Primitive Archer

Main Discussion Area => Bows => Topic started by: Badger on April 29, 2014, 04:13:29 pm

Title: Can making a bow wider lower the mass
Post by: Badger on April 29, 2014, 04:13:29 pm
   I was sugested a start a seperate thread on this. Over the past couple of years I have played around with making bows much wider than I normally do. The idea being just tiller them out and then reduce to desired weight by narrowing the limbs. I like to use the mass principle for letting me know that I have a sufficient amount of wood to work with to accomplish a specific design.

    More and more I have been pleasently surprised at how low in mass these wide limbed bows are comming out. I have also found them to be extremely low in hysteris, take very little set and perform at a much higher level. This sounds a little counter intuitive at first glance. Most of us know that if we add 25% to the width we only gain 25% draw weight, if we add 25% to the thickess we double draw weight. I am finding out that if I keep the bellies very flat I can reduce the thickess enough to overcome the added mass expected with added width. This can only be true if the narrower bows are crushing more wood than some of us thought. I find this more true on hard backed bows using flat wood backings.

    I noticed this same thing when examining Mark St Louis bows. I saw very flat bottoms, fairly wide limbs yet always low in overall mass. Any thoughts or debates welcome.
Title: Re: Can making a bow wider lower the mass
Post by: Bryce on April 29, 2014, 04:24:44 pm
I have had a similar experience, BUT! Only to a certain degree. I think for each wood there is a proper width:thickness:length ratio that adjustable for draw length and weight, and finding such is too difficult a complicated to even try bc of woods natural way of always being different than the piece before.
I find myself thinking less and less about it and focus more on just making a bow that takes minimal set and shoot a heavy arrow hard.
Title: Re: Can making a bow wider lower the mass
Post by: JonW on April 29, 2014, 04:29:09 pm
I can actually contribute to a thread! I don't do any weighing of my bow's physical weight but I can sure feel it in what you are describing. If I come across a good stave that is fairly wide and clean it is always going to be a shorty pyramid. I noticed that this design was making some good bows as far as a lack of set goes. Some of my Osage and Locust short pyramid bows are incredibly light in the hand. I rarely make anything under 50 pounds in draw and more often than not quite a bit over that. I really didn't give much thought to it but when Steve made that comment the proverbial "bulb" lit up. There is definitely something to this line of thought.
Title: Re: Can making a bow wider lower the mass
Post by: Badger on April 29, 2014, 04:34:05 pm
I have had a similar experience, BUT! Only to a certain degree. I think for each wood there is a proper width:thickness:length ratio that adjustable for draw length and weight, and finding such is too difficult a complicated to even try bc of woods natural way of always being different than the piece before.
I find myself thinking less and less about it and focus more on just making a bow that takes minimal set and shoot a heavy arrow hard.

  Bryce, you are right on, what we struggle with is trying to identify the character of the stave we have in our hand durring the building process before we have gone too far. I have always felt that going a bit wider and narrowing afterward was a fair way to accomplish this, I was just surprised at how wide I could actually go before the point of deminishing returns sets in. Patience is not one of my greatest virtues and the wide flat limbs are a bit more touchy to tiller.
Title: Re: Can making a bow wider lower the mass
Post by: Crogacht on April 29, 2014, 04:35:49 pm
Oh no, I was just starting to get my head around things and now you guys are changing the rules again, argghhhhh  ;D

(But really, this is interesting and excellent and I'll read what you guys come up with  :))
Title: Re: Can making a bow wider lower the mass
Post by: mikekeswick on April 29, 2014, 04:38:11 pm
If the wood cells get less damaged getting to full draw then they are going to have more stiffness per mass once there = lower physical weight proportionately for  equal draw weight.
Title: Re: Can making a bow wider lower the mass
Post by: Badger on April 29, 2014, 04:43:54 pm
If the wood cells get less damaged getting to full draw then they are going to have more stiffness per mass once there = lower physical weight proportionately for  equal draw weight.

