How far, how fast?

[StickMark]

Hickory board, with two courses of sinew on back, with a thick center strip, so 2.5 courses of sinew?
NTN is 59", with bendy handle.
1.35/8 " or   say a generous 1 and 3/8" handle.
That width stays for about 9.5 ", and then over next 20", tapers to 1/2 inch tips. Stiff tips for last 4" about.
thickness is 0.5" at center gradually changing to 3/8" towards tips.
(back is gently trapped, if that matters for calculations)

[sleek]

I'm very sorry, but this works only for self bows. No laminate or sinew. Too many variables, I could never figure that out.

[StickMark]

Sleek, how about this simple white oak bow.
White oak board:
60" NTN
4" handle, with 1 and 3/8 " width.
At fades, 1 and 6/8", going 11 ", and then
tapering to 6/8" tips. for that 17"'s. 
Bends in handle, slightly, with tips stiff about 4 inches. 4
Thickness:
6/8" at center, gradually thinning to generous 2.5/8", then thicker at tips.

Sleek, I am fascinated by that statement that we underbuild our bows. 

[superdav95]

Ok so my math may be off.  Sorry about that.  From center of symmetrical bow.  4.5”+ 12” at 1.75”+ 8” tapered to 1.5” + 3.5” tapered to 1”+ 4” tapered
To .5”  at tips. 

I’m in process of building this bow aiming for 50lbs at 28” draw.  Thanks 

[sleek]

Sleek, how about this simple white oak bow.
White oak board:
60" NTN
4" handle, with 1 and 3/8 " width.
At fades, 1 and 6/8", going 11 ", and then
tapering to 6/8" tips. for that 17"'s. 
Bends in handle, slightly, with tips stiff about 4 inches. 4
Thickness:
6/8" at center, gradually thinning to generous 2.5/8", then thicker at tips.

Sleek, I am fascinated by that statement that we underbuild our bows.

So white oak has lots of variation within its species. Up to 23% I went for its average properties and got a draw weight of 45 pounds. How heavy is the bow and what set did it take?

If a bow took set, it was underbuilt unless it has a bad tiller, but even then, it was underbuilt for that tiller profile. So yes, most people underbuild their bows by those standards.

[StickMark]

35 pounds
Set: 1.25"; 0.75"
I underbuilt.

And I think it just was a slightly weak piece

[WhistlingBadger]

Example: 
Wood type: Balsa
Nock to nock 62 inches
8 inch handle
6 inch stiff tips
1.5 inches wide at the fade for 3 inches past the fade
1.25 inches wide at 4 inches past the fade
Even taper to .5 inches wide 18 inches from fade
6 inch Stiff tips after 18 inches

Thanks for this offer, Sleek!!  I can't take you up on it as I don't have any self-bows in the pipeline at the moment--I'm experimenting with sinew and dogbane backings on all my current projects.  But now I feel this weird emotional need for someone to build a 62", balsa wood bow with an 8" handle and 6" levers...

[sleek]

35 pounds
Set: 1.25"; 0.75"
I underbuilt.

And I think it just was a slightly weak piece

If you drop the 23% of white oaks range, 23% of 45 pounds is 34 pounds. White oak has such a huge range from essentially a rubber tree all the way to stout as osage, it would require a test of that wood to know what to expect. Also did you heat treat the bow? White woods soak moisture like a sponge and moisture content in any bow will cause set. If you haven't heat treated it, perhaps try that and let me know if that makes the difference?

Like I said, this is a learning experience and I'd not considered that a single species would vary over 60% within its own species. For example, is density ranges from .55 to .83, a 66% difference.

[StickMark]

Heat treated the heck out of it.
But, this build i attempted to try the tracing method. Outlining on paper.  (1.25 set is on bottom limb. I string it w step through method.)
I went too ⁷far with sanding, those dreaded adjustments that i do at the end; your observation of underbuilding comes in play here, as leaving more wood to handle the final adjustments would have given me 43, 45 #.
I have a piece from same board, shorter by 8 ".
I am going to finish it today, but leave it much "stouter" in build: semi bendy handle, but wider. Will heat treat through out build, and get back w results.

[sleek]

Heat treated the heck out of it.
But, this build i attempted to try the tracing method. Outlining on paper.  (1.25 set is on bottom limb. I string it w step through method.)
I went too ⁷far with sanding, those dreaded adjustments that i do at the end; your observation of underbuilding comes in play here, as leaving more wood to handle the final adjustments would have given me 43, 45 #.
I have a piece from same board, shorter by 8 ".
I am going to finish it today, but leave it much "stouter" in build: semi bendy handle, but wider. Will heat treat through out build, and get back w results.

How a bow is handled over its life will case set  I can't account for, such as the step through method over stressing the lower limb like you mentioned. This method I'm using is good for a fresh dry bow, that won't take set under normal conditions.

