horsepower calculation

[skippinge]

Can someone tell me what is the correct formula for calculation horsepower or watt for a 3 cyl SA radial steam engine.
Regards Flemming

[David Thompson]

No, but I can start the ball rolling.

The formula for power is always "plan" - pressure x area x stroke x number of working strokes per second.

If you use SI units, there are no more numerical constants, but you have to get the units right. Thus pressure in Pascals (N/sq m), area in square metres, stroke in metres and rate in Hz, ie per second, which is rpm/60.

The power then comes out in the correct SI unit, Watts, which you convert to horsepower by dividing by 746, because 1 HP = 746 Watts.

The area can be the total piston area, which is one piston area times 3 for the three cylinder engine, and the area of the piston is pi x diameter squared / 4. The diameter must be in metres to get area in sq. metres.

I am not familiar with a 3 cylinder single acting radial steam engine, but I would think you get one power stroke from each cylinder in each revolution, so the formula is complete. If not, you have to look at my original wording and make the appropriate correction.
For example, for a 4 stroke car engine you have to use n/2 (that is , N/60/2) because the engine only fires on every alternate revolution. I think for a double acting steam engine, you should multiply by 2.

[skippinge]

Dear David,
Many thanks for your detailed and very good explanation. It help me very much.
Freindly regards
Flemming
Copenhagen/Denmark

[Frits]

Hi David,

I'm sorry to correct you but in my books I learned that 1 PK(HP) = 736 Watt.
Could you made a mistake or do we use different horses. ;D

Frits

[GeorgeRay]

Must be different horses or perhaps ponies. As far as know 1hp =746 watts.

[David Thompson]

Yes, it seems European horses are indeed weaker than British horses.

In Britain and the USA, the horsepower (HP) is 550 ft.lbf/s or 745.7 Watts.

Machinery's Handbook confirms this, but also quotes "horsepower (metric)" as 735.5 W. I recall being told that a German PS ( pferdestarke ) which clearly translates to "horsepower" is in fact different.

In fact, I have now discovered that 1 PS is defined as 75 kgf.m/s so then 1 W = 1 N.m/s = 9.80665 x 75 = 735.5 W. Big deal, some of you may think, but others will recognise 9.80665 as the more exact value for the well known 9.81 m/s/s which is the acceleration due to gravity. That's how you get from kg force to Newtons.

So the difference comes down to 550 ft.lbf/s being the British and American definintion of a horsepower (HP), while the metric definition (PS) is 75 kgf.m/s

I realise I may be the only person interested in this.

[Deleted]

Hi

Remember that the pressure is the avaerage throughout the stroke, I think it is called mean effective pressure, this will be a lot less than boiler pressure or even steam chest pressure

Hope this helps

[David Thompson]

Ah, quite right, I should have remembered to use indicated mean effective pressure (imep).

This is the average presure difference across the piston so will be less than boiler pressure for several reasons, such as losses up to the steam chest, the back pressure of the exhaust, the pressure drop through the valves and expansion of the steam in the cylinder, which in turn depends on the cut-off.

Since we are talking about power rather than tractive effort, we are talking high speed rather than low speed, so cut-off will be short for economy but possibly not all that short in a model, especially if you are trying to maximise power rather than economy.

The Greenly/Steel book shows graphs of imep against cut off with allowances for real effects in models. At 50% cut-off you could expect between 60% and 75% of the steam chest pressure - use the lower figure for small models. The steam chest pressure I suppose could be 80 to 90% of the boiler pressure.

At 20% cut off, the imep is down to 30-40% of steam chest pressure but this cut-off may be too short for models because of condensation.