   Its not really changing the rules as much as it is understanding them better, same rules would still apply. For my personnal program I intend to start them off about 25% wider than I had been in the past. If I am comming into heavy I can always reduce the width after.
Title: Re: Can making a bow wider lower the mass
Post by: JonW on April 29, 2014, 05:10:30 pm
I started using a bendy pyramid design for short bows based on what I was NOT getting in the set department. I got tired of reflexing the narrower designs and just kept getting good results from a pyramid design. If you want to go short go wide IMO
Title: Re: Can making a bow wider lower the mass
Post by: Badly Bent on April 29, 2014, 05:16:44 pm
I'm thinking there is something valid in this idea. Without really knowing why I have been thinking of going wider and thinner on the next stave that gives me enough width for it. About 6 months ago I made a buckthorn shorty that was wider than my usual and had very thin limbs for its 51# @ 24" draw. Had some natural set back at the handle and I added a little more reflex to bring the tips 2" ahead of the handle expecting 1-1/4" or more of set. Ended up taking only about 1/2" set and has taken no more after several hundred arrows shot, springs right back after unstringing too.
At 53" long it came in at around 8 oz. prior to adding handle, finish and string. Not sure where that falls in line with your mass principle Steve but it feels like a feather in the hand and cast is good for one made by me.
Ooops, just went and measured the width to make sure I was accurate in my description of this example bow and it is actually only slightly over 1-1/2" wide. Not that wide I guess, but like I stated very thin limbed for the draw weight.
I'll be looking through my stave collection to find an good candidate of black locust, buckthorn or other wood to try
for a wider thin limbed bow. The thinner limbs do seem to be a challenge to me to tiller well though

Title: Re: Can making a bow wider lower the mass
Post by: Bogaman on April 29, 2014, 05:29:33 pm
I think experimentation in our craft is great. I think all of us owe a debt to people like Tim Baker, who has provided us with gobs of bow building info. I also think close to 90 some percent of what we know today is ancient history that we have just rediscovered. It's to  bad some one wasn't writing all that prehistoric info down.
Badger, I suppose I've done a little experimentation  over the years, but it isn't my forte. I just like to whittle on the wood and hope I get a keeper while I'm at it. But, I'm sure I'll keep an eye on this thread to see what you come up with, either for or against;^)
Title: Re: Can making a bow wider lower the mass
Post by: tom sawyer on April 29, 2014, 05:32:27 pm
The physics don't support your contention.  I think what you are seeing is that craftsmanship trumps all, and that you can't really ever compare two bows because there are multiple variables that can't all be controlled.  Craftsmanship being one important variable.  A well-made bow is going to be low mass by default.  But all things being equal, the narrowest limb that maximizes the tension/compression without damaging the wood, is going to be most efficient.  All things are never equal though.
Title: Re: Can making a bow wider lower the mass
Post by: tom sawyer on April 29, 2014, 05:36:25 pm
You definitely only know if your bow is suffering a bit from hysteresis by observing it right after unstringing after a nice long shooting session.  You'll quite often see an inch or so of set that disappears as the bow recovers.  That temporary set is is more indicative of the relative strength of the spring during use.
Title: Re: Can making a bow wider lower the mass
Post by: Badger on April 29, 2014, 05:47:32 pm
The physics don't support your contention.  I think what you are seeing is that craftsmanship trumps all, and that you can't really ever compare two bows because there are multiple variables that can't all be controlled.  Craftsmanship being one important variable.  A well-made bow is going to be low mass by default.  But all things being equal, the narrowest limb that maximizes the tension/compression without damaging the wood, is going to be most efficient.  All things are never equal though.

   Tom, that is my contention that craftsmanship is the determing factor, thats the only thing that could explain wider bows having less mass. Another thing, maybe what many of us thought to be the norrawest effective width might really be a smidge wider than we thought.
Title: Re: Can making a bow wider lower the mass
Post by: Badger on April 29, 2014, 05:49:18 pm
You definitely only know if your bow is suffering a bit from hysteresis by observing it right after unstringing after a nice long shooting session.  You'll quite often see an inch or so of set that disappears as the bow recovers.  That temporary set is is more indicative of the relative strength of the spring during use.

