Anvil size vs hammer size, 2% or 10:1 or 15:1

[Gerald Boggs]

Hi Gerald.  The analysis assumes no contact between anvil and earth.  Thus, it produces an pessimistic answer (underestimate of efficiency).  Accounting for a connection is not trivial.  This calculation is significantly beyond the textbook applications of conservation of energy and momentum.  Before calculations of this type are made, the hammer-anvil impact force needs to be estimated.  This estimation will open the door to the above and other interesting statements, and will appear in the second and forthcoming parts of the paper.

 

A significantly simplified and more approachable set of articles is running in the CBA magazine as well as some other local publications.  As expected, they have attracted quite a bit of controversy, primarily due to the author's gaps in clarity and anticipation of the kinds of questions.  There should be another installment appearing soon, perhaps in the next issue.

Without including the earth, how in even a little way, is this useful knowledge?

I read the article published in 2011/early 2012?  (I'm a member of CBA)  You could call it "controversy" if that's the word you use for "not supported by practical experience."

[evfreek]

Without including the earth, how in even a little way, is this useful knowledge?

I read the article published in 2011/early 2012?  (I'm a member of CBA)  You could call it "controversy" if that's the word you use for "not supported by practical experience."

It is useful knowledge in that it provides a pessimistic estimate (or worst case).  Any connection whatsoever to the earth will act to improve the efficiency.  So, if an efficiency number of 92% is computed, a naysayer cannot jump in and say it must be less than 80% if the anvil is sitting on anything, even a rubber pad.  He can reply that it must be higher than 92% since the anvil is welded to an I'beam which is buried 8 feet into solid ground, but the model does not address that side.  Therefore, this model is not very useful for those little 25 lb striking blocks that seem to work so well with 12 lb. sledge hammers.  That is not the place to apply it.

[evfreek]

In the case of that specific analysis, I think I'm far more skeptical of the applicability of its findings to the real world question than I am to its contents, given how different the scenario it envisages are from the one we are actually using.

It is a worst case analysis.  Any support will increase the efficiency. 

[Gerald Boggs]

On 2/6/2014 at 4:18 PM, evfreek said:

It is useful knowledge in that it provides a pessimistic estimate (or worst case).

 

No, it has no application.  My take on the article, is it's nothing more then an attempt by the author to get attention.
This is part of the opening paragraph.  "If it is necessary to do more work or larger jobs, just use a bigger hammer and/or swing it faster. But, should the anvil be correspondingly larger? That seems to make sense, since the anvil could no longer be considered immovable when hit with a larger hammer. Not only might the anvil no longer be immovable,but it might be damaged."
To the novice blacksmith this might sound both clever and true, but true it is not.  Trying to use a bigger hammer then one is use to or swinging faster are the hallmarks of the poorly trained smith.  If the author believes this...
Then there's a bunch of gobbledegook that has no application to the working smith
The conclusion of the article  "There you have it. Tell your partner that for good forging efficiency you just gotta buy a bigger anvil."  The only reason to use a bigger anvil, is because you like a bigger anvil.

[dbrandow]

It is a worst case analysis.  Any support will increase the efficiency. 

 

I suppose, but again, because it doesn't take into account what material the anvil is made out of, or the fact that it cannot move but instead can only compress, it doesn't seem to me to be taking enough of the real world variables into account to be a useful enough model. It might establish a lower bound, but it doesn't sufficiently answer the question at hand. If the equation in consideration, this or any other, doesn't take into account whether the anvil is made of mild steel, hardened tool steel or wood, then I can't consider it applicable enough to be of much value. A professional engineer wouldn't design a bridge without taking into very careful consideration what materials its made out of, the same thing applies here.

[thingmaker3]

Nor would said engineer refuse to use individual equations describing how said materials react. There is no "bridge equation." Nor would said engineer have learned all those equations simultaneously. (Anybody here learn the whole suite of smithng skills at once?)

 

On 2/7/2014 at 8:16 AM, Gerald Boggs said:

No, it has no application.

That nail over there is useless. So is this board. That whole pile of nails has no application. This whole stack of boards has no application. I wanted a shack, not a bunch of useless items!

[Gerald Boggs]

So be kind to us and give us a example of where a working smith would use this information.  I don't fight change, I had been working in blacksmith shops for seven years and one day a smith came up, watched me hammer and said "Try doing it this way"  In a moment I when from one method to the next and never looked back.  But I won't just nod my head and agree to something I think is not valid.

[rockstar.esq]

Gerald, dbrandow,

 

I can't pretend to answer your questions but I do have an observation that may serve to bridge the gaps you're identifying.

 

The math involved with physics is derived primarily around motion of rather than the specific properties of a given material.  The means to calculate the center of gravity are the same if the object is wood, metal or gelatin.  An awful lot of materials have similar densities, modulus of elasticities, and so on.  By giving the math a chance, you can arrive at some interesting solutions and you can waste a lot of time.

 

I was working with structural steel calculations in a class thinking to myself that any given section deep enough to pass requirements for moment (sag in a horizontal beam) would also pass requirements for shear at their end points.  

