Building an Aligator

[f350ca]

Need to do some actual engineering design work now, and would like some input on paddle size.
My thought is paddle size would be based on the boat sitting stationary and applying steam pressure to the engine to get it moving. Too much paddle area and you won't move the paddle through the water, too small and you won't get enough thrust to move the boat at a reasonable acceleration.
The dia of the paddles will be 8 feet. That gets the shaft at deck level and the bottom of the paddles even with the bottom of the boat.
Rotational speed would be set to give hull speed plus a certain amount for slip. How much slip?
Once the speed is determined I can calculate the torque available at the paddle shaft based on the bore and stoke of the steam engine and boiler pressure.
So for a given torque and a 4 foot arm how do I determine how much area on the blades can be moved through still water at startup?

Any thoughts would be appreciated, there's not much in the way of engineering formulas out there on the net for paddle wheelers, wonder why?