Chopping Physics 2

[the possum]

Well, between the two hatchet the one with the 20oz head has obviously the greater kinetic energy at the same angular velocity (whether one outchops the other I leave up to you). The double headed (how do you hold such a thing? ouch!) has a kinetic energy of 2*20*(R/2)^2, the single head hatchet has one of 20*R^2. You moved the COM way forward. Between the double headed hatchet and the knife, the hatchet wins (kinetically) precisely because it has a larger moment of inertia.

Well, I thought this is the way it should be, but then again, how do you know I moved the com forward? Aren't your examples based on keeping the com & velocity the same, while only changing the mass distribution?

Well, with the MBP: You need to balance both sides of the POI. For that you have to have at least some mass on both sides. At precisely the tip or beyond, you have mass only on one side...no balance possible.

OK. Yet, this explaination fails to describe things I've noticed when chopping near the tip with various knives.
Same thing when you say it's so important to move the COM forward in order to gain chopping power. Both are readily described by the pivot points. If we move mass to the pommel, the COM moves back. Yet, because of the rotational principles, that mass in the pommel will act just the same as though you placed it out on the blade (equidistant from the new pivot point), thereby giving the same effect as moving the COM forward- when in reality it went back. At the same time, it also improves several other nice qualities we're choosing to ignore for the sake of this discussion, but prove worthwhile in their own right in real life.

For those who want to calculate the pivot point with the momentum balance. The location of the pivot point is rp=Sum(mi*ri)/m. The expression Sum(mi*ri) is as illustrated on my handwritten sheets the sum of the mass of each segment times the distance of that segment from the axis. (the 'i' referes to the ith point). So written out it means: m1*r1+m2*r2....... The expression for the pivot point is by the way calculated for an object that travels (like in Turners Figure 2) initially linear.

Tell ya what. It's getting too late for me to do math. But I am still interested in these ideas and how they may relate to my next big project. I'm making a falchion, which does by nature have more mass forward than on a double edged cut & thrust type sword, so it would be cool if I could find some blend of both ideas that would give me the "ultimate" blade.

 

[Cliff Stamp]

... don't see how others can't just "feel" what is working and roll with it.

They can, the above isn't mean to illustrate how a user would evaluate a knife, it is how a maker or user would change a knife in an efficient manner to optimize a knife for a particular type of performance. You can very easily measure the dynamic balance point very precisely on a knife with no handle, no edge without ever leaving the shop. You can also do it right at a makers table and it is a non-destructive test which you could do on a $1000 bowie with no objections from the maker, aside from a bit of a odd stare from most.

I am still not understanding why we can view this as mass rotating around the com.

Ok some brief comments on the underlying physics. If you look at a two body collision you can define a reference frame where the momentum of the system is zero. The position of this coordinate system is the center of mass of the system, this is actually how the center of mass can be defined. Now having a system where the momentum is zero is obviously of benefit because zero is a nice number to work with.

If you don't know what a reference frame means, imagine you are driving a truck and you look at the guy next to you. What speed do you see him moving, zero. What speed do you see the house that you just passed moving, negative your speed. In your reference frame you see basically the opposite of what someone in the house looking at you would see. Obviously you can define any reference frame, the speed of the air, the truck, the house, a bee flying into the windowshield, or even the sun.

Why use the center of mass system? Well it has a number of benefits. If you look at the kinetic energy of the system (knife and water bottle/2x4/possum etc. ) it can be wrote as the kinetic energy of the center of mass :

K_cm=1/2*(total mass)*(speed of center of mass)^2

plus the kinetic energy of the bodies moving relative to the center of mass (that is a bit of an ugly term because you have to calculate the relative velocites in the center of mass reference frame but I'll get to that shortly). This is very important because of the following :

If there are no external forces then the velocity of the center of mass does not change

An external force means something outside the system, in this case, not the knife or what it hits. This means that since the velocity of the center of mass does not change then its kinetic energy does not change either. This means that during a collision that only the other part of the kinetic energy can be transformed (which generally means into heat or phase changes, i.e., damage to the objects).

