Having approximated the engine’s steam consumption at a given speed and having calculated the consumption of fuel for the boiler I should now be able to calculate the Steam Engine and Boiler Efficiency.

In my previous post on steam and methylated spirit consumption the final calculation looked like this:

The engine design for my traction engine is 12mm bore and 12mm stroke. Volume of working fluid consumed per revolution:

π x 0.6

^{2}(bore in cm) x 1.2 (stroke in cm) x 2 (double acting) = 2.7cc / revat 300rpm x 2.7cc => 810cc/min

At the end of the stroke the steam will still be under pressure. I’ve assumed the steam will still be at 1.5 atmospheres

810 / 880 x 1.5 =

1.38g water per minute => 0.26g fuel / minuteThis feels like a fairly simple walk through of the steam and methylated spirit consumption.

Steam and Methylated Spirit Consumption

### Engine Power

With a 12mm bore and 12mm stroke engine running at 300rpm and with steam at 3 atmospheres then the peak force:

3atm at beginning of stroke, 1.5atm at end of stroke, approximately 2.25atm when the crank is at 90° to the piston main axis:

- Bore = 12mm, Area = π x 6
^{2}= 113mm^{2} - Force = 225,000 x 113 / 1,000,000 ~ 25N
- Torque = 25 x 0.006 = 0.15Nm

Power = Torque x Speed / 9.5488

Watts = Nm x rpm / 9.5488

Engine power = 0.15 x 300 / 9.5488 ~ 4.7W

A piston and crank create a sinusoidal torque with a double acting piston, this means that my effective average torque is 0.7x this value, so my power out of the engine is approximately, 0.7 x 4.7 ~ 3.3W

### Heat Input Power

From the previous calculation we had the following:

810 / 880 x 1.5 = **1.38g water per minute => 0.26g fuel / minute**

we have a heating value for the methylated spirits of 29700J/g

0.26 x 29700 = 7722 J/minute = 128.7 J/second = 128.7 Watts

### Efficiency

I now have an input power of 128.7 Watts and an engine output power of 3.3 Watts, the Steam Engine and Boiler Efficiency is a ratio of the output and input:

Steam Engine and Boiler Efficiency = Output Power / Input Power

Miniature Traction Engine Efficiency = 3.3 / 128.7 = 0.0256 = 2.56%

So, my calculated efficiency is 2.56% that feels very high for this small system and I expect a lot more losses when I put this into practice.

The LittleLEC 2019 competition that measures the overall efficiency of steam trains recorded results between 0.057% up to 0.428%, an order of magnitude lower efficiency than my simple calculation.

LittleLEC 2019, Reference 2

I need to go back to the steam indicator diagram and take a look at the real losses.

### References

- Condensers and Boilers for Steam-Powered Cars, NASA Technical Server
- LitteLEC Model Steam Train Efficiency Competition

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