Why is a crowned back favorable?

[Marc St Louis]

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

[George Tsoukalas]

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

[George Tsoukalas]

Marc, good point. I agree. Jawge

[Badger]

  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.

[willie]

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.

[joachimM]

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 
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.

[willie]

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

[George Tsoukalas]

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

[son of massey]

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

[Jim Davis]

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?

[joachimM]

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

[Jim Davis]

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.

[SLIMBOB]

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.

[willie]

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

[bradsmith2010]

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,,,