Catapulting & Trebuchet Physics: A Beginner's Guide

[badger5149]

I will try and cut to the chase here. My recent hobby involoves variations of catapults and trebuchets. I am finding a need for some physics in rotional mass type situations. I have no background in math beyond basic arithmatic but I have always been pretty good with math logic in a general sense.
My question is this, I don't have a need for precise answers as much as I do rounded reasonable figures for starting tuning processes and exploring feasability of designs. One method I have been using that I am not too sure of is to find the point on a rotating mass that seems to be the center of mass and then applying all the mass at that point of rotaion and simply calculating the kinetic energy based on the speed at the particular radius point I have figured to be the center. Will this give me reasonably close numbers? Steve

 

[thespaceman]

I am a little unclear on the question so if I fail to answer it please let me know. Are you simply trying to calculate the kinetic energy of a projectile? If so the center of mass is an unnecessary. It is true however that you can assume that the mass of an object is concentrated at the center of mass. The kinetic energy is given by K=(1/2)*(mass)*(velocity)^2. Therefore all you need is the mass of the object and the velocity at which it travels.
Why is it that you need the kinetic energy of the projectile?

 

[badger5149]

You did partialy answer the question and thank you for the reply. What I am building is a cross beween a centrifical machine and a standard trebuchet. One of the challeges of this sport is t try and reinvent the wheel so to speak and my particular facination is with efficiency as opposed to brute force. The model I have in mind is similar to a yo yo that does not come back up, I think I need to know the speed at the center of mass so that as this spinning weight releases a sling with a known weight projectile so that I can determine the length of sling needed to sap the energy out of the spinning weight in a relatively short time span. The only constants I have are the weight which is 5,000# and will be raised 20 ft, the weight of the projectile is 10# and will require about 60,000# to get it up to 600 fps. At present 50% efficiency is considered a super machine and my goal is to reach 60%. Primarily by reducing friction and virtual mass of the machine. In all honest the design does not look all that promising but I do want to play it out as sometimes a new idea is spawned while I have a work in progress. The yo yo, axle and sling length just need to be ballanced out as to make it workable so the efficiency can be physicaly tested. Idea is based on 80% transfer to yo you and 80% of that transferred to sling. Thanks again, Steve

 

[thespaceman]

From what I understand you want to store energy in the form of rotational kinetic energy so that you may use it in addition to the counterweight to produce an overwhelmingly awesome trebuchet. For a rotating object the center of mass is also the rotating axis and therefore does not have any velocity, it is still. Now to store the energy I suggest a fly wheel which can store it in the form of rotational energy given by
K=(1/2)*(moment of inertia)* (angular velocity)^2.
The moment of inertia depends on the geometry of an object, but for the simplest case of a solid cylinder it is given by,
(moment of inertia)= (1/2)*(mass)*(radius).
The angular velocity is given by,
(angular velocity)=(linear velocity)*(radius). Where the linear velocity is taken to be any point on the wheel and the radius is the distance from the center to that point.
I think this is a really cool idea and I am interested in how you plan on transferring the rotational kinetic energy to the projectile.

 

[badger5149]

Spaceman, my biggest challenge here is to efficiently as possible use a very large weight to propel a very light projectile. The projectile will be about 1/5000 of the potential energy. This is close to a dryfire so keeping the virtual mass of the machine low is the biggest challenge. I am using a centrifical drag system to introduce the sling into the rotating mass. The sling ideally will be much longer than is now considered feasbale, I am hoping a tuned release may make this possible. The throwing arm is probably the biggest robber of energy in the treb, I think normal ratios are slings no more than about 2/3 the length of the arm, I want the sling at least double or triple the length of the arm. I am somewhat isolating myself from the current thought processes on building these machines for a reason even though I do find myself checking in on certain aspects here and their. Thanks for your help. Steve

one last thing, the reason I needed to know about the center of mass in a rotating object was so that I could figure out how much of the potential energy was being transferred to the wheel in the form of kinetic energy, I was using the speed at the center of mass point as a place to measure kinetic energy. Steve

 

[Feldoh]

I have been using that I am not too sure of is to find the point on a rotating mass that seems to be the center of mass and then applying all the mass at that point of rotaion and simply calculating the kinetic energy based on the speed at the particular radius point I have figured to be the center. Will this give me reasonably close numbers? Steve

The only way I could see your method working is if the lever arm is really light compared to the projectile AND the projectile's radius would need to be a lot smaller than the length of your level arm. That way your system would approximately consist of just a point mass at some distance from the point of rotation. A great way to do this might be carbon fiber composite as the lever perhaps?

The problem is that the lever arm also has (probably) a decent mass which needs to be taken into account at the system is rotated.. What you want to do is calculate the moment of inertia of the lever/projectile combined and then you would be in business.

EDIT: I just read your last post and you seem to be on the right track to making your approximations come out to be somewhat correct.

 

[Donaldson]

I will try and cut to the chase here. My recent hobby involoves variations of catapults and trebuchets. I am finding a need for some physics in rotional mass type situations. I have no background in math beyond basic arithmatic but I have always been pretty good with math logic in a general sense.
My question is this, I don't have a need for precise answers as much as I do rounded reasonable figures for starting tuning processes and exploring feasability of designs. One method I have been using that I am not too sure of is to find the point on a rotating mass that seems to be the center of mass and then applying all the mass at that point of rotaion and simply calculating the kinetic energy based on the speed at the particular radius point I have figured to be the center. Will this give me reasonably close numbers? Steve

Just curious but is this for some kind of LARPing stuff? I just wondering because I can't think of a use for trebuchets unless your planning to besiege a castle.

 

[badger5149]

Greg, actualy my background is in primitive archery flightshooting, going for world record distances. I have set a couple of records here. I was asked to build a giant bow for the discovery channel on a Doing Da vinci series catapult and it got me interested in the siege machines which are used in the pumpkin chunkin contest. I want to try and set a new record in that competition. Being a begainer I figure it might take me a few years to be competitive, I am hoping for two years.
One more question, I am building scale models to start, the best system I can come up with is each time I cut the unit in half I divide the counterweigt mass by 8, the projectile mass by 4 and the projected velocity by 2, does this sound reasonable to you. These numbers would give me an identical projected efficiency so I am thinking they are correct. Thanks for your time, Steve