Primitive Archer
Main Discussion Area => Bows => Topic started by: joachimM on January 21, 2015, 04:38:44 pm
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Hi folks,
I've been thinking on the exact reasons why a crowned back is often/sometimes favorable to bow design. Maybe this explanation has been given before on this forum (and suppose it's right, it was probably a better one than mine), but since I always have the feeling that to understand something really well, you should be able to explain it someone else. So here's my attempt at doing so. If you disagree, please tell me, and tell me why so I might learn something from my mistakes.
Most if not all woods are much stronger in tension than in compression. As far as I interpret the data from wood databases correctly, most woods are about twice as strong in tension than in compression. That is, a beam of wood that is bent takes set (non-elastic deformation of the belly due to compression) way before the back breaks. This is also what comes out of the standardized bending tests of Tim Baker (and later bowyers). So typically, the thickness of a bow is dictated by the ability of the wood to withstand compression rather than tension, unless you allow set to occur. At least, that's the principle behind no set tillering. In flight bows one evidently wants to avoid set, so the belly dictates the thickness.
In David Dewey’s (aka Woodbear) spreadsheet the amount of strain the back can take before the belly starts to take set is termed the proportional limit, which is on average half of the rupture modulus (the tension at which the back starts to fail). If I'm not mistaken, this difference in tension and compression strength can also be deduced by the difference in crushing strength (compression failure) and modulus of rupture (tension failure).
When wood is stronger in tension than in compression and the surface of belly and back is equally large (rectangular cross-section), the neutral plane will not be exactly in the middle, but shifted towards the back of the bow: more belly wood is required to withstand the compression dictated by the back, because the wood is stronger in tension. The thicker the part that has to deal with compression, the easier the wood takes set at the same bending radius.
This can be avoided by having a broader belly than back, which is the case in bows with a crowned back. It doesn’t stop there: in a crowned back design, the neutral plane of the bow shifts more towards the belly (because back and belly are more in balance), as a result of which there is less belly thickness in which set can occur, as a result of which the bow can bend further before taking set. Or put otherwise, a bow with a crowned back and flat belly has a higher proportional limit than one with a rectangular cross-section.
Toasting the belly has a similar effect. For reasons not entirely clear to me, toasting increases the the crushing strength of wood.
I'm sure there's plenty of leeway for improvement of my reasoning, so shoot!
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I am not convinced that the thinner parts of the limb are doing their share of the work. Just a small change in thickness equals a large change in beam strength. I sometimes trap when I want lateral stability but want an area slightly bending more. I am not conviced trapping or crowning has any benefit.
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well I have no proof other than what experts have written,,, that the flat back and belly can bend further without taking a set or breaking,,, but I am open minded as to what you say if someone can show me an example of such design and performance obtained :)
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i use a lot of ash, which is known to be excellent in tension and rater bad in compression. since i started trapping the back i noticed that bows on te narrow side tend to get quite a bit less follow. with wide limbed bows this effect seems to be smaller.
this is of course by no means a scientific research but only some observations from a guy who is a bit mathematically challenged but has a few hundred bows under his belt :D
i'd like to see the engeneers jump in and tell te true story...
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Badger, I'm not sure I understand your comment on thinner parts of the limb not doing their share of work.
Suppose you have no thickness taper at all (pyramid design), and you trap the back. If that indeed means that the neutral plane shifts a bit to the belly, there's also less risk of set at same bend radius. This allows you to make a slightly thicker (and therefore stronger) bow or to draw the bow further without taking set (because trapping increases the proportional limit due to the shift of the neutral plane). As you say, a slight increase in thickness will strongly increase draw weight (and that's because draw weight follows a cubic relation with thickness; this makes tillering such a critical procedure: a small error has large consequences).
As Bradsmith2010 says: the proof of the pudding is in the eating:
I mostly make bows with a crowned back, and nearly all of them weigh way (20 to 30%) below what the mass principle tells me to expect, probably because I take off excess back wood, shift the neutral plane to the belly and make the bow thicker for the same draw weight and barely taking set.
If I take Woodbear's spreadsheet for a no-set bow (I have a few bows without any set), the intended mass of the bow is a lot more than what I actually have with my trapped or crowned backs. this makes my recent hawthorn branch bow (heavily crowned) shoot very well (173 fps at 9 gpp for a 33# draw at 27"), weighing 216 g instead of the expected (mass principle) 297 g. With a proper string (I chronied it with a nylon string that stretches enormously) I could probably gain a few fps. It doesn't seem to me the thinner parts of the limbs aren't bending (see for a pic http://joachimm.paleoplanet69529.yuku.com/photos/view/pid/3856371)
Another bow I tillered today is another crowned branch bow (plum). It draws 40# at 27.5", is 151 cm long (just under 60") and weighs 333 g (with the bark still on; removing that will reduce mass further, it's starting to flake anyway). It has very little set (it keeps 1.5 " of resting reflex after heat treating the entire belly; immediately after shooting it still has 0.75" of reflex), outside the fades it's 1.85 cm thick (.73") (by 2.8 cm or 1.1" wide) and even midlimb that's still 1.4 cm or .55" thick. Intended weight according to the mass principle is approx 439 g. Woodbear's spreadsheet intends such a no set bow with flat back and belly to weigh even 510 g (at a pyramid design). My crowned design is thus 24 to 35% lighter in mass than expected with no crowned back. Yet it doesn't break, because the wood is stronger in tension than compression. The reason for this mass difference is that the allowed thickness (at no set tillering; Woodbear's spreadsheet) for the limbs is only 0.4 cm with a max width of 5.4 cm. My bow limbs are at most 2.8 cm wide but much thicker.
