How efficient are 3:1, 4:1 and 5:1 pulleys?

We’ve always been taught that doubling a winch line back to the vehicle is a 2:1 mechanical advantage (MA), so if the force required to move the car is 1000kg then the winch need only generate 500kg. Similarly, for a 3:1 pull that same winch would only need generate 1/3 of the force required, or 333kg. The physics-minded amongst you will now be saying the correct unit is newtons, not kg, and you’re quite right but if you knew that you won’t need the explanation and may perhaps forgive my simplification. In the video below I explain a few configurations of rigging for MA:

What you may not know is how much efficiency you lose, and I can tell you as I’ve measured it. What’s efficiency? Well, pick up a snatch block. Turn the sheave (the wheel bit) by hand. Doesn’t take much to turn it, does it? But it takes *something*, takes some energy. Now spin that sheave. Does it spin forever? No. Friction, air resistance all conspire to slow it down and bring the spin to a halt.

Now take your rope. Hold it straight. Now bend it. Then unbend it. Doesn’t take much energy, but it does take *some* energy, same way as the flexing of a tyre as it contacts the road takes energy.

Some of that energy is lost as heat, and we can see this by looking a pulley as it is put under load. Check out this thermal-camera view:

So when a rope or wire goes around a pulley of some sort energy required, to turn the sheave and flex the rope. The amount of energy lost relative to the pulling force is efficiency. In a perfect world, a double-line pull would exactly halve the force required, so that’s the 2:1 MA. But the world has friction. I’ve done testing for various configurations of multi-line pull to find real-world figures for friction loss, and you can see the results here:

I then looked at the results and tried to create a formula to model pulley efficiency. It turned out to be harder than “just add 10% per pulley” because first off, is that 10% of the winch load, total load, or what, and in either case that simple solution doesn’t work.

Eventually I decided on a 60%-50%-40% rule for a double-line pull (2:1), a 3:1, and a 4:1 rigged as a Spanish Burton (see video for how that’s done. This means that say you have a 1000kg pull if you rig a 2:1 then your winch load would be 600kg, rigged as a 3:1 it’d be 500kg, and as a Spanish it’d be 400kg. Those numbers are conservative, but I feel reasonable based on my testing.

A reader sent me an army manual which had figures of 2:1 actually 1.8, 3:1 actually 2.5, and 4:1 actually 3.1. Those are in line with my results which are 2:1 actually 1.7-1.9, 3:1 actually 2.1-2.5, and 4:1 actually 2.5-3.4. The difference in equipment between the army and my tests is that I used snatch rings which are less efficient than the snatch blocks the army would have used, and they didn’t use a Spanish Burton for their 4:1, but overall the results have a close correlation. The lower numbers for my results are rings, the higher blocks.

Now if you really want to get technical here is the formula I did come up with to determine friction loss, but decided there were too many numbers for the video and it was too complex for an in-field guide. The 60-50-40 rule works quite well I think.