Author Topic: Bow Calculator  (Read 7035 times)

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Offline gfugal

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Bow Calculator
« on: March 08, 2017, 12:50:50 am »
Here is a calculator that I put together. If you want to plug your own numbers in quickly online just go to this link: https://docs.google.com/spreadsheets/d/1G-FvwGUGZMzUsHSAVZ5aIz9qHArbLxbIR14PmN396pM/copy
to make a copy of the google sheet. You need a google account for this though. If you want to download the Excel sheet go to this link: https://drive.google.com/file/d/0B0oOIHJuFoYBT3VlWm4xZnNIQUE/view?usp=sharing
or maybe you can get it from the attachment on this post. Let me know if there are problems.

The info that I have default in there already is from Simson's most recent Osage Bow. Simson if you're reading this I hope you don't mind that I used it. It was a great bow! Your one of the few who post a force curve, or in your case draw weights all up the draw. I haven't made a real worthy bow yet, so I hope you don't mind. I don't know what your real velocity was, so I just pulled one out of thin air. From your stored energy it's clear your velocity is going to be high. Anywhere from the high 160s to possibly the 180s. It just depends on the efficiency.

I personally would like to know what efficiencies people get from their bows at specific arrow weights. I've been calculating in the 50% range but Badger reports that he gets them in the 60% and even 70%. I want to get a rough idea of what to expect from a bow. As you can see in the calc, if you can get in the ball park then you can get a pretty good guestimation of what your arrow's speed will be. Speaking of arrow weight, I also threw in the virtual mass calculations Badger introduced me to in Selfbowman's thread: http://www.primitivearcher.com/smf/index.php/topic,59797.0.html. It got me wondering what the significance of GPP (grains per pound) is? I've seen it thrown around here and there and was hoping someone could enlighten me. 
« Last Edit: March 08, 2017, 12:54:06 am by gfugal »
Greg,
No risk, no gain. Expand the mold and try new things.

Offline willie

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Re: Bow Calculator
« Reply #1 on: March 08, 2017, 12:49:43 pm »
Lots of work building spreadsheets, and I have not had a chance to look at the calcs,

Have you compared your sheets results to similar projections in Alan's or Woodbear's sheets?

Offline gfugal

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Re: Bow Calculator
« Reply #2 on: March 08, 2017, 01:16:12 pm »
I have not. I didn't know there were other sheets. Where can i find them to compare?
Greg,
No risk, no gain. Expand the mold and try new things.

Offline willie

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Re: Bow Calculator
« Reply #3 on: March 08, 2017, 01:41:43 pm »
here's a link to recent thread that may help

http://www.primitivearcher.com/smf/index.php/topic,59828.0.html

I have also accumulated some other helpful associated info, and could email I think.

Offline simson

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Re: Bow Calculator
« Reply #4 on: March 08, 2017, 02:08:36 pm »
Well I saw the sheet and I'm not completely in, but will study.
What I will say:
Meanwhile I have made hundreds of bows and have an eye when a bow seems to be a good or a bad one (at least I think so, hahaha).
But, I've learned there is a wide variaty in efficiency coming from marginal design changing and also proper design for the specific wood. And I mean not only the species, it has a lot to do with the sg. At the moment I have some very good osage, it is thin ringed but it is almost homogen ( the early wood isn't that spongy crispy stuff than usual). I will try more extreme design on that wood.

Well, I think I can make quite bows in the middle range. But some are way more better that the others. I cannot explain 100% why.
Below are links to 3 bows which shoot extra fine.
The first, a common design. I got 185 fps avarage.
The second, with an extreme high drawweight in the beginning of draw.
The third with an extra high reflex.

http://www.primitivearcher.com/smf/index.php/topic,36225.msg476616.html#msg476616
http://www.primitivearcher.com/smf/index.php/topic,41624.0.html
http://www.primitivearcher.com/smf/index.php/topic,56785.0.html

I have no chrony, but have sometime access to rent. All these three bows shoot over 180 fps with 10gpp

Looking at the first one I have no explanation for the results. well, the bend is concentrated more on the inner halves of the limbs.

Huuh, it's hard for me to talk about that theoretical stuff in English, sorry.

So Greg, feel free to ask for info or use anything from me for your sheet.
Simon
Bavaria, Germany

Offline joachimM

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Re: Bow Calculator
« Reply #5 on: March 08, 2017, 04:55:57 pm »
Gpp is a way to standardize bow performance of bows with different draw weight.
10 gpp is a standard way to compare bow speed of traditional bows.
A 300 grain arrow shot from a 30 # bow or a 600 grain arrow from a 60# bow will give you a clue on how they compare to each other. Any bow shooting >175 FPS at 10 gpp from 28" draw is excellent, even superb. >180 is exceptional, flight bow material.