 

It was easy to think that because I'd spent most of  the class looking at structural sections that were long relative to the loads and in all those cases the shear calculations required less section depth than the moment calculations did.

 

A heavy load on a short span tends to fail in shear as opposed to moment.  Those relationships would be true with wood, concrete, steel, carbon fiber, or whatever.  

 

It's very rare to find a situation where someone actually bumps up a short joist's depth to account for that in residential construction.

 

It's very easy to come to the wrong conclusion by assuming one factor is more important to the system than it really is.  One little shift in the system application drives entirely different priorities.

 

Glu-lam beams utilize premium material for the top and bottom with lower quality wood in the middle.  The lower quality wood drives the beams mass for sure.  What the lower quality wood is actually doing is moving the tension and compression forces further apart in the beam thus offering greater stiffness.  That's why "I" beams are skinny in the middle.  Adding mass doesn't correlate to compressive strength directly so focusing on it draws the wrong conclusions.

 

Picking futher, it's also an energy calculation.  Potential energy is converted to kinetic energy which is bounced around.  Heat is generated.  In some cases light is generated.

 

My physics professor turned off the lights and struck a piece of paper with two ball bearings in each hand.  It not only sparked bright enough to see - it actually burned little holes in the paper.  Two masses suspended by naught reacting in kinetic energy.

 

To physicists, there doesn't have to be a practical application which at least for me was why they're so frustrating to understand.

[Gerald Boggs]

Thank you for taking the time.

 

To physicists, there doesn't have to be a practical application  And that's fine, but in the article it was presented as having practical application to blacksmiths.

[evfreek]

Hi Gerald and others.  Physics definitely has applications.  But, sometimes they are far removed from the task at hand.  Many years ago, I was hanging out with a physics professor who was installing a 3 story tall particle accelerator.  The installation was kind of tricky, because these things are top heavy, kind of like a power hammer.  I asked him if it was like moving a power hammer, and if he was doing calculations.  He said that the riggers do all that, and they should do fine.  It would not be done in a day or even a month.  So he didn't have any role?  Well, he said, if the riggers get in trouble, they will call the engineers.  And, if the engineers get in trouble, they will call the physicists.  I asked him if that happens much, and he said hopefully not.  But there is one famous time that the engineers got in trouble and had to call the physicists.  That was the o-ring low temperature failure that let to one of the greatest space exploration disasters in history, and it had to be diagnosed by a physicist.  I talked to another physicist about this, a fellow who did not have much good to say about the investigator.  He said that many engineers could have solved the problem but they were held back by a cultural problem.  Seems that there is a big problem with mistaking skepticism for intelligence.

 

As for practical applications of the hammer and anvil calculations, here are some:

 

1.  There are two numbers given from two different calculations.  One of them says that a bigger anvil is needed for the same efficiency.  The cost difference between the two calculations is not trivial.  As I recall, there is a factor of 4 there.  What the inelastic model says is that you do not need as much mass as previously thought to attain decent efficiency.  In fact, there is even some efficiency at 1:1 ratios.  In other words, if you suspend a 2 lb hammer on a thread and strike a target up against it with a 2 lb hammer, you will do some work.  The elastic model says all energy will be lost.  This is clearly wrong.  And it can easily be demonstrated with a string, a couple hammers and a finger (or piece of modeling clay).  Interestingly, it was not a physicist who introduced me to this idea.  It was a blacksmith, the web personality FredlyFX, who I met at a CBA spring conference.  This observation contradicts the figuring from the guru at anvilfire.  The distinction is not trivial.  It is the difference between wanting a 400 lb anvil vs a 100 lb anvil.

 

2.  As was correctly pointed out, the model does not account for anvil strength.  That was considered a fatal flaw, since the idea of the rubber anvil was brought up.  Far from being fatal, it highlights the importance of thinking of efficiency as the battle against energy loss.  There are all sorts of ways that energy can be lost, but by doing the calculation, the maximum energy loss due to low mass ratio can be calculated.  This is incredibly valuable.  Once the mass ratio is brought to the desired value, it can be ignored when the question of material strength is asked.  This meta-analysis is called decoupling.  In other words, one can make the statement that when the anvil is less than 100 lb, material strength is not so much a worry, since too much energy is lost in the mass moving, while at greater weights, attention can now be directed to the material strentgh.

 

3.  There has been an excessive focus on the limitations and assumptions of the model rather than its (rather simplistic) conclusions.  One important thing that it shows me, which I did not realize until doing a couple of web searches, is that it is also useful to ask where does the lost energy go?  Does it disappear into thin air?  No!  The emphasis on conservation of energy in the model directs us to ask this question, which is more important for power hammers.  The energy, even if it is only a few percent, goes into movement of the anvil.  In a power hammer, this is transferred to the foundation and creates noise and nuisance vibrations.  There is one company which analyzes this transfer and recommends its padding instead of increasing the anvil mass.  Why?  Increasing the anvil mass helps, but it reaches a point of diminishing returns quickly.  The model beautifully illustrates this.  In the end, it is cheaper to buy a dissipative rubber pad whose main function is to waste energy.  But the naysayer will complain that energy wasted is money wasted.  The manufacturer uses the model to show that this wastage is limited as the conservation of momentum and energy show.  The object is not to harness this energy, but to keep it out of the foundation, where it can cause problems.  In that way, I think that skepticism is less a measure of intelligence than is the rational quest to save money without accepting mediocrity.

