Scaling down, can you help my maths?

[stuckinthemud]

There is a bow I want to copy but my stave is 10% too short. If I reduce width, thickness and draw length by 10%, what will be the reduction in draw weight?  Any ideas? The calculation is beyond me but I suspect it is more than 10%. 

[willie]

 if you posted the actual lengths you are working with, I could plug it into a spreadsheet, but need to know if you want to change width and draw weight and drawlength.  what wood? what style?

alternately,  if the bow is to be the same weight, and the same width, and the same drawlength, then the shorter bow would need to be slightly thinner to accomadate the tighter bends.  not much really , so you could procede  as normal and expect to take of slightly more on the thickness, watching for set etc as you go.

[stuckinthemud]

Well, the original is 44 inches long yew 2 inches square at centre, bend through handle, draw length is 12 inches but my billet is 6 inches shorter,  not exactly 10% but near enough. So, if I took the centre down by 5mm and reduced draw length to 11 inches then I should be able to get a decent model for how the original performed. Alternatively I could use a really nice wytch elm billet and go full size.   How does elm compare with yew for performance?

[willie]

took the center down by 5mm

in width or thickness?



your brace height ?
are you looking for the original draw weight also? approx what is it?   if something has to give way to make the shorter stave work, what would you prefer to give up? draw weight or draw length?

[George Tsoukalas]

Multiply any figure you want to change by 0.10. So 44 x .1= 4.4. Subtract 44-4.4=  39.6. Jawge

[RyanY]

Is this a crossbow prod? 2” square in any wood will not bend in the handle unless massively long.

[Hawkdancer]

I panicked!  Math ain't my strong suit, but everything should drop 10% or so, maybe!
Hawkdancer

[bownarra]

Yew and elm have very different bend resistance.

[stuckinthemud]

Ok, so a 90% scale model in yew is the  better approach with a 10per cent reduction in length, width across back and belly, thickness and draw length.  Cool.  Is there a way of using the data from that bow to calculate the performance of the original bow?

[willie]

stuck,
I am willing to plug it into a calculator if you are willing to provide a little more data

brace height?

do you want to keep as close to the original as possible but just build to a slightly lower draw weight?

your messagebox is full

[stuckinthemud]

Thanks for the heads-up, I have cleaned up my inbox.  The original looks like this
My estimates are of 110cm length overall, brace height of 4 inches, thickess 4cm, height across back 3cm, draw length 12 inches.  Draw length is a guess,  I haven't properly analysed the drawings of possible tillers yet.  Also, the centre has definitely had compression damage, possibly by being crushed into a too narrow bridle, My reconstruction will probably use a slightly fatter section . Brace height is a guess but looking at the string notches the original brace height looks quite deep.
 

[Badger]

 A bow is not something you can really scale down, Every bow is just built to bend properly. I think the best you can do here is just copy the style with the length you have to work with.

[willie]

@ 12" draw, and 42" ntn, and 4" brace and 2" wide   .......  and a rough guess of how much you can bend yew

compared to the same with a 38 ntn means your thickness will come in at about 80% of the longer stave.

if you keep the same width, your poundage with the 38 ntn will be about 70% of the longer stave.

[stuckinthemud]

Ok, thank you,  that's really useful. 

[willie]

as you noted, it looks like the original took set, so its thickness at the center was a bit thin relative to the rest of the bow. 

my calcs are just a ball park estimate, and the shorter bow will only be a few mm thinner than the longer, but the longer needed to be relatively thicker in places, so, as others have mentioned, you are best off to tiller conventionally with the usual precautions. It would be nice when you finish to see how close this estimate came.