Chopping Physics

[HoB]

Read the following with a bit of a smile. It hopefully will be somewhat entertaining and not be a dry physics lecture.

Well this is a topic that got started in the Rogue review, but I think it merits a new thread. After thinking on it for a few hours I am a bit bothered by Cliff’s term of “dynamic balance point”. There is no such physical quantity and I don’t think it is very sensible to define one. However, the point he is making is a valid one.

There are really only three physical quantities that are relevant to chopping. Those are the mass of the knife, the center of mass (COM or balance point) and moment of inertia. For those that yet have to encounter moment of inertia in school and for those it has been too long ago: The moment of inertia is the integrated mass over the distance from the center of mass…..huh? Ok, what does that mean? It is a quantity that determine how easy a body engages in a rotation. A sphere has, of all symmetric solid bodies, the smallest inertia (it spins up quickly), while a dumbbell has the largest, since the masses are furthest from the center of mass. Makes sense? The moment of inertia must always be INSIDE a solid body (if that is not obvious, I would like to ask you to trust me on this). So it cannot be at the tip of the knife and in no normal shaped knife it will be even close. A knife that has its moment of inertia close to the tip is called a war-axe with counterweight .

Ok, during a strike, I don’t tend to spin the knife in my hand like a tambourine stick , I rather swing my arm, I would imagine most of you do the same. The motion is a rotation of either the shoulder and elbow or the wrist or all together, doesn’t really matter. Since the entire weight of the knife (including handle) is OUTSIDE the center of rotation, its moment of inertia is completely irrelevant to the power of the swing (this is assuming that the knife doesn’t have a massive pommel that protrudes beyond the wrist. Since the weight of your arm doesn’t change, the center of mass is the ONLY determinant for a knife of a given mass (a heavier knife will obviously also increase power). The further out (towards the tip) the COM the more powerful the swing. This is again assuming that neither the weight nor the COM is so extreme that the maximum velocity, that I can generate with my arm, is affected. This is only basic physics so far and it is the reason why it is hard to believe that a 7” blade will ever come close to the chopping power of a 10” blade if both are of similar design, as the 10” blade will both be heavier, as well as have the COM further out. Again, this applies ONLY to swings against a stationary object. The moment we are talking about an object that has give (like a thin branch) this all changes and power becomes much less important while speed becomes essential.

Ok, what I said above applies unfortunately only to an iron connection between the hand and the handle. And when I say iron, I mean “welded to it”. This is obviously not physically possible (now not talking about physics but about the physical abilities of the human hand). As long as the knife is struck on the COM the moment of inertia is still irrelevant and the wrist and hand have to compensate only for the torque induced by the reach (distance of impact point from closest center of rotation, either in the hand or on the wrist) but not for the knife rotating in my hand. But to maximize efficiency I would like to maximize my reach. If I hit the blade in front of the COM the knife wants to rotate around the COM. The larger the moment of inertia, the slower the rotation will be at a given energy. Meaning: the larger the moment of inertia, the smaller the transfer of vibrations and backlash. In other words, a knife that has its mass centered around the COM will kick like a mule, to the point were a lot of the power of the swing is lost in the give of the hand, while for a knife that has the two centers of weight distribution away from the COM will remain relatively “calm” as the weight further up in the blade will help carry the blade through while the counter weight in the handle will help compensate rotation of the knife in the hand (this is what I meant when I described the weight distribution of the Rogue as “bi-modal”: It has a large moment of inertia at its given mass). Now this is comparing two knives with the same COM (and mass) and obviously this effect is aggravated the further away from the COM the blade is struck. Which means, instead of increasing the moment of inertia, I can simple move the COM forward (so I strike closer to the COM) to increase the efficiency of the strike. The balance point (and I mean static balance point or COM for those that got lost) is therefore absolutely CRUCIAL!

So the (Possums’s) experiment that hardheard described is a very clever way of comparing the moment of inertia for different knives. However, the height of the weight of the pendulum is arbitrary as it depends on the mass of the weight (or weight of the mass ?), so it is physically not sensible to take the height of the weight as “dynamic balance point” as it can be adjusted. But for a given weight of the pedulum, a longer pendulum indicates a larger moment of inertia (very cool idea, by the way, Possum, in case you should read this!).

