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Hammer Physics Math (Myth?) Manual Manipulation Something Or Other
May 3, 2013
12:14 am
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Lee Cordochorea
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I'm starting this as a new topic, because I didn't want to side-track the other thread...

Larry L;17865 wrote: A hammer that was half the weight swung at twice the speed would produce 8 times the result ( I think, I am too lazy to look it up to verify so someone prove me wrong)

I really don't want to pick on Larry, he's just saying what a lot of us have heard said. I just want to point out that I can only swing my empty hand so fast. I don't think anybody can really do what this formula says. I don't think this formula takes the weight of the arm into consideration either.

Has anybody hereabouts actually tried this? Can you really swing the smaller hammer faster?

No matter where you go... there you are.

May 3, 2013
1:10 am
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Eric G
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welllll... I used to use a 3.3lb hammer and now use a 2lb 10 oz hammer ind i believe i do swing the lighter hammer faster... I have never measured my hammer speed tho and I imagine there are practical limits. I can say that many light blows do not equal a few heavy blows so if you go lighter hammer you will need to swing faster to make up for the difference of weight.

May 3, 2013
2:04 am
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Zach Stroup
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Depends on how much I've had to drink and what she looks like... 😀

My rainman concept of physics says that mass x speed= impact

You can only swing an empty hand so fast, so much like a golf swing, the hand>hammer joint utilizes centrifugal force like any other lever system. So scientifically speaking I disagree with Larry's theory, unless you manipulate the leverage... Larger hammers are usually shorter and more stout, while you're lighter hammers might have longer handles... You can most definitely swing a lighter hammer with a longer handle faster than a shorter/heavier hammer, but I think the comparison of the end product would be infantecimal.

When I'm in my love shack, with what little experience I have smithing, I'm more comfortable swinging a lighter hammer under the wisdom that "One errant blow takes seven to correct"... So in my case in particular, under the guise of little skill and considerable strength, I move way more metal with the lighter hammer...

Furthermore, I don't have any experience with hammers over 3 pounds, so I'm comparing potatoes to potatas... I'd love to acquire I 5 to 4 pound rounding hammer, and foresee them moving way more metal...

May 3, 2013
4:02 am
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James vonMosch
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What should be taken into account is the "snap" factor. The flick of the wrist when smacking a racquetball or throwing a frisbee makes all the difference in the force imparted to the ball or frisbee. The velocity of the hammer head is not necessarily limited to the speed of your hand. It can be greatly increased by snapping your wrist -- a-la-crack the whip. If the end of the whip were only able to go the speed of your arm and hand it would never break the sound barrier. Thus if the flick makes the hammer head increase in speed 4x you will indeed get 8x the force....IMHO

May 3, 2013
4:08 am
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Steve McGrew
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Energy is proportional to the weight of the hammer times the SQUARE of the hammer speed. So if you can, for example, swing a hammer of half the weight twice as fast, you get twice the energy (1/2 x 2 x 2).

Energy is not the only factor, of course. I think a light hammer will typically deliver a smaller fraction of its energy to the workpiece than a heavy hammer will.

Bottom line in my opinion is to use a hammer light enough that you can control it well and swing it all day without hurting yourself. Use the fingers on your hand to "whip" the hammer instead of exerting more force with your arm and shoulder, and you will get a lot more speed without a lot more effort.

May 3, 2013
4:11 am
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Larry L
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Yep, what James said.... It has a lot to do with skill and little to do with how fast you can swing your hand.... Mark Aspery picked on me one day until I finally got it and when I did get it I was stunned at how much less effort resulted much more work... Its all about the snap....

Whatever you are, be a good one.
Abraham Lincoln

May 3, 2013
4:35 am
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Lee Cordochorea
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Can I "snap" a one pound hammer twice as fast as two pound hammer? An eight-ouncer four times as fast?

Is my "snap" force, like my swing force, limited by my muscles? And doesn't my hand rotate when I snap? (Thereby including the mass of my hand?)

