Chopping Physics

[the possum]

I'm not sure how to answer this without sounding contradictory. Basically we want the most mass that we can still move at very high speeds. All the things we've been discussing affect this; not just mass.

 

[hardheart]

Okay, so you want to move the mass, not remove it. I was wondering because I know you removed steel from your kukri-but you had to to move the balance around, it was a finished piece. You added the heavier pommel, but still made an overall lighter tool, IIRC.

 

[the possum]

Okay, so you want to move the mass, not remove it. I was wondering because I know you removed steel from your kukri-but you had to to move the balance around, it was a finished piece. You added the heavier pommel...

Yeah, that's probably a good way to describe it. As it was made, I considered it far from ideal, so I had to move the mass around. Of course if I was starting from scratch, as I'm doing right now with a big falchion, I just make it that way from the start.

...but still made an overall lighter tool, IIRC.

Well, it only ended up about 2 ounces lighter when I was done, but it's still about two ounces heavier than my bowie, too. Even with proper dynamic balance, I guess this is about the most mass I feel comfortable swinging for a tool like this. But really I would have liked to get a bit more weight in the pommel, but the blade design wouldn't allow it.

 

[Cliff Stamp]

Mass is factored into calculations of impulse, momentum, force, and such, but so is acceleration and velocity.

Those general equations are predicated on very simple situations. In any real non-trivial situation you would have to look at the base equation which is a differential one (or integral) because the variables are not independent. When you swing a knife then the speed at which you can move it is dependent on its mass. Basically up to some point the momentum keeps increasing as you can still reach maximum speed, but as you move beyond it then the speed decreases, and eventually the momentum drops to zero because you can't move it.

This is one of the many misconceptions about balance (as a general term meaning issues such as weight and heft), that there is some ideal mass (or any physical quantity) which is independent of the user, i.e., people say "This is balanced for a fighting knife.". That is just as silly as saying something like "A size 10 hiking boot is optimized for survival." That of course would be obviously absurd, but that type of statement about balance is just as foolish.

Even a casual reflection should make it obvious that a stronger person would find optimal a heavier knife (and I use heavier in a general sense there including both linear and rotational motion). A stronger person would also be able to rotated a larger inertial moment. They would also have to adjust according to their attributes. If you are very slight and fast then you would not pick the same tool as someone who is much larger but inhernetly slower. Hence the likely development of the many different types of fighting knives, all of the existing sword patterns which are just long knives.


You also raise a very valid point in that momentum and kinetic energy are not dependent in the same order on velocity. This is one of the reasons why long blades are so versatile because the multiple points of contact allow impacts with maxium inertia or maximum speed and these have different applications. An axe for example just has the one impact point and it is of maximum inertia which is why axes are horrible for light brush.

If one can greatly increase acceleration of a smaller, or even the same, mass, then something like chopping could be done more easily. I guess it's the baseball bat versus a bullet thing-they could both have the same momentum, but the bullet has greater kinetic energy. And it would be better if you could get the tip of the bat moving as fast as the bullet. Or something like that.

That is a fairly astute point. Note however that both momentum and energy are conserved in a collision, however the momentum conservation is quite straightforward, the energy one is not because it can change forms. As a sort of general rule, this is why speed is more of a factor than mass, meaning that it is better to make an increment in speed than in mass. Of course if you can increase the mass without decreasing the speed (which will happen up to some point) then that is always productive, assuming you want to carry it.

As a general note, it is also worth noting as Possum has mentioned that the dynamic balance point effects how the blade responds and thus you don't use the knives the same. He has discussed this in detail elsewhere but basically you use the fact that you can rotate it to minimize the effort of linear movement.

-Cliff

 

[the possum]

Well, I lost a big reply during the server upgrade this morning...

You also raise a very valid point in that momentum and kinetic energy are not dependent in the same order on velocity.
...As a sort of general rule, this is why speed is more of a factor than mass, meaning that it is better to make an increment in speed than in mass. Of course if you can increase the mass without decreasing the speed (which will happen up to some point) then that is always productive, assuming you want to carry it.

