Chopping Physics III

[the possum]

Quite some time ago, HoB started this topic here- Chopping Physics
And there was a follow up thread here-
Chopping Physics II

I keep thinking about the subject from time to time, but haven’t really gotten back at it since I haven’t had any time in the shop to work on that big chopper. I’m going through some bad times personally… But for some reason the mood caught me to ponder it again.

Since those earlier threads, I found a wonderfully informative thread on the topic at MyArmory, here-
Balance Points, Pivot Points, and Nodes on the Sword

I highly recommend reading it, for those interested in these topics. Someone was able to piece together several parts of the stuff we already knew, to come up with something new (to me, at least). Such as, I don’t think we need to worry about coming up with mass at every inch along the blade in order to calculate moment of inertia. We can calculate it for any point on the sword if we have the pivot points. (I think. Not sure if it could translate to the CoM itself or not.) I was struggling to figure out how I should make that falchion, and how the mass should be distributed. This thread confirmed what I was suspecting- I shouldn’t be so concerned about getting that forward pivot point all the way to the tip on a design like this. (I was also surprised to learn original rapiers do not have their dynamic balance point at the tip either, but the explanation for this made perfect sense.) I knew where I wanted the pivot points to lie, but couldn’t do any real calculating without the center of mass, and since small changes in its location would really affect the numbers, I didn’t feel comfortable just guessing at it. But, now I have made up some simple geometric diagrams to find about where the CoM should be based on the pivot points, from this illustration in that thread:

Again, maybe some of you guys already figured that out on your own, but I thought it was really cool to lean how the pivot points and CoM are connected by right angles. I just wasn’t clever enough to see this before.

So guys, does this give us enough tools to calculate moments of inertia, etc., so we can more easily refine designs, optimize chopping power, as well as speed/maneuverability?

edit- Bah. Can't get the illustration to work. It's on page 2 of that thread.

 

[the possum]

I've made up a few illustrations of my problem, to show how the above information helped me.

This is a big fantasy chopper thingie that a special customer (my father) has asked me to make. In order to calculate things like moment of inertia and impact stuff, you'd need things like the mass, center of mass, inertial moments around the CoM, etc. These things are all pretty easy to measure, but since the piece is not yet made, I've been trying to figure out how I could come up with a model to play with the numbers, and try out various scenarios with the mass distribution to figure out how I should go about distributing the mass.

I knew roughly where I wanted the pivot points to be, and the final mass of the piece, but didn't really know where the CoM would end up. By using the equations given in the MyArmory thread, I can now figure out where the CoM should be. Here's a rough line drawing I did in Paint. (again, this design is not exactly my cup of tea, but I want it to work as well as it can.)

Here I've added a red line indicating that I want an impact point right on the hump of the spine to correspond to a pivot point just behind the crossguard:

Now I've added a second set of blue lines giving another set of desired pivot points.

From these two sets of points, I played around with the drawing in Word, rotating some rectangles on top of the picture until I could get their tips to coincide as best I could.

This determines where the CoM should lie, as indicated by the brown line.

Now, I just need to figure out how to add some kind of measuring device/scale. Numbers could probably be arrived at via calculations as well, but I like working with pictures more than math.

 

[Cobalt]

I stand by this which that chart in the sword forum hints at:

I asked the puppet in the corner of my room this question and this is what he said. He's had a few t many drinks though. The equation process that Hob went through is a very simple adaptation of what really happens when a knife is moving through the air "attached to a hand and an arm, shoulder and body" The dynamics of what is happening is more akin to a 3 dim. dynamic motion equation than a simple linear pivot point equation.

Think of the motion generated on a swing. Look at a cutting competition for free hanging rope or chopping wood. Shoulder and back rotate along one axis, arm, shoulder and knife rotate around another axis. If your doing everything correctly, the entire mass is rotating around some virtual point near your body's center of mass. The knife is just an extension of your hand, arm, shoulder, torso. The pivots are all the joints and they all have different individual properties. The equation of motion would be similar to one of a body rotating around another body both of which are rotating around a third body, simplified. Like the moon around the earth which goes around the sun. Gravity is your connecting arms and the only difference is the mass. Of course your equation would not be circular in nature or linear for that matter, introducing a more complex equation for the path of the hand or blade. But it would be slightly simplified in that there are less options for the limbs to follow.

you would need to formulate your differental equations from a correct free-body diagram.

 

[the possum]

We're bound to see things a little differently, Cobalt. After all, I generally prefer bourbon over scotch, and enjoy smoking my pipe more than cigars.

Just keep in mind that the impact mechanics do not rely on your body, shoulder, and arm. The sword will react the same to the impact regardless of how you swing it. And, especially in swordplay (as opposed to chopping wood at a steady pace), not every swing will be powered by the whole body. Just last night I used some quick sniping cuts powered by mostly wrist rotation against a moving target.

 

[thombrogan]

Hi, Mr. the possum!

From your diagram, it looks like one would emphasize his or her grip in the index finger area to get more powerful cutting with the tip and emphasize the ring and pinky finger area of the grip to place more force along the middle of the blade. Is that correct or did I get it backwards?

 

[the possum]

Hi, Mr. the possum!

From your diagram, it looks like one would emphasize his or her grip in the index finger area to get more powerful cutting with the tip and emphasize the ring and pinky finger area of the grip to place more force along the middle of the blade. Is that correct or did I get it backwards?

Greetings, Thom.
Well, umm... Really I think you've got things closer to being backwards...

If you were just to grip the handle right behind the guard with your thumb and forefinger, and wiggle the sword around just using torque on this point, then the hump or "beak" area on the spine (designated by the other red line) should pretty much stay still. (This is the "waggle test" described in Mr. Turner's article.) A pivot point on the handle cannot exert torque on it's corresponding pivot point out on the blade.

