Calculating the correct Propeller (or Wheel) pitch can be quite simple. There are a couple things you should know first. Maximum desired engine speed (RPM) at hull speed, which on most steam driven boats this is equal to propeller speed unless a reduction drive or gear box is being used. Hull speed is the next part of the equation you should know.
As most of you know already propellers are almost always advertised with two measurements. So if you had a 3" x 4" propeller. This means it is 3" diameter and 4" pitch. Now picture these measurements like a thread on a bolt, the pitch tells you how far it moves in 1 revolution. E.g. a thread with a 1mm pitch will move into a hole by 1mm in 1 revolution of the bolt. So with a propeller, given there is no resistance, as the propeller turns, it will push its self through the water, 1 revolution giving 4" of forward motion in this example.
Calculating Prop Slip
Unlike a threaded bolt being tightened in to a threaded hole, propellers will slip in water when there is resistance. The source of this resistance is called a boat. Although a propeller does 1 complete turn, instead of traveling 4" it may only travels 3". Working out the propeller slip is very straight forward. You need to know your propeller speed and hull speed. In the ideal world, you want 0% slip. In reality, anywhere between 10% and 20% would be acceptable, but on the smaller steam launches you can often find the slip is as much as 25% or more.
For example, the hull is doing 3mph and the 3" x 4" propeller is doing 1000 rpm.
1000 rpm x 4" = 4000" a minute.
3mph = 3168" a minute.
3168 / 4000 x 100 = 79.2% (This is the % of used thrust.)
Thus 100% - 79.2% = 20.8% slip.
How to choose the correct prop
This can be a lot simpler than just having to guess. The important thing is to know your engine speed which is the same as your propeller speed when using a direct drive. This will have been for the most part designed into the engine. So if the maximum recommended RPM is 1000, it is best to aim for that. You should also work out your hull speed.
Calculating Hull speed
Hull speed (knots) = 1.34 x Square Root of (Length of Water Line in feet)
1 Knot = 1.150779 mph
E.g. for a 3 foot boat, the hull speed is:
Hull speed = 1.34 x Sq Rt(3 foot)
Hull Speed = 1.34 x 1.732
Hull Speed = 2.32 knots = 2.67 mph.
Say you calculated a running speed of 3mph, and you want to aim for 15% prop slip, all you do is calculate the correct pitch.
Adding this into the calculation:
So if 15% is the target slip, that means that there will be 85% of useful thrust.
3mph = 3168" a minute.
"Pitch Distance" = 3168 / 85 x 100
"Pitch Distance" = 3727" a minute (This is the distance the propeller would move with 15% slip.)
"Pitch Distance" / RPM = Pitch
3727 / 1000 = 3.73"
Meaning the pitch required is 3.73".
You may want to go for an 4" pitch in this case, since it is usually better to have the engine producing slightly slower RPM's with the larger pitch than slightly faster with the smaller pitch. This greatly reduces steam consumption thus extending running times.
Propeller Diameter
In most cases for steam engine powered boats, the bigger the better (within reason). The larger the propeller the better their efficiency.
Historically Steam launch propellers generally have 3 large blades although four blades have become common over the years. This also adds to their efficiency as we are not running them at high speeds. As long as the pitch is suited for the engine speed and hull speed, you shouldn't go far wrong.
Typically for steam powered models you want to try to fit the largest diameter propeller possible that the model will take. While pitch is closely related to hull speed and final desired engine rpm, finding the correct diameter of a propeller is closely related to the torque output of your engine.
How far down the rabbit hole do you want to go?
Currently I am running experiments with my own steam models that closely relates to the subject of finding the correct propeller size and pitch.
As I mentioned, propeller diameter closely relates to the engines B.H.P. & torque. The method I'm choosing to use for determining final torque output at a desired final engine rpm is through the use of a "type" of "Prony Brake". For my own personal purposes, I am picking a desired steam output pressure (let's say 60psi) that I would like my boiler to maintain while operating at the desired final engine's rpm's (let's say 800 rpm) while moving through the water at hull speed. The boiler's required heating surfaces will then be calculated to maintain the desired rate of steam production. To find the engine's final torque output the "Prony Brake" will be used to apply resistance to the engine thus slowing it down until the rpm's reach the desired final rpm's. A final torque output reading will be calculated by taking the information gathered through the experiment. The torque output will then be used to calculate the most ideal diameter propeller and pitch for my personal steam launch model. I'll get into all the math required for determining the correct propeller diameter at a later date since most of you will not know what the final output torque of your engines will be anyways. Most model steam engine manufacturers don't even know it.
Conclusion
There is a lot more to it than what I have added above regarding finding the correct pitch and diameter propeller for a STEAM MODEL but this is meant to be just the basics for getting you close to choosing the right prop. If you would like to really go overboard regarding learning all about sizing propellers than I would recommend finding a copy of Dave Gerr's Book: Propeller Handbook. You can find copies on Amazon for reasonable prices. This book is considered by most in the full size boating community to be the Bible on propellers.
