Operational Theory

Piston Displacement Velocity, and Acceleration (page 1)

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Mean Piston Speed.

This is often quoted by engine manufacturers. It is obtained by the formula 2nL where n is the engine speed in revs/sec, (rpm/60), and L is the piston stroke in metres.

For example: engine speed 102rpm, engine stroke 2.5 metres.

n = 102/60 = 1.7revs/sec × 2 × 2.5 = 8.5m/s.

Remember, this is only the average speed of the piston and not the instantaneous speed at any crank angle. Mean piston speed is limited because loading on the bearings is proportional to the (piston speed)2.  As bearing technology has improved, mean piston speeds have increased. In 1970 mean piston speeds for slow speed crosshead engines and large medium speed engines were about 6.5m/s. Today they are around 8.5 - 9m/s. Piston speed is also directly linked to the power developed. The higher the piston speed, the greater the power.

Piston Displacement.

Starting at at Top Dead Centre (TDC) and moving downward to Bottom Dead Centre (BDC), the crankshaft will rotate 180°, and the piston will move 2 × crank radius or the stroke of the piston.

Hands up those who think that when the crank is 90° after TDC, the piston will have moved half of the piston stroke (i.e. the crank radius).

Sorry guys, you are wrong!! The drawing above shows a unit of an engine with a crank radius r of 1metre, and a con rod of length l of 2.5 metres at TDC and BDC showing a total stroke of 2m If the engine is turned to 90° after TDC as shown above, then a right angled triangle is formed by the crank radius, the con rod and an imaginary vertical line of length x between crank centre and top of con rod. Using Pythagoras' theorem to solve for x:

x = √(2.52 - 12) = 2.29 metres

If we now subtract this distance x from the con rod length + crank radius (l + r) the distance moved by the piston is:

(2.5 + 1) - 2.29 = 1.21metres.

1.21m is about 60% of the total stroke, so the other 40% (0.79m) is the distance moved between 90°ATDC to BDC.

In this particular case the piston will have moved  half the stroke at a crank angle of  about 79°.

If the ratio between con rod and crank radius is increased (in other words make the con rod longer) then the crank angle at which the piston has moved half the stroke gets closer to 90°, but it will never actually reach that. point. For example, if the con rod in this particular case was increased in length to 10 metres then at 90° ATDC the piston would have moved 1.05metres. and it would have reached mid stroke at about 87° ATDC.

The piston position for any crank angle can be calculated.

This is shown on the NEXT PAGE.

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