Though the pivot points are a result of mass distribution, and this configuration has lots of benefits regarding handling, I'm mostly illustrating impact behavior rather than dynamic handling behavior here. If you want "more powerful cutting", you swing it as hard and fast as you can, any way you can. What actually happens on impact is almost totally up to the sword's mass distribution; not what portion of the grip you're trying to emphasize during the swing. If you want to talk about handling properties, I'd be glad to discuss that separately.

In other words, if you'd strike with the beak on the spine, then the sword should naturally want to rotate just behind the guard. This ensures A.) Your hand doesn't feel much shock from the blow, since the pivot point does not suddenly change motion. If the pivot points get several inches or even feet away from the grip, then you get terrible and painful shock to the hands. B.) This location is also the furthest point you can be from the pommel and still be within the grip. The farther away the pivot point is from the pommel, the more good the pommel does. (I'm planning to hide a pommel beneath the handle material to fine tune the pivot points as needed.)

I chose to make the forward pivot point of the guard (What Cliff has termed the "dynamic balance point"- a useful description) correspond to the beak on the spine because A.) This blade will be so massive I don't think I could push it all the way to the point if I wanted to, and B.) I am less concerned about tip precision with this thing. It's a big freakin' Franken Chopper, after all. I want max power at the beak for smashing through shit. I expect some of the empty 55 gallon drums Dad has sitting around the farm will die a horrible death. There is evidence historical falchion were used edge up like this- possibly against armor. See this thread by Tinker.

The set of pivot points represented by the blue lines are more of an educated guess. Will see how it goes as I shape the blade.

By the way, the blue line on the handle would probably be more like the area gripped by the first finger- of the left hand. Sorry there's no scale on the drawing, but that handle is almost a foot long. Dad found a ginormous piece of elk antler he wants me to use for the handle. I can barely wrap my fingers halfway around it. I'm gonna have to slab out the center section and make it a mortised tang just to make it somewhat grippable. (Don't want it flying out of his hands mid swing!) Really it's just crazy by my estimation, but it's what he's always wanted.

 

[Cobalt]

We're bound to see things a little differently, Cobalt. After all, I generally prefer bourbon over scotch, and enjoy smoking my pipe more than cigars.
.

BLASPHEMY!!! bourbon over scotch? blagh!

 

[thombrogan]

Well, umm... Really I think you've got things closer to being backwards...

Though the pivot points are a result of mass distribution, and this configuration has lots of benefits regarding handling, I'm mostly illustrating impact behavior rather than dynamic handling behavior here.

In other words, if you'd strike with the beak on the spine, then the sword should naturally want to rotate just behind the guard. This ensures A.) Your hand doesn't feel much shock from the blow, since the pivot point does not suddenly change motion.

Please pardon the snippeting. I almost understand now. Place hand at junction A and it won't get easily broken when demolishing telephone pole B although the generated and applied force comes from shoulder C, elbow D, hip E, and knee F. Is that closer?

BLASPHEMY!!! bourbon over scotch? blagh!

Jody the Voracious (a Hog's Hog by every estimation) prefers bourbon over scotch and that's proof it's good stuff. :grumpy:

 

[Cliff Stamp]

This blade will be so massive I don't think I could push it all the way to the point if I wanted to, and B.) I am less concerned about tip precision with this thing. It's a big freakin' Franken Chopper, after all. I want max power at the beak for smashing through shit.

I think there are a few points that people need to understand, as you noted, handling, precision of cuts and then power. They are all based on similar properties but different in regards to specific influence. I would be curious to look at the tribal knives currently made by smiths with no math/physics background and see how they are broken down and how they achieve the performance. Most of the designs involve little customization and are repeated patterns so it may just be the result of 100+ years of trial and error.

-Cliff

 

[the possum]

Jody the Voracious (a Hog's Hog by every estimation) prefers bourbon over scotch and that's proof it's good stuff.

I prefer to evaluate each bottle of whatever on its own merits, rather than lumping groups together. There are good and bad examples of everything. I also generally prefer Armagnac over Cognac, yet I fondly remember a certain Cognac as one of the most interesting and complex spirits I've ever had the pleasure of sniffing.

Cliff-
If you find anything out regarding "tribal" knives, let me know. Just beware that there are still pitfalls out there not necessarily rooted in performance. Some of the alien looking designs from Africa come to mind, and keep in mind what I had to do to my HI Khukri to make it acceptable (to me).

I played around with some more illustrations so we have a better frame of reference when discussing what balance does for both handling and impacts. Here are two different extremes that I could do with this design. Again, the CoM is designated by a brown line, and the guard pivot point & dynamic balance point in red. Also note that since these are just quick illustrations based off one set of pivot points, they are not to scale.

This first picture demonstrates what happens to the pivot points if I leave the blade really massive, with little distal taper, and don't add a pommel weight. This could be called a "balance forward" design, like so many folks seem to think is necessary to get good chopping power.



The next one is at the other end of the spectrum, and shows a CoM right near the crossguard, which I could accomplish by making the blade light & thin, and adding a very heavy pommel. This is what a lot of folks think is needed in order to make a blade that's quick handling. Notice how the dynamic balance point has gone clear off the page somewhere.



Notice how with the first one, people usually focus on impact mechanics, while with the second one, the focus is on handling dynamics. If you've read the reference articles or my thoughts on the subject before, you probably already know why neither one is correct. Discussion?

 

[Cliff Stamp]

Indeed, I am not arguing that all traditional designed are optimal in function. I would just be curious as to how close they are and to discuss such issues with the makers. Not from a math/physics point of view but just the concepts of performance/design.

-Cliff