A couple more diagrams on axe balance.

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The claim was that on most the plumbing falls in front of the eye just outside the handle. I have provided pictures showing that this is not the case with several patterns. Including bit heavy patterns like the Dayton and the Michigan. As well as the jersey, as well as a couple of boys axes. As a matter of fact, the only ax I hung with a plumb line that actually did what 42 was describing was the Hudson Bay Wetterlings.(Obviously double bits fall in the center. And there are exceptions. But as "most" American axes are sold on 36" curved handles you would be hard pressed to find one new that does what he claimed.) Even the cheapest hardware store axes seem to all hang inside the handle and eye. So I feel quite confident that his claim is false and I have provided sufficient evidence to the contrary. He will however, never admit this, because that would mean when he wrote his paper it was based on assumption....
(I think this Council is a the first and only picture of him hanging a plumb line I on an American pattern. He actually used a Council Dayton 4lb Velvitcut on a 36" curved handle as the original drawing to show the claim, but never backed it up with a picture. And that is really odd. )
.... Or False claims. Just as he will not address the fact that anyone and everyone who owns or has ever tested a Council tool classic Jersey has shown it to be bit heavy, yet he claims it has perfect balance.

 

You said most. I'm sure I can provide a screenshot if you like I have provided pictures of American axes on plumb lines. You, as far as I have seen have not with the acception of the one Jersey. You have not even been capable of providing evidence that this one singular claim is true.
The problem being if the Council on the left isn't like you claimed, you have a BIG issue. And most American felling axes balance quite all right on the hang, in my experience and with evidence I have willingly provided to anyone and everyone.
From Benjamins paper

 

No, not the red line. The "simple leverage" I described uses an actual lever (the axe handle), not an imaginary red line.

 

You just demonstrated that the axe is bit heavy. Congratulations.
That ax will do the same thing with the straight handle on it.
A double bit will balance center balance of the head, and any point on the handle. (Balanced)
A Michigan will balance towards the bit, (bit heavy ax)
A classic Jersey will balance towards the bit,(bit heavy ax)

As a matter of point and the "blue line" your handle brought more of the handle into the blue line. It did not "balance" the ax. BUT judging from your photos, it made the ax more bit heavy than the straight handle if the blue line is the reference point.


Again, I can do this same thing with a well known ax that is known and agreed to to have poor balance. For your claim that you balanced the ax with the handle on the horizontal to hold water, your "experiments" or "evidence," can not be repeatable with a known bit heavy out of balance ax.

 

"Rotation takes place around the red line" is your premise, and a lot of your theories depend on it being true, but... it doesn't hold water.

The red line is useful for determining the location of Center of Gravity, and it will be the axis of rotation for cases where you are dangling the axe upside-down from a loose pinch point (with no other constraints), but if you add other constraints (like two hands gripping the handle, or even just one hand firmly gripping the handle), then all bets are off.

To illustrate the fallacy, all that's needed is a hardback book (and if no books are available, then a Kindle can be used ). Let the book dangle from one corner using a pinch grip. The "red line" will pass through the book's Center Of Gravity, from the gripped corner to the diagonal corner. So we've determined where the "red line" is. Now, change the pinch grip to a firm grip on that same corner of the book, and hold the book a few inches above a tabletop, with the spine down. Rotate the book back and forth, while keeping the spine of the book parallel to the tabletop. It's not difficult to do. By rotating the book around it's spine (instead of around the diagonal "red line"), the "rotation around the red line" theories have been disproven.

Try it with two hands gripping the spine of the book, and it's even easier to do. The same goes for one hand with a sliding grip along the spine, while the other hand has a firm grip.

But a book is not an axe, right? So try it with an unbalanced axe, holding it with two hands, keeping the handle parallel with a tabletop for reference. It likewise won't be difficult to rotate it around the axis which connects the two hands (which is not the "red line"). It can similarly be done with a sliding grip for the hand closest to the head.

But what about one grip holding an axe handle? To make it easier to hold, try it with a hatchet, and it will again be possible to rotate it around an axis that's not the "red line".

This is because the "red line" defines the axis of rotation for the axe when it is not constrained in any other ways (beyond dangling it from a loose pinch grip). Just by holding the handle in the same place, but with a firm grip, additional constraints have been added and the "red line" doesn't apply (unless the handle, where it's gripped, happens to already be aligned with the "red line", like with a double bit axe).

 

Could you clarify what you mean by "there'd be no change in the power of the twisting force between the two hands"?

 

I feel (EDIT, this is EXACTLY what cook was talking about) this may have been what cook was talking about when gripping the bottom of the curved 10 degree bottom part of the handle that would in effect be moving the "red line" behind the ax head and magnifying or amplified the wrist movements in the bit. Decreasing accuracy. But it has been a while since I looked at his writing.

Here have a picture.
Cook

 

I'm not parroting Cook, though. I'm basing it on the physics that's easily demonstrated (as I described earlier). Cook's assertions have some similarities, but I'm not taking it as far as he goes.

 

I've debunked Cook's 2nd diagram before so will do it only briefly here.

The axe would only pivot along the axle of the grip if one were to relaxe their grip and allow it. But that doesn't happen. Instead the grip is just a more comfortable interface between the arm and the haft. The actual rotation takes place in your forearm. Grab an axe and rotate it and you'll see this is so.

 

Re: "That doesn't mean it's impossible to cause it to rotate around a different axis, but doing so is not its natural axis of rotation and so will induce torque that you have to fight in order to cause that rotation."

That effect, when present, is not very significant (relative to the forces being applied to the axe) and is easily overridden (as apparent in the demonstrations with the book and the axe).


Re: "Now, as you yourself previously established, if you're rotating the axe around the handle when that handle does not align with the center of gravity, the head will be prone to torque on the handle. However, torque you apply to the handle (presuming no difference in handle shape at either point) will be identical and so it's fallacious to say that the upper hand will have any mechanical advantage over the lower hand when it comes to twisting the axe and causing wobble."

Not true. The upper hand will indeed have mechanical advantage over the lower hand, and it can cause wobble from off-center applications of force on the handle, as well as purely lateral applications of force that push the imbalanced head out of alignment.


Re: "Take such an axe and stand the butt end on your palm and encircle the handle with your forefinger and thumb of the upper hand and wobble it side to side. You'll see the path the handle wishes to trace is conical rather than vertical."

Again, the motions of an unconstrained handle do not translate into a significant effect on a gripped handle.

 

I'm not sure what this means but here's another avenue of thought for you all.

If the real rotation of the axe takes place in your forearm, and I think I've demonstrated that it does, then the hand, the grip and the haft are working together to align the axe to THIS axis of rotation. Energy is spent in the wrist and hand to make this alignment. The more efficient this interface is the less energy is spent in the wrist and hand. Handle forms likely developed to create a more efficient interface. Whether that increases accuracy or just allows you to work longer I'm not sure - maybe it does both.

 

Sounds like the "guilt by association" fallacy. If this is a way of asserting that I am making a number of errors, then how about listing them specifically?

 

I remember when you first brought up the forearm aspects, and it was a bit of a revelation to me. Those influences make sense to me, along with other effects regarding the motions of the shoulder and elbow joints, which all combine to make the axe swing more complicated than my limited understanding. The rotation of the forearm is definitely happening in the demonstrations I suggested (with book, axe, and hatchet).

 

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I was just making the connection out loud.