 

4.  Left as an exercise to the reader:  these calculations provide the foundation for more advanced observations, including three which might be of interest in the blacksmithing community.  How hard does the top have to be (yield stress), what is the effect of anchoring the anvil on a softer substrate, what is the loss associated with a lose top, and what is the loss associated with off center blows whose axes miss the center of mass.  One of the questions that always comes up is why is a full pen weld needed to join a hardened top to the anvil body.  A naysayer will complain that any porosity in the weld renders it useless for this purpose.  This paper will help the enlightened reader understand that rarely is the problem black and white, and there are other more cost effective ways that ignore the non-full pen weld after its contribution to loss drops below a certain threshold.

[thingmaker3]

and what is the loss associated with off center blows whose axes miss the center of mass.

 

That's a really good question. A lot of work is done with half-faced blows at the near or far edge. How big of a sledge may a striker wield without fear of damage? And just how much worse is it to work on a bottom tool in the hardie hole than to use a similar die over the waist?
 

[Gerald Boggs]

You have written many words, but you still have't wrote anything of practical use.  In short, the article has no practical applicaiton for the working smith. 

 

 

Practical: of or concerned with the actual doing or use of something rather than with theory and ideas.

[evfreek]

That's a really good question. A lot of work is done with half-faced blows at the near or far edge. How big of a sledge may a striker wield without fear of damage? And just how much worse is it to work on a bottom tool in the hardie hole than to use a similar die over the waist?

These questions require understanding the mechanical properties of the material and are beyond the scope of simple applications of the conservation of energy and momentum. The next installment should shed some light on this topic. Briefly, one is pretty much safe as long as the maximum impact stress is less than the elastic limit of the material. Otherwise, there is a risk of leaving a dent. The maximum impact stress is a function of the hammer momentum (not energy) and contact area. That is why the radius of the edge is important.

You have written many words, but you still have't wrote anything of practical use. In short, the article has no practical applicaiton for the working smith.


Practical: of or concerned with the actual doing or use of something rather than with theory and ideas.

The article had some use to me. It helped me figure out what size of anvil to make/buy. It helped me understand why putting silicone rubber under the anvil to quiet it down wasn't such a bad idea. It did not sap all of the precious hand hammering energy. It helped in the construction of my latest fabricated anvil in that it didn't have to be over-welded.

Theoretical does not have to mean useless. Some people over at anvilfire said welding was a waste, because it used so much electricity and it was not worth welding up an anvil. Looking up some welding guides gave some theoretical breakdowns of labor vs electricity costs per pound of deposit for different electrodes. Now, these guys over at anvilfire have way more hood time than I do, but a simple test backed up by smart meter data proved them wrong. Now, a lot of armchair experts will insist that those smart meters are inaccurate, but it agreed with the theoretical deposition tables. I would say that theory had proved itself against "the experts".

It reminds me of what I told an engineer. Your design failed in Spice, then it failed on the bench, and then it failed in the prototype. What more do you want?

[thingmaker3]

Gerald, what would make you happy?

[Gerald Boggs]

An honest explanation of the practical application.  But that's not going to happen, as this math has no application to the blacksmith.  All I'll get is more words, but no answer.

[rockstar.esq]

With all due respect Evfreek I think you'd agree that nothing shown thus far has precisely defined a ratio of hammer weight to anvil weight.  

 

I believe that you're correct that there is some information to be gleaned from what's been presented but it falls well short of answering the original post for a variety of reasons.

 

You've made good illustrations regarding the padding and it's utility to preserve foundations, limit noise, and increase rebound.  There's surely some aspect of mathematics and physics to explain why any given thing is good or bad. Without a solid practical output - the majority will view the effort as a pedantic exercise.  Philosophy often get's the same treatment for the same reasons.

 

None of which is to denigrate science of those who pursue answers.

 

I once participated in a debate regarding the ballistic advantages of one cartridge over another.  The tiny differences in the cartridges fueled weeks of mathematical debate which all hinged on one guy's belief that just because he'd found nano-meter scale difference that impacted an ecosystem - there must be a corollary in cartridge selection.

 

In the end - he wanted a weird ,expensive, and under-performing cartridge simply because he liked rattling off insignificant statistics.  I'd like to stress that is absolutely fine with me.  I occasionally like something offbeat, unpopular and downright impractical.  

 

Among some folks I know, Blacksmithing falls into all three of those categories!

 

Getting back to blacksmithing, I think it's somewhat unlikely that groundbreaking mathematics are being conducted on anvil selection.  Maybe I'm wrong and next year we'll see a nano-tube anvil.  In the mean time I'm enjoying learning what I can.  A huge reason I enjoy blacksmithing is the many ways that complex problems get solved - often by people who didn't have the advantages I've enjoyed.