For those people that think they can cheat physics by applying an “iron grip” on their knife handle a couple of numbers (and shameless bragging on my part ): I can support about 20 lbs on a 9” handle (that is an iron grip for you ). I can move in a slow chopping overhead motion with one hand about 75-80 lbs. Meaning: On impact close to the tip of a 10” knife your hand and wrist system doesn’t stand a chance if the weight distribution (moment of inertia) isn’t helping. In fact it will directly determine the power of a swing you can apply effectively.

Now, it is 3:55 am my time so please take this into account, when reading this….please… . Good night, I can sleep now .

 

[db]

HoB very well done. Even I now understand it thanks.

 

[the possum]

Uhhh..... No.


I don't have time to dissect this right now, and though there are a number of points pretty close in that, with all due respect he's way off on several of the more important ones.

Later...

 

[HoB]

with all due respect he's way off on several of the more important ones.

Possum, you know I value your oppinion, so let's not worry about respect. Rip in, tear it appart and let's have a discussion .

 

[talonturbo]

I think you meant to say centroid a bunch of times and kept saying moment of inertia. Moment of inertia isn't a location last I checked, just a measure of resistance to rotation about a specific point (regardless of torque applied), but not necessarily about the Centroid.

And BTW, a centroid can be "outside" an object, and often is. Look at pipes (or anything hollow and semi-symmetrical), C shaped beams or clamps, donuts, etc. Even L brackets, offset T beams, etc etc.

 

[SteelDriver]

HoB, have you read George Turner's ARMA article? After reading it I understood possum's dynamic balance concept a lot better .

 

[the possum]

First off, hope I didn’t come across like too much of a jerk with the above post. I was in a bit of a hurry at the moment. And, I'm kinda in that "getting down to business" frame of mind here, so I may sound a bit short, but please understand in person this would all be said with a smile, preferably over a cold beer.

I first started trying to draw attention to this subject over three and half years ago now, after reading an article on sword performance written by George Turner. Some of his ideas and sniping created a bit of a commotion, but I believe his ideas about impacts and rotations are quite sound. I have used them in my own knives, and to modify existing knives with repeatable and predictable results. I highly recommend reading it first: Sword impacts & motions
I don’t think I can do any better & it would save a lot of typing.

After thinking on it for a few hours I am a bit bothered by Cliff’s term of “dynamic balance point”. There is no such physical quantity and I don’t think it is very sensible to define one.

Indeed, the point is “dynamic” and changes depending on where you impact. But, most folks seem to like the idea of quantifying things with one easy number, and it would also be nice if we could come to a consensus on the terminology so we all know what each other are talking about. Now, once you find one set of points, you can calculate all the others, so really all you need is one anyway. The impact point that produces a rotational center at the guard is probably the easiest one to feel and measure, so that’s usually what I’m talking about when I say “distal impact node” or “rotational centers”, while Mr. Turner call them “pivot points” and Cliff calls it the “dynamic balance point”. All the same concept. But again, every spot along the edge will produce a different corresponding center of rotation.

There are really only three physical quantities that are relevant to chopping. Those are the mass of the knife, the center of mass (COM or balance point) and moment of inertia.

Not quite.
They are all parts of the equation, but so are the pivot points. The COM affects how we can move the knife linearly, such as if we kept our wrist locked and swung from the shoulder. The moment of inertia only comes into play when the blade is rotated via a snapping motion with the wrist. Both factors affect each other when we do a full arm swing combined with the snapping motion, and rotation is a good thing. This is because at the start of the swing, with the blade cocked back over your wrist, it’s easier to get moving. And on impact, you have the linear momentum from your arm, plus the rotational momentum from the blade spinning.

All factors are involved upon impact (chopping) too, but the pivot points determine how the forces are applied. If we change the moment of inertia via extensive tapers vs. using a pommel weight, the results on chopping (especially near the tip) can still be very different.

For those that yet have to encounter moment of inertia in school and for those it has been too long ago: The moment of inertia is the integrated mass over the distance from the center of mass…..huh? Ok, what does that mean? It is a quantity that determine how easy a body engages in a rotation. A sphere has, of all symmetric solid bodies, the smallest inertia (it spins up quickly), while a dumbbell has the largest, since the masses are furthest from the center of mass. Makes sense?

