That formula has served riggers well. I works. It gives the right answer. It is based on the laws of physics.
The problem is not with the formula. The problem is with identifying whether a pulley is fixed or is moving.
A couple of people have explained why a pulley attached to a tree can be a moving pulley. It isn't a moving pulley in the first photo in that "Expedition Portal" article because the end of the cable is not attached to the same vehicle as the winch. It would become a moving pulley if the cable end went back to the vehicle.
This article offers another explanation of why an apparently fixed pulley behaves as a moving pulley.
Simple Machines -- Mechanical Advantage
Here are examples where the fixed point is not obvious:
A man sits on seat that hangs from a rope that is looped through a pulley attached to a roof rafter above. The man pulls down on the rope to lift himself and the seat. The pulley is considered a movable pulley and the man and the seat are considered as fixed points; MA = 2.
A velcro strap on a shoe passes through a slot and folds over on itself. The slot is a movable pulley and the Mechanical Advantage =2.
You are quite right in saying that a single fixed pulley offers no mechanical advantage. That has never been in dispute. The issue is that it is not always immediately obvious whether a pulley is effectively fixed or effectively moving.
One reason riggers can rely on the formula you mentioned is because the way cranes are used does not resemble the way a winch can be used on a vehicle.
If the cable goes from the winch, through the snatch block and onto another tree or another vehicle, that is like a crane (except that things are horizontal, not vertical).
The only way a crane setup could duplicate the common 4WD setup where the cable comes back to the winching vehicle would be if the crane was attached to the load it was trying to lift with the cable through a single overhead pulley. I don't believe that a crane would be likely to be used like that, so that the crane goes up with the load. I have searched a lot of rigging documents and have never seen a crane set up like that.
I can't think of a situation where a crane would be used where there would be any confusion about whether a pulley was fixed or moving. However, there are obviously situations where people could be confused about whether a pulley was effectively moving or not.
That is why I offered that alternative way of calculating MA. There is no problem with the formula. As you say, it is based on the laws of physics. The problem is with understanding whether a pulley is fixed or moving. In the world of rigging and cranes it is obvious . Unless a crane was bolted to the load it was lifting, it will continue to be obvious whether the pulley is moving or not. In some other situations, such as the two in the article I quoted, it is not as obvious.
That alternative way of calculating MA avoids the need to understand whether a pulley is effectively moving or not and that is obviously not as easy as you might imagine.
The formula works as long as you know whether a pulley is effectively moving or not.
The argument is not about the laws of physics or the formula that riggers use. The argument is just about whether a single pulley attached to a tree can be effectively a moving pulley.





Keeping it simple is complicated.
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