Link to: Piston Cylinder Surface Area Applet
Derivation of Slider-Crank Model
The volume of the piston cylinder can be determined as a function of crank angle from the compression ratio, the stroke, bore and connecting rod length. The geometric parameters of the piston cylinder are represented in Figure 1.
Top dead center refers to the position of the crank shaft at an crank angle of 0o. This position is otherwise known as the clearance volume, Vc. At bottom dead center the crank angle is at 180 o. In this position the cylinder volume is at its maximum, V1. The difference between the maximum and minimum volume, V1- Vo, is defined as the displacement volume, Vd. The displacement volume can also be represented as a function of the bore and stroke:
The final form of the Slider-Crank model is given as a non-dimensional relationship by dividing both sides of equation (6) by Vd.
Derivation of Surface Area of the Piston Cylinder
In order to study the effect of heat transfer within the piston cylinder, the surface area of the cylinder has to be evaluated. The combustion chamber surface area is given by:
The equation can be further approximated by: