Scaling down, can you help my maths?

[stuckinthemud]

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.

[Digital Caveman]

Wasn't this posted a while back?

[stuckinthemud]

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

[Strelets]

 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%.

[stuckinthemud]

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.

[willie]

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#

[Strelets]

Do you know the maths behind the spreadsheet?

[willie]

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/   for  other sheets

[Digital Caveman]

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.