  I agree with you Tom, a bow that stays the same right after unstringing is better to me than a bow that gains reflex.
Title: Re: Can making a bow wider lower the mass
Post by: George Tsoukalas on April 29, 2014, 05:51:42 pm
Steve, I always let the stave decide on width.
Here is what I mean.
I start out with a certain width...perhaps 1.5 inches. Let's say I want 48#.
As I tiller I may note the wood not responding to thickness removal. Than. I begin to narrow the  width to bring the tiller in.
There seems to be a certain width to length to poundage relationship that is specific to each stave.
My last bow (hickory)  turned out 1.25 in wide 65" in length and 48#.
I will admit that I wanted a narrow bow but the bow is light in weight.
That's all I have for now. :)
Jawge
Title: Re: Can making a bow wider lower the mass
Post by: Badger on April 29, 2014, 05:56:02 pm
Steve, I always let the stave decide on width.
Here is what I mean.
I start out with a certain width...perhaps 1.5 inches. Let's say I want 48#.
As I tiller I may note the wood not responding to thickness removal. Than. I begin to narrow the  width to bring the tiller in.
There seems to be a certain width to length to poundage relationship that is specific to each stave.
My last bow (hickory)  turned out 1.25 in wide 65" in length and 48#.
I will admit that I wanted a narrow bow but the bow is light in weight.
That's all I have for now. :)
Jawge

  I know what you are talking about Jawge, I just finished an osage bow 66" long 1 1/8 wide, which is pretty typical even though I had started at 1 3/8 and the bow allowed me to narrow it. I have several osage bows that are 1 1/2". Learning how to read the wood is the real key.
Title: Re: Can making a bow wider lower the mass
Post by: blackhawk on April 29, 2014, 05:58:02 pm
Ha...Im sealing up a narrow hoohornbeam with a crowned belly that is borderline adhering to the 5/8's rule and I'm loving it ;).... the narrow, round n crowned belly guys are gonna flip hearing this,and i hope some of them chime in.....ya know I love making all kinds of bows from all those of different woods with all kinds of widths and cross sections.... it just depends on what type of bow I'm making,and the intended bows stats, and the type of wood that dictates width and cross section....I find if I do my job well they all perform well for me as long as they all have acceptable mass...and I find you can be plus a couple ounces or even a lil more than a intended target weight and still have a smoking good bow...the mass theory is still very credible IMO,and a good tool and guideline for folks wanting to lose some unwanted "fat" from there bows...it makes them reduce mass where it needs to be reduced(outer limbs),and put mass where it needs to be(inner limbs)..and yes a good bow will be by default lowest possible mass without eventually breaking down and taking too much loss from the start....to me its not so much about hitting a intended target weight as it is about having the right amount of wood where its needed,and NOT needed...I think Tim bakers "mantra" says it best in simple layman's terms..and I quote " make inner limbs wide or long enough for virtually no set. Make midlimbswide enough for little set. Make outer limbs and tips narrow enough for lowest possible mass". That statement is so simply understood and said,but at the same time it is an extremely difficult thing to understand as well as it takes a lot of bows made and experience to start to comprehend how to layout and make a bow with that in mind beforehand...
Title: Re: Can making a bow wider lower the mass
Post by: George Tsoukalas on April 29, 2014, 05:59:32 pm
Sure is, Steve. It can be a hard lesson to learn. :) Jawge
Title: Re: Can making a bow wider lower the mass
Post by: George Tsoukalas on April 29, 2014, 06:02:19 pm
Oh forgot to mention, Steve, that this bow started straight and ended up with less than an inch of set.  Jawge
Title: Re: Can making a bow wider lower the mass
Post by: Bryce on April 29, 2014, 06:40:41 pm
Yep! Tension/compression value is an ever changing variable.
Title: Re: Can making a bow wider lower the mass
Post by: Marc St Louis on April 30, 2014, 12:14:10 pm
I was thinking about this last night Steve and I think that in many cases you may be right.  Take for instance a HHB bow, no heat-treating.  If what you want to make is a stiff handle bow pulling 60# at 28" and you want to make the bow 64" ~ 65" long with 1 3/4" wide limbs, which are acceptable dimensions.  This would give you a bow with low set and of a certain mass.  If you narrow the limbs by 50% and increase the thickness appropriately then the bow will likely have slightly less mass but will also take more set so to compensate for this, to maintain the same low set, you would have to make it longer.  This would increase the mass again and you could very well end up with a bow of the same mass as the wide limb bow or perhaps even more mass.  I'm sure that there is an optimum mass for every wood type, bow style.  It is certainly something to think about
Title: Re: Can making a bow wider lower the mass
Post by: Badger on April 30, 2014, 12:27:13 pm
  Mark, I have noticed your bows are all relatively low mass but not unduly narrow in profile. I always attributed that to flat limbs and good tillering. I have been rethinking how I treat different designs and woods lately. I have always felt that my biggest personnal challenge is perfecting methods for reading the condition of the wood as a bow progresses. I hate tillering flat bellied bows so usually end up slightly rounded but I have much better results with dead flat.
Title: Re: Can making a bow wider lower the mass
Post by: tom sawyer on May 01, 2014, 02:57:13 pm
I wouldn't necessarily say that a bow that shows no hysteresis after unstringing is better.  My thought is that just a little of this, an inch or less, indicates that the bow is not overbuilt.
Title: Re: Can making a bow wider lower the mass
Post by: dragonman on May 01, 2014, 04:17:18 pm
I have also experimented with this....my experience is that the softer more elastic woods like yew and elm need to be narrower and thicker to get the wood to  "work"...but the stiffer and less flexible hard tropical woods work better  with the limbs flat and thin ( that is thin in depth)
With bamboo if you dont stress it enough you dont  get it working properly because its so flexible, the same with horn.....some woods work better when stressed more.....the harder woods like ipe are so stiff that wide thin flat works best...common sense realy

