falling 101

[smokechase II]

lever arm drawing

Jpeg for reference attached.

 

[moray]

Originally posted by juststumps
...driving a 1" wedge into a 17" cut is easier than driving a 1" wedge into a 12" cut...

Then Moray's response: "With all due respect, juststumps, these two statements flatly contradict each other."

**********************

Moray; I believe Juststumps is correct.
All other things being equal, face - hinge - wind - lean - wedges etc., the closer a wedge is to the hinge the harder it is to drive.
If Juststumps is driving wedges at the very back center of the back-cut in both instances the longer distance is a longer lever.

What we have here is an incline plane lifting a lever. [EXACTLY]

The incline plane requires less force to drive if it is working with a longer lever. [EXACTLY]
The bottom of the butt log in the back-cut is [one arm of] a lever. [EXACTLY]

Besides the sloping back-cut being more work to make, if wedged its tendency is to push the tree off the stump (break the hinge) rather than pivot at the hinge.

He also said: ".....the only mechanical advantage you are getting is in driving the wedge....." The reason I called this a contradiction is there are two sources of mechanical advantage: the wedge itself, and the lever arm length. You and I seem to agree perfectly in every detail. By the way, smokechase II, nice diagram. Also, please pardon me for inserting notes in your quoted remarks (square brackets).

I measured the slope of one of my wedges--about 5.5 to 1. That's its MA, and it's favorable. The MA of the lever is very much against us. The center of mass of the tree might be 50 feet in the air, but the lever arm from wedge to hinge might be 18 inches. We are trying to move the long arm of the lever (50 feet) with the short arm (1.5 feet). That's a MA of 1:33. With a sloping back cut of 45 degrees, the short arm becomes about 2.1 feet. This would improve the MA to about 1:23, which, of course, is why it is easier to drive the wedge.

Loosely speaking, the hammer is another source of MA. Otherwise we would just leave it at home and push the wedge in with our hands.

 

[windthrown]

Amusing thread. As a semi-retired (or is it retarded?) engineer, I think that a flat cut is more stable, and seems to hold a wedge better for falling. Wedges can and do weird things. They seem to float around more in angled back cuts, and vere sideways. They also tend to force the grain apart in an angled back cut, spliting the stump open more, which gives them less leverage.