Yeah, I can pretty much agree with that. But…

The moment of inertia must always be INSIDE a solid body (if that is not obvious, I would like to ask you to trust me on this). So it cannot be at the tip of the knife and in no normal shaped knife it will be even close. A knife that has its moment of inertia close to the tip is called a war-axe with counterweight .

…you’re losing me here. I’m just a farm boy, but I thought the moment of inertia was a quantity or value or whatever, not a physical point. The moment of inertia will be different at various points along the blade, and is simply a measurement. Here it almost sounds like you’re using it to mean the pivot points or “distal impact node” I was talking about above. And if so, then yes, a rotational center at the guard could easily have a corresponding impact node at the tip, or even beyond it. Which simply means there is no physical part of the edge where an impact will make the knife rotate at the guard. All rotational centers will be very far away from the hand, which produces hand shock. And a bunch of other stuff regarding handling.

Ok, during a strike, I swing my arm… The motion is a rotation of either the shoulder and elbow or the wrist or all together, doesn’t really matter. Since the entire weight of the knife (including handle) is OUTSIDE the center of rotation, its moment of inertia is completely irrelevant to the power of the swing. Since the weight of your arm doesn’t change, the center of mass is the ONLY determinant for a knife of a given mass.

First off, we need to break this down into the two separate ideas it really is. The way a blade behaves while swung does not determine how it behaves upon impact. You can swing the blade any way you wish, but impacting at a given spot on the edge will always make the knife rotate the same. Likewise, static and dynamic balance are two different things.

Next, as I said above, the two do influence each other during the swing. The COM really comes into play with linear motions, and the moment of inertia for rotating the knife. The COM may be the dominant factor in how you can make full arm swings with no rotation, but likewise the moment of inertia plays a huge role in swings that involve a lot of wrist snapping. In fact, it’s the main factor when making quick snap cuts at things like running raccoons.

The further out (towards the tip) the COM the more powerful the swing.

Hogwash. I proved this entirely to my own satisfaction when I nearly doubled the tip cutting power of my khukri while bringing back the COM almost three inches. That’s an observed phenomenon, before and after the modifications, and was perfectly predicted by the principles outlined in the article.

The moment we are talking about an object that has give (like a thin branch) this all changes and power becomes much less important while speed becomes essential.

Very true. And that’s one of the beauties of good balance. It allows you to accelerate the knife quicker for the light targets, without sacrificing max power for the heavy ones. As I’ve said before, proper balance allows my bowie to swing/maneuver faster than a machete, and still have more chopping power than my 32 oz Khukri. (before I modified the khuk, that is.)

If I hit the blade in front of the COM the knife wants to rotate around the COM.

No, it doesn’t. It will want to rotate around some point on the other side (the hilt side) of the COM; not the COM itself. I.E., the “pivot point” or “rotational center” or whatever we want to call it. (Centroid? Is that what we’re talking about here?)

The larger the moment of inertia, the slower the rotation will be at a given energy. Meaning: the larger the moment of inertia, the smaller the transfer of vibrations and backlash. In other words, a knife that has its mass centered around the COM will kick like a mule, to the point were a lot of the power of the swing is lost in the give of the hand…

Again, the rotational centers determine this; not the moment of inertia. And I’ll use my khukri example again to back that up. Some of the main reasons I modified it were because it was so slow & heavy (very large moment of inertia) and yet at the same time it transmitted terrible shock to my hand. It was actually enough to completely numb my fingers. I fixed this by centering the mass around the COM more- the difference is night and day, and exactly the opposite of what’s written above.

… the counter weight in the handle will help compensate rotation of the knife in the hand

This much is true, and is why it’s far more effective and efficient to put that counter weight at the very butt in the form of a pommel than to leave a bunch of dead weight in the center of the grip with a slab tang.

(this is what I meant when I described the weight distribution of the Rogue as “bi-modal”: It has a large moment of inertia at its given mass).

Just out of curiosity, whose words are these? Did you write all this, HoB? If I had known you were so interested in this stuff I would have gladly shared sooner. I generally don’t bother any more since Cliff and one or two other guys are the only ones I’ve been able to get really interested in three years of trying.