I think they take little set because the crowned back shifts the neutral plane to the belly (because the crown forces more wood to take the tension load). So for the same draw weight I have a bow that is much lighter than a flat back bow because I made it thicker because I could do so. And I could do so because the proportional limit was increased due to this shift of the neutral plane.
Need more convincing? 70" bow, red oak. trapped back (back is 67% width of belly). 29" draw, 77#. Pyramid design 4.5 cm wide at belly (3 cm at back) to 0.8 cm wide at nocks, 1.85 cm thick throughout the toasted limbs (tension of 0.95% compared to expected neutral plane, but likely even higher due to shifting of the neutral plane! That's what you would expect for an osage or yew bow). Bow mass=588 g (still needs sanding to remove tool marks) instead of expected 737 g. That's 20% lighter than suggested by the mass principle. I admit, it shows 1" of set right after shooting and has 0.4" of permanent set. I still need to find a 800 grain arrow to chrony it at 10 gpp. This thickness is four times the allowed thickness by the no-set method.
You said it yourself: increasing thickness a bit makes a bow far heavier. So the eternal trade off is how to make the bow as thick as allowed by set. Shifting the neutral plane to the belly shifts the proportional limit, allows for thicker bows, with lower bow mass for the same draw weight. Crowning or trapping the back (according to my train of thought) does exactly that.
I may not be able to convince you (right now), but as long as I'm thinking it works and it allows me to make better bows I'm satisfied :-)
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shoot the 70# bow with any arrow,, and it will give a good idea of performance ,,,sounds like a great bow,,, I am old school so if you shot it with a 500 grain arrow, I could compare with many of my own results,,, thanks for posting the info B
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Too tired to digest the science and watching a Hallmark movie with my wife. :)
But heavily crowned saplings have only worked for me when I've left them a few inches longer. In a crowned back I believe the tension stress to be concentrated down the middle.
I like my bows to be 64-66" long unless heavily crowned then I go 2 inches longer.
Jawge
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When you build a bow from a sapling with a high crown you have basically flat sawn wood on the back and quartersawn wood on the belly. The best of both worlds. Not to mention the closer to the center of a log you get the better the rings generally are.
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So conversely, when should a person de-crown a stave? Last year I de-crowned a hackberry stave and flipped the tips. No particular reason, just wanted to experiment. It turned out to be a nice, light weight shooter, but don't know if anything was gained from flattening the back.
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I would not decrown. Just leave it longer. Jawge
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Jawge, you are certainly correct about the tension being concentrated along the center of a crowned back. As long as that center has somewhere near 1/3 as much width as the belly, all will be well. (Most wood is closer to 3 times stronger in tension, not 2 times, as offered up top.)
joachimM, Wow. Way too many words (not too much science, just loquacious).
Now that I think of it, yes, too much science in one post. To answer all the points would take an equally extensive reply.
What's more, there is at least one source of all those issues that was written by engineer Paul Klopsteg in June of 1935 and reprinted in the book "Archery, the Technical Side." "I don't have that book!" comes the collective lament. Okay, neither did I for years, but I managed to get a copy and so can you.
Trying to rediscover those established principles without engineering background seems to me certain to produce a less dependable understanding.
If you can get the use of Archery the Technical Side, one of the best of several pertinent sections begins on page 146 with the title, "Getting the Most out of the Bowstave." Worth every word.
Jim Davis
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Jim, that makes sense. Jawge
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Thanks everyone for your suggestions. Will try to find that book, will chrony with 500 gr arrow.
And for the record: no I'm not an engineer, I'm a scientist (with a PhD). Yes that makes me write lengthy and maybe tedious messages. Sorry for that :-)
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Jawge, I agree with you, I tend to use more working limb on high crowned bows than I do flatter staves. I feel the same way that the tension is concentrated down to middle. Wood is much more elastic in compression, there is no reason to try and put the nuetral plane somewhere near the middle. If you do manage to get the tension side to stretch a little bit it is right at failure. I like to use as little working limb as I can get away with. I find flatter allows me to get away with less working limb.
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Steve,
You seem convinced that wood is more elastic in compression than in tension. Permanent set in a bow is caused by the collapse of wood cells in the belly, hence by failure to resist compression. The observation that bows take set before they break, isn't that evidence that wood is stronger in tension? That is why the proportional limit (the degree of tension above which there is set) tends to be lower than the breaking strength.
Take for example the wood database (http://www.wood-database.com/) and pick any tree species. You will see that the max tension strength (given by the modulus of rupture) is roughly twice as high as the crushing strength (aka Compression Strength parallel to the grain).
This clearly shows beyond any doubt that most woods are twice as strong in tension than compression. Osage is right in that ball park. In many conifers the ratio is a bit smaller, and is smallest in juniper (which explains why Juniper is a good bow wood for sinew backing: it's light in weight, but withstands more compression relative to its SG than most other species). In Hickory this ratio is higher, which makes hickory a better than average wood for backing.
Chief RID: Sassafras has the lowest ratio I've seen so far (tension/compression strength = 1.36 instead of 2), so whenever that wood starts to take set in a crowned design, you know you are close to breaking the back of the bow.
So far I haven't read any sound argument against my reasoning. I've read arguments like "I do things differently", but not the actual theory behind why that is supposed to work better. So I'll give it a try myself :-)
I do realize that a thin broad limb (as you advocate) allows you to have less working limb, and thereby reduce hysteresis (internal friction among wood fibers in the bow), as a smaller portion of the fibers are moving, which in turns increases efficiency. But in another way than a crowned limb, which increases efficiency by reducing (inner and outer) mass (at the cost of higher hysteresis). In a thin limb, trapping doesn't reduce as much mass as in a thicker narrower limb, so I agree that in thin limbs trapping will have little effect. I also agree that outer mass is what matters most, so broad, flat and thin backs in the inner part of the limb are allowed to be heavy, as long as the outer limbs are light. The mass principle isn't only about mass, but also about how that mass is distributed.
