Tuomas Pöysti 2020
As we know, pulley efficiency has more to do with sheave/rope diameter ratio than bearings, bushings or other technical nuances of pulley design.
To get rid of any doubts considering potentially different bearings on commercial pulleys of various sizes, I built a pulley with interchangeable sheaves. The sheaves range from 20mm to 80mm in diameter.
The sheave sizes follow a geometric series: 20, 28, 40, 56, 80 mm. The groove profile is copied from Rock Exotica Omniblock 2.0. The sheave material is acrylate polymer, 3D printed.
Here are results of a test series (@1kN):
Efficiency plotted against sheave diameter:
Mr. D. Reeve, someone I’m happy to consider an Internet friend of mine, noticed something about the curve. If we assume the force difference between the sides of the pulley is directly proportional to force and inversely proportional to sheave diameter:
F’ = kF/D
Then pulley efficiency is
e = F/(F + F’) = F/(F + kF/D) = 1/(1 + k/D)
1/e = 1 + k/D
If we now plot 1/e against 1/D:
The plot is linear. Additionally, if we fit a trace curve on the data, we get something like
1/e = 0.98 + 6.21/D
How beautifully close to the theory, with k = 6.2. Parameter k will of course vary with rope diameter and material at least.
Thus, we can quite safely conclude that pulley efficiency is a function of sheave diameter.