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I thought that pitch more directly affected thrust while diameter affected slippage, and ultimately speed for a given RPM.
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1. Yes, pitch more directly affects thrust,
2. No, diameter does not more exactly directly affect slippage, that's really more the function of rake and rake progression, although diameter does have an effect. "Cupping" a prop is nothing more than an abrupt change in rake progression at the outer edge of the circumference of rotation.
3. Yes, pitch has a more direct effect on thrust and speed (which are not the same thing) than diameter.
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wouldn't the 5.4% improvement be applicable to the slippage percentage of say 7% for example, leading to only a possible 0.38% improvement in speed?
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The improvement is in thrust, not speed. The question then is how much of the improvement in thrust is lost because of slippage, and how the ratio of slippage is changed by the difference in diameter.
If I figure this right, assuming the slippage for the new prop is the same rate as before, (let's use your 7% number), then 7% of the improvement in thrust is lost to slippage, making (before all other relevant calculations are figured in) a NET thrust improvement of 93% of the total.
But don't forget, a change in diameter also makes an effective change in total rake, rake progression, angle of attack/entry, etc. It's a rock in a pond thing.
Unfortunately, I don't know how to figure all that out. I don't do math well, so if I have unwittingly inserted a fallacy here, I apologize.
I do know this, back in the 80's, when I was driving the Excaliber and Scarab boats for Wellcraft to prop them, as drivers we looked at diameter as more of a turbulence factor than a thrust factor.
Our "idiots rule of thumb" was to keep 1/4" of clearance to the cavitation plate PLUS about 1/8" for each increment of 10kts of speed to minimize ventilation and turbulence up to 40 kts, and an additional 1/8" for each 20kt increase above that. Get too close to the cav plate and the prop tip will ventilate, losing thrust. We focussed more on shape, length, and rake for the blades, and just used rule of thumb for diameter.
But every now and then, the engineers and we drivers would be stumped or baffled.
Like the case of the Wellcraft 23' Aruba. It actually ran 6-7 kts faster and used almost 10% less fuel at cruise rpm with a 4-blade surface piercing cleaver propeller, than with the Mirage II prop we finally gave it. It just was an absolute pig to plane with the cleaver (nearly 7 seconds). Yet our experience and the slide rule people said the cleaver should not have worked at all. Sometimes you just don't know.
If you want more detail about all this, contact PowerTech. When I ordered a custom prop for my Seafari, their engineer gave me a dissertation on the physical science of propeller application technology for an hour. The end result, though, was I got a great custom prop for my boat.
