Steam & Excursion > Estimating steam locomotive horsepower

Assuming you know boiler pressure what other calculations would be needed to estimate a steam locomotive's horsepower?

I would think you'd need to factor in all sorts of things. The size of the cylinders, the size and number of the drive wheels, boiler pressure of course, engine weight on the drivers (factor of adhesion?). I'm just guessing here really. Locomotives are often rated by their horsepower at speeds, like "4000 horsepower at 45mph" or some such in my casual reading.

-K

This is one of those things where you really have to ask the right question to the the answer you're looking for. There are many kinds of horsepower relating to locomotives. With a diesel, you're talking mechanical horsepower: 550 foot pounds per second....or Brake Horsepower...or Indicated Horsepower...or Shaft Horsepower. It doesn't work that way with a steam locomotive.

For the 1876 Centennial Exposition in Philadelphia, some old guys got together and cobbled together this idea of Boiler Horsepower. Pretty much since 1876, boiler people tried to get away from Boiler Horsepower, at least as it was then defined. One Boiler Horsepower = the evaporation of 34.5 pounds of water in one hour from and at 212 degrees f. To really figure out how much Boiler Horsepower your boiler makes, you have to measure the steam output and have test equipment.

What heating surfaces are there in a steam locomotive? It depends on what you've got. Total area of surface in contact with hot gas and below the normal water level as long as it's part of the circulation system of the boiler. Area of: firebox sheets (minus door hole, stoker, tube & flue holes, etc), arch tubes (OD), siphons, circulators, combustion chamber, tubes & flues (ID) from sheet to sheet. Superheater area is figured seperately.

You probably don't want to get into all those formulae and steam tables and stuff....and there's drawbar horsepower....aww, just use the easy way ALCo looked at it:

Saturated Steam HP = 0.0212 X P X A
Superheated HP = 0.0229 X P X A

HP = Horsepower
P = Boiler Pressure (in Pounds per Square Inch)
A = Area of One Cylinder (in Square Inches)

For most of the locomotives out there, you can easily find out what boiler pressure they run at and what the cylinder diameter is. Use this simple formula fore every two-cylinder steam locomotive you want to know about. You do the math on your cell phone and can make the comparison for your self. Leave all the egg head stuff to the egg heads who can then argue amongst themselves over minutiae.



Edited 1 time(s). Last edit at 03/05/13 00:00 by AdamPhillips.

And, for a steam locomotive there are two kinds of horsepower, cylinder and drawbar.

Wow! Look at the brain on Adam! ;)

Brian

Horsepower is the rate of doing work, for a RR locomotive it is the rate of delivering drawbar pull. Horsepower is limited by the ability of the boiler to deliver steam at the design pressure and the rate that the cylinders can apply the steam to the pistons, and exhaust the other side.
In internal combustion engines the power is similarly defined on the input end by the cylinder pressure, cylinder displacement, and number of power strokes (e.g. rpm) but is also confined by the gas flow constraints on both the intake and exhaust sides.
Apparently the numerical factors applied to the calculations of BP, piston size, and speed are attempting to quantify these other variables.

> Assuming you know boiler pressure what other
> calculations would be needed to estimate a steam
> locomotive's horsepower?

People used various estimates (based on square
footage of heating surface, for instance) but
no one was surprised if the estimate
turned out to be off by, say, 30-40% for a
particular engine. An educated guess would be
about as good.

AdamPhillips Wrote:
-------------------------------------------------------

> You probably don't want to get into all those
> formulae and steam tables and stuff....and there's
> drawbar horsepower....aww, just use the easy way
> ALCo looked at it:
>
> Saturated Steam HP = 0.0212 X P X A
> Superheated HP = 0.0229 X P X A
>
> HP = Horsepower
> P = Boiler Pressure (in Pounds per Square Inch)
> A = Area of One Cylinder (in Square Inches)

So are you defining Area as the area of the inside surface that the piston travels along, and not the small dead volumes at either end, or just take the total length of the cylinder from cap to cap?

Mike Massee
Tehachapi, CA
Photography, Railroading and more..

Thanks Adam, I was curious as to the horsepower the Southern 630 might be capable of and plugging in the figures says almost 2800.

Reply to Harlock:


The the "area" referred to should be the the area, in square inches, of the Piston Face.

A handy approximation of the (circular) square inches allows you to multiply the the Square of the DIAMETER of the piston (the bore size) by .7854.
Thus a piston of a nominal 25" diameter has a surface area of (5625 X .7854 = 4417.875 Square-Inches).