So in no way does what I am saying question the performance of your bows or the quality of their design (the numbers speak for themselves...). It's just another pathway to the same goal: having a faster bow. And it all depends on what bow wood you start with and what design you aim for. If you start with a thin stave with narrow limbs and crowned back you can still get a fast bow by taking advantage of the crown. As Marc St Louis mentioned in your flight bow post: it's all about balance (between back tension and belly compression). How you achieve that balance will depend on which design you are constrained by (due to the stave properties).
Does that reconcile the apparently contradicting bow designs? Either flat, thin and broad inner limbs are one proven optimum. You can also get to another peak (it may not be as high) with thicker narrow but heavily crowned backs and a flat (toasted) belly.
Joachim Mergeay
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joachimM,
I don't know how to post links but I posted a bow a couple a weeks ago that had a super high crown and had very flat belly called { Ocean Spray Bow "Inspired by Half Eye }... This bow shocked me in that it was 49" ntn 57@25 reported weight gain and half inch of reflex by half eye...I don't know or understand what mechanics are going on other than maybe wood species...This bow was tillered to 26 1/2" and shot by me at 26" before shipping to Rich. Now I'm in know way blowing my own horn just wish I knew what was really going on with this sapling high crown compared to my semi flat back bows...Anyway it's something for you to check out and I'm going to make some more high crowned bows and see what gives, open minded and still learning... The bow has not been shot 1000 times yet though ;)
Don
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A high crown or trapped back is not favorable in all designs...it depends on what design you are trying to execute. I think your misunderstanding what badger is saying. When a bow has short working limbs its more favorable to have a lower to not much crown. This allows you to be able to make a wider limb...with a high crown its not feasible or possible to establish the width needed because shorter working limbs need more width than normally. And you also can run into tension problems with too much crown in a shorter working limb. I've experienced this first hand,and make a lot of bows with short working limbs. With a lower to no crown the tension is now spread a lil wider across the back. I've seen hickory(king of tension woods) and other strong tension woods break in tension with a high crowned short working limb. After these failures I realized and learned that the crown was too high,and now when I build a bow that is going to have short working limbs I look for a piece of wood that has a low to almost no crown. Now this doesn't mean every piece with a high crown and short working limbs will break...just that it will be much more prone to doing so.
Again...moral of the story is it depends on the bows design
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In hindsight, the topic title should have been "when is a crown favourable", not why.
I agree that it all depends on the bow design.
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I agree with Blackhawk. I tend to make any bow based on the width of the belly. I disregard the crown initially.
With a narrow-high-crowned-stave (nhcs) the width reduces quickly as you remove belly. So I start with the belly where I want it then I take a look at tiller/weight and decide if I need to remove that crown, and how much crown.
I think the fact that everyone here has mentioned that the short working limb needs to be flat says it all.
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I will be the first to admit that I have little understanding of how tension and compression forces work in conjunction with one another. I do know of quite a few woods that I use with high crowns frequently without problems. Elm, plum, yew, ocean spray, and even osage are all good examples. I still seem to do better without the crown though.
How would you define strength? I have been under the impression that strength refers to how much it resists bending. I have read in many sources that wood almost always fails in compresion before it breaks and I don't neccessarily buy that one either. I just don't see evidence that this is true. Its a good discussion and I am admittedly not comming from a place of a good understanding. I have relied more on just knowing what to expect from a piece of wood.
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I think that's stiffness, not strength.
The trouble with comparing strength of tension versus compression is that failure past the elastic limit manifests differently.
Compressed wood can visually appear fine while stretched wood is going to be broken.
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A good visual overview on wood properties, including what compression failure represents (set; wood strain) and how that works can be found here:
http://forest.mtu.edu/classes/fw1035/2011/Lecture%2010%20-%20Mechanical%20Properties%20of%20Wood.pdf
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if someone would post I have a 50# bow flat back and it shoots 170fps
and i have a 50 bow it is crowned from the same stave and shoots 180 fps same draw and arrow weight etc,,
I would understand better :)
I think the performance improvement so far is from heat treating as to reduce the mass of the bow,, and not so much about the crown,,
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Joeachim
I have read your explanation of proportional limit many times and am a bit confused by
proportional limit (the degree of tension above which there is set)
It is my understanding that a materiel being stressed may reach its proportional limit in either compression or tension. These limits would be different for each stress in wood, just as the tension strength and the compression strength differ widely. we easily see the proportional limit in compression first, as it develops quite a bit before failure.
the link you posted for the overview pdf is a good intro to the basics of the engineering principles. Please look at the chart that shows the "factors affecting wood strength" p 12. You can see here how if a bow were to be designed to have three times the stress on the back as the belly, it would be ok at 12% mc, but would fail on the back at 6% mc.
In a back failure, the proportional limit in tension is not often apparent, as it occurs very close to the breaking point, and any "set" that occurs on the back is not easily seen apart from the set on the belly.
It is certainly possible to build a bow that performs exceptionally well at the optimum mc, but as Tim baker mentions on p 118, Design and Performance in Tbb4, "a bow is still a bow until its back breaks, so its generally safer to avoid trapping". That is of course, if you are concerned about charging grizzly bears. If your interest is making the ultimate flight shot, then by all means, push your design to the limit.
I have not seen the usual posts about breaking bows this winter, perhaps it is warmer (moister) than normal this season. As always, wear your eye protection when you shoot.
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Willie,
Thanks a lot for bringin this information to the attention.