Now this is comparing two knives with the same COM (and mass) and obviously this effect is aggravated the further away from the COM the blade is struck. Which means, instead of increasing the moment of inertia, I can simple move the COM forward (so I strike closer to the COM) to increase the efficiency of the strike. The balance point (and I mean static balance point or COM for those that got lost) is therefore absolutely CRUCIAL!

Nah. If striking close to the COM is so critical, then maybe you could explain to me how swords with 35”+ blades and 5” COMs work at all. And, if it’s better to move the COM further out, why is the Rogue balanced right at the guard? The COM is a piece of the equation, but no more important than the others.

So the (Possums’s) experiment that hardheart described is a very clever way of comparing the moment of inertia for different knives. However, the height of the weight of the pendulum is arbitrary as it depends on the mass of the weight (or weight of the mass ?), so it is physically not sensible to take the height of the weight as “dynamic balance point” as it can be adjusted. But for a given weight of the pedulum, a longer pendulum indicates a larger moment of inertia (very cool idea, by the way, Possum, in case you should read this!).

I really wish I could claim credit for it, but I’m just not that clever. But, we really need to clear up that the pendulum is NOT dependant on weight/mass. It is swinging under gravity, and gravity affects heavy objects the same as light ones. The pendulum’s period (or time of swing/oscillation) is only dependant on the length of the string.

Meaning: On impact close to the tip of a 10” knife your hand and wrist system doesn’t stand a chance if the weight distribution (moment of inertia) isn’t helping.

If I’m understanding you correctly, I agree. Even a strong wrist cannot exert enough leverage to the end of a long blade to compare with the blade’s inertia. That’s why we *chop* with long blades rather than just touching them to the wood & trying to press them in with wrist strength alone.

In fact [the moment of inertia] will directly determine the power of a swing you can apply effectively.

Well, not sure what to make of this since earlier you said, “moment of inertia is completely irrelevant to the power of the swing”. ??? Perhaps I’m misunderstanding you here.


Hot diggety damn. I really didn’t plan to write so much here. Hope I don’t sound like an a$$ with all this nit picking and stuff. That ain’t my intention. I think I’ll go back and add a few smilies or somethin’… Really feel like I have only been saying what I disagree with here, and not explaining things that might actually help folks understand this stuff. Bah. Take a look at the article linked above and I’ll see if I can offer any pointers after taking a break…

 

[HoB]

I think you meant to say centroid a bunch of times and kept saying moment of inertia. Moment of inertia isn't a location last I checked, just a measure of resistance to rotation about a specific point (regardless of torque applied), but not necessarily about the Centroid.

And BTW, a centroid can be "outside" an object, and often is. Look at pipes (or anything hollow and semi-symmetrical), C shaped beams or clamps, donuts, etc. Even L brackets, offset T beams, etc etc.

No, I didn't mean to say centroid, I meant to say moment of inertia, but if centroid helps you to think about it, that is fine, too. You are right on the moment of inertia not being a point though. The moment of inertia is a tensor of second rank and every body has three principle moments, one of which is completely irrelevant to knives, the second comes only into play if we talk about the weight distribution between spine and edge, so we are talking mainly about the last. On a simplified system like a knife or a rod, the moment of inertia can be viewed as a weight rotating on a string around the center of mass. You are right in so far as you could replace the system with a weight that is so small that you would have to place it outside of the body, which doesn't make much sense though. I think it is most sensible to take the moment of inertia as the sum of the masses on one side of the COM, weighted by the distance from the center of mass devided by total mass on that side of the center of mass. This way you can calculate a moment of inertia of a rod/knife on each side of the center of mass and even a theoretical one for a rotation around any impact point. The moment of inertia thus defined (which by the way is very close to the physical definition) is hence a distance.

Well you are right with your examples, this is what I meant to say with "solid bodies". A donut is not a solid body nor is a pipe. You are right that I should have made the description such as to exclude C-clamps as well. Most knifes don't look like C-clamps. Let's ignore Kurki's for the moment, or rather lets ignore that they are severely curved for a moment, because then you would have to look at the second principle moment which isn't really helping. I assume that the objections to what I have written are of different nature.

SteelDriver, no I haven't, thanks for the link.

 

[hardheart]

I don't quite get why the moment of inertia is dependant on the COM. I thought it was just mr^2, and the radius is determined by the axis about which the mass rotates-does that have to be at the COM?