Before this gets too vague, as an example of what this means, first consider the expression of this part of the kinetic energy, this again is just a lot of highschool algebra by which you transform the relative velocites back to the ones in the stationary frame and do some juggling of variables to get :

K'=1/2*(m1*m2)/(m1+m2)*(v2-v1)^2

That mass factor is usually called the reduced mass and if one mass is a lot bigger than the other it pretty much equals the larger mass, that should make some things pretty obvious when it comes to collisions. It also says that the quantity of interest is the relative velocity of the objects not the difference of the squares which you might think may be the case which would change the physics completely. It also has some fairly direct and obvious implications.

Case 1:

Lets consider a knife (object 1) hitting a large rock (object 2). The rock is very large and stationary, this means that m2 >> m1 and v2=0 and thus the kinetic energy which can act to damage the knife (and rock) is approximately :

K`=1/2*m1*v1^2

This isn't surprising, it says that basically all of the kinetic energy of the knife can be destructive.

Case 2 :

A knife hits something which is very light and also stationary, again knife is object 1 and the small branch for example is object 2 :

K'=1/2*m2*v1^2

This makes more sense like this :

K'=(m2/m1)*1/2*m1*v1^2

or

K`=m2/m1*(kinetic energy of knife)

This says that the only part of the kinetic energy of the knife which can be transformed (cause damage) is the relative mass scaled kinetic energy of the knife. Thus if a knife hits an object which has 1/10 the mass then only 1/10 of its kinetic energy can be used to damage it.

There are of course many other considerations because you also have to look at how the kinetic energy can be used to damage the objects. For example a knife is extremely strong when resisting compressive motion compared to lateral deformations. This is why a light object which can move is often much worse to chop into than a heavy stationary object.

This is why for example you can take knives and hit rocks/concrete with only minor damage but have them be grossly damaged on hardwood branches. The branches can bend violently and induce severe lateral torques, all a piece of concrete can do is try to compress the steel and unless the impact toughness is exceeded then nothing significant happens.

With the momentum calculation I outlined above, you can actually calculate very easily the pivot point without resorting to some area calculations.

HoB, the people doing these calculations or those interested in the results often have little to no math background. This is why Turner and others have used the methods and quantities they do. Anyone can easily measure the period of a pendulum or do a waggle test and do an area calculation. Not everyone however can follow motion decomposition and realize that you can always talk about the motion of an object relative to any point or any speed (or even acceleration) not just the center of mass. This doesn't mean the motion is inhernetly at that point or at that speed or acceleration, just that you chose to look at it from that point of view. It just so happens that if you pick the center of mass as a relative point then the equations tend to be simple and have direct and useful consequences.

By the way, there is a fairly easy way to determine the acceleration characteristics of any knife and any user. Take a camera (digital or analog doesn't matter) and set it to long exposure and take a strobe light with a known frequency and start chopping from a fixed stance illuminated by the strobe in front of a black screen. On the picture you can then see where the blade was at any given time and even calculate the velocity at any given point.

There is free software to calculate such quantities if you have digital video, even highschools use it now. Even the price of the senors to directly record acceleration are very cheap, last I checked they were much less than even the cost of a cheap bowie. You can even plug them into a TI calculator and thus measure velocities/forces directly.

By the way, Angus Trim has reported recieving back a couple bastard swords for repair that were bent in the plane of the edges (through the width) rather than through the thickness.

On hardened steel? What kinds of impacts?

-Cliff

 

[HoB]

Well, when I calculated the hatchets and the knife, I did this very quickly in my head assuming zero mass for the hatchet handle, so obviously the COM of the two hatchets is not the same.

Well, I forgot to say that the calculation for the pivot point is only valid for a tip strike, but since I am on a roll here I can tell you what other games you can play with this. Since striking at the point of maximum momentum transfer (which is the MBP) does not allow to minimize shock since the pivot point would be infinitely behind the handle, you can now calculate for a given mass distribution at which point you would have to strike in order to obtain the largest possible momentum transfer while still be able to hold the knife at the pivot point....

 

[HoB]

HoB, the people doing these calculations or those interested in the results often have little to no math background.

There is free software to calculate such quantities if you have digital video, even highschools use it now. Even the price of the senors to directly record acceleration are very cheap, last I checked they were much less than even the cost of a cheap bowie. You can even plug them into a TI calculator and thus measure velocities/forces directly.
-Cliff

Yes, I understand, this is why I try to tread as lightly as possible. It is very important to me that we don't lose anybody that is interested in the equations. This is why I wrote these three pages as reference with many examples. In order to get a good idea of the underlying physics here, you have only to be able to add, multiply and taking the square.

