# Displacement

Animation of a four-cylinder four-stroke engine. The cubic capacity is colored orange.

The displacement or stroke volume designated for the cylinder of piston engines the enclosed volume , which consists of the working path of the single piston stroke and the effective piston cross-sectional area is obtained. It therefore defines the volume that is displaced in an engine by the stroke of all pistons.

## definition

The effective piston cross-sectional area is generally the circular area enclosed by the piston ring or the inner cylinder wall : ${\ displaystyle A}$

${\ displaystyle A = \ pi \ cdot r ^ {2},}$

where is the radius of the piston surface. ${\ displaystyle r}$

In contrast, a larger piston surface, which results from a curved instead of a flat piston end surface, is not to be used . In machines whose piston has a continuous piston rod , such as B. common in steam locomotives , the circular cross-sectional area of ​​the piston rod must be subtracted from the piston cross-section to determine the stroke volume.

The piston stroke is the distance covered between the two extreme positions of the working piston, usually referred to as top and bottom dead center in internal combustion engines .

The stroke volume thus results as the effective piston area and as the stroke path ${\ displaystyle V}$${\ displaystyle A_ {w}}$${\ displaystyle h}$

${\ displaystyle V_ {h} = A_ {w} \ cdot h,}$

usually cubic centimeters or liters are used as the unit of measurement .

With the same parameters ( speed and effective mean pressure ), the displacement is an indicator for comparing the performance of different machines and one of the parameters of an internal combustion engine . A distinction is also made between the individual cylinder displacement and the total displacement of a machine, which is equal to the sum of all cylinder displacement and, in the case of identical cylinders, results from multiplying the cylinder displacement by the number of cylinders. ${\ displaystyle V_ {h}}$ ${\ displaystyle V_ {H}}$${\ displaystyle Z}$

Depending on whether the piston stroke is larger or smaller than the diameter of the cylinder, one speaks of a long stroke or a short stroke . If the stroke and bore are the same size, one speaks of a square stroke ratio .

## calculation

Important sizes:

${\ displaystyle V_ {h} =}$ Cylinder displacement
${\ displaystyle V_ {H} =}$ Engine displacement
${\ displaystyle V_ {c} =}$ Compression space
${\ displaystyle V =}$ Combustion chamber
${\ displaystyle Z =}$ Number of cylinders
${\ displaystyle d =}$Cylinder diameter ( bore )
${\ displaystyle r =}$Cylinder radius ( )${\ displaystyle = d / 2}$
${\ displaystyle h =}$ Piston stroke (also stroke path or stroke for short), the designation is also common ${\ displaystyle s}$

### Cylinder displacement

The displacement is the volume between the bottom and top dead center of the piston of an engine cylinder and is usually specified in cm 3 or in liters. The following applies:

${\ displaystyle V_ {h} = r ^ {2} \ cdot \ pi \ cdot h}$.

### Engine displacement

For multi-cylinder engines with cylinders, if the individual cylinders have the same cubic capacity, ${\ displaystyle Z}$

${\ displaystyle V_ {H} = V_ {h} \ cdot Z.}$

### Combustion chamber

The combustion chamber is the volume enclosed by the cylinder, piston and cylinder head. It depends on the position of the piston, i.e. time-dependent during operation. If the piston is at bottom dead center, then applies

${\ displaystyle V = V_ {h} + V_ {c}.}$

In double-piston engines, two cylinders have one combustion chamber in common; the situation is more complicated.

## Internal combustion engine specifications

Due to the larger cylinder cross-sectional area, short strokes allow larger valves to be accommodated. At the same speed  , they have a lower piston speed than long-stroke engines , so they are more speed-stable and are therefore mainly used in sports cars and motorcycles.

Long-stroke engines enable better combustion chamber design and better combustion.

In general, shortly after ignition, i.e. when the gas is at its hottest, the combustion chamber resembles a flat cylinder, i.e. it has a large surface area in relation to its volume. The smaller the cylinder bore and the longer the stroke, the less flat the shape of the combustion chamber at this point in time, the smaller the surface area of ​​the combustion chamber and the lower the heat conduction losses through it.

