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A mild convex grind will provide the greatest strength in the blade.
Andy, you still have to wonder about a few things... first, did Sears design the knife linearly? or did an existing specimen influence his knife?
What is "thin"? He, as you said, clearly disapprove of heavy "bowie" style knives but those ran the gamut from 1/4 inch and a hair, down to 3/16th or a little less.
Lastly, how long was his original knife. If we are to believe the illustration, then you can start with the moose pattern: a big moose patten of the day would measure 5 1/5 inches closed, compare that with the axe handle and the nessmuk. On my screen, the moose measures 2 7/8 (2 and 14/16ths or 2.875), the nessmuk 4" with a blade of 1 11/16 (1.6875) , and the axe handle 4 7/16 (4.4375).
So...
"if" the moose pattern folder is a 5 1/2" closed knife, the scale is 1: 1.869
Thus the axe handle as pictured is 8.29 inches in length
the nessmuk is 7.47 inches in length with a 3.15 inch blade...that sound small.
or was the entire engraving "out of scale"??
All of your questions are outside of his writing, and drive us into theory.
His "light thin knife" of just over 7" is very small to me..A knife made of 3/16" and 9"-10" long is only a medium sized knife to me..