AKKAMAAN
ArboristSite Guru
I think maybe this is wrong..
If you are swinging the shorter axe with "x" energy to achieve an axe head speed of "y".. lets say 200fps. With a longer handle, still swinging at "x" energy and achieving 200fps at the 28" point on the handle, the axe head is now 8 inches farther out in the arc, it HAS to travel faster to get there at the same time. So mass times velocity squared says the longer handle has more potential energy from the same swing..
You are assuming that a certain fixed energy input, will maintain the same angle velocity no matter what the length of handle it is....
That wont work, because the longer the handle, the more "resistance" it will be from MOMENT OF INERTIA...
Let us say you swing a 4.25lbs mass at a radius of 40" at 0.5PI rad /sec (90 degrees/sec).....
Do you think you can maintain that angle velocity with a radius of 80" (or what ever longer than 40"), with out adding more energy???