Langhuber therefore have a slightly higher efficiency .

The trend in motor vehicle construction is increasingly towards smaller and thus lighter motors, as these have lower thermal losses due to the smaller heat transfer surfaces with the same output. However, this does not necessarily mean that large-volume motors are less efficient.

### Displacement and torque

For a given cylinder mean pressure, the size of the displacement determines the torque . Cubic capacity, mean pressure and speed together influence the performance.

Rule of thumb for naturally aspirated engines : The value for the maximum torque is around 100  Nm per liter of displacement. However, there is often a deviation in the torque value of around 10 to 15 percent - usually downwards, but increasingly also upwards.

example

If a naturally aspirated engine has a displacement of 2000 cm 3 , the maximum torque is usually 170 to 210 Nm. If it is significantly higher (over 240 Nm), it can be assumed that the engine has an engine charge such as B. an exhaust gas turbocharger or a compressor .

### Cubic capacity and road tax

The cubic capacity is often used for tax assessment , whereby the so-called tax formula is used here (situation in Germany). Since the taxes are usually staggered, engines with cubic capacities just below these limit values ​​have been built again and again, for example 1998 cm³ instead of 2000 cm³. The type designation of a motor vehicle often has the displacement in the more precise designation.

The calculation of the displacement of reciprocating piston engines according to the tax formula has been carried out in Germany since 1989 using two different methods:

• Old StVZO tax formula: total displacement = ( bore, stroke, number of cylinders; bore and stroke are to be rounded off to half a millimeter before the calculation, the result to full cubic centimeters. Note: is rounded down to 0.78, so the displacement according to the old tax formula differs slightly clearly downwards from the actual cubic capacity).${\ displaystyle 0 {,} 78 \ times d ^ {2} \ times h \ times Z}$${\ displaystyle d =}$${\ displaystyle h =}$${\ displaystyle Z =}$${\ displaystyle d}$${\ displaystyle h}$${\ displaystyle \ pi / 4}$
• New EU tax formula: total displacement ( bore, stroke, number of cylinders; bore and stroke are commercially rounded to full millimeters ; here they are rounded up to 0.7854).${\ displaystyle = 0 {,} 7854 \ times d ^ {2} \ times h \ times Z}$${\ displaystyle d =}$${\ displaystyle h =}$${\ displaystyle Z =}$${\ displaystyle d}$${\ displaystyle h}$${\ displaystyle \ pi / 4}$

Since in some cases other rounding rules apply to the tax formula, which has been changed several times, than are customary in technology, there have been and still are deviations in the cubic capacity information in the manufacturers' technical data on the one hand and the administrative data for taxation on the other. Bores enlarged by cylindrical grinding during an engine overhaul are not taken into account for taxation. When the cylinder capacity tax was introduced in Germany, the legislature intended to tax engine output; However, since this was not easily measurable at the time, the displacement - according to different formulas for two-stroke and four-stroke engines - was used as a measure of the engine power, for more details see under tax horsepower .

Numerous laws, such as the German Motor Vehicle Tax Act , also use the cubic capacity as a basis for assessment, for example driving license classes for small motorcycles . In the new registrations of passenger cars in Germany in 2008, 30.3 percent of the vehicles had a displacement of 1800 to 1999 cm³.

## Related topics

• The compression ratio describes the ratio of the combustion chamber volumes before and after compression.${\ displaystyle \ epsilon}$

## literature

• Hans Jörg Leyhausen: The master's examination in the automotive trade part 1. 12th edition, Vogel Buchverlag, Würzburg 1991. ISBN 3-8023-0857-3 .
• Peter Gerigk, Detlev Bruhn, Dietmar Danner: Automotive engineering. 3rd edition, Westermann Schulbuchverlag GmbH, Braunschweig 2000. ISBN 3-14-22-1500-X .
• Max Bohner, Richard Fischer, Rolf Gscheidle: Expertise in automotive technology. 27th edition, Verlag Europa-Lehrmittel, Haan-Gruiten 2001. ISBN 3-8085-2067-1 .