# Basic geometric parameters of the ICE’s piston and cylinder

In order to characterize the basic performance of an internal combustion engine, over its operating range, we can use some parameters and geometrical relationships of the piston and combustion chamber. Engine performance relates to both fuel efficiency and dynamic output (power and torque), which are influenced directly by the basic parameters of the engine.

To recall the working principles of an internal combustion engine works read the article How an internal combustion engine works.

The main geometric parameters of the cylinder, piston, connecting rod and crankshaft are depicted in the image below.

where:

IV – intake valve
EV – exhaust valve
TDC – top dead center
BDC – bottom dead center
B – cylinder bore
S – piston stroke
r – connecting rod length
a – crank radius (offset)
x – distance between the crank axis and the piston pin axis
θ – crank angle
Vd – displaced (swept) volume
Vc – clearance volume

The piston moves within the cylinder between TDC and BDC. In order to complete a full combustion cycle, the piston executes four strokes and the crankshaft makes two complete turns. The displaced volume is the volume in which the piston moves, the clearance volume is the volume left in the cylinder when the piston reaches TDC.

In this tutorial we are going to look into how to calculate the volumetric capacity of the engine , what the compression ratio is and which are the main geometric parameters of the engine.

For one cylinder, the displaced volume Vd is the product between the stroke of the piston and the area of the cylinder (nearly the same with the area of the piston):

$V_d = S A_c$

The area of the cylinder is:

$A_c = \frac{\pi B^2}{4}$

This gives the volumetric capacity of one cylinder which is equal with the displaced volume:

$V_d = S \frac{\pi B^2}{4}$

To find the total volumetric capacity (displacement) of the engine, we only have to multiply the volumetric capacity of one cylinder with the number of cylinders Nc:

$V_d = N_c S \frac{\pi B^2}{4}$

Let’s take an example of engine and calculate the volumetric capacity. In the article BMW’s iPerformance plug-in hybrid electric vehicle (PHEV) powertrain architecture we have the technical specification of the internal combustion engine:

S = 94.6 mm
 B = 82 mm
 Nc = 4

Replacing the values in the expression of Vd, gives:

$V_d = 1998336.9 \text{mm}^3 = 1998.3369 \text{cm}^3$

The technical specification states that the engine capacity is 1998 cm3, which is the same with the calculated volume.

Engine displacement is usually given in liters L, cubic centimeters cm3 (SI) or cubic inches in3 (US). The bore and stroke are given in mm so we need to apply a conversion in order to get the requested unit for the volume:

$1 L = 10^{-3} \text{m}^3 = 10^3 \text{cm}^3 = 10^6 \text{mm}^3 = 61 \text{in}^3$

The displacement of the modern internal combustion engines varies between 1.0 L and around 6.0 L, with the average of around 1.5 – 2 L. There is a clear tendency of decreasing the volumetric capacity of an engine (downsizing) in order to fulfill the more stringent fuel emission standards.

The basic geometry of a piston (reciprocating) internal combustion engine is defined by the following parameters:

• compression ratio
• ratio of cylinder bore to piston stroke
• ratio of connecting rod length to crank radius (offset)

The compression ratio is calculated as the ratio between the maximum (total) volume of the cylinder (when the piston is at BDC) and the minimum (clearance) volume (when the piston is as TDC).

In the technical literature the Greek letter epsilon ε is used to define the compression ratio of an engine.

$\varepsilon = \frac{V_{max}}{V_{min}}= \frac{V_c + V_d}{V_c}$

Most of the modern spark ignition (gasoline) engines have compression ratios between 8 and 11, while compression ignition (diesel) engines have compression ratios in the range 12 to 24.

Usually internal combustion engines which are supercharged or turbocharged have a lower compression ratio than naturally aspirated engines.

The higher the compression ratio, the higher the combustion pressure in the cylinder. The maximum value of the compression ratio depends mainly on engine materials, technology and fuel quality.

Because it depends on the geometry of the engine, the compression ratio is fixed. There are various attempts to develop engines with a variable compression ratio which should have a better overall efficiency.

The ratio of cylinder bore to piston stroke is most of the time defined as the Greek letter zeta ζ:

$\zeta = \frac{B}{S}$

For passenger road vehicles the bore to stroke ratio is usually from 0.8 to 1.2. When the bore is equal to the stroke, B = S, the engine is called square engine. If the stroke is higher than the bore the engine is under square. If the length of the stroke is less than the bore diameter the engine is called over square. For our example the bore to stroke ratio is 0.87.

The connecting rod length to crank radius ratio is usually defined as R:

$R = \frac{r}{a}$

For small engines R is between 3 and 4, for large engine starts from 5 up to 10.

For a fixed volumetric capacity of the engine, a longer stroke allows for a smaller bore (under square). The advantage is a lower surface area in the combustion chamber and correspondingly less heat loss. This will improve the thermal efficiency within the combustion chamber. The disadvantage is that the longer stroke, the higher piston speed and higher friction losses, which reduce the effective engine power.

If the stroke is reduced, the bore diameter must be increased and the engine will be over square. This results in lower friction losses but increases heat transfer losses. Most of the modern automobile engines are near square, with some slightly over square and some slightly under square.

In the table below there are several examples of internal combustion engines with their main geometric parameters.

 Manufacturer Fuel # of cylinders Engine capacity [cm3] Bore [mm] Stroke [mm] ζ [-] ε [-] Fiat Gasoline 2 875 80.5 86 0.94 10:1 Renault Gasoline 3 898 72.2 73.1 0.99 9.5:1 Audi Diesel 3 1422 79.5 95.5 0.83 19.5:1 Renault Gasoline 4 1149 69 76.8 0.9 9.8:1 Mazda Gasoline 4 1496 74.5 85.8 0.87 14:1 VW Diesel 4 1598 79.5 80.5 0.99 16.5:1 Renault Diesel 4 1598 80 79.5 1.01 15.4:1 Honda Gasoline 4 2157 87 90.7 0.96 11.1:1 Mazda Diesel 4 2184 86 94 0.91 14:1 Porsche Gasoline 6 2893 89 77.5 1.15 11.5:1 BMW Diesel 6 2993 84 90 0.93 16.5:1 Ford Gasoline 8 4951 92.2 92.7 0.99 11:1 VW Diesel 10 4921 81 95.5 0.85 18:1

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