Primitive Archer

Main Discussion Area => Bows => Topic started by: stuckinthemud on May 05, 2021, 04:56:25 pm

Title: Scaling down, can you help my maths?
Post by: stuckinthemud on May 05, 2021, 04:56:25 pm
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%. 
Title: Re: Scaling down, can you help my maths?
Post by: willie on May 05, 2021, 05:34:00 pm
 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.
Title: Re: Scaling down, can you help my maths?
Post by: stuckinthemud on May 05, 2021, 06:35:57 pm
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?
Title: Re: Scaling down, can you help my maths?
Post by: willie on May 05, 2021, 07:16:49 pm
Quote
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?
Title: Re: Scaling down, can you help my maths?
Post by: George Tsoukalas on May 05, 2021, 08:06:20 pm
Multiply any figure you want to change by 0.10. So 44 x .1= 4.4. Subtract 44-4.4=  39.6. Jawge
Title: Re: Scaling down, can you help my maths?
Post by: RyanY on May 05, 2021, 08:07:26 pm
Is this a crossbow prod? 2” square in any wood will not bend in the handle unless massively long.
Title: Re: Scaling down, can you help my maths?
Post by: Hawkdancer on May 06, 2021, 03:12:13 am
I panicked!  Math ain't my strong suit, but everything should drop 10% or so, maybe! (lol)
Hawkdancer
Title: Re: Scaling down, can you help my maths?
Post by: bownarra on May 06, 2021, 03:16:30 am
Yew and elm have very different bend resistance.
Title: Re: Scaling down, can you help my maths?
Post by: stuckinthemud on May 06, 2021, 02:04:36 pm
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?
Title: Re: Scaling down, can you help my maths?
Post by: willie on May 06, 2021, 02:18:09 pm
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
Title: Re: Scaling down, can you help my maths?
Post by: stuckinthemud on May 06, 2021, 02:51:27 pm
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.
 (https://stuckinthemudsite.files.wordpress.com/2020/10/screenshot_20201021-225415_duckduckgo980863592428033768.jpg)
Title: Re: Scaling down, can you help my maths?
Post by: Badger on May 06, 2021, 03:04:50 pm
 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.
Title: Re: Scaling down, can you help my maths?
Post by: willie on May 06, 2021, 04:02:27 pm
@ 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.
Title: Re: Scaling down, can you help my maths?
Post by: stuckinthemud on May 06, 2021, 04:43:23 pm
Ok, thank you,  that's really useful. 
Title: Re: Scaling down, can you help my maths?
Post by: willie on May 06, 2021, 05:12:49 pm
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.
Title: Re: Scaling down, can you help my maths?
Post by: stuckinthemud on May 06, 2021, 06:33:49 pm
Not sure it took set, it seems to me to be reflexed a couple of inches but the  drawing also looks like it shows a rectangular dent at centre.   This kind of dent could well be a result of being braced against a narrow crossbow stock, especially if the bridle edges were left square or a leather buffer pad wasn't fitted between bow and tiller.
Title: Re: Scaling down, can you help my maths?
Post by: Digital Caveman on May 06, 2021, 06:50:30 pm
Wasn't this posted a while back?
Title: Re: Scaling down, can you help my maths?
Post by: stuckinthemud on May 07, 2021, 07:42:02 am
Wasn't this posted a while back?

I posted the diagram a while back asking what people thought of it.  My research following that thread led me to a French website which described the reconstruction of the original in a French museum, the description of which which one of the guys on the Arbalest guild translated  to be of elm.  I duly ordered up some very nice wytch elm.  I carried on researching, finding a picture on an Italian blog (love google translate) which said the name of the book the image came from.  I then contacted the author, once I'd managed to locate her to a French university who very kindly informed me the bow - in fact all the bows from the site - was definitely not elm, it was yew.  AArgh!  Turns out the museum reconstruction was incredibly poor in all directions - wrong materials, wrong dimensions, just all wrong.  Now people are using that reconstruction to state categorically what the original 11th century bow was capable of and they are literally describing a powerful (for the time) hunting/war-bow as a kids toy/youths training bow.  I don't know for sure, but I would have thought the bow would be well above 150lb, but some sources state it was about 30!  Rant over.