No matter where you go... there you are.

May 3, 2013
4:51 am
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Zach Stroup
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1.5 pound hammer - 1.5 (weight) x 2 (Speed)^ 2= 6

3 pound hammer - 3 (weight) x 1(Speed)^ 2= 3

5 pound hammer - 5 (weight) x 2(Speed)^ 2= 20

Sweet!

So don't fart around, and hit it hard.

May 3, 2013
4:52 am
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James vonMosch
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Nope. The snap comes from holding the hammer loosely between the thumb and forefinger with other fingers mostly open, and just before the bottom of the swing closing the last 3 fingers to snap the hammer down. The wrist does snap some, but most of the velocity seems to come from closing the fingers. If you grip the hammer tightly you can't get that last little bit of snap...and it increases the shock to your taut muscles and thence to your brittle bones = tennis elbow.

May 3, 2013
5:09 am
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Zach Stroup
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If you watch a golf swing in slow motion (very similar in nature) the shoulder precedes the elbow, which precedes the hands, which leads the club the whole swing, and "all" parallel the club at the exact instance the ball is struck.... now apply it as arm, hand, fingers, hammer....

May 3, 2013
5:08 pm
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Ries
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You forgot some numbers in your calculations--
Like how old I am, and how much I have worn out my arm by 30 years of holding a damn 4 1/2" grinder.
And how close it is to the end of the day.
And how many hours a day I swing a hammer.
And how many inches around my biceps are.
And how much HGR I inject, that I get mail order from the ROCK.

In other words, for most of us older guys who dont look like Arnold, there is a finite limit to how hard we can hit, no matter what size the hammer is.

Thats why I got a power hammer.

May 3, 2013
7:19 pm
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Lee Cordochorea
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Excellent point, Reis! But right now my power hammer is named "Michael" and he only comes over once every few weeks. :giggle:

It would certainly be interesting to know how much final velocity is imparted by the descent and how much by the snap. I do know that "snapping" by itself won't work. I also know I can "snap" any hammer I can swing accurately.

Anybody got one of those expensive high-speed cameras?

No matter where you go... there you are.

May 4, 2013
1:33 am
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billyO
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To calculate the velocity, you need to know the radius of the arc of the hammer head. With a 'snap' you have 2 arcs, and I think you would add the velocity of the hand and the arc with the arc of the wrist to hammer head. but maybe you would multiply it. It's too hot to think that hard right now.

as always

peace and love

billyO

May 4, 2013
3:04 am
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D_Evans
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Years ago I coached a little league team.
The hardest thing to get the batters to do was swing fast instead of hard.
You can hit a baseball MUCH farther if you swing faster.
I remember my first baseball coach telling me that- and was convinces that he was wrong. Finally I tried it just to shut him up.
He was right.
And I believe Mark is correct also.
After reading his advice I went out to the shop, heated a piece of steel and started swinging fast instead of hard.
The extra force wasn't a little better- it was way better.
Same deal as swinging a baseball bat.

You can swing however you like, I am sticking with faster.

Dave

No one really listens to anyone else, and if you try it for a while you'll see why.
- Mignon McLaughlin

http://WinDancerKnives.com

May 4, 2013
2:42 pm
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Lee Cordochorea
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I don't want to argue one way versus the other. I want to understand the physics of it.

If smaller & faster is better, then why not apply same to power hammers? Why won't a 12 oz hammer be better for working at the anvil than a 32 oz?

What is it that's going on here that we've not looked at yet? Since there can indeed be such a thing as too small, what principles really govern this stuff?

No matter where you go... there you are.

May 4, 2013
3:07 pm
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craig
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D_Evans;17889 wrote: Years ago I coached a little league team.
The hardest thing to get the batters to do was swing fast instead of hard.
You can hit a baseball MUCH farther if you swing faster.
---cut--

You can swing however you like, I am sticking with faster.

It is also important when hitting a baseball or golf ball to swing through the ball and finish the swing,
the swing is finished when the bat nearly hits you back.

