Just returned from a trip to t'frozen north, Tynemouth to be exact. Went to Durham, Beamish (brilliant), Alnwick & Warkworth Castle. At the latter I bought a working scale model of a trebuchet!
Haven't built it yet, but it will be around 200mm high when finished. Always been fascinated by trebuchets and the plan is to scale up this model so I can build one around 1.2m high.
So, is scaling parts up as simple as it seems? For example, one piece in the kit is 240mm long, if I multiply x 10 it would be 2400mm long - about right. The cross section is 20mm x 12mm, so that would end up as 200mm x
No because if you multiply each dimension by 10, you end up with the volume (and hence the mass) going up by a factor of 1000
240 * 20 * 12 = 57600
2400 * 200 * 120 = 57600000
57600000 / 57600 = 1000
But that doesn't tell us if your original model uses that particular x- section just because it was readily available, or possibly because it "looks right" - rather than it be designed correctly for the stresses on it.
I doubt the medieval designers of the real thing could calculate the stresses either though (and it's a far from simple problem), so maybe just go on experience and instinct.
Masses of online resources:
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simply throwing bricks at non-paying customers would be a lot less hassle.
The maths is really quite fun (this from the Wiki link)
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is the maths of the Roman cross-bow type catapult, which is also very dependent on the properties of the sinew which they used for the springy bits.
Whilst the designers didn't have the modern tools, there was a Scientific American article on the latter a while ago that suggested they had got quite close to the optimum
Basically if you double the size of something (ie, double all dimensions), then the strength of the object is increased by fourfold (ie, 2 squared). However, the volume and weight of stuff required to make it increased by eightfold (ie, 2 cubed). The problem you then run into is the fact that your structure may have trouble supporting its own weight. Triple the size and strength increases by a factor of 9 but the weight of it increases by a factor of 27.
OTOH it's not likely that you'll build a big one out of identical materials to the little one...
I could make this a commercial venture! The original 'Warwolf' could chuck a 100kg ball 200m. It was 20m high, so transport might be a problem, but how much a day could you charge for destroying places like Bluewater?
Actually it sort of does: however the material you use will go up - in the model airplane world - from balsa, to spruce, to aluminium as you progress towards that full size spitfire. ;-)
Trebs are sized by their beam length when dismantled. Mine is exactly one Citroen XM length 8-) (about 2m beam)
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're easy to make and good fun. A 20-bricker is a good starter, in this size. You need a _large_ ratio of weights between projectile and weightbox. IMHE, 20x is just enough and more is definitely more.
Smallest I've had was a beam of carbon fibre kite spar and lead cast into a Coke can, for throwing boiled sweets around the office.
Caerphilly Castle has a nice collection of siege engines, including treb and perrier (aka traction trebuchet)
Get yourself a copy of Payne-Gallwey's splendiferous "The Book of the Crossbow" which has an awful lot on trebs , ballistae etc. Then you can build one of these:
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's a 12" hammer shaft as the throwing beam. I did a 9" for my son.
Scaling is tricky - it defeated Napoleon III when he tried to recreate a medieval castle-smasher. One of the best science books I have _ever_ read is Pennycuick's "Newton Rules Biology". It's an analysis of biological structures in terms of Newtonian scaling laws. Make something twice as long and it will have 2^2 = 4× the area and 2^3 = 8× the volume. This also implies a ratio of surface area / volume that reduces with increasing size, thus making it hard to cool an elephant. Elephant leg strength is also proportional to their leg bone cross-section (i.e. area) which is why they can't jump.
So if you scale up your trebuchet to a 2m beam in 4"×4", it'll be fine. But if you go to a 4m beam, things will start snapping, even if you double the beam thickness. It's impossible to make a trebuchet of military scale, without getting into the innovation of tapering the beam along its length - even if you make it from carbon fibre.
Trebuchet design / simulation programs like WinTreb (probably others too) will help to explain how important the sling and the sling release hook are.
You'll also discover how the trajectory of a treb is a random factor of the release point. They are _not_ controllable, not safe to fly in, and easily capable of hurling bricks either backwards or vertically upwards.
The Spitfire was inspired by medieval trebuchet design, The wing spar is a tapered beam, formed by laminating simple aluminium box sections of varying length. Although broadly constant in cross-section, the wall thickness tapers outwards.
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