My main goal is to understand better why some bows shoot faster/better than other, why some break and others don't. MC is a critical factor, so it seems. Here in belgium we always have humid winters.
I'll let you know if the backs break next summer or so :-)
Over here bowhunting is illegal, and we have no bears either.
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Joachim
I guess I should add that storing or building the bow in a heated building is usually the culprit, as the relative humidity typically goes much lower in the winter when we heat outside air. some like to keep their bows in an unheated space for this reason.
if you can weigh the bow mass to the gram when you do a draw weight test, you
might be surprised how easy it is to watch the values change in conjunction with each other.
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About moisture content and the relation it has with the proportional limit:
I measured ambient moisture where I store all of my bows, curing staves and other bow wood: At c. 65% ambient moisture at 25°C the equilibrium MC of the wood would be around 12%
So I reckon I'm definitely safe there.
A note on Badger's former posts on hysteresis and the mass principle (http://www.primitivearcher.com/smf/index.php/topic,17294.0.html, http://www.primitivearcher.com/smf/index.php/topic,48766.msg665748.html)
I really should monitor hysteresis (through no-set tillering) next time I tiller a crowned or trapped bow, to see if there is indeed an high cost of hysteresis, and if these crowned bows indeed have a lot of hidden (not apparent) set.
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I think Badger meant to say that wood is stronger in tension than compression.
So what design would be improved by a high crown?
Jawge
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Jawge,
I've tried to put a simple overview together. Here's the short (!) explanation.
As for tension-compression ratios: look at the wood database and compare Modulus of rupture (tension strength) with crushing strength (compression strength). As of elasticity, that's given by the modulus of elasticity. The lower, the more elastic the wood is.
This database has thought me that we have an equivalent to osage orange in Europe, namely common pear. Hawthorn (Crataegus laevigata) is probably very close to that (my preferred bow wood).
I'm trying to add an image, which says more than my explanation (Hope this link works now).
https://www.milieuinfo.be/dms/d/d/workspace/SpacesStore/d05ff317-a04e-4cbc-960e-148d65813f0b/Trapping-toasting-thinning.jpg
To avoid set, we need to find the balance at which the belly wood is never compressed beyond the proportional limit (the amount of stress at which the wood starts to surrender, either in tension or in compression; typically this is in compression). The closer the belly surface is to the neutral plane (NP), the less compression each fiber is exposed to. So we want to bring the neutral plane as close as necessary towards the belly.
We can achieve this in at least three ways, abbreviated TTT, for trapping, toasting, thinning:
1) thin the limbs. This brings the NP closer to both back and belly. The trade-off is a weaker bow limb. This can be mitigated by making it wider, at the cost of a higher bow mass. Since bow mass matters most at the outer limbs, the solution is to have a wide but thin working upper bow limb, and a narrow stiff outer limb for minimal mass. The maximum width is mostly constrained by the stave properties.
2) Heat-treat the belly. Heat-treating or toasting makes the belly wood stronger, so less belly is required to counter the tension load. Hence, the neutral plane shifts downwards.
3) Trap the back, which results in more belly relative to back surface. As a result, the belly is now stronger relative to the back, which also shifts the neutral plane towards the belly. Trapping reduces total mass, increasing cast.
In all three cases, the belly is less strained, as a result of which the bow can be drawn farther before taking set than in the reference condition. In the latter two, the bow can be made a bit thicker for the same draw length before taking set. Since a change in a bow limb from 1 cm to 1.1 cm gives you a 33% increase in draw weight but only 10% increase in mass (and less if trapped), the advantage of a trapped back –provided your wood can take it- is self-explanatory.
Under what circumstances is a crowned/trapped back favorable?
1) when you cannot make the limbs broad enough. There’s plenty of bow wood that never gets 2 or 3” wide. And a crowned stave is easier to find than a flat stave.
2) When you have very tension-strong wood (relative to compression strength). This is why Elm bows perform best when crowned.
3) When you are a rookie and tillering mistakes are easily made and hard to mend (the thinner the limb, the more careful you need to tiller to avoid hinges)
Under what circumstances is crowning unfavorable?
1) when you have tension-weak wood (relative to compression; e.g., Eastern red cedar and other true Juniper species, Sassafras). This is why Juniper is often backed with sinew, to provide a tension-strong back to compensate for the compression-strong juniper (as far as I’ve seen, relative to its elasticity the wood that is strongest in compression).
2) when you decide to have broad thin limbs anyway. Trapping thin limbs yields only minor mass reductions.
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Joach, have you considered the following into your calculations. Something all spring have in common is that they have a rate of increase. We usually rate them at how much they build per inch. As we compress the belly on a bow and it starts building pressure it would not take long before it built enough to force the back to start working in tension. In most cases the belly will still have available elasticity to continue to compress while the back will fail rather quickly once the compression forces become equal to the tension limits. Back don't like to stretch. I know this goes counter to a lot of experts who claim the belly is always the first to fail. I believe in most cases the beack fails first because the belly catches up to it with opposite forces.
In other words, when a bow is at rest the bback is twice as strong as the belly,( twice the resistance to stretching than the belly has resistance to compressing) once you start to bend the bow the forces will quickly start to equal out until one gives.
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High crown is relative. What may be high crown to me may not be to someone else. You should first define what one considers to be a high crown. When I talk of a high crown I'm referring to a bow made from a small diameter tree of less than 3". With such a piece of wood you won't be able to get more than 1 1/2" wide limbs before the limb edges become too thin, for my taste at least.
I believe some has said before than MOE is nothing more than a measure of a woods resistance to bending and says nothing about a woods ability to bend without deformation. It really has no application in bow building. As I have said before, balance is key
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joach,
Thanks for taking the time and because you did I will engage you on this issue.
