Percent of energy storage to draw weight ratio

[sleek]

On most my short bows I am getting a stored energy to draw weight ratio of 72-89%. Id like to know how these numbers compare to larger bows? Are these good numbers for stored energy effeciency or too low?

[Badger]

 89% is not bad for a shortbow at all, about average for a mid length bow. The way we have been figuring I found out is not that accurate, add up all the numbers under the curve and divide by 12. It doesn't allow for the slope and will actually be a bit lower I believe. I still do it that way for my own purposes but it really isn't accurate. I need to find out the right way to figure that.

[sleek]

Thanks Steve. Would we be better off if we measured every half inch and devided by 24? Or am I looking at this in the wrong way?

[DC]

There is a formula called Simpson's Rule that boat builders use for figuring the area of oddball shapes. Is that what you're trying to do?

[loon]

could just calculate the kinetic energy of a shot arrow. would be a bit easier given just its speed and mass
Custom Thumb Rings has done energy measurements. Peter Dekker's website has a graph somewhere, maybe an excel spreadsheet where you can input draw weight values and it makes a curve ... and finds stored (potential) energy. backyardbowyer has also done such measurements in his blog

the potential energy should be higher than the kinetic energy due to inefficiency (inertia from limb mass, limb vibration, string mass, string stretch)

there are more accurate ways.. there's ways of better approximating integrals like the trapezoid rule. another would be to use software to find a fitting curve and then just make it take the integral.

Thanks Steve. Would we be better off if we measured every half inch and devided by 24? Or am I looking at this in the wrong way?

yes

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I'm not the best at physics but. potential energy is sort of like work
(force times distance). Could find the average draw weight over all the
measurements from brace to full draw and then multiply by (draw length -
brace height)?

alternatively the energy is just the integral from brace to full draw with
respect to distance.. so that's basically adding them all, then dividing
such that there's a unit which is not needed if there's a measurement
every inch, which implies given # of data points = powerstroke = draw
length - brace height

((SUM draw_weights) / powerstroke) * powerstroke
SUM draw_weights

more math

PE = mgh due to gravity where m = mass, g = acceleration, h = distance

deriving potential energy in a bow from this

F = ma => a = F/m

PE = m(F/m)d = Fd

but the mass of what? the arrow.. in both cases

if you're dividing by 12, you're just changing the unit to feet from
inches? let's prove this

((SUM draw_weights) / datapoints) * (powerstroke/12)
where datapoints = powerstroke

= (SUM draw weights) / 12


what if every half inch..

((sum draw_weights) / datapoints) * (powerstroke/12)
where datapoints = 2*powerstroke


(sum draw_weights) * 1/(2*powerstroke) * (powerstroke/12)

(sum draw_weights) / 24

yes

[sleek]

I dont have a chrono or id do kenetic energy....

So to add to this, i am getting an average of 2.5# gained per inch of draw. Its stays consistant through the range of draw.


What is really hurting my stored energy is low initial draw weight.  I need to fingure how to increase it. Every time I heat the limbs, take deflex out, reflex the mid limb, or recurve the tips, initial draw weight goes up, but of course, so does the final draw weight. When I tiller it down, initial draw weight always goes back to where it was. The initial draw weight is sad. Down to 5 poinds at 10 inches with a 7 inch brace.

Perhaps if I make long sweeping recurves that work, that will trick the bow into thinking its shorter than it is, the long recurves will apply tension, and still work to add draw length without over stressing the bow.

[loon]

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https://www.buildyourownbow.com/articles/force-draw-curve-template/

[sleek]

Loon, i love that link. Than you.

[sleek]

89% is not bad for a shortbow at all, about average for a mid length bow. The way we have been figuring I found out is not that accurate, add up all the numbers under the curve and divide by 12. It doesn't allow for the slope and will actually be a bit lower I believe. I still do it that way for my own purposes but it really isn't accurate. I need to find out the right way to figure that.

What percent do most good flight bows have?

[DC]

110%, like football players

[Badger]

  Slle, flight bows are looking more for high efficiency and low virtual mass. Anything above 95% I think would be considered very good.

[gfugal]

http://www.primitivearcher.com/smf/index.php/topic,59964.msg834378.html#msg834378

Here's a calculator I made to determine stored energy and force curves and stuff like that. The 8th post I explain the equation I use to calculate stored energy. It's the trapezoidal  rule https://en.m.wikipedia.org/wiki/Trapezoidal_rule?wprov=sfla1. It should be very accurate.  If you open the calculator and plug in your own numbers it will tell you what your energy to draw weight ratio is. Anything over 100% is excellent like mentioned.

[gfugal]

Correction, to the previous post. The way I calculated the area under the curve is not the trapezoidal method but rather the midpoint rule. http://www.dummies.com/education/math/calculus/how-to-approximate-area-with-midpoint-rectangles/. Basically, you find the areas of rectangles by multipling their base (distance between two measurments on the graph) and their hight ( the average midpoint between the two y values you measured) then adding the areas of all rectangles together. The website and I both have examples. I'll post pictures of those now.

[DC]

I believe that's how Simpsons rule works.

[sleek]

So the old method of adding the numbers and dividing by 12, does that give me higher or lower numbers than I actually have?
And, what percent is it off by in average?