Limb design. reply

blakey

Active member
Sorry if this one is a bit off topic but it reminded me of a longbow design article I read once. The comment was regarding traditional D-section versus a triangular or even removing material to make a concave shape on each side of a central point in the belly of the bow. As I recall the conclusion was that it was a way of getting increased speed but at the expense of durability and possibly shootability. I wonder whether modern laminates could make the design viable?

There wasn't any comment on bow shape as I recall, just cross-section. Also, I don't remember who it referred to but I think someone well known had experimented with the design.
I've read something similar. I think a couple of Americans in the early 20th C did some comparative studies of ELBs v Flatbows. (Hickman?). The findings were that the flatbow is superior, and they designed one to knock over Horace Ford's York record. Cheating Yanks of course according to the purists. The D-section does have a tendency to fail under compression according to engineers. I do sometimes wonder though whether abstract mathematical calculations can fully analyse the properties of natural materials that have evolved over millions of years? Horn is the one that impresses me. It is just compacted hair. It has incredible compressive strength. :)
 

Darth Tom

Member
you need to read the bowyers bibles. Vol1 2 and 3.

they tell you what you need to know.

but in short in a limb you have three main stresses.
compression, tension and sheer.
sheer us up the nutral axis.
you also have a bit of compression between the laminates.
the core needs to withstand the back to belly compression, as well as the sheer stress.
the laminates need to withstand the compression and tenson.
so if you had a triangular cross section, i assume peak in the belly, how do you handle compression?

laminated wooden bows are just the same, compression tension sheer....

I beams, have a top and bottom.... and a vertical (core) to keep the two other parts appart...
So in a triangular section bow all the compression force would be concentrated at the apex of the triangle. What happens to the front of the bow where the back has been cut away? Would it be unsupported in compression, thus introducing a force across the limb as well?
 

JohnK

Well-known member
Hi Sid, that's what I assumed, but in this quote from your first post in this thread you say: "the fastest bows in the world ..... are the ones that store the best energy. Examples of this are the ACS longbow, the Centaur Longbow, and our longbows."
So I was wondering whether I was missing something? Obviously not. :)
Read the next line: "and the fastest recurves ever produced, all look at stored energy as the main remit, and not at mass reduction as the main game.
granted to be the fastest, you need both mass reduction and stored energy."

So, no, he isn't saying that flatbows are faster. He's talking about which makes of flatbows are the fastest, and what the qualities of the fastest recurve limbs are.
 

BorderBows

New member
Read the next line: "and the fastest recurves ever produced, all look at stored energy as the main remit, and not at mass reduction as the main game.
granted to be the fastest, you need both mass reduction and stored energy."

So, no, he isn't saying that flatbows are faster. He's talking about which makes of flatbows are the fastest, and what the qualities of the fastest recurve limbs are.
the arguement has been that longbows store 0.9sepdf, and recurves have been storing 0.92 sepdf. so the limb mass becomes the deciding factor in bow speed.
with longbows having skinny limbs, its possible to say that the limb mass is sufficently less that it can keep up with a recurve.

but the game on what a longbow has been (longbow being a UK flatbow) progresing more and more towards a recurve, with Hybrids.
there is a fine line in design between a very aggresive hybrid that has ignored vertical stability, and a very mild recurve. is the recurve is simply a longbow thats been even more reflexed at the tips.

but the game changes, when you look at super recurve.
the term longbow means it CANNOT have string wrap. so its limited in its reflex. while the term recurve can include super recurves.
with a super recurve its possible to store 1.2sepdf. so that simply leaves longbows standing.

considering 4fps is regarded as a considerable step forward.

a super recurve doesnt come with a mass penailty.

longbows simply cant keep up.


the other "cheat" in the marketting in longbow vs recurve comparisons. is that the longbow is vastly carbon powered, Carbon laminates are available for bow makers to play with.
so the comparisons are with glass powered recurves.
but when compaired to a carbon powered recurve (not one thats carbon but BOUND in glass)
 

BorderBows

New member
So in a triangular section bow all the compression force would be concentrated at the apex of the triangle. What happens to the front of the bow where the back has been cut away? Would it be unsupported in compression, thus introducing a force across the limb as well?
for exactly the same reason its pointless to only have one torsional stability layer, you need an opposit to counteract the equal...

if you have a flat front, you spread the stress over that flat area in a equal way. as you say, the peak concentrates the load into that peak...
 