Remember that the bowyer has no control over the shape of the back. Basically, we work with what we have.
Let me respond to:
"Under what circumstances is a crowned/trapped back favorable? "
There are no circumstances. IMHO.
(1) I'm not saying a crowned stave should not be used. I've made lots of bows from saplings with crowned backs. You don't have a choice. 99.99% of saplings are heavily crowned.
(2) The tension forces are always greater than compression. It's not a question of "when".
(3) I don't agree that a crowned back favors the rookie. Perhaps a not so wide bow with a flat back does. Different issue.
(1) Of course
(2) Of course
I am confused as to what you believe. Are you saying that bows with crowned backs are easier to make? Are they better?
Like I said I've made many bows with crowned backs. They are better left a little longer. When I haven't they raised a splinter right down the middle.
If I have a choice of a flat backed stave or one with a crowned back I'm going for the flat backed one. How about you?
Board bows shoot faster than stave bows, in my experience. Boards have flat backs.
I'm afraid these esoteric discussions confuse beginners.
Anyway, thanks for taking the time to respond. Remember we are spending time rediscovering principles the ancients knew already. They learned and passed these principles down father to son over untold bows.
I've an idea that they made use of saplings quite a bit. Green saplings are easier to turn into bows with stone tools. Most of the ancient bows are pretty long for the size man back then.
Anyway, good debating with you. :)
Jawge
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Marc, good point. I agree. Jawge
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I agree Jawge and Mark, there really isn'tmuch we have control over. Ballance is something we tend to learn with experience and working with different woods. I don't know of any way to determine what is actually happening between tenion and compression beyond just learning how different woods respond. I use to think that strong tension woods would overpower weaker woods. Anymore I just have good backing woods and good belly woods. As long as the backs aren't too thick they all seem to work together pretty well.
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joachim,
perhaps what causes some confusuion to beginners is the the word "elasiticty".
As Marc pointed out, MOE...says nothing about a woods ability to bend without deformation
, which of course is crucial to working with bow designs that stress wood near it's breaking point. much of the commonly found engineering data on wood was developed for building applications which are very conservative and mostly constrained by a small allowable deflection.
when working with wood at such high levels of strain, other factors play into bow designs that need to be considered. Have you seen?
http://paleoplanet69529.yuku.com/topic/28706/Picking-a-wood-for-a-bow?page=1
it is a discussion of the interrelationship of some other pertinent factors when working with wood as a bowbuilding materiel.
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Hi folks,
I must admit that I am already way outside of my comfort zone, but it is very good exercise to be challenged all the time. To force myself to rethink over and over again why some things do what they do.
So Steve, I cannot really answer your question on the spring thing other than that I haven't considered that yet.
Willie, I'll have to consider the MOE thing. However, if you look at what we think is good bow wood, and at what the numbers call good bow wood, we get similar results: see http://www.wood-database.com/wood-articles/bow-woods/
That isn't the whole story, as compression qualities need to match. But mostly, they do. I'll post a thread later on on wood qualities.
But now I'll have to give you parts of the long answer :o
First: a working link (now really) to my drawing on the effect of trapping, toasting and thinning on the distance between belly and neutral plane. Is there any discussion about that?
https://www.milieuinfo.be/dms/d/d/workspace/SpacesStore/d05ff317-a04e-4cbc-960e-148d65813f0b/Trapping-toasting-thinning.jpg
I do realize I have very few credentials in the art of bow making, but mark that nothing I've written here is new, I'm just standing on the shoulders of giants, and putting pieces of a puzzle together to see if they fit. And to me it seems they do.
Firstly: trapping does result in a shift of the neutral plane. There's very little arguing about that. David Dewey has made all sorts of hard calculations about how a change in the cross-section of a bow results in a shift of the neutral plane. His data are still accessible on the old Paleoplanet support site https://groups.yahoo.com/neo/groups/PaleoPlanet/files
Secondly: who am I to challenge Tim Baker (by now you must have realized that I don't care too much about challenging master bowyers ::))? TBB4, p 118-119 (trapezoidal sections). The only thing I'm adding to his reasoning is that the neutral plane is now closer to the belly, and that this might be the key to understanding why it works. (and Gianluca100's earlier reply to this post seems to confirm my reasoning).
Thirdly: Consider a cable backed bow. This is the extreme version of a crowned stave: the wood is supposed to take all compression, the cable some to all of the tension. If the cable is weaker than the wood's compression strength, some of the wood will also take a portion of the tension. The neutral plane will be in the wood. Now take a cable with a breaking strength ten times as strong as the compression strength of the wood. The cable bow is clearly overbuilt on the back. The neutral plane will virtually hover above the back of the wood, as the cable cannot take compression. The wood belly is too weak to withstand the huge compression and takes enormous set. This can be avoided by either make the cable lighter (~trap the back of the bow), or by providing a stronger belly. This is what composite horn-sinew bows are all about (which are typically also crowned). The neutral plane is back where it belongs: inside the wood core of the sinew-wood-horn bow.
a rectangular cross-section is nothing but an intermediate between a trapped and a reverse-trapped cross-section. There's little reason to believe that a rectangular design is, by its symmetry alone, superior to trapped designs. It all depends on the properties of the wood, and where you want the neutral plane to be.
What I believe is subordinate to the entire discussion. I tend not to believe a lot unless I'm entirely convinced by hard facts. I thought I had a good hypothesis, and that backing it with facts wouldn't be too difficult. But you guys make me doubt. Which is a good thing. But only doubting a little :)
I consider it a hypothesis, and let tests in the future make out if it stands or falls.
