Sumner and Flynfol, thanks for the discussion (and the spread sheet), I learned some things here.
I have to correct something I said "
The thrust must be traveling backwards faster than the boat is going so no matter what the prop pitch"
As the boat moves through the water, it must accelerate backwards some mass of water in order to move forwards. But the water accelerated backwards from the prop just needs to exit faster than it came in in order to get forward thrust. For example, if the boat is going 20mph, the water exiting the prop needs to be moving at 24 mph going out of the prop relative to the boat (ie, the water was accelerated by 4 mph by the prop). The water coming out has been accelerated backwards as the boat moves forward (F=MA). The slippage referred to earlier is a measure of difference in boat speed to "prop actual travel" so slippage is necessary in order to get thrust.
From the quote below "prop slip is NOT the same as propeller efficiency" and I think this is correct. Interesting to note about the term prop slip is that it to some extent tells you how efficient a boat is at traveling through the water. For a very efficient hull (like light planning powerboat), it takes relatively little mass*acceleration to propel the boat so I think you would get a low slippage percent number - ie, the speed of the water coming out of the prop is not much faster than the speed going in. A larger diameter prop would accelerate a larger volume of water so might also reduce the slippage number.
As you get to a more inefficient planing hull (like Mac M simply because of its size/weight and relatively small motor), you need to accelerate more water to make the boat move so the speed of the water exiting the prop increases compared to the speed going in. Ie, you have a higher slippage factor. Again, "prop slip is NOT the same as propeller efficiency" so no problem.
In the displacement hull where you are pushing up against hull speed and with a small outboard (and small diameter prop), you may need to accelerate water out of the prop a lot faster than what is going in to get the necessary M*A to move the boat. This pretty much matches what I see with my outboard where the water coming out of the prop looks like its moving a lot faster than the boat is. In this case, the displacement hull is operating at a relatively high slippage percent. Yet again, "prop slip is NOT the same as propeller efficiency" so this is OK - just the way a displacement hull with a small outboard works - and works fine.
If we were to just look at prop efficiency, Fylnfol suggested that a highly loaded foil moving at a slower RPM (ie, high pitch number) might be more efficient than a lightly loaded foil (lower pitch number) moving at a faster RPM. Plus, the outboard would be operating at a lower RPM. I cant back this up with a reference but also believe this is likely true.
The problem is that is that the high pitch number tends to operate at lower RPM for the same amount of thrust so in some cases wont allow the outboard RPM to get up to levels where the outboard is putting out its rated HP. If you want the outboard to get to its peak RPM power band for a given boat speed, you need to go to a lower pitch prop. The prop calculators give you a ballpark for this.
However, in the case above, we went to a lower pitch prop operating at a faster RPM so we could get more HP delivered because of the higher outboard RPM. But we also (according to what Flynfol and I think) went to a less efficient set of foil conditions. We noted that with a boat like a 26S and a 9.8 hp outboard, you "normally" don't need the peak HP so the trade-off was questionable.
The "high Thrust" 4 blade prop I have now I think will allow me to punch out a lot of water when the boat is going slow because it will allow the outboard RPM's to get up into the power band. This prop will also likely get max hull speed out of the 26S at full throttle as it should allow the outboard to get into a better power band. But I think it will not get as good of gas mileage when I run it on long trips because its lightly loaded with lots of blade area (high parasitic drag) and generally higher RPM's. Most of the summer, I use maybe 2 gallons of gas total so the efficiency wont be an issue and the high thrust will be nice to have (and fun to have) for most of the things that I do such as motor around the lake a little and for docking. Sumner said I will like this prop, I think he is correct.
But.. maybe if I get a spare prop, it might be a high pitch one and if was trying to squeeze the gas mileage, I could swap to this prop for my trip where I motor a lot and have limited gas.
One final thing.. for a given prop diameter, it must accelerate some mass out the back end in order to propel a boat at some speed. The speed of the mass determines the slippage number. Note that no matter what pitch of prop you use, you have to accelerate the same mass out the back so the slippage number is independent of prop pitch. No problem once again because "prop slip is not the same as propeller efficiency".
The quote from the web site Sumner referenced is below:
Prop slip is a measure of how efficiently the boat is going through the water. Prop slip is not the same thing as propeller efficiency.
If the prop did not slip at all as it screws through the water, each rev theoretically propels the boat the forward a distance equal to the prop pitch. (a 15 inch pitch prop theoretically propels the boat 15 inches in one revolution). The propeller revolution rate is the engine rpm divided by the gear ratio. This propeller rpm times the prop pitch determines the theoretical distance that the boat should have moved in one minute, which can be converted to a theoretical boat speed in miles per hour. Due to prop slip the boat is actually going slower than the theoretical speed. Normally on the nature of 10 to 20% slower at top speed. This ratio is found by dividing the actual boat speed by the theoretical boat speed to get a ratio. Then, this ratio is subtracted from 1. The result is the propeller slip. In real life, you also have to do a number of unit conversions between hours, minutes, miles, feet, inches, etc. All of these calculations and conversions are done for you internally in the RBBI Prop Calculator.