Per (W)-Weight at a given (A)-Angle of
line bend; a specific line (T)-Tension is achieved.
Per specific (A)-Angle, there is a specific leverage
multiplier, to multiply by the (W)-Weight that will give the leveraged
rope (T)-Tension.
Below is a spreadsheet calculator, that you can change the weight in
the 1st yellow shaded area, to see what a line bearing that weight, will
raise the line tension to. This will pull on each of the 2 line
support spars etc. As anything else, pulling along it's length, is
not a leveraged angle, so the line tension is the same as the load.
But pulling across/perpendicular to the line (as pictured), leverages
the line. Now the line tension is a multiple of the load, so the
given angle, is a leveraged multiplier.
A) At 150 degrees, the
line tension, pulling on each support; is ~ 2x the load; after that
the leverage multiplier rises sharply.
B) At
120 degrees, the line tension is equal to the load, so the supports
don't share the load, they both carry the equivalent of the load.
C) At Zer0 degrees (a tight 'U' shape), the line
tension is 50% of the load, so now, the 2 supports each only carry
1/2 the load a piece. Pulling 1 end of the line, gives
2/1 power on lifting the load. That advantage would dwindle
down to breaking even at 120 degrees. At 150 deg. the effect
has inverted, you are pulling 2x the load to lift, above there it
gets intense quick etc.!
Non working picture of the above
calculator/spreadsheet.
example: User enters 400# in the
yellow shaded box, and sees that at 150 degree line bend, the line
tension is 772.7# that pulls at at each of the 2 line supports.
These numbers are generated in
rigging, pulling, speedlining, sweating a line tight, even bending
the tiedown line(s) to your dirt bike properly will secure it more
with higher tension! etc. daily. These numbers can help,
hinder, cause a line to snap, a support to give, a control man to
get over powered by pull etc.
This is why heavy power lines are hung with slack!
Theoretically, the line tension is infinite on real loading in
center of a line sitting at 180 degrees flat, so the line will
always bend out of that range when loaded. This is no magic,
it is a mathematical equality. At 120degrees, the line tension
will equal the load etc.
The weight of the load hanging on the system,
empowers the chain of forces, through the multipliers of:
Angle (A) of the bend in line gives leverage on the line; so is
the first multiplier of the weight. This increases the
line tension as spreadsheet shows. Angle (B), is how
leveraged an angle the spar receives that line tension.
Just like the line, pull down the length is not leveraged, a
pull directly across/ perpendicular to the spar, is most
leveraged. So Angle(B) induces another compounding
multiplier, onto the leveraged line tension, against support.
The Length from the hitch to the ground, giving final,
compounding multiplier.
So the total force is Weight X AngleA factor X AngleB factor
X Length factor.
Notice, that the leveraged line tensions, then in turn apply that
tension to each support In top picture), pulling across. Once
again, like the line, if the loading is down the length of the spar/
tree it is not leveraged; but line pull will be at an angle.
Now, the force of the weight /load in the bend of the line gets
multiplied by the leveraged angle of the line, then again multiplied
by the leveraged angle of pull placed on the spar, then that
multiplied by the leveraged length to the ground of that spar from
the tie in point! That is one way to get into trouble quick,
stacking these multipliers etc.! This is visualized as a
pulley floating on the bend in the line, carrying the load.
But, it would be all the same, for separate lines, per their angle!
8/1/4 (Always Under
Construction & Expansion!)