The first choice. The perfect wood is good straight grain ash that grows quite fast, if you get more than 6-8 rings per inch, it's more fragile, 4-6 rings per inch is perfect. It has been said that such an axe almost always uses one hand, and the handle does not get the same pressure as the cutting axe, so I will use the wood you have well, although I prefer more fiber species, ashes, oak, elm, etc. Redistribute your log in half. If it is a fat log, you may be able to go down to 1 / 8 section.
Your goal is to cut some wood that looks like this, a little bigger than the axe. Pull the eye inside the eye onto the grain at the end. The particle orientation is independent of ash content. I often see that this shows that the direction with the ear head relative to the growth ring is good, and the radial direction is not good. I found no difference. All the technical data, I can find the same information. I think the repeated pictures of grain direction may be from the old American sources, referring to the Old Hickory. In my experience, ash is good, and I usually end up using Ti in another way just because when I separate the wood, it finally comes closest to the shape I want. Bows do the same.
Next, if you have another axe handle, you like to draw on the profile, or just a shape you like. Straight handle is very good. I like this shape.
Cut the profile to try to keep the edge at 90 degrees. At this stage, we are not looking for a circular profile but a nice clean rectangle.
If necessary, relax face down and aim for a clean, flat plain.
Now work on the surface with a knife to smooth the curve and leave a nice clean cut on the surface.
So now we have a rectangular part, about 10-15% on the head, and slightly larger on the handle. We leave it dry. The wood is very dry, so 48 hours may be enough indoors. When it's dry, if I click on its stuff, it will ring, not UD, and feel beautiful and elastic. You can keep it for a month, make sure, but I'm always impatient.
What do you think about it when it's finished. This is a cheap old man, I don't know what mode it is, or where they are made, but I have such a pair of car boots that they don't seem to be common, and I like its appearance as a carved axe. Another old man will be the perfect replacement for a small forest axe for the budget. See how to install the axe handle here.