Jawge, I do think that trapping backs can be favorable under some circumstances, because you end up with lighter bows for a relatively high draw weight and take less set. Turning it around: would decrowning a crowned stave (2-3") yield a better bow? and why?
It seems that the fact that bows do break is viewed as evidence against my reasoning. But it isn't. Irregularities in wood make that a small flaw in the back effectively yields a weaker than expected back and can be enough to yield back failure (a chain is only as strong as its weakest link). In reverse, a small flaw in the belly will only yield minor set and often go unnoticed. so a stronger back than belly is a requirement for bows to function.
I get the feeling balance is becoming a rather meaningless word. it just defines (to me) where the neutral plane is, so that means we can have control over it.
But the proof of the pudding is in the eating. Standardized bend tests on trapped, reverse-trapped and identical rectangular sections should be a good test. Trapped designs should show less set at the same amount of deflection. Reverse-trapped designs should show the highest set.
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the link to the dutch site just brings me to the log-on page
Joachim-
But you guys make me doubt. Which is a good thing. But only a little
Please do not think that it is my intention to make you doubt, as there is much to be said for understanding the basic science. One of the things that makes bowmaking interesting to all posting, is that after 10,000 years of bowmaking, we all are learning something new as we share our experiences, and to find that bowyers in antiquity have built better bows than we can now is................... rather humbling.
I have found that many who are able grasp the more technical aspects of the art, find it difficult to put into words just what they have learned. For me anyway, technical writing is harder than making a bow.
Much of what has been posted here I don't see as doubt. Many are just saying....
"there's more to it than that"
willie
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joachim,
The disagreement we are having is that you are saying that crowned backs are always favorable. No, they are not ever favorable. I've reread your initial post several times now.
What are you going to do with a stave that is flat on the back? Not use it?
When you have a stave with a crowned back you deal with it. I deal with it by leaving it longer.
As for trapping, that can be a useful technique to deal with woods that are weak in compression.
That has nothing to do with a heavily crowned back.
I feel that I am repeating what I said earlier so I may just let this ride and go on with my life.
Jawge
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Not that I have a horse in this race, but I don't know that it is fair to say that trapping has nothing to do with a crowned back-they are extreme examples of the same thing. I am also not sure he said it is always better-Joachim did say in retrospect the topic ought to have been something like 'when is a crowned back favorable' which presupposes cases in which a crowned back is indeed not favorable.
In fact, thinking about the neutral plane argument and high crown being at one end of a spectrum with a trapped board bow at the other...has anyone tried to decrown a high crown sapling only partially? Instead of having a very narrow ridge along the back there could be a half or three quarter inch flat plane...it would be essentially the same as decrowning and then trapping.
SOM
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There are some absolutes in this issue that are being ignored or forgotten in the maelstrom of observations.
First, according to various engineering sources, including the Forest Products Laboratories, the tension strength value of a wood is almost always midway between the modulus of rupture and the compression strength parallel to the grain. In every one of the half dozen I worked out, the math backed up the statement from the same sources that NEARLY ALL WOODS ARE ABOUT 3 TIMES STRONGER IN TENSION THAN COMPRESSION.
So, in bending, the tension side fails when the compression side has crushed to the point of putting the neutral plane very near the tension side--THE WOOD FAILS FIRST IN COMPRESSION. This is not just an observation by some of us bowyers, it is established fact in the world of engineering and as provable and repeatable as gravity. This also has been known and reported for close to 75 years now.
Second, If the back of a bow is strong enough at half the width of the belly, leaving it full width will not make it less likely to fail, because the belly will still fail and move the neutral plane toward the back.
Third, making the back narrower, will not make the back stretch more. Wood is almost inelastic in tension. The yield before rupture is about 1 percent. (Again, you can do the research as I did to find the engineering support for this.)
Trapping the back of a bow improves performance only if the reduced mass allows the limbs to return faster--seldom much of a factor since very little wood can be removed from the outer, faster moving parts of the limbs.
I for one, weary of the repeated conjectures whose merits or falsehoods have been proven for years. Does no one read books anymore?
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Hi Jim,
thanks for adding your expertise to this discussion.
So am I right to conclude that, according to you, a trapped back (or a broader belly than back) does not shift the neutral plane towards the belly, and is therefore not advantageous by itself (without the effect of reduced mass)?
This would confuse me a lot, as heat-treatment does the same (yielding a stronger belly than in the reference condition) but not by weakening the back but by making the belly stronger. I finally managed to add the drawing of what I think trapping does in the cross-section of a bow limb. For simplicity, I gave an arbitrary identical shift of the neutral plane for all three treatments.
"Making the back narrower will not make it stretch more". I'm not sure I agree. If the neutral plane indeed shifts towards the belly in bows with stronger bellies (see drawing), then the bending radius to which the back surface is exposed will be a bit larger, hence the back will be forced to stretch more at the same draw length. So, again, it comes down to whether or not the neutral plane shifts when the ratio of the strength of back and belly wood changes.
Forgive me my ignorance of the vast bowmaking literature I am completely unaware of. I'm mostly trying to learn here how different bow designs affect performance.
As you pointed out, as bow takes more and more set, the neutral plane moves towards the back (set reduces the functional thickness of the bow but not its mass). This is what is represented in the "thinning" treatment, but imagine this for a bow with set a small zone at the belly consisting of crushed wood. (because the functional thickness is reduced by set, the NP shifts not only towards the back, but also towards the functional zone of the belly).
