Chopping Physics 2

[tsdevanna]

Very impressive gentlemen. Now lets see if we can apply this wealth of knowledge to actual application and please keep it as simple as possible.
I compete in cutting competitions. The chopper I use has an overall maximum length of 15 inches - maximum blade length of 10 inches and maximum blade width of two inches - blade thickness is wide open but most choppers are running about .250" thick. Lastly choppers I currently use are approximately one pound, 4 ounces in total weight with COM approximately 7.5 inches from the end of the blade - or 2.5 inches from ricasso.
We cut 2 X 4s, hard wood dowels, ropes, soda cans, water bottles, etc. but I am most interested in a chopper that will cut through 2 X 4s quickly and effectively. Any suggestions on blade shape, weight and COM ???

 

[the possum]

The chopper I use has an overall maximum length of 15 inches - maximum blade length of 10 inches and maximum blade width of two inches - blade thickness is wide open but most choppers are running about .250" thick. Lastly choppers I currently use are approximately one pound, 4 ounces in total weight with COM approximately 7.5 inches from the end of the blade - or 2.5 inches from ricasso.
We cut 2 X 4s, hard wood dowels, ropes, soda cans, water bottles, etc. but I am most interested in a chopper that will cut through 2 X 4s quickly and effectively. Any suggestions on blade shape, weight and COM ??? ...and please keep it as simple as possible.

Let's hear some more. For starters, where is the 'dynamic balance point' we've been discussing? That will quickly tell me quite a bit about the mass distribution on your knife. Your CoM is right at 50% of the total length, and 25% of the blade length. Historically most cultures that needed extreme speed combined with adequate power settled on a location a bit further back, but again, the CoM doesn't tell us much unless we know how the mass was distributed to get there. What kinds of tapers are you using in the blade and tang, if any? What kind of handle material? Any guard or pommel?

How do you use the knife when chopping? Do you choke back further towards the butt of the handle, or keep it in position close to the guard area?

Regarding weight, how many other comp knives have you made before this one? I'm trying to understand whether you've changed the design for a knife that was lighter, or if you felt you could go heavier, or whatever. Does this one feel about right to you? I.E., a good mix of weight and speed for your abilities?

As I recall, my old bowie was right about that same weight, except it was 21" long overall. Really, the first thing I'd do if I wanted fast chopping power is make the knife a fair amount larger than 15" overall. And a fair amount smaller for the finer tasks. I personally think the competitions would be neater if they did away with the size restrictions and devised a *testing regimen* that would naturally weed out designs too focused on one specific set of useage. (such as chopping, wear resistance, whatever.)

 

[HoB]

Hi, tsdevanna: Glad you join the discussion.

Unfortunately, I can not give you a straight answer to your question. Like I told possum, this is not how it works or even should work. I know much less about chopping than you do, so who am I to tell you how your knife should look like. Also, the weight distribution will depend very much on the preferences of the user.

However, what I can do is give you preditions what will happen to certain properties if you implement certain changes. If you have for example a specific blade that you are not completely happy with. I can tell you how much kinetic energy you gain/lose when you move the COM by a certain amount or if you change the weight distribution around. I can tell you where your sweet spot will be, and can make an approximation on how wide the sweet spot will be, I can make a resonable guess on the shock you might feel if you have a certain blade position that you would like to hit the blade. I can also give you ideas on how much faster/slower the blade might be if you make certain adjustments to the weight distribution.

But for all that, I need a starting point first. Meaning you have to give me a weight distribution to work with first. This could look like the following, let's say you have a knife that has the following weight distribution: 1 1 1 2 2 1 1.5 1.5 1 1 1 1 1 2 2 and you what to know, how much faster or slower will the knife be if you change the weight distribution to 1 1 1 2 2 1 1 1 1 1 1 1 1 2 3, how the sweet spot will be affected how much energy you gain or lose if you still swing it with the same velocity etc. That I can tell you before you do any modifications to your blade. It could also work this way. You give me a weight distribution of an existing blade and you ask me how to change it to get the maxiumum momentum without changing the COM. Then I can make a suggestion and tell you how much you gain, and how certain other parameters like the pivot point will change. And you might reply that you don't like my suggestion because you don't like how the pivot point moved. Now I can make a different suggestion and we can work back and forth till you think you have a reasonable trade-off. Of course with the sample calculations you could do that all yourself, but I am more than happy to assist anybody who doesn't want to slug through the math.

But for me to give you a starting point would be taking advice from the wrong person. Possum might help you with this, and as I see he has already started with it.

Edit: You should view the mathematics as a playground: The role of the model is not to tell you what is best, but to test your theories. It takes a lot of time and money to make a blade, you can make up 10 different blades in minutes for the expense of a pencil and some paper and see what happens and more importantly even quantify the differences if you make your adjustments to the blade. You will also realize that you can not optimize all parameters at once. You can construct a blade that gives the maxium power but if you do not have the strength to swing it, it is no use to you. My brother was once part of a workshop that build high performance human powered boat, so called waterbikes. They build an amazing design: double hull carbon fiber driven by a single bladed carbon fiber air propellor with counterweight which, at ideal opperating speeds would reach supersonic tip speeds. The whole thing was calculated to be able to reach close to an incredible 20 knots.........well....turned out that no humans were actually strong enough to get the propellor to full operating speeds.....ooops. The calculations were all correct an when the put in a very small motor that was strong enough to actually get the propellor up to speed, the thing was flying. Unfortunately, the calculations overestimated the human element substantially.

