A knife, because of its having a sharper edge and more acute blade angle, WILL out hack an average hatchet given that the amount of effort or energy is equal. This is only because of the more efficient cutting edge on a knife. Because of the weight and balance of an average knife, it does not offer the kinetic potential of an axe, with all of its weight on the end of the handle where it can develop inertia more efficiently.
The drawback to having a sharp angle for impact cutting is that the edge will be much more suseptable to damage. Axes have fairly blunt grind angles, and are more so intended to retain their shape more than an edge. The inertia incurred by swinging the axe will more than overcome their not having a keen edge.
Given that wood cutting efficiency is matter of edge geometry and kinetic energy, it would not surprise me that there are a few large knives that would outhack a hatchet. A khukuri is a prime example. Larger hunting/camp knives that are heavy in the blade would be another. Then there is the venerable machete. I have one that I keep in the truck for trail clearing, and it is much more efficient to use on small trees than a hatchet or an axe. For larger trees I break out the 12 guage, but that is another story....
Axes do have their use, of course. In a area where there is plenty of swinging room, axes offer the the potential to get more work done. Axes and hatchets are better than knives in splitting wood because of their wedge shape, and because all of their energy potential is in the head of the axe/hatchet where the bulk of the weight of the tool it.
Ugh...Hopefully someone out there can decipher what I just said.....
YeK
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"No, it's a Vaquero Grande in my pocket, but I am happy to see you!"
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