Author Topic: question: twice as big => twice as strong?  (Read 609 times)

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Offline leif

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question: twice as big => twice as strong?
« on: May 17, 2019, 10:01:22 am »
Let's say we have made a simple pyramid flatbow 50# @28" and we want to put a bow of similar efficiency on a gastraphetes but with double draw length, would doubling it's size in every direction (2x width,2x thickness,2x length) work with the same efficiency?

the only thing I now : it would be 2x stronger due to width and 8x stronger due to thickness but don't know how the length increase will decrease the strength.

Offline jeffp51

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Re: question: twice as big => twice as strong?
« Reply #1 on: May 17, 2019, 10:05:56 am »
my math is a little sketchy, but you are doubling in three dimensions, so I think that increases every thing by the cube (factor of 3) instead of the square (factor of 2)  so you wouldn't need to make a bow twice as long to double strength
 

Offline leif

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Re: question: twice as big => twice as strong?
« Reply #2 on: May 17, 2019, 10:14:04 am »
don't forget I want to double the draw length 56", which means to avoid stacking/ breaking needs to be 2x as long

Offline SLIMBOB

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Re: question: twice as big => twice as strong?
« Reply #3 on: May 17, 2019, 10:19:53 am »
Roughly, you only need to double the width to double the draw weight.  A 2 inch wide bow of some proportions, that draws 50 lbs at 28 inches....2 of those bows held together would draw 100 lbs at 28 inches.
OK...misread the question....interesting question...and I believe the answer is yes.  just a guess.
« Last Edit: May 17, 2019, 10:23:48 am by SLIMBOB »
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Offline Hawkdancer

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Re: question: twice as big => twice as strong?
« Reply #4 on: May 17, 2019, 09:14:14 pm »
Don't tangle with a dude/damsel who can draw 56" >:D (lol)!  I ain't got a clue about your premise!
Sounds a bit theoretical, though!
Hawkdancer
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Offline Del the cat

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Re: question: twice as big => twice as strong?
« Reply #5 on: May 17, 2019, 10:30:40 pm »
My take is to look at it piecemeal.
Call the draw weight W
1. Double the width you double the the draw weight... so that 2W
2. Double the thickness, that gives 8 times the draw weight so it's now 16W
3. If you double the bow length and double the draw length..... that's where I'm stumped  :o
Does it stay the same poundage? That's my guess.

But the real problem is you can't simply double the thickness of a bow and expect it to bend the same amount.
I'd suggest increasing the thickness by a lesser amount is more realistic
E.G 25% would almost double the draw weight (1.25 cubed is almost 2).
Increasing the thickness by 50% would give 3.3 times the draw weight.
So double the width, increase the thickness by 25% and double the length would be my first try and I guess/reckon that would give 200# if scaled from a 50# bow. That would seem a manageable thing to try.
Del
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Offline Hrothgar

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Re: question: twice as big => twice as strong?
« Reply #6 on: May 18, 2019, 12:26:31 am »
All math aside, a person could go to the lumberyard and purchase a 12' long oak 2x4 and start from there
" To be, or not to be"...decisions, decisions, decisions.

Offline Del the cat

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Re: question: twice as big => twice as strong?
« Reply #7 on: May 18, 2019, 02:44:23 am »
All math aside, a person could go to the lumberyard and purchase a 12' long oak 2x4 and start from there
Good point... easy enough to do a quick test with with some lumber 6' of 2 x 1 compared with 12' of 4 x 2
Del
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Offline Jim Davis

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Re: question: twice as big => twice as strong?
« Reply #8 on: May 18, 2019, 04:52:47 am »
+1 for Del

It is said that Thomas Edison once saw one  of his engineers struggling with a math problem and asked him what he was doing. The engineer said he was trying to calculate the volume of a light  bulb. Edison said, Why don't you just fill the glass globe with water, then pour it into a graduated cylinder and read the volume?

The math for this  bow question is beyond most of  us and the answer can be found directly by building a bow to the suggested dimensions.

Or, you can, for variety, argue about how many angels can dance on the head of a pin.
Jim Davis

Kentucky--formerly Maine

Offline SLIMBOB

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Re: question: twice as big => twice as strong?
« Reply #9 on: May 18, 2019, 05:10:19 am »
12. Exactly 12.
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Offline George Tsoukalas

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Re: question: twice as big => twice as strong?
« Reply #10 on: May 18, 2019, 05:16:30 am »
Thank you. I had never heard of one of these and I am of Greek ancestry.
I watched  you tube video just now.
Very interesting.
Jawge
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If you ain't breakin' you ain't makin!

Offline leif

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Re: question: twice as big => twice as strong?
« Reply #11 on: May 18, 2019, 06:28:48 am »
Thanks for the replies they made me want to look more into it.
the question is theoretical.  just imagine tillering a 12' 2x4 with hand tools :P
I really had to get an answer so i did an experiment.
I used a metal ruler instead of boards
below are the pictures of the set up and the data(if you can understand anything)

The results: doubling length will make the spring 8-9 times weaker, of course there are errors in the experiment but it seems that it follows a cube pattern like  thickness does (but weakening instead of strengthening).

so 2x width 2x thickness 2x length =2x8x1/8=2x strong.
but we also have 2x draw length so it goes 2x draw weight (from hooke's law) but this is a big assumption to make.

i guess the resulting F-D curve would be more aggressive 200# @ 56" (100# @ 28") rather than 100# @ 56"
it would store 8x the energy of the normal bow (about time to double the arrow ::) )

I thought that someone would have made a miniature bow and scale it up to man sized, the same principles would apply here.

Offline Hrothgar

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Re: question: twice as big => twice as strong?
« Reply #12 on: May 18, 2019, 06:52:30 am »
Leif, kudos for your perseverance and calculations...something I wouldn't do. I hope, for curiosity's sake, someone will try to build this.
" To be, or not to be"...decisions, decisions, decisions.

Offline Del the cat

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Re: question: twice as big => twice as strong?
« Reply #13 on: May 18, 2019, 07:24:27 am »
@ Leif.
Nice work :)
I like the combination of experimentation and a bit of physics with a pinch of assumption/approximation :)
Del
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Online Badger

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Re: question: twice as big => twice as strong?
« Reply #14 on: May 18, 2019, 09:25:02 am »
+1 for Del

It is said that Thomas Edison once saw one  of his engineers struggling with a math problem and asked him what he was doing. The engineer said he was trying to calculate the volume of a light  bulb. Edison said, Why don't you just fill the glass globe with water, then pour it into a graduated cylinder and read the volume?

The math for this  bow question is beyond most of  us and the answer can be found directly by building a bow to the suggested dimensions.

Or, you can, for variety, argue about how many angels can dance on the head of a pin.

  Several years ago I had to build a bow for a TV show about 24 ft long I think. It was configured slightly different than a bow but was basically a bow that operated a catapult. I built 3 scale models to calculate the increase and it came out very accurate when I was done. I wish I could remember how it worked out but I don't.