Hi Don,
Assumptions: Tree is hinged at ground level, it has been cut off!
Let T = tension in rope in pounds
W = weight of tree in pounds
H = distance from hinge (ground) to where rope is tied to tree as measured along the tree
Theta = angle between tree and ground
alpha = angle between rope and tree
L = distance from ground to the center of gravity as measured along the tree,
this is the point where a cable attached to the tree could lift it in a balanced position????????
Sum torques about the hinge (butt of tree)
T = L*W*cos(theta)/( H*sin(alpha))
Checks: IF theta = 90 degrees the tree will fall over Thus T=0
IF alpha= 90 degrees the tension is a minimum
The larger H the smaller the tension
Hope this helps,
Mitch
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