Job

New member
I see that the thread 'Limb Design' in Archery Forum Australia which precipitated this has degenerated into puerile inanity. Not sure how this reflects on the "Science" of the opinions expressed, but suppose it means their influence will be negligible.
 

BorderBows

New member
I see that the thread 'Limb Design' in Archery Forum Australia which precipitated this has degenerated into puerile inanity. Not sure how this reflects on the "Science" of the opinions expressed, but suppose it means their influence will be negligible.
the thinking behind leverage vs efficent use of materials comes down to limb mass.

if the leverage provides more stored energy, but the stored energy is so incumberd by the mass of the limb, then there is NO point in increasing the leverage. (klopsteg)
this would be Parks point, i beleave, with the likes of even distribution of stress along the limb.
where as Adock, with his ACS design, argued that with light mass outer limbs the Longbow could keep up with recurves.
the ACS concept stiffens the outer limb without adding mass. (by shape)

So my point is that use of materials impacts on the bias of the maths.

if you have materials that allow you to stiffen the limb without adding extra mass, then the bias changes.
if you have materials that reduce the limb mass by a WHOPPING amount, then the bias changes.
for example if the stored energy increases faster than the mass increases then its worth doing.

Carbon is ALOT stronger than glass, and glass is alot stronger than wood.
this strength can equal limb mass reduction.
so look at the changes in limb design when moving to a glass limb from a wood limb.
so why is carbon stuck to the same old designs as glass limb.

either that or its a different issue, such as mass production not wanting to change its production line... and with market dominance, why bother...
 

blakey

Active member
the thinking behind leverage vs efficent use of materials comes down to limb mass.

if the leverage provides more stored energy, but the stored energy is so incumberd by the mass of the limb, then there is NO point in increasing the leverage. (klopsteg)
this would be Parks point, i beleave, with the likes of even distribution of stress along the limb.
where as Adock, with his ACS design, argued that with light mass outer limbs the Longbow could keep up with recurves.
the ACS concept stiffens the outer limb without adding mass. (by shape)

So my point is that use of materials impacts on the bias of the maths.
I've tried to follow the argument on Archery Forum, and haven't really been able to understand it. The claim that longbows are more 'effective' seems facile. We all know that recurves are faster, and super recurves even more so. Apparently numbers do not lie, so it's the application of the maths that must be flawed, or the modelling? I've seen some comments of yours about leverage. I'm wondering if the maths relates to a stiff lever, that doesn't flex? This would give a simple mechanical advantage to a short limb. However the leverage of a curved limb that unrolls as it is drawn is totally different. Would its energy not be compounding as it expands? Also the nature of the material that would be wanting to return to its static formed shape would also have to be taken into account. I'm no mathematician, but it would seem to be extremely difficult to formulate this in abstract?
I like your idea of thinking up a design, and testing it. That's more of an evolutionary approach. If it fails it disappears. If it works it's the basis of the next step? :)
 

blakey

Active member
Well I've decided to read Kooi. I mean I've ploughed through Ascham so how bad can it be? The maths is beyond me but the language is interesting. On Mathematical models for bow performance Kooi starts with Hickman, who models a bow with 2 linear elastic hinges (at the fadeouts?) and rigid limbs. Ie they don't bend. Next Schuster who " made a mathematical model assuming the Recurves limbs to be part of a circle which unroll along the initial tangent."
Sounds interesting?
But:
"Observe that we do not discuss the results of Schuster's model, because we are not able to deal accurately enough with the dynamic performance of the working recurve bow. "

So basically Hickman's model, which James Park is using, is simple levers. And not relevant to your design at all.
And the maths to explain recurve, let alone super recurve, did not exist in Kooi's time?

There is of course more, but I will leave you with this nugget:
"It is even possible that the drawing force can decrease in the neighbourhood of maximum draw." Kooi 1983 (predicting the design of the Hex series?)
 

