# How tall is Otto Thorwarth

## Internal combustion engine (3): displacement, compression ratio04.01.2010, 12:55

When calculating the combustion chamber, the displacement, the stroke-to-bore ratio and the compression ratio are key terms. They are explained and supported by calculation examples.

### Calculations on the engine

1. Displacement

Image: The cylinder space consists of the displacement VH and the compression space Vc. The compression ratio ε (epsilon) indicates how many times larger the cylinder space is than the compression space. For example, if ε = 7: 1, then the cylinder space is seven times larger than the compression space (see below).

When the piston moves back and forth, its direction of movement changes at the upper and lower turning point. These reversal points are the top and bottom dead center (TDC and BDC).
Because the piston area is a circular area, the displacement is a cylindrical volume with the calculation parameters: cylinder bore meter d in cm, piston stroke s in cm. This results in the calculation formula:
Cylinder displacement = cylinder cross-section times stroke or
Fo 1: V.H = A • s (cm3)
If the cross section A = d2 If π / 4 is inserted into the formula, then the cylinder displacement is:

Fo 2:V.H = d2• π / 4 • s (cm3)
The units of measure for cubic capacity are: cm3 or dm3 (1 dm3 = 1l (liter)).
Note: The bore diameter d and the stroke s are given in mm; Before inserting them into the calculation formula, they must be converted into the desired unit of measurement, cm or dm.

Both the stroke s and the bore diameter d can be calculated from the cylinder displacement. To do this, the displacement formula must be converted according to the size you are looking for:

Fo 3 and Fo 4:

In the case of multi-cylinder engines, the total displacement of engine V resultsH from the cylinder displacement VH multiplied by the number of cylinders z, i.e. (Fo 5):

2. Stroke-to-bore ratio

In practice, there are three different options for designing the combustion chamber: The specified displacement of an engine can either be achieved with a large cylinder bore and a small stroke (short stroke); if the stroke and bore are the same size, an speaks of a square hub. Finally, a combination of small bore diameters and large strokes (long stroke) is possible. Each of the three different types has its advantages and disadvantages. The ratio between the motor bore and the stroke is referred to as the stroke-to-bore ratio α.
Fo 6:α = s: d
Like all ratios, the stroke-to-bore ratio is dimensionless.

3. Compression ratio

The cylinder space consists of the displacement V.H and the compression space Vc. The sucked-in air (diesel engine) or the sucked-in fuel-air mixture (gasoline engine) is compressed to the volume of the compression chamber in the compression stroke when the piston has reached top dead center.

Compression ratio ε = (VH+ Vc): Vc
or Fo 7:
ε = (VH: Vc) + 1
In it are:
ε = Compression ratio
V.H = Cylinder displacement (cm3)
V.c = Compression space (cm3)

1. What is the cylinder displacement VH (in cm3) of a tractor engine with a bore diameter of d = 114 mm with a stroke of s = 122 mm?

2. The cylinder displacement of a 4-cylinder VH = 1032 cm3. How big is the bore diameter with a stroke of 72 mm?

3. The cylinders of a six-cylinder engine have a bore diameter of 106 mm and a stroke of s = 125 mm. How big is the total displacement in liters?

4. What is the compression ratio of a gasoline engine with a cylinder displacement of V?H = 470 cm3 and a compression space of Vc= 58 cm3?

5. A cylinder with a bore diameter of 120 mm has a stroke-to-bore ratio of 1.1333. How big is the hub?

6. A gasoline engine has a VH = 230 cm3 and an ε = 7.5: 1. How big is the conurbation?

### solutions

1st V.H = A • s = d2 • π / 4 • s = (11.4 cm)2 • π / 4 • 12.2 cm =
V.H = 1245.26 cm3

2nd V.H = VH : 4 = 1032 cm3: 4 = 258 cm3
V.H = d2 • π / 4 • s -> d see formula Fo 3 -> d = 67.55 mm

3. Calculate in dm to get liters:
V.H = d2 • π / 4 • s • z = (1.06 dm)2 • π / 4 • 1.25 dm • 6 =
V.H = 6,619 l

4.ε = (VH: Vc) + 1 = (470 cm3: 58 cm3) + 1 = 9,1 = 9,1 : 1

5. α = s: d -> s = d • α = 120 mm • 1.133 = 136 mm

6.ε = (VH: Vc) + 1 –>
V.c = Vh: (ε - 1) = 230 cm3 : 6,5
V.c= 35.38 cm3