Speed of an arrow is often little informative when gpp is not mentioned. Many bows can shoot 200 fps, at 6 gpp or so.

Mark that glassfiber bows are often rated for speed  at 8 or 9 gpp, compound bows at 5 gpp.
Take a bow, shoot far, aim high

Online Badger

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Re: Bow Calculator
« Reply #6 on: March 08, 2017, 05:00:34 pm »
  Greg, I need to go over with you how to figure your stored energy. I think your numbers are too high dropping the efficiency. Instead of just adding up all the numbers and dividing by 12 another step is involved. I need to check with Allen Case on that as I haven't done that for awhile. Getting accurate force draws and stored energy is not that easy. Without real accuracy everything else that comes out is worthless.

Offline joachimM

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Re: Bow Calculator
« Reply #7 on: March 08, 2017, 06:58:47 pm »
I have not. I didn't know there were other sheets. Where can i find them to compare?

Have a look here:
https://bow-simulator.sourceforge.io/resources/

I haven't used bowsimulator yet. David Dewey's and Alan Case's simulators haven't been updated for a while. I still have different versions of both available though. I thought there was a bug in Dave's program, but I just forgot a part that was explained in the manual well enough. So it's still working pretty neatly.

Dave's program takes set into account, Alan's doesn't. But bow design-wise, Alan's spreadsheet worked better for me, allowing to design recurves more easily. Both programs include predicted stored energy and FD-profiles. Dave's spreadsheet also estimates arrow speed for the GPP you enter for a certain bow design. 

Try them out, you will learn at lot from them.
Take a bow, shoot far, aim high

Offline gfugal

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Re: Bow Calculator
« Reply #8 on: March 09, 2017, 12:15:36 am »
  Greg, I need to go over with you how to figure your stored energy. I think your numbers are too high dropping the efficiency. Instead of just adding up all the numbers and dividing by 12 another step is involved. I need to check with Allen Case on that as I haven't done that for awhile. Getting accurate force draws and stored energy is not that easy. Without real accuracy everything else that comes out is worthless.
So for the stored energy the calculation continues on to the other sheet page. For the sake of appearance it isn't on the front page. Basically what I did for each measurement was this (Y1+Y2)/2•(X2-X1), then added those together before I divided by twelve. I also put the function sign() in the calculation, therefore if there was a blank cell it wouldn't calculate it since it would essentially multiply it by zero. The above formula is what I know of for calculating the area under a plotted graph. If you can find me the other method I would love to learn about it.
Lots of work building spreadsheets, and I have not had a chance to look at the calcs,

Have you compared your sheets results to similar projections in Alan's or Woodbear's sheets?
So my sheet isn't really a projection. It's more informative if you want to figure out your bows stored energy, and efficiency. It does project hypothetical velocities based off of efficiency, virtual mass and stuff. What it doesn't do is offer any design advice. I downloaded both the supertiller and the woodbear's selfbow design sheet. They are comprehensive, and complex. A wonderfull tool that's for sure. I just don't know quite how to use them yet and it will take quite a bit more study. I haven't read the instructions for woodbear's but I spent some time messing around with the supertiller. From what I could gather although, is that their sheets are more there to help you theorize different designs rather then give information on existing already made bows. That's cool and all, but that wasn't the purpose I was going for with this. I don't think my sheet is as good as theirs by a longshot, but it's not complex. I just wanted to offer a simple tool for people to plug in values they may already have from existing bows in order to calculate basic properties they may be curious about. I don't know if you can do that with these other sheets. I'm sure you can and I definitely need to look more into them.
« Last Edit: March 09, 2017, 12:21:03 am by gfugal »
Greg,
No risk, no gain. Expand the mold and try new things.

Offline joachimM

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Re: Bow Calculator
« Reply #9 on: March 09, 2017, 04:11:37 am »
Greg,
indeed these sheets are primarily intended for bow design, but they also allow you to input dimensions from existing bows and calculate the parameters you want. But indeed these sheets are rather complex and may be a bit terrifying to a lot of users.

So if you have a shortcut for some of the properties of bows, I'm certain that's a positive thing. I made an extremely simple sheet to estimate the effect of shortening (or lengthening) a bow on draw weight, and the effect of removing or adding belly thickness on draw weight, and calculating strain on belly and back. You could find it in both complex sheets as well, but my shortcut has helped me a lot already.

Bear in mind, as Badger already wrote, arrow speed hinges on a lot of estimates, and for some parameters a small change in can give a large difference in arrow speed.
Take a bow, shoot far, aim high

Offline willie

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Re: Bow Calculator
« Reply #10 on: March 09, 2017, 10:03:13 am »
yes, some of those other sheets are rather complex and have a bit of a learning curve if you wish to use them to their full potential. Although I have explored most of the features of David Deweys sheet in the past, more often than not, I usually just run a beam test on a sample of the wood I am using to get a look at MOE and set, (to estimate a Design Strain value), then get a basic idea of the shape required before roughing the bow out. I then do most of my build and tillering in a conventional manner, but it is interesting sometimes, to go back and compare the finished bow with the design dimensions on the spreadsheet.



