Edward wrote:Bret ,
First work out the volume of steam that will be used per hour at a given RPM , lets say 200 RPM .
The volume of your HP cylinder is 3.142(Pi) x 2.25(Radius squared)x 6(Stroke) = 42.4 cu" , say 42.5.
Assume a fairly typical cut-off of 8% : Volume per minute at 200 RPM will be 42.5 X .8 X 400(400 not 200 because the engine is double acting)
=13,600 cu" per minute or 816,000 cu" per hour which is 472.222 cu' per hour .
At 150 psi 1 lb of steam takes up 3.015 cu' so 472.222 cu' will weigh 472.222 divided by 3.015 or 156 .62 lbs. Realistically your steam is unlikely to have a dryness factor of much more than 90% unless you superheat , therefore the final figure will be 156.62 +10% = 174.02
So I believe your engine will use around 174 lbs of saturated steam per hour at 150 PSI and 200rpm .
As a very rough rule of thumb a firetube boiler will produce about 5 lbs per hour per sq ' of heating surface , so you should aim for a boiler with around 35 sq' .
Regards Edward .
PS . Having written this the boiler size seems rather large . I've checked my sums but can't see any obvious errors (but it is half past midnight !) Perhaps some one else could check them for us .
1. All steam calculations regarding weight, etc. should proceed from
pounds per square inch absolute (psia). Absolute pressure starts at absolute vacuum ( -14.7 psi, call it -15psi). Steam at 150 psi gauge (
psig) at sea level is equivalent to
165 psia. The weight (from Marks' Steam Tables) is 2.75 lbs/cu.ft.
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2. When using the PLAN/33,000 formula for horsepower remember that P (pressure) is the Mean Effective Pressure (MEP or average piston pressure during it's stroke) expressed in
psi. Any back pressure (condenser or atmospheric exhaust) must be subtracted from this intial figure to give correct MEP.
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3. One this side of the pound, the cutoff on a small compound engine is usually between 60% and 65% to allow the LP cylinder output to approximately equal the HP cylinder output. This, however, will reduce the overall pressure on the piston during its stroke (the MEP) and a corrective factor must be introduced. In this case, the corrective factor for 65% cutoff is 0.9306. The pressure at the HP cylinder valve chest (I'll use boiler pressure to keep this easy) is multiplied by this factor and any back pressure (condenser or exhaust - in psia) is subtracted - I'll use a condenser vaccum of 20" mercury or 5 psia. So (165psia x 0.9306) - 5 = 148.549 psi - call it 148.5 psi for an MEP
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4. The end result is the theoretical horsepower. But small steam engines are not perfect. Two semi-retired, licensed mech engineers working with steam with whom I am acquainted suggest a diagram card (the actual pressure/expansion/work of the steam in the cylinder) factor of 66%. This brings it more in line with reality.
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So now: PLAN / 33,000
148.5 X 0.5 X (1.5 X 1.5 X pi) X 200 X 2 (power strokes per revolution) / 33,000 = 6.36HP. But this is for a simple engine. An easy American "Rule of Thumb" for small engines is to multiply by 1.5 (150%) for a compound. Then: Theoretical Horsepower = 9.54HP. Adjusting this to Indicated Horsepower (IHP) multiply by 66% yields
6.36 HP. So you could probably push a displacement hull (curb weight) of 6000 pounds at about 6 knots.
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Amount of steam used: Volume in cu.ft. X Number of Strokes X 60 (one hour) X 65% (cutoff)/ 2.75:
[(1.5 X 1.5 X pi x 6) / 1728] x (200 X 2) X 60 X 65% / 2.75 = 139.23 - call it 140 lbs/hr. This works out to 22 pounds of steam (weight) per horsepower/hour.
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However, we have not taken into account some other items that affect all this. There is steam line/cylinder condensation and leakage around valve stems and piston rods which can account for as much as 20%. So the 140 lbs/hr is on the low side. Size the boiler for the Theoretical Horsepower of 9.54 at 22 pounds of steam/hp/hour or 210 pounds of steam/hour. A 42 sq.ft. boiler would be suitable. However, remember to oversize for future steam auxiliaries and
whistle blowing.