 

[HoB]

I still have to read Possum's post and really look forward to it, so I am going to take some time with it. But to answer the easy question first. Mechanically any motion can be decomposed into a motion of the center of mass and into a motion around the center of mass. Therefore, the inertial tensor is a function of the weight distribution of the body only and independent of the axis of rotation. You try to simplify the problem to a one-body-problem with is represent by a point mass rotating around an axis at a certain distance.

 

[the possum]

I don't quite get why the moment of inertia is dependant on the COM. I thought it was just mr^2, and the radius is determined by the axis about which the mass rotates-does that have to be at the COM?

No. That's partially what I was getting at earlier when I said, "You can swing the blade any way you wish, but impacting at a given spot on the edge will always make the knife rotate the same." Just try looking at how you swing a knife. Does it appear to be rotating out on the blade? If you're just doing a quick cut with wrist action, the center of rotation will be about at the center of your grip. With a snap cut where this wrist action is combined with linear motion from your arm, the center of rotation may be more at the pommel. But no matter where the rotational center is when swung, the blade will rotate the same upon impacting in a given spot, such as the tip.

That's part of the beauty here. You can swing in one rotational center and make the impact occur in another. Then recover and redirect in yet another. Once you grasp this, you can see the really cool stuff with proper balance. You can distribute the mass so it's easier for you to swing/rotate, but harder for the object you hit to move it back.

On a simplified system like a knife or a rod, the moment of inertia can be viewed as a weight rotating on a string around the center of mass.

Again, it does not have to rotate around the center of mass. This misunderstanding might be partly why you seem to think the COM is so important. Just play around with a stick or ruler and you can see this. I'm adding an illustration:

You are right in so far as you could replace the system with a weight that is so small that you would have to place it outside of the body, which doesn't make much sense though.

And again, it is not dependant on the weight of the pendulum. Only the length of the string. Feel free to check it out yourself with some string and different sized fishing weights or something.

I've used measurements from the pendulum to find the weight/ineria (but not the moment of inertia) at several different points along the blade. When it comes to measuring or calculating the moment of inertia, the hard part for me is trying to come up with a measurement or estimate of the velocity.

 

[Alberta Ed]

Head... hurts..

 

[Cliff Stamp]

The moment of inertia must always be INSIDE a solid body

The inertial moment being discussed in the above isn't a location, it is a scalar quantity and basically the rotational mass.

However, the height of the weight of the pendulum is arbitrary as it depends on the mass

It just depends on the length, it comes from the gravitional acceperation which isn't dependent on its mass. Of course you can calculate this length from the distance from center of mass and moment of inertia, so it isn't another independent quantity, however it is a lot easier to understand and measure. It also directly corrosponds to the dynamic version of a center of mass hence the term dynamic balance point.

I can support about 20 lbs on a 9” handle

The goal isn't to actually fight an induced impact rotation with your wrist it is to actually get the blade to rotate and thus impart a rotational soruce of energy and to have the dynamic balance point so positioned so that there isn't a huge shock through the wrist.

Head... hurts..

That is why I prefer defining a dynamic balance point instead of detailed discussions on tensor quantities and integral calculus. If you understand the role of the static balance point then what a dynamic one should mean is fairly obvious and it is very easy to measure directly. The measurement is also very straightforward to apply in terms of how it effects the performance of the blade.

-Cliff

 

[db]

Albert yup mine was starting to also. It is much easier than it seems by just getting a stick and hitting with it and holding it at different points. I'm still not sure what terms mean what in all the discriptions, but I think I'm starting to figure out the concepts. Btw I'm finding this topic very interesting and I'm not one much for large knives.

 

[hardheart]

IYou try to simplify the problem to a one-body-problem with is represent by a point mass rotating around an axis at a certain distance.

Isn't that what the pendulum test does?

 

[HoB]

First off, hope I didn’t come across like too much of a jerk with the above post. I was in a bit of a hurry at the moment. And, I'm kinda in that "getting down to business" frame of mind here,

Hot diggety damn. I really didn’t plan to write so much here. Hope I don’t sound like an a$$ with all this nit picking and stuff. That ain’t my intention. I think I’ll go back and add a few smilies or somethin’… Really feel like I have only been saying what I disagree with here, and not explaining things that might actually help folks understand this stuff. Bah. Take a look at the article linked above and I’ll see if I can offer any pointers after taking a break…

Possum, I really enjoy this, you don't come across like a jerk at all and you bring a lot of experience to this discussion.