Also, in the Rogue review thread, Cliff said:

Rotational tip speed is proportional to length but that is only part of the total energy and the linear part isn't dependent on length at all. The power has more to do with the total mass and the balance points and you can vary these a great deal in a given length, but at most you are looking at a less than linear effect. The 75% comes from actually comparing a number of similar blades of varying lengths which I did before I looked at the physics, experimentalist after all. Swaim looked at this on rec.knives years before I did. He also assumed there would be a bigger influence on length. Note as well that the total length is what factors into things like the inertial moments.

This is why things can get a little complicated and why I didn't want to give the impression that it's always better to "lighten" the blade to increase angular velocity. The heavy targets still need some inertia via mass, and it may or may not be so important depending on how you're chopping.

If you're just chopping wood at a steady pace (i.e., not trying to move near your maximum speed), providing power with the whole upper body and arm, then maybe the moment of inertia is less important, and likewise a few extra inches of blade length won't add much in comparison to the length of the whole system. (your arm)

But, contrast that with another of my favorite applications. I need to move the blade as fast as possible for quickly moving targets, and I may be running myself & straining for reach, so I can't rear back with a full swing. As I alluded to earlier, I need to make a lot of very fast, short, cuts with heavy wrist action. So I need a lower moment of inertia, but also depend on the blade's length for speed (angular velocity). When the cut is almost completely powered by the blade rotation alone, then the length can indeed make quite a big difference. A quick wrist cut like this will easily go halfway through a coon; sometimes all the way.

 

[sevenedges]

Man, I could read all of the above posts understand them all, and not gain one bit of chopping performance with my knives. When I pick up a knife I immediately know where the sweet spot on that blade is, and when to break my wrist and how to swing my arm. So I'm a happy hound just scanning this thread. Looking at all the techno babble.

Jeff

 

[the possum]

That's not really the point here, Jeff. We're not talking so much about changing the way you use an existing knife, because most of this stuff is predetermined by the way the knife is made. It's more about changing the design of a new knife, or selecting a new knife that better meets your needs/uses. Unless you want to do extensive modifications to your knife, or it already happens to be perfect, that is. But glad you're enjoying it either way.

 

[sevenedges]

Possum, I only buy knives that are as perfect as possible for my uses. So mods arn't needed. And neither is changing the design of a new knife except for reprofiling the edges. I Just look at the blade and can tell what that knife is capable of 99% of the time, without even touching it. I am rarely suprised. The only thing I really can't tell for sure about is the handle. Although I still have a pretty good idea by looking at it if it will eat my hands. Everyones hand is different and until you use the knife under hard use for an extended period of time, sometimes not so extended you can never be quite sure.

 

[the possum]

Possum, I only buy knives that are as perfect as possible for my uses. So mods arn't needed. And neither is changing the design of a new knife except for reprofiling the edges.

Very well then. You are of course entitled to that opinion, and I don't even know what knives you own that are "perfect". Though if I may say so, I see a lot of chopping blades that could use some work in these regards.

 

[sevenedges]

perfect is opinionative of course.

 

[the possum]

There seemed to be a fury of interest in this topic for the first two days, but is sliding now.

Just curious- HoB, have you had some time to mull over/digest some of these ideas?

I still haven't been able to come up with a simple idea for measuring angular velocity. Any perspective here you could share from your physics background? The easiest way I've come up with is simply to do a bunch of chopping & see what happens, but it would be nice if I could use numbers for a more precise comparison that doesn't require so much effort.

 

[HoB]

Sorry, Possum, yes I have worked out three handwritten pages with some numerical examples, but to post them will take some time and my work came crashing down on me so I just haven't had the time to post them. I hate when my work imfringes my hobby time . Maybe I do it peace by piece.

I will admit I stumbled over a few things that were a bit unintuitive to me, and I found some honest mistakes in my first post (unlike the pendulum thing which was just a temporary laps), even though the general idea seems to hold.

Maybe, I post something tonight, it is certainly more interesting than the stuff I am supposed to think right now.