Tim,

I like a belly to my chainsaw blade, rather than a flat one. I like a belly to my crosscut. I like a convex curve to my drawknife, and I like a curve to my axe heads.
The reason, is because if you want to cut a straight line, you should use a curved tool. If you want to cut a curved profile, you should use a flat tool. My carving drawknife I use for making bows is flat, which makes shaving a curved radius a lot easier. My big shingle knife is curved, which makes it easier to carve things flat.

Even so, the belly of a saw makes it easier to get a flat-bottomed cut, otherwise you tend to get a high middle. When I use a chainsaw, I pull it through the cut, rather than going straight down. This in combination with the slight curve of the bar creates a flat bottom.

When I use an axe, I pull the axe slightly toward me as a slice (not chop). With a carved bit, this creates nice straight lines. With a flat bit this does little good.

I also use a chisel to clean up axe-cut joints. However, my understanding is that a really good axe wielding carpenter does not need to do this. But I'm not so skilled, so I like to try and leave somewhere in the range of a good 1/8" or so to make a nice clean face with the Stichaxt, or with chisel. Often times my good 1/8" ends up more of a good 1/4".
It should also be said that a felling axe is not the proper tool for this job. You need to use an axe with a flat side, like a small broadaxe. The Gransfors 1900 works well, and the carpenters axes of the German tradition do as well, since this is precisely what they are designed for. The two are almost exactly the same thing. I use my 1900 not for hewing, but for joinery and carving.

just so you know what I am talking about, here is a Gransfors 1900 compared to a German carpenter's axe.


DLB


Was de eine ilüchtet isch für angeri villech nid so klar.
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