 

[HoB]

Sounds like something that would be interesting, and help me learn the concepts at the same time. Rather than using quadrille paper though, I think it may be easier for me to draw a simple line graph freehand. I know the mass at the base will be 3.8 oz (since at the choil it will likely be the full stock dimensions of 2 1/4" wide and 3/8" thick, and steel is about .283 pounds/cu inch.), and basically half that just ahead of the shoulder, and zero at the very tip, so I can use those reference points to draw a curve to represent the tapers in between.

Sounds like a plan. I will be gone next week but the week after I will be back online.

All church services locally were still conducted in German at least until the 1930's, and my grandparents would often speak to each other in German. I'm not fluent myself though.

Wow... . I think the spelling "grosse messer" is probably more due to a spelling error of someone who knew less about german than you do .

If you don't mind me asking: Southern Illiois.....how far away are you from Terre Haute, IN?

 

[the possum]

About 165 miles or so. Actually I have a couple college friends from Terre Haute. Sparticus, and Spam, and Wheelchair...

 

[HoB]

That is still quite a ways away. I used to live in Terre Haute for a while.

 

[Cliff Stamp]

To someone that does not want to rotate the blade at all, and instead use it in the same manner as they would with a paring knife with static cuts, handle heavy balance may make sense.

It is usually that way simply because people want the knives to be light when they pick them up, how they cut is usually not a factor.

Any suggestions on blade shape, weight and COM ?

Thicker stock, say 3/8", distal taper and pommel weight. Adjust to put the dynamic balance at the tip and have the static and intertial moments just at the point of personal maximal acceleration. You can tell when they are optomized because you put maximum effort into the swing and it snaps down and sweeps out at maximum speed. If you are too heavy (inertia and dynamic) the blade will feel sluggish and if you are too light (again inertial and dynamic) then you have more to give to it but nothing to push against. You can also easily tell if it is too light/heavy either statically (center of mass) or dynamically (moment of inertia) and adjust accordingly.

You also need to get the optimal edge geometry which is pretty much minimum (unless you are getting binding issues on the woods) so I would start about 0.025/10 degrees with a 15 degree micro and reduce this through the tip as the bottle and rope cutting don't need the same edge thickness/angle as 2x4 chopping. Given all the materials are soft and thus impact toughness isn't a concern you might be able to refine this geometry a little by increasing the hardness of the steel. But given how strength is quadratic in cross section you can't hope for a lot.

I can tell you how much kinetic energy you gain/lose when you move the COM by a certain amount or if you change the weight distribution around.

You could tell how the blade would respond under a constant force if the static and inertial moments were changed but the actual force a person will apply depends upon those quantities so such a comparison is inherently invalid.

-Cliff

 

[HoB]

That is no necessarily true. Depends very much on the weight range and size of the knife. I would say from my own experience, that there is a weight and size below which I swing all knifes at the same velocity, because my arm is more limited by a max velocity rather than by strength. Once strength plays a role, you can make the calculation dependent on the accelerating force.

 

[Cliff Stamp]

I would say from my own experience, that there is a weight and size below which I swing all knifes at the same velocity, because my arm is more limited by a max velocity rather than by strength.

Yes, that is what I meant by too light (again general, not just meaning the weight), you will feel a lack of effort on the swing as you don't have enough resistance. The energy of the blade is simply the work done on it by you which is given by the force integrals. Of course it isn't just the energy which is important, a very heavy blade could impact with a lot of energy but lack cutting ability as it isn't fast enough.

You again simply adjust the static/dynamic moments accordingly based on how the blade moves. The only complication is that chopping a 2x4 and cutting a water bottle are two very different cuts. The water bottle needs a very high speed while the 2x4 needs a lot of inertial impact. This is why I suggested a heavy distal taper to provide both options in the same blade.

As a possible experiment, you could have a blade with a variable static/dynamic balance by using either metal shot or a heavy liquid. This would be fully optimal because the actual force you can apply maximally isn't the same throughout the full range of motion so a really optimal blade would actually have its linear/rotational inertia match the force responce of the user through the swing. The actual force curves for people are very well known, the tricky part would be getting the knife to respond to match.

-Cliff

 

[HoB]

Or you could use the same approach as many match pistols: Mill a grove close to the spine and attach a sliding weight. But I don't know if any of that is legal in competitions.

 

[the possum]

Though I've never participated in a cutting competition, I believe the water bottle part is going to depend on inertia too, because of the way they do it. If you just had one bottle sitting on a stand, you'd want to snap the blade around with max speed. But when you have 10 of 'em sitting in a line on a table, you have to contort your swing into a straight line, or you'll simply miss the bottles at the beginning or end of the line. Since you won't be able to add much snap with the wrist and have to follow through in a linear motion, you'll need some blade inertia to keep the blade from losing speed or cocking back at the end.