Badger have you concluded then, that the 8:1 width to depth ratio you talk about and BB talks about is no longer aplicable?
Title: Re: Can making a bow wider lower the mass
Post by: PatM on May 01, 2014, 04:36:22 pm
Most people say the exact opposite about Ipe, that  it needs to be deeper and narrower to show its best qualities.
 I have made many elm bows of wide and thin dimensions. Some woods work very well no matter what shape or length you give them.
Title: Re: Can making a bow wider lower the mass
Post by: Badger on May 01, 2014, 04:45:47 pm
I have also experimented with this....my experience is that the softer more elastic woods like yew and elm need to be narrower and thicker to get the wood to  "work"...but the stiffer and less flexible hard tropical woods work better  with the limbs flat and thin ( that is thin in depth)
With bamboo if you dont stress it enough you dont  get it working properly because its so flexible, the same with horn.....some woods work better when stressed more.....the harder woods like ipe are so stiff that wide thin flat works best...common sense realy

Badger have you concluded then, that the 8:1 width to depth ratio you talk about and BB talks about is no longer aplicable?

   I din't even know I subscribed to a width to depth ratio? I think the depth depends on elasticity and design while the width depends on draw weight. The contention I made starting this post actually applies more to backed bows than self bows because of the flatness we have to work with. I just seem to be getting better results starting off a bit wider than I had in the past. I use my own mass formula as a guage as well as how the wood is reacting. If I have a bow that is say 2" wide but well within my own mass requirements and behaving well I will leave it wide. If the bow is behaving well but very high in mass I will start reducing width until it conforms but monitoring the condition of the wood as my draw lenght increases. I have found anytime I can't get the mas down where I want it high moisture is usually the cause.
Title: Re: Can making a bow wider lower the mass
Post by: dragonman on May 01, 2014, 04:50:56 pm
maybe there are too many variables to draw conclusions?  My ipe recurves definately show less set  and a faster return after unstringing with  wider totaly flat  limbs, but I'm only talking small differences...I would call narrow 1"- 1 1/8"  and wide 1 3/8"   , I have even had compression fractures on the belly with narrow ipe bows of heavier weight.... just my subjective experience, not saying it proves anything....and I think ipe comes in sub species and diferent qualities..so hard to draw accurate conclusions
Title: Re: Can making a bow wider lower the mass
Post by: dragonman on May 01, 2014, 05:05:40 pm
badger sorry I didnt explain propery and our messages overlapped

what I meant was that if you increase the width by 8mm then that is equilivent to increasing the depth by 1 mm ,in increasing limb strength.....I think you said that; if we add 25% to the width we only gain 25% draw weight, if we add 25% to the thickess we double draw weight. isnt this saying the same thing as 1:8?
Title: Re: Can making a bow wider lower the mass
Post by: Badger on May 01, 2014, 05:28:12 pm
badger sorry I didnt explain propery and our messages overlapped

what I meant was that if you increase the width by 8mm then that is equilivent to increasing the depth by 1 mm ,in increasing limb strength.....I think you said that; if we add 25% to the width we only gain 25% draw weight, if we add 25% to the thickess we double draw weight. isnt this saying the same thing as 1:8?