Nothing in this thread should be taken in any way as deminishing any of the cited work. This is really not the point I am trying to make. I am just asking myself, what can I contribute to this topic and figured, the contribution that I can make is providing a mock-up, a numerical model, that anyone can play with and see what happens when you change the numbers: move weight forward or backwards or spread the weight out or increase the mass or the length etc.

The ultimate goal is of course to map out the weight distribution of an actual blade. This way, when someone reviews a knife, the reviewer can give the weight distribution and the reader can then compare that to a blade that he has at home and from the model can estimate what effect the weight distribution might have. This way, a reader can decide whether the reviewed blade has a good or bad balance for him/her (the reader) without having to hold it.

Ah, see, I am am a photographer. Video didn't even come to my mind. You are of course correct.

I was always interested in these motion sensors, but I am really not a computer geek and electronics is by far the weakest part of my experimental skill. With these sensors I am always afraid of being to dumb to interface it with a computer (and I have always been a HP guy as far as calculators go, reversed polish notation rules ).

 

[the possum]

Cliff, thanks for the illustrations. It will take me a while to digest though. In the meantime, -

On hardened steel? What kinds of impacts?

He mentioned this nearly three years ago, so I mis-remembered it slightly. He was more talking about the tips of blades that taper for thrusting.
Bent blades
He mentioned five examples, and he uses 5160 hardened to 55-52 Rc, as I recall. But still, I was quite surprised. It never even occurred to me that's what he was talking about; I assumed he meant bent through the thickness at first.

 

[Cliff Stamp]

This way, when someone reviews a knife, the reviewer can give the weight distribution and the reader can then compare that to a blade that he has at home and from the model can estimate what effect the weight distribution might have.

The dynamic balance point does that to a large degree if you give this, the static point and the mass. Note for example when I did this recently possum commented that the bowie was not what he would prefer at all and how he described it would handle is just as it does. Of course things like inertial moments are just proportionality constants, someone who is stronger will "see" a smaller moment of inertia / mass becuase if they determine the effort/acceleration ratio (i.e., the mass or inertial moment) it will be smaller.

The benefit of the dynamic balance point is that it isn't a proportionality constant, it doesn't matter how strong you are, the blade will have a fundamental difference in handling, just like a longer blade has more reach. This is no different for example than stabbing with a point in the centerline of the handle vs one which is heavily upswept or dropped. It doesn't matter how strong you are, a point in the centerline on a knife which is symmetrical in that plane will be inherntly much more accurate on a stab, just like a narrow axe bit is much more accurate than a very wide one.

I was always interested in these motion sensors, but I am really not a computer geek and electronics is by far the weakest part of my experimental skill. With these sensors I am always afraid of being to dumb to interface it with a computer

You just plug it in, the software auto detects it. It will even calibrate it, set up the data collection to defaults, etc. . All you basically have to do is press start. The only time you need to do something significant is when you want to do extra calculations to show midpoint behavior, or track multiple objects and do center of mass calculations, etc. .

...and I have always been a HP guy as far as calculators go, reversed polish notation rules

You can't buy them locally plus TI's are more common and thus as a student it is much easier because you can then trade data/programs with a larger group. This is unfortunate as RPN has many benefits for computation both on calculation and indirectly as it teaches people to think about the calculations. Automatic ignorance of equation evaluation is a horrible problem. The majority of computation mistakes students make could be eliminated if they simplified the calculations a little before they started in on the numbers directly.

It will take me a while to digest though.

There is a reason that most people don't take math/physics by mail. All of these things are much easier to understand in person with active examples.

I assumed he meant bent through the thickness at first.

I'd like to know the cross sections in detail, as stiffness is cubic in the dimension of the bend it is hard to see how you could bend something in that plane as even the vastly reduced lateral forces would tend to dominate because that cross section is just so much weaker. Unless of course you are talking about a tip which is similar in width as it is in thickness of course.

-Cliff

 

[sevenedges]

I'm all for makers trying to improve the knives they sell for a specific task. As many knives I see today just arn't properly made in all the different ways mentioned. A lot of makers seem to make a knife based on looks rather than the functionality.

