Yep, I stand corrected, you are all right regarding the necessity of the axe.
The axe is also great when you see a weepy, oozy, wound spot on the tree, Best to carefully chip away at it to inspect for metal such as an eye bolt or railroad spike, before cutting with the chainsaw.
.As a side note, Buckin Billy Ray has a 2 year old youtube video called "Tree Felling-Wedging, And The Importance Of Holding Wood". If you go to the 12:00 to 12:17 you get a real good look at his leather harness/tool belt. I wonder where he aquired that harness? All the ones I see offered like at Bailey's are the very expensive kevlar/nylon/cloth units.
Where'd he buy that leather set up?
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