Re: Bow lift, Planing speed, and number of blades.
The advertisement for a particular prop usually tells you what it is designed for.
Bass Boat props got a lot of attention because of the multitude of the design having a desire for high speed......beating your buddy to the honey hole. Other thing was these boats had hulls that were shaped such that the boat would ride on only a very narrow part of the hull called a "pad". This helped the top end but hurt the hole shot because you didn't have a flat bottom for transom lift.
Props were tweaked with material...thin blades for better speed and strong materials for resistance to damage; bending the blades back referred to as "rake" that helped to lift the bow and get the boat on the pad once underway; cupping which was the slight bending of the trailing edge of the blade to help in holding onto the water better since the engine was usually mounted as high as possible to reduce the LU drag; and increased number of blades for thrust enhancement since BBs had a large mill hanging off a jack plate, plus the jack plate, plus 3 size 27 batteries and a 20 gallon live well and 30 gallons of fuel plus a couple of 200# guys, all in the rear half of the boat.
On the number of blades just think about it. If you only had one blade and you were running at xyz rpm, you would only have one paddle connecting the engine to the water. The prop design specs would dictate the diameter to pitch ratio for a given job (area of the blade). Since horsepower wasn't an issue (250 hp on an 18' boat), the more blades the more paddles you had to push through the water and the better your thrust when you needed it the most. Problem was that once you were up and running, the blades competed with one another for clear water to push and reduced the efficiency of each blade.
So they came up with another trick and that was to reduce the number of blades but to deliberately put holes in the prop (porting) which would force exhaust gasses over the blades when you needed the most thrust (hole shot). The gas would reduce the density of the water flowing over the blades and allow the engine to wind up much faster. Since RPM is one element of the HP equation, the faster you could get it to wind up the more power you had to turn your prop and the hole shot was faster.
Then, when you were up and running and didn't want that extra blade or two in your way, your holes would close off and you had the best of both worlds.
Then there are stern drives which do not have all these restraints and are usually stern heavy so that requires a different design and then you have the barge engine, or the tin fishing boat with the tiller engine with yet other variables.
On the force vector, there is a variable and that is the fact that the water is not a solid. It's called slip and it interferes with the application of the force vector i.e. thrust.
That's the way I see it. QC and MrDHadley are more versed on this than I as they have professional experience in the area.
Mark