 

[the possum]

Been trying to get through this in small bites... and have a few questions.

If you look at a two body collision you can define a reference frame where the momentum of the system is zero. The position of this coordinate system is the center of mass of the system, this is actually how the center of mass can be defined.

First off, are we still actually talking about what is traditionally called the center of mass on a knife? I.E., the static balance point? Or are we selecting another point (such as the pivot point, since it's motion does not change) and simply calling it the center of mass for the system?

Obviously you can define any reference frame, the speed of the air, the truck, the house, a bee flying into the windowshield, or even the sun.

Why use the center of mass system? ...If you look at the kinetic energy of the system (knife and water bottle/2x4/possum etc. ) it can be wrote as the kinetic energy of the center of mass :

K_cm=1/2*(total mass)*(speed of center of mass)^2

plus the kinetic energy of the bodies moving relative to the center of mass This is very important because of the following :

If there are no external forces then the velocity of the center of mass does not change

So again, are we talking about the regular balance point here? Since during an impact (collision) from my point of view, the velocity of the balance point does indeed change. Or are we acknowledging that and choosing to use this point as our reference point/frame, and calculating the rest based on what the CoM sees? (I'm assuming so, considering your comments further down.)

It almost seems to me it would be more intuitive to use the pivot point(s) rather than the static CoM, since their velocity does not change during impact as it is.

this again is just a lot of highschool algebra...

Yes, and high school was the last time I really did any sort of algebra. Math was always my worst subject, too. I got a 29 on the math subsection of the ACT test. (most midwest colleges use this entrance exam rather than the SAT's)

the contribution that I can make is providing a mock-up, a numerical model, that anyone can play with and see what happens when you change the numbers: move weight forward or backwards or spread the weight out or increase the mass or the length etc.

I find it a noble and worthwhile effort, HoB. I should not have been so dismissive of you ideas based on my ignorance and misunderstanding.
However I have not been able to reconcile the differences between the ideas you've proposed and what I have done on my end. The main ideas I'm getting from your examples are that we need to move the CoM forward and distribute the mass like a dumbbell, or better yet, use an axe. And this is all good and true if we ignore the other things that happen at the same time.

But, deer season is this weekend, so I expect I'll have a lot of time to ponder this subject. I may even bring a calculator with me in the stand.

...I can tell you what other games you can play with this. Since striking at the point of maximum momentum transfer (which is the MBP) does not allow to minimize shock since the pivot point would be infinitely behind the handle, you can now calculate for a given mass distribution at which point you would have to strike in order to obtain the largest possible momentum transfer while still be able to hold the knife at the pivot point....

Yes, this does sound like something I'm interested in.
And since it's better to learn this stuff with examples, maybe I could take advantage of both of your knowledge here with a fantasy falchion project. I'm working under a few special constraints from the customer, namely that I use a huge piece of elk antler for the handle. I wanted to make something along the style of this original piece:

Except it will have a two handed grip, more like a grosse messer. The profile is about shaped already (with more of a bowie like influence, again per customer request) but this thing is 3/8" thick at the base, 3" wide, and will total around 42" long. (about 32" blade or so) I'm shooting for a fairly heavy finished weight of around 3.5 pounds (I think the customer would be thrilled if I handed him a 10 pound display piece). As you can see, the fuller will reduce some weight at the base of the blade, and there will be some mass concentrated near the widest portion of the blade after the fuller runs out. I want this area to provide max chopping power (for smashing lighter armor with the sharpened false edge), but I need to retain power and control all the way to the point, as the end third of the blade will see the most use.
Aside from this, as mentioned, I will have a lot of leeway to distribute mass via the thickness.

So, how should I make it?

 

[hardheart]

Yes, and high school was the last time I really did any sort of algebra. Math was always my worst subject, too. I got a 29 on the math subsection of the ACT test. (most midwest colleges use this entrance exam rather than the SAT's)

That's a good score, actually. I only got a 27 (but got a 36 in science reasoning ) and figured calc I was my limit in college, since I got out of there with a C.

3.5 lbs?

how about one of these, the dragonslayer from Berserk
http://amethyst-angel.com/cosimages/swordpose03.jpg
from the actual manga
http://img273.imageshack.us/img273/6228/berserk202kf.jpg

lol

 

[the possum]

3.5 lbs?

