Physics of the Trebuchet
The trebuchet is actually two things- a lever and a sling. A lever is a simple machine that gives a mechanical advantage when given a fulcrum, or pivot point. It is often used to move heavy loads with less effort.
A sling is simply a piece of cloth or looped strap in which a stone is whirled and then let fly.
There are three types of levers, a first class
lever is like a see-saw. One end will lift a
The basic parts of a trebuchet include the frame (base), beam (arm), counter weight, sling and, of course, the projectile. Looking at the pictures, you should be able to see that the fulcrum, or pivot point is the place on the base where the arm (beam) balances. When building our trebuchet, this fulcrum, or pivot point was the one place that we had trouble. We couldn't get a dowel big enough to work correctly. In the end, we used the handle of an old shovel (cut off, of course!).
The counter weight is a large mass that hangs on the short arm of the beam. On older models, a person would pull down on the arm to throw the projectile and this would make the person pulling down the arm the counterweight.
The sling is a sack used to hold the projectile until there is enough energy to launch it.
A trebuchet is powered by either gravity (like a heavy load) or by a force that is strong enough to be able to throw the projectile (like a person pulling it back).
When the sling accelerates, it creates an arc shape (actually a parabolic arc) until one end slips off of a pin. The angle at which this happens is called the release angle. Using its own momentum, the projectile continues to fly in an arc shape until falling to the ground.
This is because the motion of objects under the influence of gravity are already going to make parabolas.
Lets describe this in mathematic terms (with a bit of physics):
We have an object being thrown and want to know it's velocity (speed/distance in relation to time)
We can determine the velocity using with a rate of g m/s per second.
This is called the acceleration of gravity. It uses absolute value for gravity (32.2 ft/s2 ).
Let's understand the abbreviations: velocity = v, gravity =g and seconds(time) =t the falling body is dropped.
We can determine distance:
Given the velocity formula , with the integration results in:
where x is the distance an object falls over a time t.
For example, an object falling for 3 seconds would travel 32 x 3 x 3 / 2 = 144 feet
Next, we can think about the velocity with respect to time-
If all of this would be graphed, you would get a parabola! Opening downwards, of course!
If a body is projected upwards with an initial velocity v, then at some time t = v/g, it comes to rest and then begins to fall back. The motion is described by y = vt - gt2/2 at any time, so if this time is substituted, the height of the turning point is found to be y = v2/2g. By a proper choice of the three constants in the general quadratic y = at2 + bt + c, motions under gravity (or any constant acceleration) in one dimension with arbitrary initial position, velocity and time can be described.
So- Get your axes x horizontal and y vertical (going up!)
(Click here for a projectile game from Davidson University, Physics Department)
1) As a machine, the trebuchet is actually a first class lever.
2) The trebuchet makes use also of a simple sling.
3) The sling was able to double the power of trebuchet causing the projectile to go twice as far as it would without it.
4) The sling achieves this with the parabolic arc, thanks to the effect of gravity.
5) The velocity can be determined using the formula- v=gt (velocity equals gravity mutiplied by the amount of time the projectile drops.
6) The projectile moves in the form of a parabolic arc and we can graph this, using the formulas for velocity with respect to time and distance.
7) We also learned that the length of the arm decided the position of the counterweight. We learned that the longer the arm, the more power and velocity could be created.
8) We also drew the conclusion that the weight of the projectile and the the weight of the counterweight are almost as effective as the length of the launching arm.