Steam engine horsepower?

[crueby]

Hi all,

Something I've wondered about for a long time - is there a (relatively) easy way to estimate the horsepower of a full sized steam engine, without putting it on a dynomometer? Seems like there should be a rule of thumb formula(s) that would get a close number. I have tried reading up on it, but the old technical books spend chapter after chapter of complex formulas detailing the little frictions and losses from each moving part, speeds of steam through pipes, etc, to get really accurate calculations.


Wondering if there is an easier way to get the sales-brochure-accurate guestimate for a non-compound two cylinder double acting engine? I know compounding is more efficient, but its a lot more complex to calculate, so am asking about just your garden variety twin cylinder mill engine style. Say running at 150 psi, and varying the bore/stroke. For example, how does the power of a 4" bore/5" stroke engine compare to a 6" bore/8" stroke?

Anyone have any rough estimate formulae, back of the envelope style, without the usual 87 pages of calculus (been too many decades since I've used the more advanced maths!)

Thanks for any info!!
Chris
  

[AVTUR]

The "No Pale Ale" formula usually used on IC engines could be used. Since it ignores friction losses it will be an over estimate:

         Horsepower = Engine speed x Steam Pressure x Cylinder Volume (if my memory serves me well)

It obviously ignores cut off and compounding. With the latter the low pressure cylinder pressure could be estimated using steam chart/tables.

AVTUR

[mklotz]

Here's something I put together ages ago for a club I belonged to at the time.  Lots of simplification but I think most of the key parameters are represented.  Friction is completely ignored.



                 ESTIMATING HORSEPOWER OF A STEAM ENGINE
                              M. W. Klotz

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
piston rod has to be subtracted from the piston area to get the effective
area on which the steam acts.

Let:

   d = diameter of piston rod (in)

Then the effective piston area on the piston 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


[Kim]

Great explanation, Marv!  I appreciate you tracking it from the basic units like that.  It really helped me follow.
Thank you!
Kim

[Jo]

There are many horse powers associated with Steam Engines:


Nominal horsepower is derived from the size of the engine and the piston speed and is only accurate at a steam pressure of 7 psi 

Indicated horsepower is the theoretical capability of the engine.

Brake Horse power is the power measured at the crankshaft - equals indicated horsepower minus frictional losses within the engine (bearing drag, rod and crankshaft windage losses, oil film drag, etc.).

Shaft horse power is the power available at the output shaft.


In 2023 a group of engineers modified a dynometer to be able to measure how much horsepower a horse can produce: This horse was measured to 5.7 hp - as we have just seen other horses are available 

Jo

[crueby]

Thanks very much Marv, thats exactly what I was looking for!!      I'll print that out and work through the calculations for a couple of engine sizes to see if I can follow it and not wind up with 10 billion horsepower for a 3" engine!   

Jo, thats a good point - 'horsepower' by itself is too vague a term!  And that horse qualified for a "5.7 HP" sticker on his side!  Or maybe it should be in "human-power" for a horse?       Sort of like 2+2=5 for suffiently large values of 2...   
 

[crueby]

Question on math and units for you Marv:
Where you have:----------------------------------
   P = steam pressure (psi)
   A1 = piston area (in^2)
   F = force (lbf)

Then:

   A1 = (pi/4) * D^2         (in^2)

And:

   F = P * A1            (lbf)---------------------------------
Okay, P is in pounds per square inch, A1 is also square inches, how does P * A1 give pound feet?  What am I missing?

Also, minor nit - later on you take the diameter of the 'connecting' rod, I think that should say 'piston' rod.
Thanks!

[mklotz]

...
Okay, P is in pounds per square inch, A1 is also square inches, how does P * A1 give pound feet?  What am I missing?

Also, minor nit - later on you take the diameter of the 'connecting' rod, I think that should say 'piston' rod.
Thanks!

lbf = pounds force  (to distiguish it from pounds mass)  Don't you just love the screwed-up inferial system? 

You're correct about the piston rod.  I'll change it.

[crueby]

...
Okay, P is in pounds per square inch, A1 is also square inches, how does P * A1 give pound feet?  What am I missing?

Also, minor nit - later on you take the diameter of the 'connecting' rod, I think that should say 'piston' rod.
Thanks!

lbf = pounds force  (to distiguish it from pounds mass)  Don't you just love the screwed-up inferial system? 

You're correct about the piston rod.  I'll change it.

Aha! I was mis-interpreting the letters!  Thanks!!

[Jo]

Another thing to bear in mind is that a Steam Engine's Horse Power was defined when the engine was running at a speed that it could continue at "indefinitely" under load. Yes you could put higher pressure steam into it and it would go faster/deliver more power but the engine could not do it for over 100 years, which clearly would not be acceptable to the owner Hence smaller engines horse power output was defined at faster speeds than much larger engines.

(Unlike ICE which are defined by the peak of their power out, which for many cars occurs at a very narrow window and is not where they rev when they are normally driven  )

Jo

[Charles Lamont]

Work done is force x distance moved. Power is work done per unit time.

The easy one to remember is P L A N / 33,000

P - Pressure estimated average cylinder pressure - typically take half the boiler pressure in psi

L - Length of stroke in feet

A - piston Area in square inches

N - Number of power strokes per minute

1 HP is 33,000 ft lbf / min

[crueby]

Another thing to bear in mind is that a Steam Engine's Horse Power was defined when the engine was running at a speed that it could continue at "indefinitely" under load. Yes you could put higher pressure steam into it and it would go faster/deliver more power but the engine could not do it for over 100 years, which clearly would not be acceptable to the owner Hence smaller engines horse power output was defined at faster speeds than much larger engines.

(Unlike ICE which are defined by the peak of their power out, which for many cars occurs at a very narrow window and is not where they rev when they are normally driven  )

Jo

Back when building the Stanley steam car engine I learned that they advertised a lower HP than the engine could maintain  since the boiler they used could only generate steam at the lower rate. All sorts of conditions  on any specification!


 

[crueby]

Work done is force x distance moved. Power is work done per unit time.

The easy one to remember is P L A N / 33,000

P - Pressure estimated average cylinder pressure - typically take half the boiler pressure in psi

L - Length of stroke in feet

A - piston Area in square inches

N - Number of power strokes per minute

1 HP is 33,000 ft lbf / min

Good way to remember  it!  Thanks!

[Rich Carlstedt]

Work done is force x distance moved. Power is work done per unit time.

The easy one to remember is P L A N / 33,000

P - Pressure estimated average cylinder pressure - typically take half the boiler pressure in psi

L - Length of stroke in feet

A - piston Area in square inches

N - Number of power strokes per minute

1 HP is 33,000 ft lbf / min

PLAN is a great calculator, but I believe the "L" length needs to be multiplied by two when the engine is a double acting

Rich

[Charles Lamont]

Well, you could do it that way, if you took N to be the revolutions per minute instead of the number of power strokes.