When my dad and I cut and split wood, the ax was mostly used for de-branching a felled tree. Once the splitting process started, the ax would be used to cut the remaining fibers on bigger logs that didn't split cleanly. Cutting down a tree with an ax is hugely non-productive. This is why saws were invented. Dad and I used a bow saw, sledge, wedges, and an ax.....until he brought home a chainsaw. Oh Man! Gimme a chainsaw any day, even for de-branching. And a hydraulic splitter.
I agree, a hatchet is used mostly to hack sharp points on tent pegs, or banging them home. Maybe for making rustic wood pegs, stool legs, and such. A saw is much more productive in making firewood....any saw. Breaking up firewood can be accomplished as well with a baseball bat sized piece of wood used as a club, as can an ax or hatchet, in most cases.
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