Which is hard to do when your swing hits a anvil!:hot:

May 5, 2013
5:35 pm
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Lee Cordochorea
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Velocity comes from acceleration, and acceleration comes from force. Force comes from the muscle group actuating the swing, the muscle group actuating the "snap," and from gravity. Gravity is easy math because the Earth is so darn big: velocity imparted by gravity is directly proportional to distance. But what about the swing and the "snap?" What is the real description here?

I've been thinking about this a lot at odd moments. So I finally took some time to work out the equations. If you don't like math, skip down to "English Translation Of The Above" below.

The smith's muscles produce a finite force. How much will depend on age, health, sobriety, distractions, and lots of other stuff. But for our purposes right now, we just need to remember it is a value independent of the hammer mass. The physics texts tell us F=m*a (Force = mass * acceleration). Re-arranging algebraically, a=F/m (acceleration = force divided by mass).

Another fixed variable is distance. Mass of the hammer does not change the size of the smith or the height of the work. The physics texts say d=0.5*a*t^2 (distance = 1/2 * acceleration * square of the time). Re-arranging algebraically, a=2*d/t^2 (acceleration = twice the distance divided by the square of the time).

More algebra: since a=F/m and a=2*d/t^2, F/m=2*d/t^2. Solving for t, we get t=sqrt(2*d*m/F) (time = square root of (twice the distance * mass divided by force)).

This gives us time, and since distance is fixed, we can dig out our final velocity. The physics texts say Vav=d/t (average velocity = distance over time). They also tell us Vav=(Vo+Vf)/2 (average velocity = half the sum of original velocity and final velocity). Since our original velocity (Vo) is zero, Algebraic manipulation yields Vf=2*Vav.

Now all we have to do is substitute in the equivalences: Vf=2*d/sqrt(2*d*m/F). And that shows us our final velocity is proportional to the square of the inverse of the mass. Myth BUSTED!!!

ENGLISH TRANSLATION OF THE ABOVE:

Nobody can swing a hammer that weighs half as much twice as fast. You can swing (hammer + arm) that weighs half as much only 1.414 times as fast. The total energy coming from the smith is dependent entirely on the smith, not on the mass of the hammer.

Let's re-phrase that: We can never get more energy out of something than we put into it. Smaller hammer (not counting for gravity) means the same energy as a larger hammer. Larger hammer (not counting gravity) means the same energy as a smaller hammer.

We do also have gravity. If we use a drop hammer, we remove the smith from the descent equation and bigger clearly becomes better. But the drop hammer takes effort to raise up & be ready for use. Once again, the First Law of Thermodynamics pokes its nose in the tent. A heavier hammer wielded by any smith will hit with more energy than a lighter hammer. It will also require more effort from the smith to raise up to ready.

I think I'm finally getting a handle on this hammer math.

No matter where you go... there you are.

May 6, 2013
2:08 am
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Larry L
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I think that is the argument though Lee.... Twice/half are just arbitrary things thrown out, the point being if you swing a light hammer with some skill you can accomplish the same amount of work as a heavy hammer with a lot less damage to your body

Whatever you are, be a good one.
Abraham Lincoln

May 9, 2013
12:38 am
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billyO
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Hello all, I think I'm ready to put some of my thoughts down for everyone to read. Here goes:

What is it that we do? We move metal, and in order to move metal we need to break the forces that are holding the metal molecules in a certain positon. So what we are concerned about from a metal moving perspective is force, not work as I've read before. Therefore, from a theoretical/physics/mathematical standpoint, it's the mass of the hammer head that is important, not the speed(velocity) of the hammer head, because although it's likely that everyone can swing a 3# hammer faster than a 5# hammer, you may be able to swing a 5# hammer faster than I can swing a 3# hammer. So from a mathematical standpoint, when one simith is trying to convince another that a 2# hammer is better than a 5# hammer, and another smith chimes in with the opposite, this is an apples to powerhammers argument.