Actually, now that I read over JoachimM's post, his sheets ability to compare length with width and draw weight at a particular strain, is pretty much all I am trying to do with DD's sheet, that is, see what the stave is capable of before deciding what to make out of it.

Never have looked at the arrow speed or energy features, as I have no chrono to verify with. But I will venture the opinion, that if you start with a good piece of wood, the exceptional bow is predominately  a product of careful tillering, and having a good idea of what your stave and design is capable of, is a good place to start.
 

Offline gfugal

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Re: Bow Calculator
« Reply #11 on: March 09, 2017, 10:20:31 am »
Greg,
indeed these sheets are primarily intended for bow design, but they also allow you to input dimensions from existing bows and calculate the parameters you want. But indeed these sheets are rather complex and may be a bit terrifying to a lot of users.
I'm having a hard time with this. I wanted to see if these programs would calculate the same stored energy as I did for Simson's bow but I didn't see how i could plug his numbers in. Unless of course, I put in the dimensions and such of the bow (length, width, thickness, profile, material, etc). If I did that then it will just theorize out a hypothetical draw weight and force curve. I didn't see an option where you can manually input the force curve by typing in a weight at a respective draw.

How are people normally calculating their stored energy for their bows? I would like to double check my calculations with another like willie and badger suggested.
So if you have a shortcut for some of the properties of bows, I'm certain that's a positive thing. I made an extremely simple sheet to estimate the effect of shortening (or lengthening) a bow on draw weight, and the effect of removing or adding belly thickness on draw weight, and calculating strain on belly and back. You could find it in both complex sheets as well, but my shortcut has helped me a lot already.
This is true, thanks. Bytheway would you be able to share those sheets that you made aswell? you can never have to many haha. and I never said thank you for explaining  the GPP thing. I knew I was missing something, now it makes more sense.
Well I saw the sheet and I'm not completely in, but will study.
What I will say:
Meanwhile I have made hundreds of bows and have an eye when a bow seems to be a good or a bad one (at least I think so, hahaha).
But, I've learned there is a wide variaty in efficiency coming from marginal design changing and also proper design for the specific wood. And I mean not only the species, it has a lot to do with the sg. At the moment I have some very good osage, it is thin ringed but it is almost homogen ( the early wood isn't that spongy crispy stuff than usual). I will try more extreme design on that wood.

Well, I think I can make quite bows in the middle range. But some are way more better that the others. I cannot explain 100% why.
Below are links to 3 bows which shoot extra fine.
The first, a common design. I got 185 fps avarage.
The second, with an extreme high drawweight in the beginning of draw.
The third with an extra high reflex.

http://www.primitivearcher.com/smf/index.php/topic,36225.msg476616.html#msg476616
http://www.primitivearcher.com/smf/index.php/topic,41624.0.html
http://www.primitivearcher.com/smf/index.php/topic,56785.0.html

I have no chrony, but have sometime access to rent. All these three bows shoot over 180 fps with 10gpp

Looking at the first one I have no explanation for the results. well, the bend is concentrated more on the inner halves of the limbs.

Huuh, it's hard for me to talk about that theoretical stuff in English, sorry.

So Greg, feel free to ask for info or use anything from me for your sheet.
So I followed the link to those other bows and not suprisingly they are pretty sweet! but unfortunatley you weren't posting the draw weigths every 2 inches of draw back then so I can't construct a force curve to estimate stored energy. If its not too much to ask would I be able to get the draw weights for every 2 inches so I can calculate them? Don't know if you already have that infor or if you would have to measure it. If you have to measure it, even just the first would be fantastic. Thanks for feeding my curiousity. I really do appreciate it.
Greg,
No risk, no gain. Expand the mold and try new things.

Offline joachimM

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Re: Bow Calculator
« Reply #12 on: March 09, 2017, 04:48:44 pm »
Greg,

A few answers at a time:
1) no, Alan's and David's spreadsheets don't allow estimating directly arrow speed from FD-curves and efficiency.


2) the simple sheet I'm talking about (length, thickness, strain):
https://drive.google.com/open?id=0B3YYA3Sr_3gqLXF5OEZCN3JIM0E
These all derive from the cubic relation between length or thickness and draw weight: a bow twice as thick will have a draw weight that is eight (2 to the power 3) times higher.

