the mass principle in one sentence

[Badger]

SCP, you are changing quotes, I said mass is determined by manipulating width, you said mass is measured by width. Two different things.

  The amount of thickess you remove from a bow close to tiller is very small, the amount of width that might be removed can be significant with a much smaller effect.

The book clearly answers all the items you have addressed but I will topuch on them anyway.
There is no possible way to make a table that could allow for all bow designs, so the best way to it is to manipulate certain pertinent inputs.
Lets say you build a bow with an 8" handle and fade area which is kind of standard, this same bow has paralell limbs, mass logic or common sense or equal distribution of strain dictates that a paralell limb bow should not have a round tiller, it should be elyptical, so you change the handle figure to 10" even though it is really 8" to compensate. Lets say you like stiff tips on a bow so you leave the last 10" of the tips not bending, how much further would the bow draw if those last 10" were bending? Probably about 2" or so. So even though you will only be drawing the bow 28" you use a figure of 30 or 31 " for your draw length, this will allow a bit more mass for stiff tips. Learning to manipulate the handle and draw length figures are the key to the principle working. Not very hard actually, with extreme elyptical tiller you might use a 12" figure and extreme stiff tips you might add as much as 4" to the draw input figure. Seldom goes beyond that and estimation will get you plenty close enough. Steve

[adb]

For me, the mass princple is closely associated with set. If I remove enough wood from the limbs so I'm getting a small amount of set (when all other contributng factors causing set are minimized), then I know the limbs are as light as possible, thereby opimizing performance. That's one of the biggest reasons I think a bit of set is a very good thing.

[Badger]

   Actually one of the biggest msconceptions about the principle is that I am promoting low mass limbs. It is more about having enough mass and having it in the right places, If a bow took set in a paortion or the entire limb it is because it didn't have enough mass ( width) in that particular area to support the amount of bending it was asked to do. When we design a bow we cut out the front view of the bow, at this point we should allready know what we want the tiller to look like. The thickness controls how far a piece of wood can bend before it takes any set and the width controls how far it actually will bend when drawn. Steve

[scp]

Badger, I am not saying that you didn't say it well or fully in the book. All I'm asking for now is a simple paragraph we can use to understand the principle and to learn how to apply it, even if we cannot express it in a sentence. Of course, what I have said in my version is all in the book. Otherwise I would be calling it my mass principle.

I think you would agree with me that the mass principle is not a fixed and explicit rule but a working hypothesis that seems to be working so far or a work in progress that can be made to work. Either way, according to the mass principle, given a particular specification of a bow, its optimal total mass is reasonably predictable and attainable.

We can stop there or we can make it also deal with the proper distribution of the mass. You appear to opt for the latter as you say "It is more about having enough mass and having it in the right places." Now we need to say what it means to "have enough mass in the right places." You say "The thickness controls how far a piece of wood can bend before it takes any set and the width controls how far it actually will bend when drawn." If this is the case according to the mass principle, of course when all other things are equal, what is the relationship between the mass and the width and the thickness that makes it so?

You also said, "The distribution of the mass is determined by width only, the depth is what you use to control your bending." Does that mean we cannot control the distribution of the mass by changing the thickness?

[Badger]

   Yes, you ignore thickness when distributing mass, thickness is never negotiable if you have a particualr tiller in mind. I think it is beyond a work in progress, not perfect for sure. But well in use long before it was published. Steve

[scp]

   Yes, you ignore thickness when distributing mass, thickness is never negotiable if you have a particular tiller in mind.

That sounds like an oversimplification. Do you ignore thickness when you try to properly distribute mass in an ELB style bow? You must be talking about the case when you have reached at a certain stage of bow making, say when you have reached the target draw weight at the target draw length but still the total mass is a little high. Does that mean we are not allowed to scrape the belly and heat treat it?

[Badger]

  Yes thats what it means, if you want to remove mass you remove it from the sides of the bow, always maintaining your design. If it is a bad design the mass formula will tell you long before you get to that point.
An elb is an excellent example and played a big part in the final stages of the formula. A elb has to meet certain criteria for depth to width proportions. The thickess can be anywhere from a 7/8 ratio to a 5/8 ratio minimum. In my opinion a properly made elb never bends in an arc of the circle but bends more in an elypse. The recomended demensions of an elb support this. If an elb is too high in mass you simply scrape down the sides a bit as you tiller till it starts comming into line. If by chance the wood is a bit too dense for the length and draw weight you chose you simply make the tiller slighlty more elptical and it will raise the number for projected mass and maintain performance. Steve

[Badger]