Not really sure yet, but I figure that will be on the heavy end of things as my customer seems to like, yet still within historical parameters.
The man he bought the piece of elk antler from used the other (matched) antler to make the handle for a gigantic display bowie knife. He said it weighed 17 pounds!

 

[HoB]

I should not have been so dismissive of you ideas based on my ignorance and misunderstanding.

Nonsense, you haven't been in the least bit dismissive and after all we are here to have a discussion.

So, how should I make it?

Mmh, asking me this question would be the blind leading the one-eyed . So I propose the following: You draw up a design on a quadrille ruled paper and estimate the weight distribution by counting the squares, taking into account weight reductions that you might achieve by using tapers, fullers etc. You give me the weight distribution similar to my examples as a series of numbers as oz or gram per inch or cm or 1/4 inch or even per square on your paper. You also tell me were you want to put your hand and how far back your wrist is (and even elbow and shoulder if you want, since it seems that in this case the closest rotational center, the wrist, will be inside the body. Meaning the pommel extends behind the wrist). And I help you calculate kin. energy, momentum, MBP, residual momentum/shock, pivot point and any other values we can come up with. If you don't like what you get, you can make changes to your design on the paper and we recalculate the values until you are happy. How does that sound?

 

[Cliff Stamp]

First off, are we still actually talking about what is traditionally called the center of mass on a knife?

Yes, I was just illustrating why the center of mass is used as a reference point and the fundamental nature of its defination. It is possible to look at the motion of an object from any point of view and you can also transform forces to change perspectives. What HoB noted when he said that you can decompose a force on an object as one acting on the center of mass and another which rotates it is just a specific application of the general principle that you can always transform a force on one point on an object to a force acting on any other point and a couple (which is just a pair of forces which induces a rotation).

The reason that you do these kinds of changes or alterations to the problem is that you are usually trying to either simplify it directly or part of it, or reduce it to a problem you have already solved. Note all of these changes are artifical, they are just viewpoints. It doesn't mean that the object is inhernetly rotating around or through a point. For example, if you stand at the front of a merry go round and look at the motion of a rock on the merry go round what do you see. What does the person see who is on a roof looking down. What does the person who is on the merry go round see.

Which person is seeing the "real" motion of the rock? Is the rock moving in a circle, or oscillating in a straight line or standing still? The answer is yes because there are no absolutes it all depends on point of view. Unfortunately when people are introduced to physics they never hit relative motion for a long time and by that time it is so ingrained that motion is "fixed" that it is always the hardest thing for people to try and learn. Generally you work from the viewpoint where the motion is simplest and then apply standard transforms to other co-ordinate systems because all that math has been done in detail.

Since during an impact (collision) from my point of view, the velocity of the balance point does indeed change.

That is because there are external forces on the knife, the target for example as you are defining the system to just be the knife itself.

It almost seems to me it would be more intuitive to use the pivot point(s) rather than the static CoM, since their velocity does not change during impact as it is.

That is indeed why they are generally discussed. The math is kind of interesting as you can show for example as Angus Trim and others have noted that distal tapers will move the impact point for the grip pivot point forward. This design is also wonderfully consistent because you use the tip to cut at maximum speed and thus you want a very minimal profile to increase the cutting ability because the inertia of the tip is very low. Thus you now have a blade which cuts very well and precise through the tip but at the same time is very powerful for heavy cutting near the choil.

-Cliff

 

[hardheart]

woah, ya lost me on the distal taper, why don't you want more mass at the tip? How do you push the COM forward otherwise? I could see with a widening profile, but a lot of choppers actually go the other way-clip points. Do you need a taper tang, or other weight reducing measure at the handle?

(and I remembered my scores wrong, it was 36 for reading comprehension, 33 for science reasoning, and I'm showing little of either here )

 

[Cliff Stamp]

It depends on what you want the knife to do. The ones that have distal tapers are designed for very fast tip cuts and by using a distal taper you will push the center of mass back more than you will decrease the moment of inertia so this pushes the dynamic balance point forward. You then use a pommel weight to increase the moment of inertia (move the center of mass even further back) and push the dynamic balance point right up to the tip. This gives you maximum precison, speed, power and cutting ability through the tip. Some longer blades are not however designed for such work and are intended mainly for cuts lower on the blade closers to the maximum inertia point and thus they have heavy tips to move the center of mass forward and have no pommel weights.

