# Horsepower For Live Steam



## Tom Parkins (Jan 2, 2008)

Has anyone ever done a horsepower calculation or have the data available for a live steam locomotive? Ruby, Aristo Mikado, Aster?????

Tom P


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## Charles (Jan 2, 2008)

A good reference plus a dyno car 
http://www.twoof.freeserve.co.uk/motion1.htm 

Some interesting denotations on the 1:1 engines:

http://www.dself.dsl.pipex.com/museum/LOCOLOCO/USAhp/USAhp.htm


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## Tom Parkins (Jan 2, 2008)

Some neat stuff there, typically British mixing Kilonewtons and MPH.

What is the typical Tractive Effort for a G Live steam engine? That data along with the speed of the engine at that TE could be used to calculate the HP. 

Tom


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## Michael Glavin (Jan 2, 2009)

Boiler horsepower = 34.5 pounds of water evaporated per hour at 212 degrees Fahrenheit, or 9,809.5 watts. 

Horsepower = 150-pounds in tow while walking at 2.5 miles per hour. This works out to 33,000 foot-pounds per minute, or 550 foot-pounds per second. 

I suppose you could do a scale effort to glean scale LS hp numbers. 

Michael


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## Charles (Jan 2, 2008)

equation can be obtained (for a 2 cylinder locomotive)









where
[*]_t_ is _tractive effort_[*]_c_ is a constant representing losses in pressure and friction; normally 0.85 is used[*]_P_ is the boiler pressure[*]_d_ is the piston diameter (bore)[*]_s_ is the piston stroke[*]_D_ is the driving wheel diameter[/list] The constant 0.85


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## jfrank (Jan 2, 2008)

So Charles, does that mean then that a locomotive with 3/4" cylinders, 60psi, half inch stroke(just guessing) and 1.5" drivers gets about 1 horsepower(.956).


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## JEFF RUNGE (Jan 2, 2008)

I did it a bit differently using the piston area as: pie x ( r squared) times the available boiler pressure, now here is the tricky part, calculating the torque about the axle center line through the ever changing angle to the driver crank pin. But I cheat and just use the number achieved where the pin 90 degrees to the axle ( which would be 1/2 the cylinder stroke) (but by that time the pressure in the cylinder has already began to drop) and now factor in the wheel radius and you have a interesting (but flawed) number. Per cylinder. 
On the Aster Mikado, based on 50 psi boiler pressure, I came up with 4.18 inch pounds at the rail, per cylinder. If I did it right, sounds too simple.. hhmmmm


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## Dan Rowe (Mar 8, 2009)

The formula given for tractive effort only works if the units match to make it work the dimensions are all in inches and pressure expressed as pounds/square inch.

The formula for calculating horsepower is the same for any piston engine steam or internal combustion engines. It is PLAN/33,000
P=mean effective pressure PSI
L=length of stroke in feet
A=area of piston in square inches
N=number of strokes (power) per minute.

The problem using that formula is that the mean effective presure has to be asumed. To be accurate an indicator card has to be taken and a planimeter is used to calculate the area under the curve.
Even in a controled lab this is hard to do with out modern instruments. Taking indicator cards on a moving locomotive is not for the faint of heart.... one slip and you have lost a days work or worse.
http://en.wikipedia.org/wiki/Planimeter

Charles, the conatant of .85 was the most common to calculate tractive effort in the US but "The Steam Locomotive" by Ralph Johnson ME states that values between .6 and .95 were also used depending on the valve cut off and other factors. Some designers used .75 for saturated steam and .85 for superheated steam.


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