All beginning trebuchet builders must make such a model and study it well before attempting a larger one.
This one would throw 12 yards.
It is not made to look at.
The trebuchet is an ancient siege engine used for throwing large rocks. It was invented in China in about the 4th century BC, came to Europe in the 6th century AD, and did not become obsolete until the 16th century, well after the introduction of gunpowder.
There are various kinds of trebuchets. The latest and best kind consists of a long pivoting beam, a very heavy counterweight swinging from a hinge at one end, and a sling with a big rock hooked to the other. A frame holds it all together and there is a track on the ground. When released the weight drops, the beam rotates, and the rock slides down the track in the sling. When free of the track the sling rotates very quickly up and over the beam and slips off a hook. The rock spills out of the sling and flies away.
Trebuchets are not to be confused with catapults. Catapults are sad little things. Trebuchets are much better than catapults. A really large trebuchet can reach out and squish a catapult with a half ton rock at 200 yards or more.
It is customary to mention that trebuchets were sometimes used to hurl Greek fire, dead animals, severed heads, and live POWs; but the usual missile was simply a big round rock.
This is a little toy trebuchet that I made to learn on.
All beginning trebuchet builders must make such a model and study it well before attempting a larger one.
This one would throw 12 yards.
It is not made to look at.
The 8 pound weight is a square steel bar with a couple of side plates crudely arc welded on. Drill the holes first and pass a rod through to align them during welding. The secondary weight tied on with bailing wire was just an experiment; it did not help much.
The uprights are 2x4 lumber. The track is a pair of sticks nailed to the base. The missile just hangs on a string that loops around a headless nail in the end of the beam.
This is my first proper trebuchet.
The beam is a tapered Douglas Fir 2x4. I found this apparently unique knot free specimen at a lumber yard where they kept it indoors in a jewel case with a $15 price tag on it. The axle is a 1 inch 1 foot steel bar; weight 2.7 pounds. The blocks glued to the sides of the beam reduces side shake and improved accuracy slightly. The spacers are PVC pipe. Short end is 9 inches; long end is 37 inches. Weighs 6.3 pounds without axle. Height to axle is 25 inches.
The frame is built of scrap 2x4 lumber and a plywood base held together with screws.
It is sized so that it will just fit in the back of my Toyota station wagon
or else bolted on top of it.
The bearings are just a couple of holes drilled in the wood.
Bore two nice holes with a Forstner bit and saw down to form a round bottom notch.
The axle just sits in that notch in a little grease; there is no tendency for it to hop out.
The track is a pair of oak boards set at 45° to form a 90° trough. Make them smooth and straight; accuracy depends on it.
The counterweight is cast concrete, 8 inches wide, 15 inch radius from the pivot hole to the curve of the concrete, 108 pounds total. Mold is made of two plywood arcs with holes at the center. Nail two wood squares on the ends and sheet metal on the bottom curve. The two 14 x ½ x 1½ inch rectangular steel bars have a 1/2 inch hole in each end. (Dimensions dictated by the first suitable bar I found in my junk pile.) Grind them down to bright metal so the cement sticks well. Cross bar deep inside keeps them from pulling out. A long bar through the pivot holes and mold sides keeps all in alignment while the concrete sets. Reinforcing rods inside keeps weight from flying apart in case of cracks. Mix the concrete with minimum water; pack it in well. Keep it damp and let it cure 4 days. Gently cut off the mold and round off the sharp corners; scrub it with water and wire brush. Let it cure 3 more weeks before use. Don't skimp on the cure time. The concrete I bought happened to have a density of 180 pounds per cubic foot; somewhat denser than normal. Read the concrete sack before buying, if it says 'lightweight' keep shopping.
I don't think this is how they were made 700 years ago. They probably would have used reinforced concrete if they had it back then but it would not have done them any good because the castles would also have been made of reinforced concrete.
The Trigger is a small steel plate with a hole in it welded to a rod. The end of the rod is bent to form a lever. The angle of the plate is critical, set it at a right angle to the pin. The beam must cam down slightly when the lever is lifted; that insures that friction is not being depended upon. This design will only work on a small trebuchet; a large one made this way will break.
The sling is made from heavy cord and cloth. The cord is a continuous loop. The thimble is turned in an engine lathe from aluminum bar stock. Metal on metal friction gives consistent release and reduces wear on the cord. The pouch is a cloth tube. It is sewn to the cord in the two corners nearest the beam to keep it from slipping.
The pin on the end of the beam holds one end of the sling until it has whipped around into release position.
An angle of 20° to 30° seems to work.
The first pin was a little crooked so I pulled it out and made a new one with a little more hook.
That was a bad move; it did not change the average range but it did cause very great variations of 10 feet or more.
Probably because it was releasing while the beam was quivering at the top of it's arc.
I changed it back and all was well.
The missile is a one pound lead ball; a deep sea fishing weight. At first I omitted the sling and just tied a string to a washer. This worked fine. Adjustments were easy and there was no chance of tangling. Accuracy was good. The string makes the ball easy to find when it is sunk into the ground. Countersink and polish the washer so the cord does not fray so much. The string trails behind in flight but does not slow it down noticeably. After the ball was well mangled I found that accuracy could be improved by carefully placing the biggest dent on the track the same way each time.
The range of T1 is 145 feet. It will hit a 40 gallon garbage can much of the time. The angle of fall is slightly steeper than the angle of departure; so tall targets are easier than wide ones.
Another view of the assembly.
The statistics:
I took T1 to Burning Man 1998 where it performed very well until someone burned it.