My quandry is this.  I need to do an accurate reconstruction, or a model I can use to show what the original could do.  My stock of yew has 2 warbow staves, 1 nice 36 inch billet and a lot of stuff that is twisted and/or deflexed.  My warbow staves are beautiful grade A2, and I am keeping them until I feel skilful enough to do them justice.  I really don't want to cut even one of them up.   I think I will put the project on hold for now until I can get hold of a nice yew billet the right size and then just go for it
Title: Re: Scaling down, can you help my maths?
Post by: Strelets on May 07, 2021, 02:55:59 pm
 I will try to answer the original question.

To a first approximation, the draw weight is directly proportional to the distance of string travel as it is drawn (this is less than the draw length, because of the bracing height and handle thickness. For a "draw length" of 28", the "distance drawn" might be about 20".)
This approximation is usually pretty close if the bow is long compared with the draw length, but goes astray for bows that are very short.

The draw weight is:-
 directly proportional to the width of the bow,
 proportional to the cube of the thickness,
 inversely proportional to the cube of the length.

So, if you keep the width and draw length the same, but reduce both length and thickness by 10%, you will have exactly the same draw weight. If you also reduce the distance drawn by 10%, you will  reduce draw weight by 10%. If you want to return to the draw-weight of the original, then increase the width by 10%.



Title: Re: Scaling down, can you help my maths?
Post by: stuckinthemud on May 07, 2021, 07:07:20 pm
Thank you that's amazing, I've screenshot this so I do not lose it.  That's definitely something I can work from, I can keep the draw length and width the same which means I can keep the tiller dimensions correct to the original as well.  Fab, thank you.
Title: Re: Scaling down, can you help my maths?
Post by: willie on May 07, 2021, 10:09:28 pm
So, if you keep the width and draw length the same, but reduce both length and thickness by 10%, you will have exactly the same draw weight. If you also reduce the distance drawn by 10%, you will  reduce draw weight by 10%. If you want to return to the draw-weight of the original, then increase the width by 10%.

I ran a 65" prymid 28" draw through woodbears spreadsheet to see how it agrees with this rule of thumb.

piking 10% raises draw weight and strain

piking 10% and thinning 10% will only allow a draw lenfth of 25" if you do not wish to strain the bow any more than the original.

I had to reduce the thickness 22% to get the draw length back to 28"

without adding any additional width to make up for the loss of thickness, the bow was pulling 29#
Title: Re: Scaling down, can you help my maths?
Post by: Strelets on May 08, 2021, 12:57:29 am
Do you know the maths behind the spreadsheet?
Title: Re: Scaling down, can you help my maths?
Post by: willie on May 09, 2021, 12:56:37 am
the sheet calculates bend radius, draw length, widths and strain at stations along the limb for a given thickness, woods and draw weight.  (and much more)

My previous example was for a stiff handled prymid bow.   (which pulled 50# btw)

I also ran a 66" bend throught the handle, 28" draw through woodbears spreadsheet to see how it agrees with this rule of thumb. 45# draw weight

piking 10% raises draw weight and strain

piking 10% and thinning 10% will only allow a draw lenfth of 25.7" if you do not wish to strain the bow any more than the original.

I had to reduce the thickness 21% to get the draw length back to 28"

without adding any additional width to make up for the loss of thickness, the bow was pulling 33#

I would be glad to email you a copy if you pm your email, or you can visit

https://www.virtualbow.org/resources/ (https://www.virtualbow.org/resources/)   for  other sheets
Title: Re: Scaling down, can you help my maths?
Post by: Digital Caveman on May 11, 2021, 08:31:30 pm
I wonder how hard it would be to write a MATLAB code for this kind of work; it is impressively versatile.  It would probably not be as universally usable as Excel though.