Just out of curiosity, whose words are these? Did you write all this, HoB? If I had known you were so interested in this stuff I would have gladly shared sooner. I generally don’t bother any more since Cliff and one or two other guys are the only ones I’ve been able to get really interested in three years of trying.

Ummm, uh, yup, those are all my words. Well, you know, there is a reason why I got in touch with you by email recently. I didn't pick YOU by random . I had also hoped that if I would put chopping in the title of the thread, I could lure you here .

…you’re losing me here. I’m just a farm boy, but I thought the moment of inertia was a quantity or value or whatever, not a physical point.

Ok, that is my problem not yours. Yes, I have a background in physics, but that is no exuse not to make myself understandable. If I loose you, I have to try to explain it better what I mean. I will come back to this thread a few time and try to do better.

The pendulum’s period (or time of swing/oscillation) is only dependant on the length of the string.

Ouch, :foot:, yes you are absolutely right. Those are the affects of posting at 4 am in the morning. Currently, I am trying to convince myself, that I wouldn't have made that goof if I had been less tired. And yes, you are right, the blade is not rotating around the COM upon impact. I wonder how many more of those will show up .
But the one-body problem of a weight rotating on a string is a different problem, it is not a pendulum. The kinetic energy is both dependent on mass and string length at a given angular velocity.

Ok. I am behind. I need to quit this post read yours and post new...this is fun .

 

[the possum]

Ummm, uh, yup, those are all my words. Well, you know, there is a reason why I got in touch with you by email recently. I didn't pick YOU by random . I had also hoped that if I would put chopping in the title of the thread, I could lure you here .

By the way you phrased a few things in your first post, for some reason I got the impression you had copied and pasted this from someplace else & were just sharing it. Sorry for the misunderstanding.

Possum, you know I value your oppinion, so let's not worry about respect. Rip in, tear it appart and let's have a discussion

Ha! This is so refreshing! Wonderful conversations can be had when the participants are passionate yet share mutal respect. And that it is, by the way.

But the one-body problem of a weight rotating on a string is a different problem, it is not a pendulum. The kinetic energy is both dependent on mass and string length at a given angular velocity.

Oh, I see what you were getting at now. A big weight will have more energy if swung at a given angular velocity.

...this is fun .

It is much easier than it seems by just getting a stick and hitting with it and holding it at different points.

Absolutely!! Once you try it out & know what to look for, it seems so simple, doesn't it? Why the hell didn't I think of it?

But, guys, be warned. If you continue from this point to where you actually understand it, (and I'm not claiming to have a full grasp on it myself), you will find yourself sorely disappointed with lots of knives you liked before.


No, Seriously!

 

[hardheart]

The point is to increase the angular velocity, right? Since it's one half the moment times the angular velocity squared, you would increase the angular kinetic energy with greater velocity by a square rather than increasing the moment. Now I'm screwing with my own head, because shifting the weight around shouldn't change the moment, since it's a sloid body... but putting more mass at the extremes of tip and pommel could change your torque from a given axis while keeping the COM the same or so.

maybe...

 

[the possum]

The point is to increase the angular velocity, right?

The point is to achieve the needed combination of speed, maneuverability, and cutting power, -at the portion of the blade you want to chop with, for your physique and targets, while reducing user fatigue & discomfort. That's how I'd sum up proper balance. Obviously some applications will be different from others in specifics, but the general principles are still the same. Even if we want to talk about axes.

Historically most longer blades and swords did not have a lot of mass at the extreme tip, so I'm thinking that's not the answer. They tapered thinner towards the tip. A pommel is only needed if you want to strike with the tip of the blade, and it does help in that case. And who cares if we keep the same COM? That's not what controls the show. At least not for chopping and other dynamic use, anyway.

 

[hardheart]

so that's increasing the angular velocity, right?

I guess what I want to know is if what one should be trying to do is minimize the mass of the tool to allow it to still impact with a desired amount of force. I would think that's a reasonable goal. Mass is factored into calculations of impulse, momentum, force, and such, but so is acceleration and velocity. 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.