high gear bows
scp
Khotan or Mollegabot bows.
Cf. http://www.atarn.org/chinese/khotan_bow.htm
As they appear to shoot reasonably well, I'm wondering about the
usefulness of leverage. Dan Perry says that "Leverage may be the most
controversial element of bow limb dynamics, since most bowyers I have
talked to deny the existence of leverage and gearing in bows." TBB vol.4
p.164
The issue appears to be what is the effect of making the relatively long
portion of tips unbending. Can we apply the reasoning concerning working
recurves and static recurves here?
If someone is willing to convert a reasonable well built flat straight
bow into a high gear bow by gluing some wood to the tips and narrowing
them, making them unbending but not much heavier than the original, we
might be able to get some ideas. I am saying this here because I have
almost no experience in gluing in siyahs. Has anyone here ever done this?
scp
I think Mr. Perry is not using the term in that sense. Otherwise no one
would deny its existence and the leverage would be same whether the tips
are unbending or not.
Let's do a thought experiment. If we turn the tips of a straight flat bow
and the tips are one half in length of the working limbs, we might have
made the tips unbending. What would be the effect of such conversion? We
would probably break the bow if we try to draw it full length. What if we
start with a Mollegabot style bow with unbending tips that are as long as
the working limbs? If we turn the tips 90 degrees, the tips would bend a
least a little. Will the bow shoot faster or slower? All might depend on
the weight of the arrows. Will it shoot heavier arrows faster but lighter
arrows slower? But if there is no effect at all, does that mean
"leverage" does not exist?
scp
I'm rather math challenged. So, I would just accept an engineer's
opinion if it appears to be qualified. Meanwhile I have to think in the
ordinary language or in pictures.
So far as I can tell Dan Perry seems to think it makes a difference in
dynamics if we make the tips unbending. I suspect he thinks such
"leverage" works in a way that makes the bow shoot lighter arrows faster.
All other things being equal, especially the mass of the bow. If that is
the case, does that mean such "leverage" does exist?
scp
It's not clear yet what Dan Perry meant by "leverage" or at least whether
it's a quantitatively testable quality. Anyhow he did say that "most
bowyers I have talked to deny the existence of leverage and gearing in
bows." I guess we need to refine the question.
Let's ask the simplest, the broadest, or the silliest question first. All
other things equal, mainly all the material used and all measurable
things that affect the performance of a bow, is it possible to change the
design of a bow to make it shoot lighter arrows faster than a straight
flat bow?
scp
If I remember correctly, for whatever reason, Tim Baker does not buy the
argument for the existence of "leverage" of Dan Perry.
Anyhow, let's ask the next question: All other things being equal,
especially "the same reflex, draw weight, and draw length," is it
possible to change the design of a bow to make it shoot the same weight
arrow faster?
scp
Thanks for so many observations, all reasonable and helpful. Maybe we
should use the term "tip leverage" to avoid confusion. Now let's ask the
"tip leverage" question.
All other things being equal, especially "the same reflex, draw weight,
and draw length," is it possible to make a bow shoot the same weight
arrow faster by making its tips unbending?
scp
The issue is whether there is such a thing as "tip leverage" useful in
making the bow shoot faster. Is it even possible to make the tips
unbending while keeping the same draw length and draw weight? I don't
think so. I better rephrase the question.
All other things being equal, especially the same mass and draw weight
but not draw length, is it possible to make a bow shoot the same weight
scp
Another way to look at the issue is to ask ourselves whether the static
recurve bow shoots better than the working recurve bow and if so why.
scp
Mark, I'm mostly concerned about unbending tips in all wood selfbows. I
just love them and sincerely hope that those tips work better than any
other design. My questions are all slightly different. I'm rephrasing
them ever so slightly each time just as a hunter stalks his prey.
KIandaght, even though I think your reasoning is plausible, I don't think
we can make the tip leverage bow with same mass, draw weight, and draw
length as the straight bending limb bow. If mass and draw weight are
same, the tip leverage bow would probably have much shorter draw length.
Let's just compare selfbows of same mass and draw weight. Is there
anything measurable in the tip leverage selfbow that would make it shoot
the same weight arrow faster than selfbows of other designs?
scp
Because with unbending tips, the initial draw weight would be higher,
making it reach the maximum draw weight earlier, that is, in the shorter
draw length.
I'm pretty sure the tip leverage bows will do very well with light
arrows. But I'm mainly interested in the average weight bow shooting
average weight arrows. If we keep the same draw length and allow any draw
weight, tip leverage bows would shoot much faster because of the
increased stored energy. But the same effect could be achieved by more
reflex or setback as well. So, nothing special about tip leverage with
regard to the stored energy. But there might be a difference in how the
energy is released.