The Beam The beam must be made very light and at the same time very strong. If you have to hire a professional engineer this is the part to spend your money on. The long end is usually made about 3.0 to 4.5 times longer than the short end.
Wood is the usual material. Pick something with a high ratio of strength to weight. (In the old days you would just cut down one of the enemy's own trees; what's he going to do about it cooped up in his castle?)
If a rectangular beam is tapered so that the side view is in the shape of a parabola the strength will be the same as that of a rectangle but the mass will be just 2/3 and the moment of inertia will be even less. T1's beam was made that way except that it also had some side taper. The best thing is to make the beam maybe 3 or 4 times stronger in the vertical direction than it's side direction; strong enough vertically to hurl the rock and strong enough sideways to prevent buckling.
If you want to show off get yourself a copy of 'Dialogues Concerning Two New Sciences' by Galileo Galilei. Look for the picture of the beam sticking out if the stone wall. Pretend you got the design from him; that's where I got it from.
| d = D ( x / L ) 1/3 Where: |
|
d = Diameter at any point x. D = Diameter at the big end where the axle is. x = Variable distance starting from 0 at the small end and ending with x=L at the big end. L = Length overall from sling hook to axle. |
The picture below is of a beam with a circular cross section and tapered like a cubic parabola.
The strength of a round bar varies as the cube of it's diameter.
Half way up the beam the load is only half as much as at the pivot so the diameter at that point only needs to be the cube root of half of the diameter of the thick end or 79%.
(The cube of 0.79 is 0.5).
A plane round bar with a heavy load hanging on one end will break at the fixed end, but if that bar is tapered like this it will be uniformly strong throughout it's length.
There is no use making any given point of the beam any stronger than at any other point; it will break at the weakest point just the same.
The trouble with a round beam with this shape is that it has equal strength in all directions like a fishing pole.
You should use the first design above which is a rectangle top view and a parabola side view since it needs to be strongest in only one direction.
There are many other possible shapes. Look in any Engineering textbook for designs of a 'beam of uniform strength with the load concentrated at one end'.
The Sling
The length of the sling is very important. By changing the sling length the shot may be made to go up, forward, down, of even backward.
Start with a sling about 3/4 the length of the upper end of the beam.
The greatest range occurs with a 40-45° angle of departure.
If the rock goes too high the sling is releasing too soon because it swings too fast; lengthen it some.
If the rock goes too low the sling is too long; shorten it.
When you are getting close to 45° the range will not vary much even though the angle does.
Measure the range of each trial shot and write it on the beam opposite the end on the sling.
If the sling is made very much too short - roughly half it's proper length - the rock will go straight up.
If this should occur the correct response is to run away very fast.
The Counterweight The counterweight should weigh about 80 to 100 times as much as the missile. It does not matter whether you use 'weight' units or 'mass' units as long as they are used consistently. If the counterweight is too light the beam will swing slowly and hesitantly and the shot will fall disappointingly short. If the counterweight is too heavy the shot will go a little further but not very much. That weight is simply not going to fall any faster, Galileo figured that out around 1604. The arm and the weight will thrash about after the shot is gone and that is a sign of wasted energy. In combat that energy comes from the labor of your sweaty arrow dodging grunts; it would be a shame to waste it. If the trebuchet is 'dry fired' with no missile at all it will hop and kick and buck and threaten to tear itself apart; don't do that. When all is balanced just right the beam will swing smartly to the top, the swinging weight will bring it nearly to a stop, the sling will whip around very quickly, the rock will spill out when the beam is near the top and will fly off on a path that is tangent to the arc of the sling and 45° to the ground. The beam will stay upright and sway a little and the weight will rock gently, a sure sign that most of the energy has been transferred to the missile. 70% efficiency is not too great to aspire to.
Scaling Trebuchets scale well. The lengths scale directly. The areas scale as the square of the lengths. The volumes, masses, and weights scale as the cubes of the lengths. A trebuchet made twice as large would throw a rock twice as big, eight times as heavy, and twice as far. It's counterweight would be eight times heaver, the beam twice as long, and it would take sixteen times as much work to cock. The only problem is that the areas only increase as the square of the size. This causes the weights and masses increase faster than the strengths of those same parts. If made too large it would just collapse under it's own weight. That is why anybody can make a small trebuchet that works but few can make a successful large one. That is also the reason why giant mutant Hollywood movie insects are impossible no matter how much radiation they have been exposed to.
Order of design
Many people have made tall spindly trebuchets and then wondered why they don't work so well.
I think it happens because they start with the beam or frame and then skimp on the counterweight after they find they made the other parts too light.
Remember that skyscrapers are designed from the top down; each floor being made strong enough to support the floors above it.
This order of design should yield good results:
Here are some handy formulae.
They are very rough and their results correspond only roughly to reality.
They contain 'fudge factors' and do not account for friction.
The derivations are omitted because mathematicians can figure it out themselves, students need the practice, non mathematicians don't care, and I lost my notes.
The names of the variables:
R = V2 sin (2 AngleOfDeparture) / 32.2
sin (2 45°) = 1
PE = Wc Hw
KE = Wp T2 / k
At 45°
Energy Efficiency = KE / PE
Trebuchets are subtle and tricky things. The information above is not sufficient to enable you to make your own trebuchet. To do that you must first do the research and the place to start is the Grey Company Trebuchet Page web page in Western Australia.
And here are some paper things to read:
"Mechanical engineers design weapons;
Civil engineers design targets."
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