3) I updated my wood and other bow materials lists for MOE, MOR etcetera:
https://drive.google.com/open?id=0B3YYA3Sr_3gqb0NpazZqdUFJSTQ

4) note also this nifty tool for bow mass expectations from the mass principle (made by Dave aka Aussie Yeowman, from Badger's input):
https://drive.google.com/open?id=0B3YYA3Sr_3gqQ2o5VmpLbVpseUk. For example, it showed that the bow I'm currently making was a bit on the heavy side (mass), at least for a 28" draw at 43#. The numbers did fit perfectly for a 46# bow with a 29" draw, so that's what I tested, and which turned out fine. 

5) you seem interested in the mathematics behind archery, so you should definitely read (or browse through) Bob Kooi's archery papers:
http://www.bio.vu.nl/thb/users/kooi/

Joachim
« Last Edit: March 12, 2017, 04:09:39 am by joachimM »
Take a bow, shoot far, aim high

Offline gfugal

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Re: Bow Calculator
« Reply #13 on: March 09, 2017, 08:34:31 pm »
  Greg, I need to go over with you how to figure your stored energy. I think your numbers are too high dropping the efficiency. Instead of just adding up all the numbers and dividing by 12 another step is involved. I need to check with Allen Case on that as I haven't done that for awhile. Getting accurate force draws and stored energy is not that easy. Without real accuracy everything else that comes out is worthless.
So for the stored energy the calculation continues on to the other sheet page. For the sake of appearance it isn't on the front page. Basically what I did for each measurement was this (Y1+Y2)/2•(X2-X1), then added those together before I divided by twelve. I also put the function sign() in the calculation, therefore if there was a blank cell it wouldn't calculate it since it would essentially multiply it by zero. The above formula is what I know of for calculating the area under a plotted graph. If you can find me the other method I would love to learn about it.
I've been trying to find another calculation out there to calculate the area under a plotted curve but no luck yet. But I found the samE method I did On this site https://sites.google.com/site/technicalarchery/technical-discussions-1/understanding-the-bow-draw-curve. He found the average between two draw weights -- (Y1+Y2)/2 -- then multiplied it by the distance between those two lengths -- (x2-x1). You do this for each interval then add them up altogether. This gives you the stored energy in Ft•in, but we need Ft•lbs so I divide the sum by 12. The accuracy of the stored energy is dependent on how many measurements you collect. The more the better. they did a measurement every half an inch, so they must have had a real good scale and setup in order to pick up differences that close together. Their article is great and does a better job at describing the values I'm trying to calculate here, as well as their importance. Unfortunately, they didn't actually measure their arrow's speeds so they don't have real efficiency values. They just gave an estimation for modern compound bows, which are much higher than the bows we work with. 

Greg,

A few answers at a time:
1) no, Alan's and David's spreadsheets don't allow estimating directly arrow speed from FD-curves and efficiency.


2) the simple sheet I'm talking about (length, thickness, strain):
https://drive.google.com/open?id=0B3YYA3Sr_3gqLXF5OEZCN3JIM0E
These all derive from the cubic relation between length or thickness and draw weight: a bow twice as thick will have a draw weight that is eight (2 to the power 3) times higher.

3) I updated my wood and other bow materials lists for MOE, MOR etcetera:
https://drive.google.com/open?id=0B3YYA3Sr_3gqb0NpazZqdUFJSTQ

4) note also this nifty tool for bow mass expectations from the mass principle (made by David Dewey as well, from Badger's input):
https://drive.google.com/open?id=0B3YYA3Sr_3gqQ2o5VmpLbVpseUk. For example, it showed that the bow I'm currently making was a bit on the heavy side (mass), at least for a 28" draw at 43#. The numbers did fit perfectly for a 46# bow with a 29" draw, so that's what I tested, and which turned out fine. 

5) you seem interested in the mathematics behind archery, so you should definitely read (or browse through) Bob Kooi's archery papers:
http://www.bio.vu.nl/thb/users/kooi/

Joachim

Thanks for those. I appreciate it. I'll put them to good use!
« Last Edit: March 10, 2017, 11:16:35 am by gfugal »
Greg,
No risk, no gain. Expand the mold and try new things.

Offline willie

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Re: Bow Calculator
« Reply #14 on: March 10, 2017, 09:42:52 am »
Quote
I've been trying to find another calculation out there to calculate the area under a plotted curve but no luck

 You might try using a graphical solution at 10 x 10 squares per inch, and there are some online graphing apps around also.  But as you pointed out, the extra precision is needed with the data collection.

In actuality, I think the challenge with bows, is not measuring the energy in or out, but rather identifying and rectifying the causes of the losses. Have you had a chance to look over some of Bakers essays, in addition to Koois?

as for some of the other spreadsheets, one can find the underlying formulas. it would be interesting to see if any adjust for the mass at each station along the limb.