A question on mini bows

[KShip85]

I am curious on how the specs of small bows compare to a similar design only enlarged.  For instance, if one were to build a small scale bow testing a particular design for a particular species of wood would the draw weight be related on the same scale as the bow dimensions.  Say if I were to build a small scale long bow of a certain size pulling 10 lbs at 12 inches and then increase the scale of that bow to a full size one would the draw weight simply be the same multiple as the dimensions.  Sorry if I am making no sense, it is late and I need to get to bed.  Thanks in advance!

Kip

[CraigMBeckett]

Hi Kip,

The short answer is no. In the bending of beams, which is what a bow limb is, if you double the width of the limb you double the strength, therefore the draw weight would double, however if you double the depth you increase the strength by 8 times, so you cannot just upscale.

Craig.

[KShip85]

Thanks for posting Craig.  After I posted this I got to thinking about that.  I believe I read it once in one of the TBB.  I would think there would have to be some equation that would beable to give consistant results.  Perhaps one that took into consideration how changing certain dimensions had different effects on the bow and then multiplying those by the necessary number as it relates to the scale.  Does anyone know the impact of doubling length all other dimensions remaining the same?  Say something like doubling the length would cut the weight in half?  Would it make sense to take into account how each dimension change effects it's strength and multiply that by the scale size and cancle out the differences?  Say if doubling the length and width are recipricals of each other they would cancle out and thickness would be the determining factor.  Let's say I have a 30 inch mini dogwood bow  pulling 10 lbs at about 12 inches with scaled down dimensions that would yield a bow 76 inches long 1.5 inches at center tapering to 1/2 inch tips drawing 32 inches when scaled up.  If the scale is 2.53 to 1 would it then make sense that if thickness is our concern, assuming width and length will cancle out, and that it has 4 times the effect of either of those then taking that 4 times our 2.53 times the 10 lbs of the small scale bow we can arrive at an expected draw weight for the scaled up version.  I may be no where close to being right at all here but I would like to try and see some kind of equation develope.  Thanks again all!

Kip     

[Del the cat]

As the others have said, it gets tricky.
My 18" Ash backed Cherry bow is about 3.5 to 1 scale. The draw weight is 3 pounds at 8" and that feels plenty.
If we cube that it is 3x3x3 = 27 pounds which seems a tad low.
I havn't tested for range yet, but my gut feel is that the poundage seems to scale with the bow...the penetration test seemed ok (dunno if you saw the threads? http://www.primitivearcher.com/smf/index.php/topic,17923.0.html)
Del

[KShip85]

Hey Del, I was hoping you would chime in.  Your post got me interested in this topic.  What do you feel a scaled up version of your bow should pull?  With my experimental equation I came up with 42 lbs  for a full scale version of yours which still seems a little light to me.  I imagine that the length and width are not exactly inverse in their effect on the bow.  I might run some tests later and see what kind of adjustments I can make to the equation.

Kip

[Badger]

Another factor that plays in when scaling bows is the density of the wood, something we don't have much control over. A very dense wood will scale up closer using a lighter wood. I am working on some scale stuff right now. Actually a very giant bow. I may end up using a very light wood like doug fir if I can get enough bend out of it.

[KShip85]

Another factor that plays in when scaling bows is the density of the wood, something we don't have much control over. A very dense wood will scale up closer using a lighter wood. I am working on some scale stuff right now. Actually a very giant bow. I may end up using a very light wood like doug fir if I can get enough bend out of it.

I was beginning to wonder if density played a factor.  I decided to try my test without changing the thickness between sizes and realized that by not changing thickness I was changing the ratio of the thickness to the whole bow.  Oh well back to the drawing board.  Right now I have two pieces of flat hickory from a board, one twice the size of the other.  I am going to try and put some string on and compare bending strength and see where that gets me.

Kip

[Del the cat]

Hey Del, I was hoping you would chime in.  Your post got me interested in this topic.  What do you feel a scaled up version of your bow should pull?  With my experimental equation I came up with 42 lbs  for a full scale version of yours which still seems a little light to me.  I imagine that the length and width are not exactly inverse in their effect on the bow.  I might run some tests later and see what kind of adjustments I can make to the equation.

Kip

I'd go with 42, but when I actually build it I'll be aiming higher than that.
The reality is, I have two bits of cherry, I'm saving the good half and I'm going to play with the bad half first, which will make a rather short bow.
The good half may eventually make something like the miniature.
I think for a miniature to be representative it really should be no smaller than 1:2. Even with my 3.5 to 1 you end up whittling a stick more than making a representative test bow.
But hey it gives you something to do on cold wet evenings!
The miniature does give some sort of 'feel' but I wouldn't think it was quantifiable unless it's a big miniature
Del

[CraigMBeckett]

KShip85,

You can work out (approximately) the strength of given sections and lengths, you would use beam bending equations on half the bow, but as the load is applied in a varying direction the equations are not simple.

Craig.