BOATS.

Model boats. Displacement in lbs. / swept volume (cu ins) = 65 to 65
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For full size boats, one formula gives: 5 IHP per 100 sq. . ft. of wetted surface at a speed of 10 kts.
( To estimate wetted surface, consider the hull as a rectangular box with a triangle at the front (and rear if
appropriate) and assume the profile is also a "box" shape.

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Another gives:
IHP ( S³ * L * (B + 2D) * 0.91) / 20000

where S = speed in knots
L = length in feet
B = beam in feet
D = draft in feet
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Boats. An oft-quoted rule of thumb is: 1 HP per ton of displacement gives 1 knot.
(Although wildly inaccurate in many instances, it does give a starting point.

Propellers.

Propulsive efficiency reduces as speed increases. One formula gives the most effective diameter as follows:

Diameter = v(0.013 * L * (B +2D))
Where L= boat length in feet,
           B = Beam in feet,
           D = mean draft in feet.
     
The pitch of a propeller and the amount of slip through the water can be calculated, but it is far easier to contact one of the propeller manufacturers who have programmes (and experience) to calculate this.

MODEL BOATS.
A rough guide to engine size can be found from the following:

Length x beam x Draft (all in centimetres)
Cube root of Beam x 2

Gives the cylinder volume in CC's.

Another guide, or a check on the above, is to divide the displacement (in lbs.) by between 65 and 85, which will give the swept volume in cubic inches. 65 is for a wide beam, and 85 for a very slim hull.
Displacement can be estimated from Length (waterline) x beam x draft (all in inches) / Z
where Z ranges from 16 (wide beam hull) to 22 (slim hull)
(This seems, to me, to result in an over-large engine. I reckon that it is out by roughly a factor of 10. No doubt someone will correct me on this.)

If the boiler is working at 50 psi, its size can be estimated at 180 sq. in. of heating surface for each cubic inch of cylinder volume.

FLASH STEAM.

(Properly called a Monotube boiler.)
A conventional boiler holds a quantity of water, all of which is heated and some turned into steam, which, when used, is replaced by incoming cold water.
The boiler has to be large (to hold the volume of water required) and strong (to withstand the pressure), which means that it is heavy, and expensive to build.
The volume of water takes a long time to heat from cold, giving a long delay from fire- lighting until steam is raised.

A flash-steam generator comprises a relatively-small tube, which is usually coiled to a cone-shape, around the heat source.

A small amount of water is pumped into one end of the tube, and as the tube is extremely hot, the water immediately turns to steam, which then passes from the other end of the tube, to the engine.

The problems with flash steam generators are that the high pressures and temperatures make severe demands on the tube, and the limited number of designs and paucity of background information means that far more experimentation may be required to achieve a desired performance.

The pressure can be extremely high compared to a conventional boiler. It is very difficult, if not impossible, to
measure the pressure accurately, but pressures of around 1000 psi or above, are thought to be produced in some cases.
The temperature of steam at such pressures may be of the order of 650 degrees C (assuming, as is usually the case, that it is superheated), and this is sufficient to severely weaken copper. As the tube is often subject to heating but has no water flow to keep its temperature down, its temperature can also rise considerably.
Consequently, although the flexibility of annealed copper would make it an ideal material for flash steam generators, these temperatures mean that its life will be short. In practice, the usual material is steel or stainless steel. Both are harder to form than copper, but have a reasonable life.

A reliable pump is a pre-requisite to produce steam.

A commercial boiler (for a steam car) which was produced in the late 1930's was a single-tube forced circulation type (as described above) using solid-drawn steel tube, inside an outer case 15" high by 14" diameter. The pressure was limited to 1500 psi, with a safety valve set at 2,000 psi. It would produce sufficient steam to power a 40 HP engine.

Flash steam is frequently used in model boats, and in steam cars.

The most unusual steam engine I have built was a steam lawnmower.
At the time I only had a pocket-handkerchief size lawn so it was hardly worth the effort of starting it.
The biggest drawback was the refusal of my wife to use it, whereas she would occasionally use the electric mower, and so I spent more time cutting grass and less cutting metal.
Result, machine dismantled.

Technical information: Basis, Suffolk Colt lawnmower,
Engine, twin cylinders, each 1 1/4 x 1 1/4
Boiler started as flash steam, but due to control problems was changed to locomotive type.