## Horsepower

Despite the introduction of the SI system, in which power is measured in kilowatts (kW), horsepower cannot yet be discarded altogether. Power is the rate of doing work. In linear measure it is the mean force acting on a piston multiplied by the distance it moves in a given time. The force here is the mean pressure acting on the piston. This is obtained by averaging the difference in pressure in the cylinder between corresponding points during the compression and expansion strokes. It can be derived by measuring the area of an indicator diagram and dividing it by its length. This gives naturally the indicated mean effective pressure (imep), also known as mean indicated pressure (mip). Let this be denoted by 'p'.

Mean effective pressure is mainly useful as a design shorthand for the severity of the loading imposed on the working parts by combustion. In that context it is usually derived from the horsepower. If the latter is 'brake' horsepower (bhp), the mep derived is the brake mean effective pressure (bmep); but it should be remembered that it then has no direct physical significance of its own.

To obtain the total force the mep must be multiplied by the area on which it acts. This in turn comprises the area of one piston, a = pd2/4, multiplied by the number of cylinders in the engine, denoted by N. The distance moved per cycle by the force is the working stroke (l ), and for the chosen time unit, the total distance moved is the product of l X n, where n is the number of working strokes in one cylinder in the specified time. Gathering all these factors gives the well-known 'plan' formula:

The value of the constant k depends on the units used. The units must be consistent as regards force, length and time.

If, for instance, SI units are used (newtons, metres and seconds) k will be 1000 and the power will be given in kW.

If imperial units are used (lb, feet and minutes) k will be 33 000 and the result is in imperial horsepower.

Onboard ship the marine engineer's interest in the above formula will usually be to relate mep and power for the engine with which he is directly concerned. In that case l, a, n become constants as well as k and power = p X C X N (1.6)

Note that in an opposed-piston engine 'l ' totals the sum of the strokes of the two pistons in each cylinder. To apply the formulae to double-acting engines is somewhat more complex since, for instance, allowance must be made for the piston rod diameter. Where double-acting engines are used it would be advisable to seek the builder's advice about the constants to be used.

## Solar Stirling Engine Basics Explained

The solar Stirling engine is progressively becoming a viable alternative to solar panels for its higher efficiency. Stirling engines might be the best way to harvest the power provided by the sun. This is an easy-to-understand explanation of how Stirling engines work, the different types, and why they are more efficient than steam engines.

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