Calculations

Okay, the model is not ideal.  Before I set this up, I want to make clear that blacksmithing can be very precise in terms of results, but any time a human being swinging a hammer is the actual source of the project, there are some very real uncertainties that are very hard to calculate. 

Real life:
Some of the kinetic energy remains kinetic energy.  Some becomes sound, for example.  Some returns to the hammer and a very slight bounce occurs.  Some is transferred to the anvil and it moves slightly.  So, we are not able to really, honestly, truly get a 100% conversion.  That's life.  Entropy will have her fickle way with us, as well.

But a lot of the kinetic energy actually goes into the iron.  Which brings me to...

The Model:

The kinetic energy at the moment of impact with the work piece will be equal to the potential energy at the top of the swing of the hammer.  Calculating potential energy with the data available or easily estimated is fairly straightforward, so I will use potential energy=heat energy as my basic concept.

For these calculations, I am going to assume a "perfect" hammer blow.  What is a perfect hammer blow?  For the purposes of this problem, it is a blow that delivers all of the potential energy to the work piece.  Further, all of the potential energy will become heat energy. 

Potential Energy of the Hammer

Some approximations are made, here.  I can easily strike an iron rod 30 times in 15 seconds.  I got this figure by counting how many blows I struck the in the example video in a 15 second time interval.  (It was 31 blows, but that's close enough to 30 that it won't mess up our calculations much to approximate.)  This is consistent with other smiths, as you will see in the demonstration videos.   That means each blow is about .5 seconds from one strike of the hammer to the next. 

Assuming it takes much longer to lift the hammer than to accelerate it downward, I am going to say .1 seconds of travel time over an average distance of 25 centimeters and a hammer mass of 1 Kg.  Since my favorite hammer is a 2 pound hammer (not including the handle), that's about right for an approximate mass.

Potential energy = mgh, except I am using the acceleration of the hammer in actual video experimentation.  So, now I have to find the acceleration!

Here's a helpful picture:


picture by Patrick Woolery

Since kinematics tells us that s=s0+v0t+.5at^2, we can find the acceleration easily.  Define s0 as the upper position, where velocity = 0 and the equation becomes much simpler.  .25=.5a(.1)(.1), giving a value of 50 m/s^2 for the acceleration of the hammer.  Takes a lot longer to figure out what I need to calculate than it does to actually calculate it!

Anyway, the potential energy for each hammer blow is:
(1 kg)(50 m/s^2)(.25 m), giving us a grand value of:

12.5 J per hammer blow.

Kinetic Energy becomes Heat

Assuming, for my "perfect hammer blow" model (which I hold to be as valid as a spherical cow, so take that for what it is worth in terms of physics calculations), that all of the potential energy of the hammer blow is converted into heat energy on impact, and we get:

Yep!  12.5 J from each hammer blow!

If there is a perfect change from one form of energy to the other, we don't lose a bit of it.  Now, realistically, some of that energy heats the hammer head, and a lot of it is lost to conduction with the cold anvil surface and a fair amount is lost to the air, but looking at the instant of the hammer striking, we get more than 12 Joules of heat energy every time the hammer strikes. 

But what does that do in terms of raising the temperature?  Read on to find out!


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