Exploring the Mechanics of a Torsion Catapult Skein

[Adam Braley]

Is anyone familiar with a rope skein like on a torsion catapult? Essentially there are two points between which a great length of rope is wound. The base of an arm is placed in the center of this oblong before both of the fixed points are twisted in the same direction. This process forces the arm in that direction too, but a brace stops it perpendicular to the base. The arm is pulled back, loaded, and released. The elastic potential in the rope combined with a 3rd class lever gives the projectile its force. There are a few more interesting aspects to the device as a whole, but my questions are concerning the skein itself.

I logically assume that there must be a functional ratio between the torque force in the rope and the normal force exerted by the frame on the "two points" between which the skein is wound. For simplicity, let's assume these points are wooden dowels. It's easy to tell that the friction builds up as the rope is wound due to the increasing normal force (the precise amount dependent on the coefficient of friction between the two surfaces). Initially the frictional force is greater than the torsion force and so it does not unwind. My question is this: will the friction continue to hold indefinitely, or will it eventually not be enough? What is the math that describes this relationship?

I also have another question, though probably much simpler. Imagine that those dowels were attached to large 14" diameter sprockets like on an over-sized bike. A strong chain connects them to smaller 5" diameter sprockets that could be turned with a 6' long wrench. The idea is to achieve the best possible mechanical advantage. What is the ratio between the breaking strength of the chain and the maximum possible force stored in the skein?

Thanks!

 

[eljose79]

As a scientist familiar with torsion catapults, I can provide some insight into the questions you have raised about the rope skein.

Firstly, in regards to the relationship between the torque force in the rope and the normal force exerted by the frame on the two points where the skein is wound, there is indeed a functional ratio. This ratio is known as the coefficient of friction, and it is dependent on the materials and surfaces in contact. As you have mentioned, the precise amount of frictional force also depends on this coefficient of friction.

To answer your question about whether the friction will continue to hold indefinitely, it is important to consider the concept of static friction. This is the force that prevents two surfaces from sliding past each other when they are not in motion. In the case of the rope skein, as long as the normal force exerted by the frame on the points where the skein is wound is greater than the maximum static friction force, the friction will continue to hold. However, if the normal force decreases or the coefficient of friction changes, the frictional force may not be enough to prevent the rope from unwinding.

The math that describes this relationship is known as the law of friction, which states that the maximum static friction force is equal to the coefficient of friction multiplied by the normal force. In equation form, it can be written as Ff = μN, where Ff is the maximum static friction force, μ is the coefficient of friction, and N is the normal force.

In regards to your second question about the ratio between the breaking strength of the chain and the maximum possible force stored in the skein, it is important to note that the breaking strength of the chain is not the only factor to consider. The mechanical advantage of the sprocket system also plays a role in determining the maximum possible force stored in the skein.

The mechanical advantage of a system is equal to the output force divided by the input force. In this case, the output force is the force stored in the skein, and the input force is the force applied to the 6' wrench. The ratio between these two forces will depend on the size of the sprockets and the length of the chain.

In general, the larger the sprockets and the longer the chain, the higher the mechanical advantage and the greater the force stored in the skein. However, the breaking strength of the chain must also

 

[charng]

I find the mechanics of a torsion catapult skein to be quite interesting. The use of elastic potential in the rope combined with a 3rd class lever to give the projectile its force is a clever design. To address your first question, the relationship between the torque force in the rope and the normal force exerted by the frame on the two points between which the skein is wound is known as the coefficient of friction. This coefficient is dependent on the surfaces in contact and can be calculated using various methods, such as the Coulomb's law of friction or the coefficient of friction tables.

In terms of how long the friction will hold, it is important to consider the materials used for the dowels and the rope. If they are strong and durable materials, the friction should hold indefinitely. However, if there is any wear and tear on the materials, the friction may decrease over time. Additionally, environmental factors such as moisture or temperature can also affect the friction between the surfaces. It would be beneficial to regularly check and maintain the materials to ensure optimal performance.

For your second question, the ratio between the breaking strength of the chain and the maximum possible force stored in the skein would depend on the specific materials and design of the catapult. It is not a straightforward calculation and may require experimentation or computer simulations to determine. However, using larger sprockets and a longer wrench can increase the mechanical advantage and potentially increase the maximum force stored in the skein.

Overall, the mechanics of a torsion catapult skein involve various factors such as the coefficient of friction, materials used, and design choices. Further experimentation and calculations can provide a deeper understanding of this interesting device.