"Everything should be made as simple as possible, but not simpler"
We can make simple calculations for this sort of thing, but the more we simplify, the less accurate they will be. You may recall that early calculations of steam plant horsepower were often made on the basis of heating surface. (or was it grate area?) By the time these were applied to traction engines, the art had been improved to the extent that a 10 nhp traction engine could probably produce at least forty brake horsepower.
However, for our purposes, a simple calculation that gives a rough idea of the power to be produced is probably close enough…unless you actually plan to put the engine on a brake later and actually measure the power?
So…people are worrying about indicator diagrams. Let's simplify things by assuming that we admit steam for the whole stroke. After all if we are trying to get maximum power we will go for a late cutoff. Let's also assume some pressures…we need to know the admission pressure, the intermediate pressure (or pressures for a triple), and the exhaust pressure..all should be absolute. Ok, so simple subtraction gives us the pressure difference across each cylinder. Don't bank on getting a vaccum better than 20" (About 5psi absolute) on a small plant
So apply the formula from Roy's earlier post for each cylinder, add the resulting powers together and you have a number. (This is also what Jason is suggesting.) This will be on the high side, since we did not allow for pressure drops across the valves or between cylinders. We also probably won't run at 100% cutoff! Note that things like cylinder condensation will not reduce the power when the cutoff is late, they just mean that more steam is used.
But bear in mind that you probably don't know how much power you will actually need for a given hull anyway. Any figures provided for driving the hull with a petrol engine are pretty irrelevant when comparing to a steam plant. This is because the steam plant will operate at much lower rpm, with a much larger and much more efficient propellor. So for instance the Leak compound, described in ME in 1983 and still available as casting, is recommended for boats over twentyfive feet long. My own back of an envelope calculations suggest that at the sort of pressure and rpm likely to be used this engine will probably produce about ten brake horsepower at the shaft. That does not sound like much, but if you check out the Steam Boat Associations register, you will see that plenty of people have successfully used this engine in boats that size and bigger. If you were going to substitute a petrol engine or small diesel you would probably need more than twice the shaft power to get the same performance, since the smaller high speed propellor would be much less efficient.
All this is by way of suggesting that comparing the proposed plant to others that are already working is probably a better way of deciding what hull size the engine can push than calculating the horsepower.
John