My only point here is that you can apply engineering standards only so far, but if there are variables that haven't been accounted for, your engineering solution isn't going to be accurate. You might acquire enough of an estimate, however, to state that your peavey handle is more than strong enough to prevent any man from breaking it.
Sure, that's what engineering is all about -- having the experience and judgment to recognize what to disregard and knowing when to stop over-analyzing.
Now if you were engineering a peavey for the minimum weight handle for a 180lb man that can apply no more than 150lbs of lift, then you would need to start working up some pretty sophisticated math to accommodate that tapered handle. Otherwise, just overbuild it, and count on it lasting.
Strawman. This is the first mention of minimizing weight. But as I said in previous posts, the math is not at all that difficult. If minimizing weight is the goal, rearrange the formula I provided previously to solve for diameter (D) and plug in several evenly spaced values of d (the moment (lever) arm length). Plot the D vs. d and you have the an approximation of the minimum weight taper. You can get as close as you like to the ideal by increasing the number of points. Doesn't require anything beyond 9th grade algebra.
If you want an exact solution, you need 12th grade differential calculus. Still not difficult.
You can bet good money that the originator of those tools never spent a moment doing any math to figure out how thick to make the handles.
Almost certainly true for the earliest versions, but I wouldn't be so confident that someone didn't run the numbers before they were produced in quantity. Bangor was not some sleepy backwater full of clever but uneducated rubes at the time we're discussing. There was lots of manufacturing supporting the lumber mills. Steam engines; water power, sawmill, logging and textile machinery; automobiles; machine tools; and ships were all manufactured in the area. I'm sure there was someone capable of replicating the calculations I spent a half hour on.
The Maine State College of Agriculture and the Mechanic Arts (now the University of Maine) was 5 miles up the Penobscot from downtown Bangor.
"By 1860, Bangor was the world's largest lumber port, with 150 sawmills operating along the river. The city shipped over 150 million boardfeet of lumber a year, much of it in Bangor-built and Bangor-owned ships. In the year 1860, 3,300 lumbering ships passed by the docks." (Wikipedia)