-Cliff

 

[hardheart]

*slaps forehead* gotcha. I really don't care much for knives like that, can't cut much more than light grasses with them. I find the swing just absolutely dies when I hit something substantial.

 

[HoB]

As a complete OT: I don't know much about swords, but I happen to know a bit about german. I would guess, that the correct term for this type of "cutting instrument" is 'Grossmesser' or 'Grossaebel' not 'grosse messer. This morning, when I woke up I finally remembered another name for it that I like because it is so descriptive: 'Hechtsaebel'. It translates to 'pike-saber', pike as in the fish....looking at the shape of the blade it shouldn't be to hard to guess how they came up with that name .

 

[Cliff Stamp]

I really don't care much for knives like that, can't cut much more than light grasses with them. I find the swing just absolutely dies when I hit something substantial.

There are many ways to produce a less than optimal design. But consider the following. Take a 10" bowie with the standard no taper and slab handle construction. Now make a bowie with a distal taper of the same weight and taper the tang and use a pommel weight if desired to adjust the dynamic balance point. This knife will be much more powerful than the no taper blade in both regards to maximum inertia impacts and maximum speed. Tapers just like every other aspect have to be considered as part of an overall package and design the knife accordingly. If you don't want a longer blade then use a taper on thicker stock. This gives both a stronger base for prying and splitting and a better cutting tip for lighter work and thus is a much more versatile blade.

-Cliff

 

[the possum]

I propose the following: You draw up a design on a quadrille ruled paper and estimate the weight distribution by counting the squares, taking into account weight reductions that you might achieve by using tapers, fullers etc. You give me the weight distribution similar to my examples as a series of numbers as oz or gram per inch or cm or 1/4 inch or even per square on your paper. ...And I help you calculate kin. energy, momentum, MBP, residual momentum/shock, pivot point and any other values we can come up with. How does that sound?

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.

(and I remembered my scores wrong, it was 36 for reading comprehension, 33 for science reasoning, and I'm showing little of either here )

Cool. I also got a perfect score on the reading section, but never mention it for precisely that reason. Folks will try to hold you to it.

I would guess, that the correct term for this type of "cutting instrument" is 'Grossmesser' or 'Grossaebel' not 'grosse messer'.

I actually did spell it that way at first since it should be more correct in modern German, but then changed it to the latter spelling since that's what most folks seem to use. (also Kriegsmesser) I assumed it had something to do with differences in dialects or ancient use, which also presents difficulties to those who are reconstructing methods from the fight books. 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.

I really don't care much for knives like that, can't cut much more than light grasses with them. I find the swing just absolutely dies when I hit something substantial.

I am betting your perspective comes from blades where the concept was taken too far, such as balancing right at the guard, with a dynamic balance point only slightly further out. Such knives do indeed have very little chopping power further out on the blade. But as I've said, my big bowie is very quick in the hand with a dynamic balance point at the tip, and even chopping thick wood near the tip still performed as good or better than my old khukri did at its "sweet spot" further back on the blade.

Cliff, thanks for the further clarifications.

 

[hardheart]

I am betting your perspective comes from blades where the concept was taken too far, such as balancing right at the guard, with a dynamic balance point only slightly further out. Such knives do indeed have very little chopping power further out on the blade. But as I've said, my big bowie is very quick in the hand with a dynamic balance point at the tip, and even chopping thick wood near the tip still performed as good or better than my old khukri did at its "sweet spot" further back on the blade.

Yes, balanced right at the guard, or even handle heavy. Partial or taper tangs, the mass is kept near the static balance point. None of them were as long as your bowie, though. These 'fighters' seem to be made to be 'quick in the hand' by concentrating the mass where you hold it, but that doesn't help when you actually hit something.

 

[the possum]

These 'fighters' seem to be made to be 'quick in the hand' by concentrating the mass where you hold it, but that doesn't help when you actually hit something.

And this is what I've spoken about in the past regarding the fundamental differences in the way your use/move knives balanced according to the two different philosophies. 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. (on shorter/smaller blades, at least) But they could (in theory- it's not as noticeable until the knives get large) gain both speed and power at the same time by going with a balance designed to work with rotations, and use the knife accordingly.