Jawge: I'm not saying (anymore) that trapped or crowned backs are always favorable. That was a lapsus. Just like heat-treatment isn't always favorable. But at least the latter very often is. Since (IMO) both methods operate through a similar mechanism (bringing the NP closer to the now stronger belly), trapping should often yield a similar gain in performance. Toasting gives a stronger belly without reducing mass, but the bow mass for the now higher draw weight will lower than expected. Trapping gives a weaker back and thereby reduces mass. Again, the bow will have a mass that is lower than expected for its draw weight. And yes, I actively trap bows up to the nocks, even flat back board bows. Most of my trapped bows have a pyramid design, and are 20-30% lighter in bow mass than expected by the mass principle.
What I would like to know: Can anyone come up with technical arguments or hard facts why that reasoning (shift of the NP towards belly after toasting or trapping) would be false? And if the conclusions made thereof would be false?
If so, I must concede that I was wrong.
Preferrably, other than saying "it's written somewhere and just take my word for it this other person is or was right".
I thank all of you for contributing to this discussion. Please forgive my my tediousness and repetition throughout the replies. It's just out of eagerness to learn and understand what's going on, and making sure we are not misunderstanding each other.
Joachim
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joachimM, You say, "
What I would like to know: Can anyone come up with technical arguments or hard facts why that reasoning (shift of the NP towards belly after toasting or trapping) would be false? And if the conclusions made thereof would be false?
If so, I must concede that I was wrong.
Preferrably, other than saying "it's written somewhere and just take my word for it this other person is or was right""
I say, do your own research. Coming here to ask questions and then questioning the answers is just taking the lazy way out. The information is out there, available on the internet and in books. I have spent years reading those things, but did not take footnotes. I don't fault you for not taking my word. I would not take someone's word either if I didn't understand it. But I WOULD and HAVE gone to authoritative sources in those cases. Do that.
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Purely from an unscientific perspective, after lots of bows over the years I think your reasoning is sound and and I appreciate you taking the time to make your case. Very interesting read.
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Joachim,
your anyalsis seems to only consider the static limb. what happens as it is being drawn?
consider the graph below to be the stress/strain diagram of a bow overdrawn to failure in compression.
| F (compression failure)
| B * *
s | * *
t | * *
r | * *
e | *
s | A *
| /
| /
| /
| /
| /
| /
| /
|_________________________
strain
would this not be a representation of the rectangular cross section of a bow that is much stronger in tension than compression .....at least at rest, or having never been strained above the proportional limit (no set or point "A" in above graph)?
__________
-----------|----------------|-------- NP
|__________|
By the way, i don't think that changing the proportions of the rectangular cross section changes the relative location of the NP
Now consider a bow limb that has been stressed above the proportional limit, and has taken considerable set. the belly is being compressed, but we can continue to draw to higher and higher weights because the belly has not collapsed yet. (reached point F yet). Which way is the NP moving in the cross section as the belly compresses further? My thought is that it could be moving towards the belly if the back is stretching more than the already compacted belly is compressing, or, it could be moving towards the back, if the back always overpowers the belly. Is there a simple way to tell?
Now consider that, since the belly is experiencing increasingly higher stresses, the back is as well, and lets say that the back breaks at B before the the belly totally collapses at F. where is the NP just before the back breaks?
Understanding the scientific dynamics of plastic deformation may well be a usable knowledge to have, but as I know of no way to take a stress/strain diagram of the wood in tension and overlay it on the stress/strain diagram for compression, in order to see where the curves cross,
I would rather take Badgers word for it,........
Ballance is something we tend to learn with experience and working with different woods. I don't know of any way to determine what is actually happening between tenion and compression beyond just learning how different woods respond
........as he has built thousands of bows, and has probably broken more of them than I can build, in my remaining time on this planet ;)
Perhaps the Phd in you can be of some assistance to me. I have a wood that is said to be very good in compression, but has no tensin strength whatsoever. I wish to use this wood for the belly of a backed (composite) bow. Any ideas of how I might go about testing just the compression qualities? A bend test of the wood has not been too useful, as it just breaks in tension before I can learn much. I could build numerous samples of different composites with varying degrees of trapping, but might there be an easier way?
willie
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speculation about what the wood can and will do is great,, guys like tim baker(and many others would build 10 with a crown and 10 without,, shoot and test them,, and the results would head you in the right direction,, guys that have been building bows for decades have basically done the same thing over a longer period of time.... analysis is one thing,,,,, building the bows and shooting them can be very informative,,,
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I'm in the camp that says the main benefit here comes from a somewhat physically lighter limb, and a narrowed back that can still hold together in tension, rather than increased stretching of the back fibers.
Two things give me pause, though. Bear with me.........
I HAVE had several bows fail purely in tension. They were made of VERY thin ringed red elm, like paper thin summer rings over same thickness winter rings, in layers. I just made, then quit on, a long flatbow made from a 5" tree. I finished tillering, and was shooting the first 100 arrows or so, when I heard several little "tick"s. I inspected the bow and saw no lifted splinters. It kept happening. Upon inspection with a magnifying glass, I found that all along the bow, the back had failed in small transverse cracks through the first growth ring. There are like 15- 20 per limb. I can dig a finger under them and flake up little chips about 1/32" thick, and see the winter ring underneath.
The important thing here is THE BOW IS STILL SHOOTING.
I have overdrawn it 4" or so. No break, no set, just more lifting of these eggshell thin bits. It is decrowning itself, as it were.
It hasn't broken, has taken NO more set, and hasn't cracked again.
I am tempted to try decrowning it, but the stave is super knotty and lumpy, so I dunno.
The second thing is just Baker's test from TBB IV. Taking a rectangle x-section bow and trapping it resulted in higher mass decrease than draw weight decrease, and in another test, the bows took less set. If a trapped bow takes less set than a rectangle bow of similar wood, how do we explaine this?
