For a boat to move through the water there has to be a force applied. One way to produce a force is to accelerate a mass.

You could move your boat by throwing baseballs over the stern. A 5 ounce ball thrown by a good pitcher will give you over 1 pound of thrust for the time from wind-up to follow-through. With that kind of force a small boat might gain very slowly against a 5 mph head wind. It works, but balls are expensive and it gets hard on the arm after a while.

Take a paddle or an oar and push a chunk of water faster than the water around it and you have the same effect. The acceleration is less and the mass is greater than the baseball scheme, but the force averages to about 3 to 10 pounds on a lazy day.

A propeller is in effect a bunch of paddles doing J strokes. Push water back through the water around it and your boat moves forward. The area and angle of the blades determines the size of the chunk of water, the mass. The acceleration part is a bit more complicated and involves pitch, the spinning speed of the shaft, and the speed the boat is doing. Put them all together and you get thrust.

In the old days propellers were called screws. The idea was that they screw into the water, but it was noted that the actual headway was always less than what would happen if it really was cutting through water. Prop people refer to this difference as slip, leading some people to think it should be avoided, but slip is what accelerates the mass. If you have a small propeller and spin it fast you can generate the same thrust as a larger propeller moving more slowly, you have more slip. You’d use more power with a smaller prop because friction increases four times as you double the spin, while the force just doubles. There are limits, but generally the best efficiency comes from a big prop turning slowly with just a little slip. You’ll never see these limits approached in a motor boat but in something like human powered submarines you might see a 24” prop powered by a half horsepower set of legs. That is where the quest for efficiency turns into an obsession. Hydro jets go the opposite way and connect 300 horsepower to a 6” impellor.

As your boat picks up speed, the prop has to turn faster just to keep up with the boat. When you are at cruising speed the prop blades are just kissing the water as it passes under the boat. The real work happens when a planing hull is trying to get out of the hole and climb up the bow wave. The engine is laboring, producing less than full power. The prop is struggling to throw as much water as it can as fast as it can, a good part it sideways where it does no good. A bit of air gets sucked down from the surface and a bit of vapour gets sucked out of the water, and this ventilation and cavitation just irritates the prop. But if all goes well, the nose comes down, the boat sits up on top of the bow wave and everybody is happy. If not, you have to turn back, leave Aunt Bertha on shore, and try again. Having to get the boat out of the hole and still cruise economically is a big part of what makes prop design and selection such a voodoo exercise.