      Scp, just for the ehck of it lets have a very non tecnical discussion about wood and bending wood.
Lets say you want to bend a piece of wood 6" and you don't care how much effort it takes, the width is fine like it is. You want that same piece of wood to be able to treturn to it's original shape when you release it. Some guys would start thinning the piece of wood and pushing on it till the wood bent 6". Some guys would push a little bit and see if it returned ok and then push a bit more and check back again, if it didn't quite return they would take a bit more thickess off, repeating this till they hit the 6" point. The other guy might make it way thinner than he needed and get his 6" with no problem the wood returning perfectly to it's old position, or it might just break when he was pushing. In other words he was just guessing. For the most part the inside circumference of a bend has to stay with in about .7% of the otside circumference, some woods may go as high as 1%.
     When we make a bow we have very specific goals, we know how far we want to bend it and we know how much effort we want to expend doing this, we also should know how we want it to look when bent. The goal when making a bow is not to avoid breaking it as much as it is to stay within the elastic limits and not take too much set. I have seen great looking bows with lots of reflex and great profiles that shot like dogs because the wood was so rubberized from being overstressed.
    Most of the demensions given out on line are pretty close and work pretty good because there are lots of guys experiemnting here making bows and they know what works, but if you want to start finessing your game a bit you try to eliminate as much guess work as possible. Every little change you make in a design changes the optimum mass needed for that design.
    One of the other goals when making a bow is to even out the stresses on the limb as much as possible. The only way to do this is to make the bend match the thickness. Lets say you have a 28" long limb, 16" of that limb is straight and the last 12" tapered to 1/2". You are going to scrape that limb down in thickness until it bends the same thrughout the limb most likley. It will look nice but far from being evenly stressed because you have made the limb thinner down its length, in order to make it evenly stressed it has to bend more as it progresses toward the tapered area. If you wanted a nice circular tiller the pyramid style even thickness design is what should have been chosen.
    Everything you do to a limb that shortens the working area causes the working area to be under more stress, making it wider and thinner is the only way to compensate. A childs bow of only 10# draw weight is under no more or less stress than the curviest 80# bow you have ever seen, wood will only take so much stress and it is relative. The mass principle just keeps these things in mind when recomending how much wood you need to make a bow. Steve

[Lombard]

Badger, this is some interesting stuff, that you have presented. The take that I'm getting here, is that the Mass Principle helps in building a bow that is neither over or under built for a particular design, leaving or taking away wood in the right places for a given tiller, to achieve optimal performance. Am I seeing this correctly?

[Badger]

Lombard, yes that is the goal. It is on the conservative side for obvious reasons. If anyone is interested in downloading the calculator send me your e email address, all you do is fill in a few blanks and it spits out the number. The calculator is microsoft excel. Steve

[George Tsoukalas]

scp, never stop questioning. I didn't chime in earlier because you had Badger to answer your questions. You had Badger to badger. I used to love it when my students questioned me. I used to tell them to keep at it even if I sounded aggravated which I wasn't (not usually LOL). I'm a retired chem teacher. Here is my synopsis of the mass principle. The mass principle is a technique that allows the bowyer to manipulate the mass of the bow in order to maximize performance. Thus a 50 # rigid handle bow with a mass of 28 oz is vastly over built. It's probably too wide. Around 18 oz is better. The bowyer can control the mass by reducing the width. Osage is one of the densest North American bows at 0.8 g/cc. Density is mass per unit of volume Therefore, it should be trimmer than a hickory bow at around 0.7 g/cc. Either bow would have the same mass just that the hickory bow needs more volume to get that same mass. The mass principle is quite scientifically grounded. Jawge

[Badger]

   Thank You Jawge, I thought of you throughout this entire exchange and how patient you probably had to be. I am a diesel mechanic by trade so it doesn't come natural to me. Steve

[George Tsoukalas]

Thank you. Badger, how'd I do with the synopsis? Jawge

[Badger]

   I liked it!  Steve

[scp]

Jawge, a principle must be much more than a technique. I BELIVE in the underlying intuition. But unless you formulate the principle to make it falsifiable, you are not there yet.

Badger, I don't hunt. Not even fished lately. But I shoot at targets. I chase "principles" and understanding. I have no doubt you know what you are doing. But you might be calling the totality of your experience the mass principle. Of course, bow making is an art, not science. Still if you are going to call something a principle, you might have to provide a succinct exposition that can be used by everyone.

Your said "you ignore thickness when distributing mass." What do you mean by "when distributing mass"? It cannot mean "when we are tillering," can it? How can we ignore thickness when we are tillering? Does it mean "when we are applying the mass principle after most of the tillering is done"?

You also said, "The distribution of the mass is determined by width only." Then I have to ask when? When we are designing a bow? You might be thinking about when the bow is almost finished and you are trying to apply the mass principle to that bow. Why can't we determine the proper distribution of mass by thickness when we are designing a new bow?

Don't get me wrong. I'm not saying you are wrong. I'm saying good bowyers need to make their assumptions more explicit. Knowledge mining is never easy and can be quite irritating sometimes.
The mass principle in a paragraph, anyone?