Power (equine or otherwise) has the units of work per unit time. The first

thing to do, therefore, is calculate the amount of work the engine does in one

stroke. Work is force times distance (technically, an integral is required but

this isn't a physics lesson).

Let:

P = steam pressure (psi)

D = piston diameter (in)

A1 = piston area (in^2)

pi = 3.14159...

F = force (lbf)

Then:

A1 = (pi/4) * D^2(in^2)

And:

F = P * A1(lbf)

During the expansion stroke, this force operates over a distance equal to the:

S = stroke (ft)

(Note to the technical: That's not strictly true. The pressure in the

cylinder changes a bit during the expansion stroke. However, to model that

requires a lot more math including some dreaded calculus. Remember, the title

of this article says "ESTIMATING".)

So, the work done during one stroke is:

W = F * S = S * P * A1(ft-lbf)

Power is work per unit time. Assume that the engine is running at SPM strokes

per minute. Then:

Power = W * SPM = SPM * S * P * A1(ft-lbf/min)

Watt defined one horsepower to be 33,000 ft-lbf/min. So:

HP1 = Power / 33000

HP1 = SPM * S * P * A1 / 33000

is the horsepower.

So far we've assumed that the engine is single acting, i.e., powered on only

one side of the piston. If it's double acting we can compute the power

obtained from steam acting on the other side of the piston (HP2) and add it to

HP1 to get the total engine power.

The mathematics for doing this is essentially identical to the above with the

exception of the calculation of the area of the piston. The area of the

connecting rod has to be subtracted from the piston area to get the effective

area on which the steam acts.

Let:

d = diameter of connecting rod (in)

Then the effective piston area on the connecting rod side is:

A2 = A1 - (pi/4) * d^2(in^2)

And the horsepower developed from that side is:

HP2 = SPM * S * P * A2 / 33000

Finally, the total horsepower for the (double acting) engine is:

HP = HP1 + HP2

Marv Klotz