Mr. Devanna- could you give us a little more feedback on that?

The only sword makers I've heard who have messed around with sliding weights did not like them at all. I'm betting they are more of a gimmick for very specific circumstances rather than a blade that needs the versatility to perform a wide range of tasks well.

 

[Cliff Stamp]

I believe the water bottle part is going to depend on inertia too

All such collisions will slow down the blade, it would be easy to measure if there was video, I would bet that the speed reduction would be slight for a couple of reasons. First off all there isn't a lot of resistance by the bottles individually and secondly you are still providing force through the cutting and can thus compensate for any loss through the individual impacts.

Concerning the swing itself I would assume there is significant wrist cocking because you would not want the blade at a perpendicular impact angle with the bottles. At a first pass I would consider a swing which met initially at the choil and then swept out through the tip as I would be concerned about the last bottles being knocked over or put in motion by the initial impacts and would want maximum speed for them.

The only difficultly with that would be that during the middle of the swing the blade would be hitting perpendicular for a moment, but this is only a factor if that happens just at the start of a cut. The choil area however could also be too slow even for the first bottles and if that is the case you would need to do a fairly straight swing like you noted.

It would seem like that cutting would be very similar to cutting spring brush so it would be interesting to see how some traditional blades would fare for that work such as machetes, light parangs, etc. .

The only sword makers I've heard who have messed around with sliding weights did not like them at all.

It would seem to be very difficult to get to work well because the forces curves are different depending on which muscle groups you use and as well you have to consider that the effect of gravity is different with a horizontal vs vertical swing for example. I would wonder as to the possibility of a screw on weight, handle mainly which could be used to shift the balance for task specific work.

-Cliff

 

[tsdevanna]

A picture is worth a thousand words - check out www.cuttingcompetiton.com -see photos of water bottle cuts - new world record for water bottles cut in one swing is 17, although several competitors have done more bottles than that in practice.

 

[the possum]

Mr. Devanna-
I checked out a lot of pictures on that site, but wasn't able to get a whole lot from it. Looks like the water bottle cuts are very long in a straight line, and lots of guys seem to have their elbow leading sharply. I was hoping to see how you're gripping your knife in the cuts, and how much rotation you're using on various stages.

Have you had a minute to find out about the rotational centers/pivot points/dynamic balance point on your knife yet? You can get a rough ballpark estimate in seconds with the "waggle test" described in Mr. Turner's article.

My gut feeling is also that your dynamic balance point could probably be pushed further out, and more done with the mass distribution, as Cliff mentioned. Keep in mind this is from someone who has never been in a cutting competition, though I am very demanding of my blades in regards to speed and power.

I would like to hear more from you on this subject, and if you decide to give these ideas a try, I'd really love it if you came back here and reported what kinds of differences in performance you found, with specific comparisons to your current comp knife.

 

[tsdevanna]

I will give these ideas a try and advise. I will be attending Warren Osborne's cutting comp school December 2 & 3 and will try to test these ideas at the school. Thanks

 

[the possum]

Errr... I take it you mean you're gonna try making a different knife incorporating these ideas? As stated, this is not something you can just go try with an existing knife by changing your swing or something; it's handling characteristics and stuff are built in via the mass distribution when it's made.

Either way, thanks for keeping an open mind.

 

[tsdevanna]

Yes, different knife.

 

[hardheart]

I was wondering if the calculations could be done with some large kitchen knives. Everyone probably has models of comparable dimensions, and I actually would really like to know what levels of force we'd be looking at with thin stock. I have an old 7.5" Chicago Cutlery cheapie I've been wanting to wreck, plus those really large Old Hickories are so cheap and easy to get.

This would also lead into machetes, but I figure the kitchen knife is more readily available to all readers, and a more useful length to most.

 

[Cliff Stamp]

... with thin stock. ..

The relevant moments are integrated along the length, a proportional change in thickness would not change the position of either balance point and thus you would expect the change in maximum power to simply be proportional to the change in thickness. This will hold up to the point that the mass is so great that it reaches the point of the user to generate maximum force. Moving beyond that point the user will still generate that level of force but now it will result in a lower acceleration (both linear and rotational).

-Cliff

 

[hardheart]

Yeah, I should have also requested a scaling of the stock thickness and subsequent changes in force to also be shown. A comparison to a similar blade length, % mass distribution along the length, and grind (full flat) in 1/4 inch might show how mass would effect impact energy with some real numbers and be easier to visualize, since I'd say everyone at least has a notion that thin kitchen cutlery and thick 'outdoorsy' profiles chop differently. Then it would also help to show how it needs to be balanced against wedging, penetration, ease of swing, or other things affected by changing thickness.

Can this be combined with forces at the edge, influenced by bevel angle and thickness behind the edge? I guess that may move too fr, trying to discuss both mass distribution and grind selection.