit).
We need to accelerate the payload to 7600m/s to reach orbit. So, if we begin by following Siano’s suggestion and using a counterweight 100 times the mass of the payload, 150kg, how far will we need to drop that counterweight to reach that velocity? Pop the numbers into the energy equation above, and we see the counterweight would need to be dropped from a height of 40km.
The last thing I want to do is to trample on the aspirations of other engineers. However, I doubt that even the best among us would be capable of building a moving structure almost 50 times taller than the Burj Khalifa. Raising the counterweight would take you almost halfway to ‘space’ already – the Kármán line being 100km above the Earth’s surface.
Perhaps we could reduce the height and compensate with a larger counterweight? While Siano recommends a counterweight-projectile mass ratio of 100, his paper does not show efficiency falling after this point, rather levelling off. A ratio of 10,000 would call for a 15-tonne counterweight – unwieldly, but just about manageable with a powerful crane. Plug that into the equation, and we get a minimum drop height of 400m. No crane is large enough to hoist a counterweight that far, and – to the best of my knowledge – no material could tolerate the forces in such a massive moving structure. Even in this simplified model, it does not appear feasible to build a trebuchet large enough to accelerate payloads to orbital velocity.
Do not be disheartened. For well over a century, there has been excitable speculation about alternative ways to launch things into orbit – space guns, planes, tethers and elevators. Perhaps by deviating a little from the historical trebuchet form factor – by innovating – you too could develop a new launch system to compete with expendable rockets. I’ll be watching that space with interest!
The Evil Engineer
Sign up to the E&T News e-mail to get great stories like this delivered to your inbox every day.