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I'm thinking a wider blade, reduced diameter prop is more efficient.
Actually quite the reverse, a larger diameter propeller will usually be more efficient, as the swept area is one of the major factors in propeller design. the power is transferred over a larger swept area reducing the load per blade area. a blade thats having to work hard will often come close to cavitating, which is one of the largest losses a propeller can have!

Another is the rotational momentum imparted to the water from the spinning 'disc', which is a function of the blade lift/drag coefficients and RPM. an ideal blade is one with a high Clift and a low Cdrag, but this is nigh on impossible! lift cannot be created without drag, so a highly loaded propeller will have a high Clift, but also a high Cdrag, which decreases rotational efficiency. you also have to turn a smaller propeller faster, which results in more rotational losses.

another way of thinking of it is this: A large merchant tanker will often have a very large propeller turning at less than 100 RPM. They will often design the stern frames of the vessel to accommodate the largest propeller possible! vessels like this are all about efficiency!
Source: Currently a masters student in marine engineering :)

ps. I know this is my first post, but I have been reading sailnet for some time and thought I could help!
 

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Makes sense. Would cavitation limit maximum tip speed as is there a point where increasing the prop diameter for a given working RPM starts to reduce the efficiency?
Essentially yes, although cavitation is not caused directly by the speed of the blade, but the local pressure in the fluid surrounding the blade. When this pressure drops below that of the vapour pressure of water, the water effectively boils to form the bubbles. The tip creates a vortex from its trailing edge, and at the centre of this is an extreme low pressure, but by increasing the diameter of a similar propeller, you decrease RPM demand and increase the torque required to transmit the same power.

A well designed propeller will probably have a 'lightly loaded' tip, both to reduce blade stress and reduce the possibility of tip vortex cavitation. I should also say that the vortex is a necessary part of the blade's lift generating capacity, and is always present at any RPM, but the pressure may not be low enough to cavitate.

I recall reading that during the initial development of the screw propeller way back when that the boat speed increased when the tips of the blade broke away during trials, and I've always wondered why this was so.
I think the story you are thinking of is the development of the first propellers, which were originally a screwthread type of two full turns. full story at the link below.

https://en.wikipedia.org/wiki/Propeller#Screw_propellers

Sheldon
 

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Its not the number of blades that has this effect, its the blade/swept-area ratio. A propeller could have a huge number of narrow blades and have the same blade area as a 2 bladed prop with wide blades. the reason fewer but wider blades are preferred is to reduce the surface area of the propeller (viscous drag of spinning it in water) and to evenly distribute the pressures over as large an area as possible (reducing cavitation and reducing root stress)

I suspect that for your application (sailing yacht) wider blades would detract from sailing performance, however if you were looking only at propeller efficiency... there are several methods of optimising all the parameters of a propeller (and there a quite a few of these, see link below!)

If you ever wanted to know more about the powering calculations that designers and engineers use, I would suggest you read some of this (it is a huge resource written by several of our professors):

Anthony F Molland_ Stephen R Turnock_ Dominic a Hudson-Ship Resistance and Propulsion _ Practical Estimation of Ship Propulsive Power-Cambridge University Press (2011)

Chapter 12 onwards relates to propeller design
Its not aimed at the general public, and it gets very technical so if you have questions, PM me :)

Sheldon
 
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