Stored energy

[Buckeye Guy]

Blafair
your head ach reminds me why I don't do math
and as long as Steves numbers keep proving me right I don't have to get a head ach either
so keep up the good work Steve !

[BarredOwl]

Maybe I'm not understanding what is being asked but, wouldn't you also have to assume or know an arrow speed and weight then just calculate the foot pounds the arrow would impart upon a target.  I guess the performance of the bow material and design would have to be super uniform.

[pinhead52]

Hey everyone. Just started making bows, but I've been a nerd for a while.

If you're trying to discuss potential energy as it applies to projectiles, you technically have to integrate the force applied from release to the arrow leaving the string and apply that over time to get impulse as force translated to the arrow, then divide by mass to get flight speed or skip a few steps and assume negligible wind resistance and finish with impact force. But if you don't want to go about it the long way, Trad Gang answered this question already for us.

http://www.tradgang.com/ashby/Momentum%20Kinetic%20Energy%20and%20Arrow%20Penetration.htm

But here's the cliff's notes: A bow held at the same force, but a longer draw will then apply force for a longer time, leading to higher impulse, which translates to more force. Or, bigger numbers will always result in bigger numbers. But why bother? Shouldn't you just make the bow that is right for you?

[KS51]

Actually, the original question was which scenario would have the most stored energy.  Stored energy= potential energy.  What you mentioned above would actually be related to realized (Kinetic) energy, which includes efficiency.  Put simply  KE = PE x Eff.  Or put in full mathematical form  (WxV^2)/(gc x 2) = (D x P)/2 x eff

W = weight
V = velocity
gc = gravitational constant ( only for ft-lb systems) = 32.14 ft/s^2
D = effective draw = draw length - brace height
P = poundage at full draw

If you change P to grains/pound you will find that at 100% efficiency, your max possible velocity is about 214 ft/s for 9grains/pound arrows and a 22in effective draw (28-6), though this is not actually possible.  At 200 ft/s your efficiency has to be pretty close to 92%.  This does assume a perfectly triangular force-draw curve which may not be realistic for some types of bow designs.  This is just the "static" math that helps explain what is happening.

Ken

[Badger]

  Pinhead, to figure an arrows potential energy you don't use time you use force and distance. The force changes over the length of the stroke being the highest at full draw. This is a well established accepted archery method for measuring a bows stored energy. It has no relation to how efficient the bow is. Truth is with a wooden bow you will never get an accurate measurement of force applied to the arrow by trying to measure it because of hysterisis in the wood. But measuring the force draw curve and stored energy will get you pretty close. The chrono will tell you what actually went into the arrow.

[pinhead52]

Oh, I was just answering the question with physics, I didn't know there were already thumb rules in archery.

[Chadwick]

A few tips for getting more stored energy:
1) High early draw weight (and weight throughout draw) - So avoid string follow, and shoot what # you can handle.
2) Avoid stacking, as this gives most of your draw weight & energy in only the last few inches. Many short bows have this prob.
3) Lower brace height a bit. This lengthens the effective draw, BUT slightly decreases draw weight.
4) As mentioned above, pull it back further.
5) Release quickly upon reaching full draw --- holding it back there will decrease stored energy because of limb stresses.

And then don't waste your energy with a sloppy release or with arrows that are too light to take what the bow has stored.
It is both simpler and more complicated than we make it sound, based on your perception and which details concern you.

[redhawk55]

Did you know this guy's tests?

http://goldenhordebows.blogspot.com/2013/07/hysteresis-tests-part-2-wooden-and.html?q=draw+return

he did some videos too(bit chaotic):

http://www.youtube.com/watch?v=HcSJTObuMV0

With his tests in mind I would conclude time has a much more impact on hysteresis than I thought.

Michael