Finally, this should be super easy to test. We reverse Bakler's test. We make a trapped pyramid bow out of a maple board or somewhat. Shoot, measure, test. Then we square the sides up with the back. If the belly corners are truly "loafing", then we should lose almost no draw weight, and take very little more set, right?
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I think a lot of the bow tests seem to me to be anecdotal evidence. When comparing two bows, one trapped and one rectangular in cross section, how do we know that they are comparable with just bow length and draw weight? I think a better test would be to make two pieces piece of wood where the volume is equal, the thickness is equal, and the cross section is rectangular in one and trapezoidal in the other. This way we know that the mass of both pieces is the same but we can measure the resistance to deflection at a particular distance and compare that. The other comparison would be to test the pieces for set and breaking strength to see if the difference in cross section makes a difference in the tolerable bend radius. Maybe this has been done but I think it would be far more definitive than bow testing. It would tell us if trapping makes a difference in both energy storage and bend radius. And of course I think that several degrees of trapping would need to be tested such as 25%, 50%, 75%, to gain an idea of the benefits and risks. Unfortunately I don't have the engineering background to mathematically figure out how beam cross section effects energy storage but if I were to experimentally figure it out I think this would be the way to go. Thoughts?
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ryoon-
I woun,t normally make suggestions for the other guy to try, but since you asked, I have been giving some thought about a way to easily test limb profiles and materiels.
if one settled on a single pyramid limb width and length profile, that was designed so that the thickness could be even and easily ripped with a table saw,
then perhaps 2 easily manufactured limbs could be clamped on a universal handle riser.
one could mix or match, share with others, save for later comparisons, or just plain shoot to see if some more subjective differences between limbs exist.
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I still think going from trap to rectangle would prove at least the one element intended, which is the claim/idea that the belly corners are loafing.
Tolerable bend radius WOULD be a good thing to test. There is a lot of anecdotal evidence, by us, that tolerable bend radius is simply a threshold event.
I also think that it would be cool to purposely induce a hinge, and slow-mo film it while it breaks.
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I still think going from trap to rectangle would prove at least the one element intended, which is the claim/idea that the belly corners are loafing.
I think it would prove that, though I can't imagine anyone thinking the belly corners are loafing...
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I wish there were a Paul Kolpsteg among us.
http://www.archeryhalloffame.com/Klopsteg.html (http://www.archeryhalloffame.com/Klopsteg.html)
http://en.wikipedia.org/wiki/Paul_E._Klopsteg (http://en.wikipedia.org/wiki/Paul_E._Klopsteg)
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Actually, a pretty straightforward way of testing if trapped backs reduce set would be to start from flat boards and make ten identical pyramid bows with rectangular cross-section, for example made from maple or red oak boards or something easily accessible.
No grip, just two opposed triangles. They don't need to be live-size bows; miniature bows (75 cm from a 0.5 cm thick board or c. 30" x 0.2") could do the trick.
Pyramid bows can be made such that there is no thickness taper from fades to nocks, which makes the bows easier to compare. For ease of making, forget about the handle, they don't need to actually shoot bows, you just need to put them on a tillering stick and draw them. Use only straight grained boards.
string them with the same slack string, put them on a tillering stick, draw them progressively and mark at which draw length they start to take set. Measure draw weight at each interval for each bow. Continue, and mark at which draw length they take 1" of set. Continue and mark at which draw length the bow breaks or the back develops splinters.
There are two basic ways to test:
one is you divide these bows into two groups: one stays rectangular in cross-section as is, the other half is trapped, with the back being 2/3 as wide as the belly.
This allows you to compare some test statistics (see below) between the two groups. There are easy statistical tests (even online) where you can compare two groups of variables. (ANOVA, or t-test here, or a variant thereof)
The other method is by regression: you make a gradient of trapped (and reverse-trapped) bow-belly width going from 2/1 (back twice as wide as belly) to 1/2 (belly twice as wide as back). Here you relate draw length at which the bow starts to take set with the back/belly ratio and see if there's a linear relation.
You can also check if there's a trade-off with draw weight, and a trade-off with back failure (there's no point in having a bow that takes no set but always breaks).
I'll try to find good board wood here and test this sooner or later. But please if you have spare time and want the scoop, be my guest :) :)
Now, this won't give you a magical back to belly ratio applicable to all future bows; these result will be very specific to the wood considered, and to the moisture content of the wood being used. But as a proof of principle it may be useful.
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I think it would prove that, though I can't imagine anyone thinking the belly corners are loafing...
[/quote]
This is actually the crux of the argument. If they are NOT loafing, then you save weight, but store similar energy, and the belly is evenly strained. If they ARE loafing, then there is no reason to trap a limb or use a crowned stave, and in fact the thinner edges hurt you by adding dead weight.
Baker said that in TBB I, which champions the rectangular cross section for most woods in the Design and Performance section. His testing and extrapolation to that point indicated that TOO small diameter a tree (crowned back) resulted in thick wood in the middle taking the brunt, and the thinner edges taking much less strain, thus storing less energy.
In TBB IV, he was leaning toward trapping the limbs for weight reduction with minimal loss of draw weight.
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joachim, Baker only did the one test I remember with a poplar bow. I don't have exact numbers, but he took a poplar bow and trapped the limbs. Weight was reduced by something like 20%, but draw weight only fell by 6%, (or some such) and the bow took no new set.
Really basic pyramids like you describe would be perfect. I think you could design a practical test by making two bows, purposely over built to take low set, one trapped and one rectangle cross section. Measure and shoot, then start trapping the square one in stages to obtain the back to belly ratios you mentioned, and squaring the trapped one. Then just chart what happens regarding limb mass, draw weight, and set. You could do this in stages until they break. Square the trapped one and then trap the new narrower bow again.