Multiple Rotations Trebuchet

Growing up in Ohio, I came across this device in inter-school trebuchet competitions. It had performance comparable to a floating arm trebuchet.

This is my assessment of the device. The video clips I am using were used by the creators of the device to plot the motion of the arm, projectile, and counterweight. It was not initially shot for instructional purposes. The simulation, however, is my own.

It was done by using Lagrangian mechanics to find the equations of motion. These were in turn solved using a fourth order runge-kutta.

Conclusion-
Design advantage:

Per chasis size, it has similar counterweight fall distance to FAT and CW always moves vertically. My simulation also indicates that the design is potentially very efficient, but only if well tuned. (Similarly, FATs are only efficient if they are well tuned.)

Also important to note, the multiple rotations trebuchet is mathematically simpler than most other trebuchets(FAT or HCW trebuchet...). In fact, I would hesitate to call anything with a simpler Lagrangian a trebuchet.

-Disadvantages-
Slower reload.
Release system dependent on angle of the arm (You'd think that would be an advantage, but it's not. The sling could be 45 degrees forward or 45 degrees behind.)
If you don't know the CW weight and projectile beforehand,
Good Luck.

Explanation of advantages

In order to understand any discussion of trebuchet efficiency, we must ask what the objective is. Ignoring any discussion of throwing angle, it's making sure that as much energy goes to the projectile as possible and that as little as possible remains in the arm or CW.

A FAT accomplishes this in two ways. First there is an asymptotal relationship between the the motion of the CW and motion of the arm (let's say the vertically constrained guide wheel) as the arm approaches vertical. In other words, if I move the CW a little near vertical, the arm moves a lot. Second, there is the behavior of the sling, whose length is of critical importance to the efficiency of the FAT. (As the simulation shows, a rotating sling and arm that follows path of least action, will have most of the energy transferred to the projectile at certain times.)

In contrast, a multiple rotations trebuchet only utilizes the behavior of the sling. (This is reflected in the far simpler Lagrangian...) This means that while sling length is far more critical than in any other trebuchet, the absence of a fixed dependence on arm angle allows great freedom in deciding throw angle.

Category:

Science & Technology

Tags:

• Trebuchet
• multiple
• rotations
• science
• olympiad
• wtf
• MRT
• FAT
• Lagrange
• Euler
• Runge-kutta
• simulation
• Physics

[NoOne3234]

@ketmaniac True, efficiency gets worse as you increase the number rotations. This is mainly due to the behavior of a free hanging sling rather than friction or wind resistance (at this scale). If kept to around three rotations, this isn't much of a problem. A few more rotations and the disadvantages of a free hanging sling become very noticeable.

I've made FATs before under the same rules. Best one was only 5% better. Far easier to work with, though.

[ketmaniac]

It must have been quite a low-grade competition where this machine came second. A system that uses multiple rotations before release will eat up a big slice of the available energy in friction and air-drag. I can't see it beating a FAT, unless the FAT is not well-tuned (which admittedly they usually aren't).

[NoOne3234]

@Omnigeek6 Sort of, but that would miss the point.

First, the term centrifugal catapult isn't a good term for describing the physics behind either device. It implies that the projectile is sent radially outwards, but in reality it is released tangentially.

Second, that would ignore the value of the sling, which puts almost all of the energy into the projectile. A fixed arm will get a certain fraction of the energy to the projectile, but it really pales in comparison.

[Omnigeek6]

I guess you could consider this similar to a centrifugal catapult, but powered by a weight instead of a motor.