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# Pulleys: where is the friction?

We know that a good, relatively big pulley used with a 11mm nylon rope is actually only about 90% efficient. That is, 10% of energy is lost somewhere around the pulley. And a smaller pulley will lose even 20%.

For example: if a 100kg weight is lowered 10m distance using a descender, the descender has to transform 10m * 9.81m/s2 * 100kg = 9800J of potential energy into heat.

But if we put a 80% pulley between the descender and the load, the descender will need to deal with 80% of that only. The pulley takes care of the remaining fifth of the energy, 1960J.

To get some perspective, let’s study what this amount of heat is capable of doing.

## Do pulleys get hot?

Petzl Partner is a little pulley that is known to have about 80% efficiency used with an 11mm rope. It weighs 56g. Let’s assume Partner is completely made of aluminum. The specific heat capacity of aluminum is about 900 J/(kg-K). This means that 900J is capable of increasing the temperature of a block of one kilogram of aluminum by one centigrade.

Or that 1960J is capable of increasing the temperature of all-aluminum Partner by 39 centigrades! This means that starting from room temperature, Partner would actually get hot, not just warm. By the way, factoring in the fact that Partner really has some steel parts in it would make things even worse, because steel has way lower heat capacity than aluminum and thus gets even hotter with the same amount of heat.

## Bearing efficiency

No, actual bearings are not that inefficient. Most bearing manufacturers, including SKF, have nice online calculators.

Let’s assume we have a pulley with 50mm sheave, which has two SKF 607/8-Z’s as bearings. A rope takes a 180 degree turn in the pulley, and on both sides there are 250kg weights. This means 500kg radial load, 250kg per bearing. According to the calculator, a loss torque of 126Nmm per bearing is expected.

Measuring the sheave radius at the rope’s center axis, this moment corresponds to total friction force of 8.3N. And the rope was tensioned by a 250 kg weight, which means about 2450N. The calculated bearing friction is thus 8.3/2450 = 0.0033, in other words, in this application, the bearing duo is 99.7% efficient.

And THIS is the real level of efficiency of rolling bearings. If that was not the case, cars would need a serious cooling system for the bearings alone.

## What then?

The following is a bit old data, but still valid. I measured efficiencies of a bunch of different pulleys I owned back then. They were

• Petzl Rollclip 18 mm
• Petzl Partner 28 mm
• Camp Tethys 28 mm
• Petzl Pro Traxion 38 mm
• Camp Big Pulley Mobile 50 mm
• Rock Exotica Omniblock 2.0 51 mm
• Rock Exotica Kootenay Ultra 56 mm
• Rock Exotica Omniblock 2.6 66 mm

I tried different loads also, but that’s not the point. The general deviation of values is interesting:

Sure, there could be a correlation between sheave size and bearing quality. But it is highly unlikely the correlation is this systematic. Actually, the 50 mm value (belonging to Camp Big Pulley, of course) just might show the effect of poor bearings (or bushings). But the effect is not a game changer, just a little bump on the road.

## Conclusions

There clearly is a connection between sheave size and pulley efficiency. To be exact, not just sheave size but rather ratio between sheave diameter and rope diameter. I’ll show this in other articles.

So, even the best bearings won’t make a pulley with a 30mm sheave 90% efficient, if it is used with a 11mm rope. And the pulley will not heat up as if the friction happened inside the pulley itself. It is rather self evident that rope is an integral part of the friction.

Therefore, we should never talk about “pulley efficiency” as such, but rather efficiency of a pulley-rope combination.