Adam said "Short spring moves fast, long spring moves slower (I wrote
about the natural frequency of limbs in an article in in the book if
anyone remembers). It means the bows with the shortest bending sections
and the longest stiff tips are the fastest." Does that mean the bows with
unbending tips are more efficient? Less limb vibration and/or hysteresis?
scp
Waterlogged, thank you for the wonderful post. Frankly I don't quite
follow your steps that well. But the amount of stored energy would be
same in all cases. That means we need to look at the [release] efficiency
of the bow to see any difference.
"Tip leverage" might change the amount of limb vibration and hysteresis.
I believe that's where we should go. Now we really need an engineer or a
physicist.
scp
TBB vol.4 p.143 String Angle and Stack
The angle made by the string and arrow is the important angle. The
near-tip string angle is less significant. If limb and string are nearly
parallel for a high percentage of limb length then braced string tension
is greater, increasing early draw weight.
But as I said earlier, Tim Baker does not even buy the existence of "tip
leverage" in bow dynamics.
For now I'm only interested in comparing well tillered straight bows of
same maximum draw weight regardless of their draw length. The thought
experiment I suggest is to take a well made pyramid style straight bow
with circular tiller and turn its tips that are one half of the length of
working limb 90 degrees to make them unbending. What would be the effect
of doing so with regard to the angle made by the string and arrow, at the
same maximum draw weight? Better yet, can anyone guess at their force
draw curves?
I suspect that the curve of the bow with unbending tips would be fatter
at first. But will the draw length of the converted bow at the maximum
draw weight be as long as that of the original bow?
scp
It's good to know that I can just shoot a really heavy (over 2000 grain)
arrow and "see" the amount of the stored energy. But this "tip leverage"
is rather illusive. If it is in the change of limb vibration and
hysteresis, it might not show up even in the force draw curve. If it does
not even exist, as most bowyers think, we are wasting out time. But just
because I really love the bows with long unbending tips and Dan Perry
said that "leverage" might exist, I will keep at it for a while longer.
Working recurves can probably be made as light as straight limbs. Cf. TBB
vol.2 p.173. Can static recurves be made as light as working recurves?
scp
Dan Perry says in TBB vol.4 p.166
Non-working recurves, siyahs, or light, narrow, non-working outer
limbs on straight bows, shorten the working limb and compound velocity.
This shortened working limb, combined with leverage, helps with heavy
arrows just as with light arrows. If the mass of the outer limbs remains
low, dry fire speed goes up, but we also gain by compounding velocity by
the length of the lever from the bow tip to the beginning of the working
limb.
The key ideas appear to be the short working limb and compound velocity
"through leverage." I think I get what Adam said about the effect of
short working limb. I think Ryoon4690 is saying the same thing. He also
thinks stiff tips can be even lighter than bending tips. I sure hope so.
But I have no idea how to measure or even picture the compound velocity.
I don't think I would comprehend its mathematical representation. Still I
think this is what Perry means by "leverage" and he also says it is "the
most controversial element of bow limb dynamics, since most bowyers I
have talked to deny the existence of leverage and gearing in bows." Would
anyone care to explain this concept in the ordinary language or in
pictures?
scp
it's never easy to come up with a new idea. Dan Perry was courageous
enough to write about "(tip) leverage" that compounds velocity in bow
limb dynamics. But he was not successful in convincing other bowyers
about even its existence.
IMHO he was thinking about compound leverage.
Cf. http://chestofbooks.com/crafts/metal/Applied-Science-Metal-Workers/35-
Problems-In-Compound-Leverage.html
But it takes more than one fulcrum to have compound leverage. We don't
have the secondary fulcrums in bow limb dynamics. At least while we are
pulling the bow.
But is it possible that they appear at release? Just after the working
limbs stop moving, the unbending tips might keep on moving a little more.
I think this can be captured with a high speed camera.
scp
I think we can test it even without a high speed camera. First we make
the joint between the working limb and the unbending tip way too thick to
bend at any velocity. Then we make the joint as thin as possible without
making it break, and measure the difference in the mass of the bow. Now
we add that amount of weight to the joint using a material that is as
flexible as possible. If this bow shoots any faster, there's something
about the concept of "tip leverage that compounds velocity." What would
be the best flexible but rather heavy material we can use?
scp
Actually Dan Perry did a similar experiment but was not able to persuade
Tim Baker.
http://paleoplanet69529.yuku.com/sreply/46319/t/Bow-Limb-Dynamics.html
For your convenience I will quote several paragraphs from the link.
