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The mean of any function refers to the average value.

In the case of mean piston speed, taken in a narrow mathematical sense, it is zero because half of the time the piston is moving up and half of the time the piston is moving down; this is not useful.

The way the term is usually used is to describe the distance travelled by the piston per unit of time, taking distance positive in both up and down senses.

It is related to the rate that friction work is done on the cylinder walls, and thus the rate that heat generated there.

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how fast the piston moves up and down at the cylinder at the different stages of a revolution of the crank, being the top dead center position the reference and the degrees of the crank the graduation (360) 

the importance of it is about;calculating-managing-avoiding the wearing of the piston rings and piston skirt

naturally the higher the rpms the higer the piston speed but in high revving engines the way its managed is by lowering the stroke of the piston (the total race of of the piston from its highest position to its lower position) but thas typically applied only to engines with a high count of cylinders and pistons (6+)

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On 12/19/2014 at 7:18 PM, DrD said:

The mean of any function refers to the average value. In the case of mean piston speed, taken in a narrow mathematical sense, it is zero because half of the time the piston is moving up and half of the time the piston is moving down; this is not useful. The way the term is usually used is to describe the distance traveled by the piston per unit of time, taking distance positive in both up and down senses. It is related to the rate that friction work is done on the cylinder walls, and thus the rate that heat generated there.

This is sort of a non-puzzle. It represents a specification to be designed to rather than as a result of. I'm not an ME but I have built many engines of various types over the years and the mean piston velocity is a function of the revolutions per minute, that is, the piston at a specific rpm is going to be the same at the peak of the graph as it is at the trough, that is at 286.071 degrees on the crankshaft if the rpm is held consistent. At 0 and 180 degrees, the piston velocity is zero.

Piston velocity is a test of the strength of the piston and connecting rod subassembly. The alloy used to make the piston itself is what determines the maximum velocity that the piston can reach before friction coefficients, heat levels and reciprocating stress overcome the maximum levels that the piston can sustain before it begins to fail structurally. As the alloy tends to be fairly consistent across most manufacturers, the maximum velocity of the piston at a given rpm is determined by the length of the stroke, that is, the radius of the journal of the crankshaft.

The most common engine types in production are built to square, or below square. That is, a square engine has the same diameter of cylinder bore as the total length of the stroke from 0 to 180 degrees, whereas in an undersquare engine, the total length of the stroke is less than the diameter of the bore. The latter is mostly used in higher performance engines where the torque curve approaches the peak of the maximum piston velocity. Generally in this type of engine, the volume of the cylinder can be artificially enhanced with turbochargers or superchargers, increasing the amount of fuel/air available for combustion.

An example is found in Formula 1 racing engines, where the cylinder diameter is substantially greater than the length of the stroke, resulting in higher available rpm but necessitating greater requirements of the strengths of connecting rods and pistons and higher temperature tolerances for bearings. The cylinder diameter in these engines are fairly small (under 45 mm) and the stroke is less than that, depending on the torque curve and maximum available rpm as designed by the builder. Peak torque is reached at higher rpm and is spread over a wider range of rpm. The specifications of these are known factors and can be designed to.

Torque is a function of the length of the stroke, the shorter the stroke, the less available torque at lower rpm, but the piston velocity can be taken to much greater speeds, meaning higher engine rpm. These types of engines are much more delicate and require a much higher level of precision in the moving parts than square or oversquare engines. Up until the early 1960s, the focus by designers was on torque rather than piston velocity, probably due to material considerations and machining technologies. As materials have improved, engine rpm has increased.

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