Jock, My plans for the analysis were just to use it as a basis for treadle hammer and maybe power hammer design. As I finished it, I thought of maybe having copies available at blacksmith gatherings or as content for my own web site. But my site is currently just a few pictures thrown up for friends to look at, and Anvilfire would be a much larger and better venue if this would be helpful for the community. So, if you think it would fit in at Anvilfire, go ahead and put it up. This will probably save you a little work... I was playing around and what to my wondering eyes should appear... but a save as HTML option in MathCAD. Files attached. Sorry I don't use ZIP enough to justify buying one of the sharewares. Steve Jock Dempsey wrote: At 09:34 PM 2/8/2004 -0600, you wrote: I checked with Wordpad on my WinXP machine (yeah, I know, I plead compatibility with work), and it opened okay. I'm sure older MathCAD won't read the new format, and I can't Save As back that far. They made some major changes with V6 a few years ago. Anyway, have a look, and thanks. Steve, It will take me a while to wrap my head around this but it looks like a good study. MathCAD did a PERFECT export job. RTF is like DFX. MS products and AutoCAD products stink when exporting to THEIR "universal" formats. They almost NEVER work. But all the other users do a wonderful job. You first graph is exactly like the Chambersburg graph. They have a second graph that I will have to pull out and compare. The 40 and 50 to one ratios SEEM ridiculas but that is where the typical hand hammer and anvil work best. And even though the mathematics say there is very little difference you CAN FEEL the difference between using a 350 and 450 pound anvil with ratios well above 100 to 1. That is why I tend to believe the simple analysis. There is still some variation in that range. Your second analysis says the the difference is much less and REALLY should be imperceptable at these high ranges, but it IS perceptable to the point that it makes a difference in how you feel at the end of the day. Not very scientific but true. For power hammer designers there that are hanging on the "knee" of the curve there is a LOT of difference between being on one side or the other. SO, what do you intend to do with this? After looking at it closely I would like to publish it on anvilfire. I would have to convert to HTML. That requires capturing the graphs and formulas as JPEGs. Jock D. . [] IMG0014.JPG [] IMG0017.JPG [] IMG0028.JPG [] IMG0029.JPG [] IMG0034.JPG [] IMG0036.JPG [] IMG0040.JPG [] IMG0046.JPG [] IMG0049.JPG [] IMG0052.JPG [] IMG0053.JPG [] IMG0056.JPG [] IMG0066.JPG [] IMG0075.JPG [] IMG0080.JPG [] IMG0083.JPG [] IMG0087.JPG [] IMG0090.JPG [] IMG0092.JPG [] IMG0096.JPG [] IMG0097.JPG HAMMER AND ANVIL EFFICIENCY ANALYSIS (C) 2004 Steve Alford, Sojourner Forge Roots of this analysis go to a question I asked on Anvilfire about the relative effectiveness of different anvil-hammer weight ratios, with an eye to building a treadle hammer. The Anvilfire guru cited an efficiency table from an old hammer manufacturer - I think it was Chambersburg - and gave me the hint that it was based on an anvil and hammer in free space. This surprised me, because I was thinking that perhaps someone had quantified "how hard it hits", and wanted to know how that would be quantified. After thinking about it some more, I realize that this is at least a good, if idealized, figure of merit. When a hammer and anvil collide, energy that goes into moving the anvil is energy that is expended without going into deforming the workpiece. From Physics for Scientists and Engineers, by Serway, there are three types of collisions: 1. Inelastic, in which only momentum is conserved. 2. Perfectly inelastic, in which the objects stick together as one object after the collision. 3. Elastic, in which both momentum and kinetic energy are conserved. FIRST APPROACH The initial analysis, then, will assume a collision between an hammer and anvil in free space. The hammer will be moving, initially, and the anvil will be stationary. I will also assume a very hard anvil and hammer, that is, an elastic collision, in which no energy is expended in deforming either the hammer or the anvil. Conservation of momentum Conservation of energy v = velocity before collision, u = velocity after collision Some things I can simplify right away: The anvil is at rest before the collision, so v.a = 0 I'm concerned with the ratio of the masses, not the masses themselves, so I introduce k = m.a/m.h Subbing, multiplying through, and generally simplifying: Taking u.a out of the way, because it doesn't enter into the final answer I'm looking for: Solving this last equation for u.h, I use the quadratic equation to get: This is the hammer velocity away from the anvil, in terms of the anvil-hammer mass ratio and the hammer velocity when it hits the anvil. What I want is an efficiency, energy out over energy in, because it's energy that does the work of deforming steel. Ideally, an efficiency of 1, or 100%, would mean the hammer has the same energy going out as going in, and no energy was lost in moving the anvil. If efficiency is only 50%, then half the energy of the hammer blow was wasted in moving the anvil. Kinetic energy is: To put up a nice plot, An anvil-hammer mass ratio of 1 would be abysmal - like striking two hammers together. 50:1 represents a typical, good 3-lb hand hammer and a 150-lb anvil... So an anvil-hammer ratio of at least 6 is needed to clear 50% efficiency. At least 15 is needed for 75% efficiency, and the curve flattens out above 25 or so. A DIFFERENT APPROACH In Mechanics, Den Hartog uses the forging operation as an example in his treatment of impact, with a different approach. This example may be more palatable, because it feels more real-world. The anvil is assumed to remain at rest, as our intuition would indicate. He describes an inelastic collision, where the hammer is mass m.h and the mass m.2 represents the mass of the anvil and the workpiece. The workpiece has a coefficient of restitution e, which is nearly zero for a "sufficiently hot" piece. The kinetic energy of the hammer going in is And the kinetic energy of the hammer after impact is That is, for a low coefficient of restitution, more of the hammer energy goes into deforming the hot workpiece. For a high coefficient of restitution, as in hitting a cold workpiece, the collision is more elastic, the hammer comes back with much more energy, and the smith may have to think of some explanation as to why he hit himself in the head with a hammer. The energy that is dissipated in deforming the workpiece is (Den Hartog leaves the algebra as an exercise for the reader): If that expression is rearranged slightly, the energy that goes into the workpiece appears as a fraction of the initial kinetic energy of the hammer: Recalling that m.2 is the mass of the workpiece and the anvil together, if the mass of the workpiece is assumed to be a negligible fraction of the mass of the anvil, which certainly seems like a valid assumption for the forging projects that I'm familiar with, I can write the fraction of the initial hammer energy that goes into the workpiece as: From here, I can revert to using the anvil-hammer mass ratio k, These charts emphasize two great points of blacksmithing instruction: the importance of hitting while the iron is hot, and the value of a large anvil relative to the size of the hammer. An anvil-hammer ratio of 5 is necessary to get up to the "knee" in the curve, and a ratio of 10 or more is required to get above the knee. And although I'm not sure of an expression to mathematically relate e to forging temperature, it's clear that the energy that goes into moving the metal decreases dramatically as the temperature decreases (increasing e).