BorderBows

New member
Well I've decided to read Kooi. I mean I've ploughed through Ascham so how bad can it be? The maths is beyond me but the language is interesting. On Mathematical models for bow performance Kooi starts with Hickman, who models a bow with 2 linear elastic hinges (at the fadeouts?) and rigid limbs. Ie they don't bend. Next Schuster who " made a mathematical model assuming the Recurves limbs to be part of a circle which unroll along the initial tangent."
Sounds interesting?
But:
"Observe that we do not discuss the results of Schuster's model, because we are not able to deal accurately enough with the dynamic performance of the working recurve bow. "

So basically Hickman's model, which James Park is using, is simple levers. And not relevant to your design at all.
And the maths to explain recurve, let alone super recurve, did not exist in Kooi's time?

There is of course more, but I will leave you with this nugget:
"It is even possible that the drawing force can decrease in the neighbourhood of maximum draw." Kooi 1983 (predicting the design of the Hex series?)

We have 0.5lbs in that last inch done on a 60" covert hunter pulling 51lbs at 28".

So we are very very close.

That said i have a huge question to answer tomorrow when i get to test a few things.

Mmm...

I have a handfull of bows to string up... :)

Ill be back...
 

BorderBows

New member
We have 0.5lbs in that last inch done on a 60" covert hunter pulling 51lbs at 28".

So we are very very close.

That said i have a huge question to answer tomorrow when i get to test a few things.

Mmm...

I have a handfull of bows to string up... :)

Ill be back...

ok...

the thinking is that 70lbs bows gain 3.5lbs per inch.
40lbs bows are 2lbs per inch.

30lbs bows are 1.6lbs per inch.

0lbs per inch on a ULTRA smooth DFC would have 0 pounds per inch, irrespectve of poundage.

so 0.5lbs pounds per inch gain means very little change when you change poundage.

i can confirm it
 
ok...

the thinking is that 70lbs bows gain 3.5lbs per inch.
40lbs bows are 2lbs per inch.

30lbs bows are 1.6lbs per inch.

0lbs per inch on a ULTRA smooth DFC would have 0 pounds per inch, irrespectve of poundage.

so 0.5lbs pounds per inch gain means very little change when you change poundage.

i can confirm it
It's amazing !
 

anmactire

New member
Here I was thinking I really would love a Hex 7.5 limb (really wish I could afford a set right now!) and then Sid drops another one of his hints at progression in the works towards something magic like an even lower PPI at full draw... Maybe I should save my pennies and just wait for a Hex 9
 

Darth Tom

Member
Here I was thinking I really would love a Hex 7.5 limb (really wish I could afford a set right now!) and then Sid drops another one of his hints at progression in the works towards something magic like an even lower PPI at full draw... Maybe I should save my pennies and just wait for a Hex 9
The Hex 7.5 is excellent and IMO worth every penny. They are pushing the envelope though; I have no hesitation recommending the Hex 6 and CV series for anyone. They are built to the same tolerances and with the same excellent materials as the 7.5. They don't have the same preload or smoothness through the clicker, but the flip side of that is they have less of an adjustment period.

Remember that the CV has an improved draw force curve over other top conventional limbs, with extreme torsional stability and the extra speed from the glassless construction.

Personally I'd recommend anything from the Border range over anything else on the market. For that matter I'd recommend my 15-year old Borders over anything else.
 

anmactire

New member
The Hex 7.5 is excellent and IMO worth every penny. They are pushing the envelope though; I have no hesitation recommending the Hex 6 and CV series for anyone. They are built to the same tolerances and with the same excellent materials as the 7.5. They don't have the same preload or smoothness through the clicker, but the flip side of that is they have less of an adjustment period. Remember that the CV has an improved draw force curve over other top conventional limbs, with extreme torsional stability and the extra speed from the glassless construction.Personally I'd recommend anything from the Border range over anything else on the market. For that matter I'd recommend my 15-year old Borders over anything else.
I would agree, I own a set of Hex 6 S BB2 limbs. I don't see many borders here in Ireland and often get questioned on them. My sight marks are excellent with them. I shall just have to travel to the Sids perhaps
 
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