The .7854 figure is the area of a circle inscribed inside a square --- with a side equal to the diameter.
You wind up with 4 triangles (with a curved hypotenuse) at the corners of the square which are NOT part of the piston's circular area.

Now, multiply that by the static boiler pressure; example: 240 PSI and you arrive at the piston thrust, at the crankpin, (for one side of the engine).
Piston thrust, in pounds: 4417.875 square inches X 240 PSI = 1,260,290 lbs! (divide by 2,000 to get the piston thrust in tons).

Now, it gets more complicated since you have, effectively a 4 cylinder engine (2 double-acting cylinders).
The equations referred to earlier are a simplification to allow approximate numbers to be representative enough (to arrive at a HP number)

The 'side wall' areas do not contribute to rotative force applied to the crank pins. All of this gets you to a stalled-condition, with no motion, as the rotation begins other piston thrusts aid in the propulsion, so a steamer starts with a high torque and almost ZERO horsepower. Getting into the power curve, getting the RPMs up --- soon you have increased rate-of-work being accomplished.

The "Horse Power" comparisons date back to James Watt's factory and the sales teams' attempt to show how powerful his engines were for factory applications ---
it freed siting the factories at water falls for water power. Watts factory-steam engines meant that factories could be built at better locations!

The low-HP "first generation" diesel locomotive businesses focused on the ability of the electric transmission to apply immense rotative force to the wheels, in a stalled condition. Once underway, the DC-drive diesels were not as powerful, at speed, as promised -- so, "Multiple Units" were applied to get to the track speeds they wanted.

There is the oft-quoted addage: "A steamer will RUN with anything it can't start; and a Diesel will Start anything it CAN"T run-with" !!!

With the advent of the modern AC transmissions, all that changed, you now have an effective "chain wrapped around the axles" and the engine's crankshaft -- a very efficient electric transmission!

NOW, you can, through constant phase-manipulation, fool the traction motor's fields into seeing a near-stalled "attractive force" -- at 70 miles-per-hour strain!
THAT'S A WONDER TO SEE! But, it drinks barrels of fuel ---- they will soon be hauling "diesel tenders".

Back to steamers.... Later, if you want, you will see that at portions of the 'power-impulse circle', the cylinder head and the frame members drag the whole train, while the piston and crankpin remain stationary (fixed to the rail --in a non-slipping condition)...
The cylinder heads have to restrain the same 'applied pressure! as the pistons withstand!

Later!

Wes Camp

> just use the easy way
> ALCo looked at it:
>
> Saturated Steam HP = 0.0212 X P X A
> Superheated HP = 0.0229 X P X A

Getting an answer is always easy, long
as you don't mind wrong answers. Try that
formula for a few engines and see how well
it does. (Some will come out right, some wrong.)

Wes, I hate to disagree with you, but the face of the piston area would equal Pi X the Radius squared, or 3.1416 X 12.5 squared=490.875 square inches.

timz2 Wrote:
-------------------------------------------------------
> Getting an answer is always easy, long
> as you don't mind wrong answers. Try that
> formula for a few engines and see how well
> it does. (Some will come out right, some wrong.)

Well, that's pretty much my point. It doesn't really matter. You're not really going to figure anything out unless you do actual testing. There really is no point in trying to figure out something that the boiler engineers wanted to do away with. It was really just a swag to give a lay person something they could wrap their head around. Eventually terms involving BTUs gave the engineers hope.

I can remember one trip where Hotwater was firing for me and we ended up shoving a stalled freight up the east side of Archer Hill from Burns, WY. Well, we kept data on that little segment to take back to EMD and the engineers there pulled out the old formula. They figured we were producing 4400 horsepower with 844 shoving that 11,000+ ton freight. We got it up to 25 MPH when the crew ran out of time above Hillsdale and they had to recrew so we started all over again. My good friend, Steve, who helped me with the old steam crew videos got the whole maneuver recorded and it really sounded great. I also recall we burned 53 gallons of #5 burner oil per mile for that 25 mile journey. One part of my time on the crew that I will always remember.

Bob Krieger
Cheyenne, WY

Bob: you have any idea of the cost per gallon of oil when this occured?

Wait, wait, you forgot to include an analysis of fortnights per furlong . . .

John Gezelius
Tustin, CA

tomstp Wrote:
-------------------------------------------------------
> Bob: you have any idea of the cost per gallon of
> oil when this occured?
Tom, I did not have access to the cost of fuel then. I sent my fuel orders through the fuel desk in Omaha and they handled the orders for us. I supplied the quantities and locations.

Bob Krieger
Cheyenne, WY