How is piston displacement calculated?

Piston displacement, also known as engine displacement or swept volume, is a key measurement in determining the size of an engine and its potential power output. The formula for calculating piston displacement involves the bore (the diameter of the cylinder) and the stroke (the distance the piston travels within the cylinder).

The correct method to calculate piston displacement is to use the formula where the bore is squared, multiplied by the stroke, and then multiplied by 3.14 (which is an approximation of π) and divided by 4. This formula can be represented mathematically as:

[ \text{Piston Displacement} = \frac{\pi}{4} \times \text{Bore}^2 \times \text{Stroke} ]

This method works because it essentially calculates the volume of a cylinder, which is the shape created by the piston moving within the cylinder as it travels up and down. The division by 4 accounts for the fact that when using the bore diameter, the area of the circle at the base of the cylinder needs to be calculated, requiring a conversion to find the volume.

In contrast, the other options do not correctly apply the geometry involved in a cylinder or make use of the necessary mathematical relationships correctly. For instance,