There are several ways to create a mechanical advantage when we need to move a large load with a small force. The popular Block & Tackle system utilizes load sharing on the load side of the system to reduce the force required to move the load on the side of the system where the moving force is applied.
From the definition of Work, W=Fd (work = force x distance), the same amount of Work will be done moving the load from point A to point B. The Block & Tackle system trades a smaller force on the line, that is running through the system, for a longer distance of line travel through the system to get the same job done.
Let's pretend that friction does not exist, and only consider the static (non-moving) state of the system.
This page was created to compliment the Gin Pole notes page, so the discussion is focused on the application of a Block & Tackle system to a Gin Pole. The basic principles apply to any application of this system.
Let's look at some diagrams of the sheave at the top of the Rohn EF2545 Erection Fixture when lifting a 10 Ft section of Rohn 45G. The diagrams are drawn to make the principles easy to see. In normal use the multiple lines between the load and the support would be run around coaxial sheaves mounted in a Block.
The force diagram on the sheave for a normally rigged Rohn Erection Fixture looks like this:
1:1 Mechanical Advantage
The load on the left side of the sheave (that's a funny word for pulley) is the 70 Lb tower section. The line on the right side is the one we pull on to lift the section. It takes 70 Lbs of force on the lifting side of the sheave to hold the 70 Lb load in equilibrium (or steady, not moving either way). It takes 70 Lbs, plus whatever frictional loads are in the system, plus a little more to make the load move up the tower. Since, the sheave has two 70 Lb forces acting downward on it, it needs to push up with 140 Lb to support the loads. This means the lifting system is applying 140 Lbs straight down on the sheave.
If we make the sheave part of a 2:1 system, the diagram looks like this:
2:1 Mechanical Advantage
The 70 Lb load is now shared by two lines which each carry 35 Lbs. This reduces the force on the lifting line to 35 Lbs, and now the sheave has 3 x 35 Lb loads acting downward, so it needs to push up with 105 Lbs to create equilibrium. The 2:1 mechanical advantage has reduced the lifting line force by 50% and the load applied to the top of the pole by 25%. This system requires two times the amount of line travel thru the system to move the load the same distance as the 1:1 system.
If we rig a 3:1 system, the diagram looks like this:
3:1 Mechanical Advantage
The 70 Lb load is now shared by three lines which each carry 23.33 Lbs. This reduces the force on the lifting line to 23.3 Lbs, and now the sheave has 4 x 23.3 Lb loads acting downward, so it needs to push up with 93.3 Lbs to create equilibrium. The 3:1 mechanical advantage has reduced the lifting line force by 66.7% and the load applied to the top of the pole by 33.3%. This system requires three times the amount of line travel to move the load the same distance as the 1:1 system.
4:1 Mechanical Advantage
If we rigged a 4:1 system, the 70 Lb load would be shared by four lines each carrying 17.5 Lbs. This reduces the force on the lifting line to 17.5 Lbs, and now the sheave has 5 x 17.5 Lb loads acting downward, so it needs to push up with 87.5 Lbs to create equilibrium. The 4:1 mechanical advantage has reduced the lifting line force by 75% and the load applied to the top of the pole by 37.5%. This system requires four times the amount of line travel to move the load the same distance as the 1:1 system.
This type of system has been used for ages to make the handling of large loads more managable, and in some cases, even possible. They can be quite handy for many Amateur Radio antenna and tower tasks.
As, is customary with everything on this website, I only offer comments to stimulate thought, and hopefully help fellow Amateurs. None of the information provided is authoritative in any manner or guaranteed to be correct. The reader is encouraged to research these subjects and make his own determinations about these things, before trying to apply them in the real world.