  I see what you mean, thats just a standard engineering formula I believe, double the thickness 8 times as strong,
Title: Re: Can making a bow wider lower the mass
Post by: Marc St Louis on May 01, 2014, 05:45:19 pm
My experience is also that narrow Ipe bows are better.

Steve
You must remember the Bamboo backed Ipe blank you sent me years ago.  It was extremely narrow at 7/8" with a very thick Bamboo backing, the bow was a nightmare to tiller out.  If I remember right I tillered it out as a flightbow, 25" or 26" draw.  You won the auction at paleo and when you tested the bow you said it was extremely fast.  I was wondering why that bow was so fast, I do have a theory.
Title: Re: Can making a bow wider lower the mass
Post by: Badger on May 01, 2014, 05:59:57 pm
My experience is also that narrow Ipe bows are better.

Steve
You must remember the Bamboo backed Ipe blank you sent me years ago.  It was extremely narrow at 7/8" with a very thick Bamboo backing, the bow was a nightmare to tiller out.  If I remember right I tillered it out as a flightbow, 25" or 26" draw.  You won the auction at paleo and when you tested the bow you said it was extremely fast.  I was wondering why that bow was so fast, I do have a theory.


      I rememeber the bow but not in detail, I am pretty sure it was r/d with a couple inches reflex. Ipe seems to hold up pretty well in narrow bows most of the time. I have seen some that chrsaled but not many. I think the flat belly you use so often is a huge key. I built a hickory backed lemonwood recently and was unhappy with how much reflex I lost. I am redoing it now about 1/2" wider and with a flat instead of rounded belly. I am curious how it will turn out.
Title: Re: Can making a bow wider lower the mass
Post by: Bryce on May 01, 2014, 06:36:10 pm
Fastest boo/ipe bow I've ever made was 1 1/8" or 1 1/16" wide. Pretty narrow. With an oval belly. Extremely fast!
Title: Re: Can making a bow wider lower the mass
Post by: Marc St Louis on May 01, 2014, 06:59:32 pm
No it was a straight limb bow maybe 64" long with about 4" of glued in reflex.  You were going to shoot at the flats but it broke on you before you were able to.  I still have pictures of that bow, here it is

Title: Re: Can making a bow wider lower the mass
Post by: Buckeye Guy on May 01, 2014, 07:13:41 pm
Steve
You know that I am just a backwoods country boy and have no clue how all this works out , and do mostly Hickory which just wants to be a bow no matter what we do to it, but when I get a hold of some of you alls beloved Hedge or BL they most always tell me that  they want to be 1&1/2"wide or usally more and very flat bellied .So I try to listen to them! That is all I can do , just listen for I have no other means of education to draw on unless you folks tell me that I have missed the boat and need to do otherwise.
Thanks for all you do
Have fun
Guy
Title: Re: Can making a bow wider lower the mass
Post by: Arrowind on May 01, 2014, 11:32:26 pm
well I'm reading and trying to follow.....I usually start wider but most of my bows are pretty wide by most standards...probably overbuilt. Mostly cause I'm worried I'll break them!  I'm starting to pay much closer attention to mass and it is definitely making a difference in performance.  Not sure about the relationship between wider and less mass but I have definitely seen a difference in trying to follow the mantra blackhawk mentioned..   wish I had something interesting to contribute...so I'll sit back and keep reading.

Love to read this stuff.   
Title: Re: Can making a bow wider lower the mass
Post by: mikekeswick on May 02, 2014, 03:47:40 am
Yes just watch the set. Set tells you what is going on. One reason why I always trace the side profile of any bow i'm working on before bending it. I've found this much better than just doing it by memory.
Title: Re: Can making a bow wider lower the mass
Post by: Marc St Louis on May 02, 2014, 10:02:24 am
One reason why I always trace the side profile of any bow i'm working on before bending it. I've found this much better than just doing it by memory.

The only time I do that is when I am teaching someone, to give them an idea of what to shoot for.  For myself I just start a bit wider then reduce the width to finished dimensions as I approach final tiller
Title: Re: Can making a bow wider lower the mass
Post by: Slackbunny on May 02, 2014, 11:58:56 am
badger sorry I didnt explain propery and our messages overlapped

what I meant was that if you increase the width by 8mm then that is equilivent to increasing the depth by 1 mm ,in increasing limb strength.....I think you said that; if we add 25% to the width we only gain 25% draw weight, if we add 25% to the thickess we double draw weight. isnt this saying the same thing as 1:8?