Your next bow being 8 " shorter will stress it more,  You will need more width through more of the bow to compensate 

[StickMark]

Starting on 2" wide on this particular piece.
I am happy with the set on the above mentioned bow, in that I am getting better at this.
Amazingly enough, on my penetration test, that 35#bow does close to a 41# bow, same arrow (14.5 gpp vs 12.5 gpp, respectively.)

[Hamish]

StickMark. Have you changed your stringing method?

Step through is only appropriate for composite recurve bows, as they are a lot more resilient than all wood bows. I cringe anytime I see someone do that with their self bow. To try that when attempting to first string a bow, can leave an excess of set in the lower limb that sometimes the upper limb will never catch up with. This is fundamental to wooden bowyering.

A bow stringer is the best option, at least when first trying to get a string on the bow, as it, is more even with stresses. Then push/pull when its string able by hand.

[StickMark]

Hamish,

I need to go back to the bow stringer method. Around 2019, I built a second set of nocks into three bows, for a homemade 550 paracord stringer. Could use it in the desert scrub, by just placing the bow on a hat that was on the ground to avoid roughing up the back. Looking back, it worked, and I just got lazy.

The 35 pounder bow might have been more even then, with a stringer, and I can live with 3/4" set.

Will be a while before I first brace this shorter piece of white oak, and I will relay dimensions and set, etc,...and add that data to this thread. I appreciate this type of research.

[ssrhythm]

Ok, so, I want to see what weight a stave will give me, I am NOT chasing a draw weight.  I have a decent quality yew stave and the tapers are ones I have used before.  At the get go, the bend is good and there is zero set with the bow bending a few inches but not at low brace. There are schools of thought about teaching the bow to bend.  So, how hard do you chase the bend.  The primary aim for this build is to get as close as possible to zero set, so using the beginning of set as a guide is not one I want to use. I haven’t heated in any reflex but I want the bow to be dead straight when finished.

A bow with no set starts with a bow of the proper dimensions. I've got a formula that will tell you the exact draw weight a bow will take before taking set based on the wood type and dimensions. If you tell me the dimensions, I'd be happy to tell you the draw weight that bow will handle before it takes more than 3/8 inch set.

Disclaimer: ( of course there is one ) I've been working on this formula for YEARS and it works perfectly on osage. I've dabbled with it in other wood types but have not proven it yet with other woods. It seems to hold true and I'm looking for other woods to try this formula on. If you are willing to give it a go, I'll run the numbers for you.

I haven''t read past this post yet, so forgive me if a similar reply has already been posted.

Do you mind reverse-engineering what you proposed above?  I'm really wanting to build an Osage self bow that will hit ~54-55# at 27", and I'd really prefer it to be recurved.  I'd prefer it to be ~63"-65" overall length with a stiff handle and modern pistol type grip. What dimensions has your research shown that will reliably allow this bow to be made without taking set?
 
I know your formula likely assumes perfect tiller and perfect tillering process from start to finish, but I'm curious what dimensions your research would deem as ideal. 

Thanks!

[ssrhythm]

Doh!  Ive now read the thread.  I'm still curious if you can reverse-engineer the formula and give me the dimensions I should use.

That said...

Osage Orange recurve with no other reflex
63" total length; 62" n2n
ten inch stiff handle with grip section 1 1/4 " up from center to 2 3/4 below center and 3" fades
 
(the following dimensions are my best attempt to keep the same proportions from the TBB vol 1 67" osage flat bow that had a 4" grip and 3" fades but grip was laid out = at 2" above and 2" below center...ie = limb lengths...but applying the dimensions equally to a 63" bow with a shorter bottom limb than top limb)

Bottom limb: Fade to beginning of taper = 10 3/4" at 1.5" wide.  Beginning of taper to tip = 14 7/8" tapering evenly from 1.5" to 1/2" tip width with nocks 1/2" from tip.  Stiff tip from from 8 1/4 from tip; Recurve starting at 7 1/4 from tip

Top limb:  Fade to beginning of taper = 11 1/2" at 1.5" wide.  Beginning of taper to tip = 15 3/4" tapering evenly from 1.5" to 1/2" tip width with nocks 1/2" from tip.  Stiff tip from 8 1/2" from tip; recurve starting at 7 1/2" from tip.

These are the rough dimensions of a bow I have laid out for my son's bow.  Stave is limiting me to 1.5" wide max.  I have not yet reduced the tips or cut the handle.  I chose to keep the limbs'  max width lengths and taper lengths proportional to each other since the top limb is longer than the bottom...I figured the fact that the lower limb is shorter will result in it being stronger if the proportions are  the same relative to the top limb.  This might be flawed thinking, but I cannot find anything definitive for upper vs lower limb layout dimensions on bows with shorter bottom limbs in the books I have read.  Please point me to this info if you know where it resides.  Keeping proportional makes sense to my brain, but doing percentages with fractions warped my brain...so I got as close as I could before retiring for the evening to a Whiskey neat...or three.

Anyhoo...I hope you can give me my max draw weight possible without this bow taking set from the dimensions I've listed.  If you need anything more, let me know.  Thanks a ridiculous heap for being willing to do this for us.