Expert: James J. Kovalcin - 11/5/2009

Question
Hi James,
This is a question I have often wondered as I do a lot of sailing. When sailing we use block and tackle systems to enable ropes to be pulled. One such system for instance has a 8:1 system attached which allows the sail to be pulled on with one eighth of the effort. My question is does the diameter of the pulleys used have any bearing on the mechanical advantage achieved? Anecdotally I would have thought yes as I have used both small and large diameter pulleys and the large always seem easier to pull on. The guy in the sailing parts factory tells me otherwise though.

Thanks,
Reg

Answer
In principle it is only the number of pulleys that matters. However, that completely ignores the reality that friction matters as well. A larger, well constructed pulley [block and tackle] will waste must less energy that a poorly designed small pulley system.
In addition, the thickness and stiffness of the rope matters as well. If the rope is stiff it will be much more difficult for it to bend around a small pulley that around a large diameter pulley. Any extra effort required to bend the rope to the shape of the smaller pulley will be energy wasted.
I think that your sense that a larger pulley is easier makes sense. [However, I can also imagine a point where a larger pulley wheel begins to be more of a problem as well!]