Dan Perry:
It sounds like you see why I am challeging the Stored energy/ Mass
Period! Theory. It is not that I don't believe it, I just believe there
is more to it. I believe that the way the limbs apply the stored energy
makes a difference, especially with light arrows. I believe I have
isolated the limb design elements that make the most difference, but
because they also store more energy I had to find ways to make it store
less. Hence making the hinge narrow enough to take a set to reduce early
draw weight, and short enough for the draw to stack. I feel I have dogged
it down to an average level.
Even with less stored energy, the long lever and hinged limb act like
it was reflexed a mile when shooting light arrows.
The whole reason for these test bows was to prove that there was more
going on with the long stiff levers, and hinged limbs than just energy
storage. The dynamics of how they apply the force and transfer energy I
believe to be a large part of why they perform so well with light arrows.
Energy in doesn't always mean energy out where we want it. But I
believe using this leverage makes it as good as it gets.
Tim Baker:
The principles involved are simple. Straight outer limbs store more
energy, and extremely narrow, low-mass outer limbs transfer more of the
bow's stored energy to the arrow. That's all there is to it. This larger
energy transfer happens for two reasons: a stiff and low outer limb
reduces energy-robbing limb vibration, and light outer limbs allow
quicker acceleration of the arrow during early and mid portions of the
return. This increases efficiency, I believe, because less of the bow's
energy is then asked to rush to the arrow during that last train wreck
moment of string impact.
It's assumed that near-center-section bending wood is wide enough to
take little set, this extra width having no inertia penalty because it's
so slow moving.
The design can be morphed in width, length, and stiff handle/center
section length, depending on arrow weigh and intended use.
I disagree about gear and lever principles, and the need for the
terms, but we can argue that later.
That was 2007, now here we are. From "hinged limbs" to "inflexible or
flexible joints of same weight."
I sure hope my experiment at least makes sense to them.
scp
IMHO the real issue is how to find the fulcrum, other than the one at the
grip, that would make the compounding of velocity possible. Dan Perry was
getting there. That's why he made the joint of his test bow "hinged" (in
the bowery sense, not literally).
A lever is not just a hinge. Leverage can be compounded if there are more
then one lever and a fulcrum.The main issue is whether there can be more
than one lever in a bow limb.
As for hinged bows, Tim Baker has some interesting ides in TBB vol.3 p.97
(some theoretical designs). Can we think of a bow limb with another set
of lever and fulcrum? Just extend the bottom of the tip lever to pass the
hinge (on both side, back and belly, giving some space between them and
the working limb). Now we have a second lever and fulcrum. It might not
matter much while we are pulling the bow. But on release, the tip lever
might work more efficiently than a fixed tip. Not sure how for now, but
it might actually compound leverage, hence even velocity.
But hinged tips are difficult ot make and can be rather dangerous. I
would rather do my experiment first.
scp
We are looking for leverage (a lever and a fulcrum) that can compound
velocity. Compound leverage is simple to understand if all fulcrums are
not moving at all, at least relative to each other. But so far, it's not
clear to me how a lever can compound velocity when its fulcrum is on
another lever.
scp
Wonderful. Actually Dan Perry was inspired by "atlatls, slings,
catapults, trebuchets" and came up with the "(tip) leverage" idea. That
means, we need an actual hinge (of limited movement, of course) in the
joint between the stiff tip and the working limb. It would allow the tip
to move (actually rotate) further even after the limb stopped moving. My
experiment would tell us whether that is the case or not. Or we can just
make a bow with "hinged" tips. That's exactly what Dan Perry did, as
quoted above.
Will this be enough to convince other bowyers including Tim Baker?
scp
Dan Perry already knew the design works. Even Tim Baker agrees that it
works. Still Mr. Perry wanted to explain why it works. And after all the
exposition he made to Mr. Baker, the latter flatly denied the existence
of "(tip) leverage" Is his reasoning why the design works more convincing?
But first thing first. Do all stiff tip bows that shoot well have the
"hinge"? If not, do the "hinged" ones shoot better than those without a
"hinge"?
scp
It appears that some people just cannot get over the dogma
that a bow should not have a hinge in its working limbs.
We are talking here about the joints between the working limbs
and the unbending tips. They should be made stiff enough
not to bend too much while the bow is pulled, but flexible enough
to make the leverage, that is, compounding of velocity, possible.
Is it even possible for them to be made that way?
I think so. Especially when the pulling angle is almost parallel
to the string and the angle after release is almost perpendicular
to the string when we need the "hinge" to work,
as in the case of horn bows.