Understanding Mechanics of Bows & Crossbows - Seeking Advice

[3trQN]

I'm trying to understand the mechanics of bows, i haven't studied much material science or physics so I am having some trouble progressing.

I am trying to calculate and/or derive a method of calculating the power of a bow of specific length and curve.

To simplify it i am assuming initially that the bow is a single curve of a uniform rod. I will be comparing materials.

Does anyone have any suggestions on how best to go about this? I keep hitting a brick wall :s

 

[Danger]

I'm afraid that I can't help with any formulae or even the specific physics involved, but I do know that bows are actually quite complicated when you get into the real ones rather than the simplified one that you propose.
In your case, I suspect that you would just treat the thing as a leaf spring or a severely bent beam and use the math involved in those fields. I might be wrong about that, but it seems to me that that's what you've 'boiled-down' the problem to.

 

[SF]

Mentally imagine that you have to calculate the elastic force for the following parts: half the body and half the spring.
Manually determine the elastic constants then calculate the total force.

But remember, this is only for one curve/length; problem is: a bow with a different curve/length will have different constants.
You'll have to analyse many bows made of the same material before you can discover the pattern.

 

[3trQN]

Thanks for the advice.

I was thinking along the same lines as Danger, and attempting to simplify it initially using Hooks law for leaf spring and beam mechanics formulae etc.

But I intend to take it further and attempt to calculate certain composite and recurve bow characteristics, maybe even simulating the stresses.

 

[Clausius2]

Believe or not one can make a lot of calculations with bows. Your structure can be envisaged as an arch with two vertical supports that have an initial displacement. One can employ the so called Navier-Bresse equations, the same ones that you use for straight beams, but assuming that the aspect ratio of the beam is large enough for considering unidimensional tensional states. Some other energetic theorems of the resistance of materials can help you for calculating the total elastic energy stored in the bow. And I think that the elastic energy has to have a relation with the power of the arrow. Take a look at Timoshenko or similar books. Calculation of high difficulty level though...

 

[3trQN]

Thanks, although I'm not getting into the Finite Element method just yet, it is something I've got chalked up to learn more about later. I had never heard of Timoshenko until you mentioned him, for shame!, thanks for that.

 

[My user name]

probably the easist way without much math would be to get yourself a scale and mount so you can mesure the pull. for instance the bow i hunt with has a 60 pound pull max. that's with a 26" draw with a string length of 37". it is a compound bow and is made of synthetic material. i don't know if any of those numbers will help you once you get a formulae but there they are. or you could get a target that would measure impact by ft/lbs.

are you making a bow?

sting tension will be another variable.

if you want any measurements of my bow i will be happy to provide you with them.

 

[3trQN]

are you making a bow?

No, its just an exercise in design and a bit of fun. Much easier to buy a bow, its the principles that I'm more interested in putting together in my mind.

Thanks for the advice, i was planning on comparing with some real values (but I am not that bothered).