  I see what you mean, thats just a standard engineering formula I believe, double the thickness 8 times as strong,

Yes it is is a standard formula. The principle is contained in the formula for the moment of inertia. For example the moment of inertia of a rectangular cross-section is: I=(b*h^3)/12, moment of inertia equals the base times the height cubed all divided by twelve.  So if you double b, you simply double "I", and if you double h you increase "I" by a factor of 8. "I" is a factor that is multiplied to the denominator of the stress equation. So if you double I you divide the stress that your specimen is feeling in half, and if you double h, you divide your stress by 8.

"I" is purely a geometrical value and remains the same for any material. It only changes when the shape of the specimen changes. "I" is different for each cross-section. But regardless of what your cross section is, that relationship of doubling the thickness will always give you 8 times the strength, and doubling the width will always give you double the strength. (At least for every shape I've looked at).

But the stress formulas that "I" is used in assume certain things. For example they assume a homogeneous material which wood is not. These equations do not account for things like grain or knots or growth rings. And they certainly don't account for crushed or stretched fibers. It is in these areas of uncertainty that the engineering stops and the craftsmanship begins.
Title: Re: Can making a bow wider lower the mass
Post by: PatM on May 02, 2014, 12:08:43 pm
It also doesn't account for reflexing from heat treating or even heat treating while kept straight. You can take a material of a given value and that all changes when you apply heat and/or reflex.
 Of course the 'new" material from that process will still follow the rule.
Title: Re: Can making a bow wider lower the mass
Post by: Slackbunny on May 02, 2014, 12:47:29 pm
It also doesn't account for reflexing from heat treating or even heat treating while kept straight. You can take a material of a given value and that all changes when you apply heat and/or reflex.
 Of course the 'new" material from that process will still follow the rule.

True, also variable moisture content can have a significant affect on a bow from day to day.

I do think that it would be possible to come up with a "General Equation of Bowyery" that would take into account all the major factors. You would need all the geometrical information which given the tapering thicknesses and widths of a bow would probably be an integral of some sort. Obviously the mass and mass distrubution would need to be accounted for as well. Then you would need factors that would account for grain orientation, and grain density. Knots could probably be dealt with similar to the way stress concentrations are in traditional mechanics. You would need a factor for moisture content, and you would need results of a bend test done on a standard sized scrap peice.  Backings would add an extra layer of complexity, and multilayer composites would be a nightmare.

It would be a mega complicated equation, and there would be a lot of room for error, but it would be cool.  8)
Title: Re: Can making a bow wider lower the mass
Post by: Badger on May 02, 2014, 11:25:30 pm
  Instead of formulas I think the idea is to develop work bench techniques based on formulas that are not neccesary to actually know. Wood is close enough in behavior to start off with averages just based on density and then as you build the bow and see how it behaves modify it based on experience.
Title: Re: Can making a bow wider lower the mass
Post by: Slackbunny on May 03, 2014, 01:11:28 pm
  Instead of formulas I think the idea is to develop work bench techniques based on formulas that are not neccesary to actually know. Wood is close enough in behavior to start off with averages just based on density and then as you build the bow and see how it behaves modify it based on experience.

I agree. But the engineer in me is always drawn to elegant equations. I just can't help it. Once I get started with the mathy stuff I find it hard to break away from it. Maybe I'm a nerd, but I just love math.
Title: Re: Can making a bow wider lower the mass
Post by: Badger on May 03, 2014, 03:16:56 pm
  Instead of formulas I think the idea is to develop work bench techniques based on formulas that are not neccesary to actually know. Wood is close enough in behavior to start off with averages just based on density and then as you build the bow and see how it behaves modify it based on experience.

I agree. But the engineer in me is always drawn to elegant equations. I just can't help it. Once I get started with the mathy stuff I find it hard to break away from it. Maybe I'm a nerd, but I just love math.

   I like working with people like you, I give you the problem and you give me back the math.
Title: Re: Can making a bow wider lower the mass
Post by: Dan K on May 05, 2014, 04:30:39 pm
Math is a fail safe path to truth, if done correctly, and helps the craftsmen to understand what they know to be true but not know why?  Thanks for contributing!