Hello and welcome to this video on trebuchet
physics, design, and tuning. Keep watching and I'll not only teach you
trebuchet physics, I'll show you how to make an efficient trebuchet and improve the distance
of your throws. So, how should we view a trebuchet? Many people see it as an uneven teeter totter,
with a fat guy on the short end and a baby on the other. With a ratio of roughly one to four, the larger
guy will somehow launch the other high in the air. You see this in plenty of movies, but a trebuchet
operating purely as a lever won't throw very far. I'll show you several tricks or energy transfer
mechanisms that will allow you to throw farther. It's probably best to start with a review
of conservation of energy. Let's say that I have a stationary counterweight
on a frictionless ramp. This counterweight is height h above the bottom
of the ramp and has mass m. It will have energy, mgh. At the bottom, it will have kinetic energy,
1/2m(V)^2. By conservation of energy, E=mgh=1/2mv^2. We can add a second object to represent the
projectile and accelerate it from velocity a of 0 to v2. We do this by somehow transferring energy
from the falling weight to the projectile. This adds the projectile's Kinetic energy
to our equation Now, we have to divide the energy between
the counterweight and the projectile. In other words, the projectile is fastest
if the weight is stationary. This creates a very simple rule to judge success:
If your arm and counterweight are moving fast at the point of release, you are doing it
wrong. I am going to show several energy transfer
mechanisms. Together, these will transfer most of the
energy from the counterweight to the projectile. I'll start with the lever, which is an important
feature of all trebuchets. Levers provide a fixed movement ratio between
the projectile end of the arm and the CW end of
the arm. However, as I said earlier, a 1:4 ratio arm
isn't going to throw anything very far on its own. To do better, you'll want a sling. Contrary to popular belief, slings are not
just a convenient release system. They are an impressive energy transfer mechanism. Don't believe me? Watch this slow motion clip. Here, the sling unfurls, stalling the arm
and the counterweight. Most of the energy is in the projectile, making
this a good release point. The multiple rotations trebuchet is an extreme
example that relies almost entirely on sling stalls. As shown in this simulation, the trebuchet
undergoes several sling stall points. Since sling stall position is a major factor
in trebuchet efficiency, here are some sling stall tuning tips:
If you want an earlier sling stall, shorten the sling. If you want a later sling stall, make the
sling longer. In conclusion, sling length determines sling
stall point. Before discussing the ideal sling stall point,
we have to address an issue on the other end... A counterweight fixed directly to the arm
is an energy hog. It's big, heavy andusually retains a lot of
energy at the bottom... Medieval engineers had a very elegant solution. They would hang the counterweight from the
arm... Here's another slow motion clip... The beauty of this mechanism can be seen when
I plot the motion of the arm and counterweight. The counterweight falls almost straight down,
stops, makes a sharp turn and gets pulled parallel to the ground. This creates a counterweight-arm stall point. Here, the hanging counterweight mechanism
transfers almost all of the energy from the Counterweight to the arm. Syncing the sling stall point with this counterweight
stall point, results in a very efficient throw. Note how still everything is at the end. Be warned, past our counterweight stall point,
the counterweight actually pulls against the arm. While it's ok to release slightly after the
stall point, don't release too long after. With this in mind, knowing how far to hang
your counterweight is important. Here's how to find the stall point for a given
hanging counterweight length. Hold the counterweight at the launch position... Then pull it straight down. When you can't pull down any further without
moving side to side, you are at the stall point. This is an OK length... For reference, here is one that is way too
short. You're not going to get a good release off
of this. Of course, the hanging CW trebuchet sacrifices
counterweight fall distance for this efficiency. This means that it isn't viable for height
constrained competitions. Here are several modern designs that you should
look into. The floating arm trebuchet uses rails to constrain
the counterweight vertically and to allow the arm pivot to move horizontally. This has a counterweight stall when the arm
is vertical, but doesn't trade off fall distance. I highly recommend this design. Multiple rotations trebuchets are actually
surprisingly efficient if you can get the sling stall points right and have a certain
novelty factor... They are very unforgiving. Here is an interesting twist on hanging counterweight
trebuchets... From what I've seen, the nicest ones have
wheels or a floating arm. There are countless other variations, but
I won't discuss them. If this video was useful, please like, subscribe
or check out some of my others.
