Zemmo, all is not as it seems.
Objects of any size have a terminal velocity of 32ft/sec/squared. Yes, we all know that. but there's no way a light maul or a heavy maul can go that fast with gravity on it's own. Not from a swing height of say, 8 feet (your height plus length of the handle).
What I'm trying to say is that gravity alone doesn't yet kick in in all it's glory...several more feet of movement are required to reach that magic number. Which means we have a rather complex physical equation dealing with momentum, inertia...changing velocity...it gets ugly pretty quickly.
A more useful equation might be measuring the Kinetic Energy stored in the axe head at the moment it hits the round.
KE=Mass/2 x square of the velocity (V-squared). Now this equation yeilds some surprising results when you think about the differences you can swing a heavy object as opposed to a light one.
We might all be surprised to discover that we can swing a light axe not just twice as fast as a 10-16 lb maul, but, with proper technique, probably more like three times as fast....and this part is crucial to shortening the task of getting through x-amount of rounds in an hour: you can swing a light splitting axe far more frequently to make it do more work.
That's the crucial part. I just finished splitting some 16-18 inch Fir Rounds. After the initial split is done, I can split each half into burnable chunks at a rate that far exceeds a heavier maul. With this question on my mind, I was hitting split-halves at the rate of about 1.5 hits per second. (full swing obviously not needed with clear fir).
You know that delightful wham-wham-wham we all get when we use the right tool on clear, knot free wood? The kind of work that makes us smile? yeah...that kind of feeling.
Couldn't do it with a monster/heavyweight maul. Consequently, I can do more work faster. And that's what we're all after, right?
I was thinking about the kinetic energy equation after my last post, and the formula you mention. I'm just not sure that it's applicable. It's been nearly a geologic age since I studied physics, and I'd love to hear the take of a real physicist.
But I don't believe that the KE formula predicts penetration (which is what we are talking about, the penetration of the head of a maul into a block of wood. In firearm ballistics muzzle energy is calculated by the KE equation, thus one can have a very light, very fast bullet with the same muzzle energy as a slow heavy bullet. A 300 gr. bullet at 1500 fps, versus a 40 grain bullet at 3500 fps. Just guessing that these examples would yield a similar muzzle energy, they should be close enough for an example.
BUT, the penetration of these rounds in any medium, will not be identical. Given the same shape, the heavier, slower bullet will penetrate much deeper. Inertia (the tendency of an object in motion to remain in motion), is dependent on momentum, not kinetic energy.
About the actual speed one can swing a light maul compared to a heavy maul, I don't even have a guess, and no accurate way to measure.
The easier the splitting the less the heavy maul is needed, and since it stays as heavy as ever (heavier than needed for easier splitting), I agree with you that easy splitting is easier and faster with a lighter tool. Wet birch at 40 below is the easiest I've ever seen, you just wave a maul at the round, you don't even have to hit it. EXTREMELY satisfying
The twisted oak I was splitting today made me smile, but grimly, as sweat poured onto my safety glasses. But hey, outdoors on a beautiful NM winter day, it's a hell of a lot better than being in Cleveland--or in an office.
If you know any real physics nerds, I'd love their take. Good splitting, no quitting...
PS Objects don't have a velocity of 32 ft per second per second, they have an ACCELERATION of those values. Terminal velocity depends on a number of variables, shape, density, duration of fall, etc.