How are you sure? He never mentioned them. I'm suggesting that we do the test. I'm happy to be one of the test subjects. But it wouldn't be wise to make conclusions based on one person.
And as for the assertion that axe racers can get away with a curved handle because they only work in short bursts that makes no sense at all. If anything the curved haft puts less stress on the hand and wrist and allows the user to work longer. But aside from that, axe racers depend on exactly placed blows to get through wood in the shortest time possible. It wouldn't pay to be sloppy. If there were some inaccuracy in a curved haft would it have to be offset by some other factor or racers wouldn't be using them.
The curve in a haft matches the natural way your grip aligns to your wrist. You twist your forearm and the haft twists in line with your forearm not on some crazy line 10" above your axe head. Try it for yourself and see. Pick up a curved haft and twist it. Is it moving like in Cook's sketch or is it moving in line with your forearm. I encourage you all to try this.
I've also encouraged you all to try this. Stand up. Let your arms dangle at your sides. Grasp a pencil in your hand. Now raise your arm up parallel to the floor. Is the pencil pointing straight forward or up at an angle? This answers why we have curved hafts.
Cook used an axe enough to know the difference he felt between the types of hafts. He doesn't really clarify testing throughout any of the book, but it's clear that he put a lot of effort into analyzing the differences and geometry of the axes, and this implies there was some amount of side by side testing. I could just say, do you have any evidence that he did not do tests? and we wouldn't be any further. Anyone with a tonne of experience knows what they feel with the axe's movement, and of course results may be subjective, but various people giving feedback may give an idea of what is really going on. So I suppose I should have said, 'In any case he had enough experience that he did the equivalent of side by side testing.'
I would do some tests as well to see.
I'm not sure why the short bursts point makes no sense to you. We have not actually come to any group conclusion on where the best axe handles excel, and there is more at play than just comfort for endurance, there is also the argument of increased velocity with the curved handle, increased ability to withdraw an axe from wood with the curved handle, possible advantage to popping a chip with the curved handle, and increased accuracy with the straight handle. My argument is that the racers either have a regulation requiring certain deviations in the handle/head or they do seem to prefer the curved handle for one of these benefits (popping, velocity, backswing etc.), and as short chopping does not cause your accuracy to falter as much as long work (especially for highly trained people) it may be more important to focus on the other factors. So it makes perfect sense rationally.
I have done similar tests holding the straight and curved handle. If you hold the straight handle with the axe head in a bucking position you will feel that when turning your wrist the axe head will only spin, which affects the degree of penetration. For the curved handle you can see that the head will spin but also move horizontally with the toe, which affects the degree of penetration and the horizontal angle. This means you can miss on two planes rather than one. Cook's drawing is representative and not literal. It does not mean that your axe will miss ten inches above the head, it means that there is a proportional deviation in accuracy due to the twist of the curved haft being off line of the axis in the eye.
Perhaps a better test is to hold the handle with both hands, with your hand towards the head you can feel that the straight handled axe will spin while the curved haft tends to spin and push your hand left or right. For me one side seems to push more than the other. I would say then it is a matter of tradeoffs. Do you really conserve energy from the perceived comfort, or are you wasting that energy from inaccurate swings (and the increased likelihood of breaking a handle)?
And of course, there's also the problem that the vast majority of endurance users, fallers, used double-bit axes with a straight haft. So I don't know where the argument for the curved handle being better and more comfortable comes from. Seems like speculation to me.