However, we don't live in a purely theoretical world, but rather in a world where we -- living creatures with more soft tissue than hard -- try to shape and form materials that are almost always much harder and stronger than our strongest hard tissue. From this PT’s perspective, then, the argument is not whether to use a heavy hammer a little slower or a lighter hammer faster because from the standpoint of moving metal, the more metal you want to move, the heavier the hammer you will want to have. Period.

(I like to use what I call “Limit Theory Thinking” in cases like this, so here’s what I mean: with enough control, you could draw a taper on ¼” stock with a 500lb powerhammer, (how many have seen videos of closing a matchbook with a power hammer?) but I challenge ANYONE to draw a taper on a 3” square with a 2# hammer. )

So, the issue is not how heavy a hammer you should use, because that will vary not only from person to person, but throughout each of our lives as our bodies change. Normally, the progression for any individual would be this: lighter hammers when starting, progressing to heavier hammers as we develop our forging muscles, plateauing at whatever a manageable weight is until we age to a point where the body starts its natural deterioration process and we need to return to progressively lighter and lighter hammers (if we’re lucky to still be forging at that point).

So the argument shouldn't be about WHAT tool to use, since there's no one right answer to that, but rather HOW to use the correct tool safely.

When I get specific biomechanical reccomendations fleshed out a bit more, I'll start down that road.

PS - work is the ability to exert a force over time, so although not relevant to this theoretical part of my discussion, it is directly related to safe smithing from a practical standpoint.

as always

peace and love

billyO

May 10, 2013
11:39 pm
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Scott Rash
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Ok Billy, I’m going to disagree with you, but only slightly.

Even though comparing two smiths’ hammer swing speeds may be apples to powerhammers, as you mention, every smith can swing/snap a lighter hammer faster than a heavy one, even if only slightly faster. Newton’s second law tells us that force increases linearly with mass and quadratically with speed. That means one would only have to swing/snap a 1.5# hammer 16% faster than a 2# hammer to deliver the same force. A 2# hammer swung 73% faster than a 6# hammer delivers the same force. Speed kicks butt over mass. A longer handle increases velocity – a big part of why a striker is so effective. Of course my numbers aren’t quite right because I oversimplified; the force we exert on the hammer changes throughout the swing, the math above assumes unidirectional forces not acceleration through an arc, etc.

However, I absolutely agree with the point of your challenge; I think we’ve all tried to draw out large stock with a too-small hammer only to discover a concavity where the point should be (aha, moving the skin but not the core!). So we switch to a bigger hammer and it works. What this tells me is: I can’t actually swing/snap a 2# hammer anywhere close to 73% faster than a 6# hammer (or maybe just that I need a lesson from Aspery…).

I also disagree with an earlier comment that a heavier hammer will deliver more of its energy than a lighter hammer. By definition, each hammer delivers ALL of its stored kinetic energy to the workpiece. We know this because the hammer stops traveling downward! Some of the energy is lost to deformation of the workpiece, ‘cause we’re hitting a heated ductile material. But steel isn’t completely plastic at forging temperature, there’s still elastic behavior. So a good portion of the energy delivered to the workpiece is transferred back into the hammer, resulting in rebound.

What I actually do in practice is use the smallest hammer that is heavy enough to get the job done. If I’m presented with thicker stock, I switch to a bigger hammer. Then I switch back as soon as possible to avoid fatigue, and also because I have better control. No need to use a 4# hammer on ¼” stock.

billyO;17920 wrote: the more metal you want to move, the heavier the hammer you will want to have. Period.

Depends on the definition of more! I agree if more means all at once. I disagree if more means all day long = your definition of work…unless I’m using my powerhammer!

I’ll be curious to see your biomechanical treatise, as reflecting on the hammer physics topic made me think about my anvil height, how I grip the hammer handle, how high I raise it, my overall ergonomics. It was also a hoot watching different postures at the conference. One demonstrator was using a heavy hammer, but gripping it way up by the head. Gotta wonder if he wouldn’t have been better off with a smaller hammer and a normal grip!

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