Data Reduction to Standard Conditions

The performance of an internal combustion engine depends on the amount of air or, more precisely, the amount of oxygen, which can be burned in one engine cycle. This amount can be expressed as a function of the density of air, which is depending on atmospherical conditions. The density specifies the mass of air, which is contained in a certain volume. Because the atmosphere is a compressible gas, pressure and temperature have a strong influence on its density. Additionally, the amount of oxygen is reduced, when the humidity is increased.

For a comparison of engine test results it is common to reprocess the data as if they were taken at standard conditions. These standard conditions are selected arbitrarily and one possible set is listed in table 1 below.

Determination of the Correction Factors

We can split the correction into three parts, namely

The correction factors, derived in the following sections, are applied to the actual, measured data to find the equivalent power and rotational speed at standard conditions. Using the inverted factors, we can convert from standard to arbitrary conditions. The correction can be up to 10% of the power, depending on the conditions of the atmosphere.

Pressure Correction

The density of the air depends directly on the ambient pressure, which leads to a pressure correction of

.

Temperature Correction

The influence of the temperature is similar to the pressure and results in the correction factor

C_T = (T/T_0)^k,

where
k = 1.4 is the isentropic exponent (ratio of specific heats).

Humidity Correction

For the humidity correction it is necessary to consider the amount of water in the air to derive the mass of air which is available for combustion. Usually, the relative humidity is used to measure the amount of water in the air. The relative humidity is the ratio of the actual mass of water in the air to the maximum possible value, which depends on the temperature. When the maximum is reached, we can observe fog as the excess water starts to drop out of the air. A relative humidity of 100% does not mean, that we are under water; instead, we have vaporized the maximum possible amount of water. Hot air can hold more water than cold air - 50% relative humidity at 0C means less water in the air that 50% at 30C (in winter the air is dry, so that some people try to raise the humidity in their rooms artificially). When hot, humid air is cooled down, its relative humidity is increasing until water drops out - this can be observed in refrigerators and air conditioning units.

Using the partial pressure of the water vapor and some thermodynamics leads to the expression

C_H = P / (P - (P_H*R_H - P_H0*R_H0)),

where

is the partial pressure for the current ambient temperature T, (see tables of the properties of steam),
is the relative humidity,
is the partial pressure for the standard conditions.

Density Correction

If we use a propeller to brake the engine, we have to take into account, that not only the power of the engine depends on atmospherical conditions, but also the power required by the propeller. Recalling the performance coefficient of a propeller:

we see, that it contains the density of air. Assuming, that the Reynolds numbers are fairly close, the power coefficient for a given propeller will always be the same. Rearranging the equation and setting up the relation between two different atmospherical conditions, we find, that the velocity of rotation depends on the density and the power input. On a hot day, with low pressure, the density of air is smaller than on a standard day, which makes it is easier to turn a propeller at a given speed. The correction factors for the engine power have been derived above, so that we end up with a factor CR, describing the influence of the density of air on the propeller speed:

.

If we do not use a propeller to brake the engine, we can set this correction factor to 1.0.

Correcting Performance Data

When the three correction factors have been calculated, the power for each measured data point has to be multiplied by these factors:

.

Also, the rotational velocity has to be corrected. With the aerodynamic characteristics of a propeller, this correction leads to the corrected speed

.

 

Ambient Temperature T0 288.15 K 15 C
Ambient Pressure 100000 Pa  
Relative Humidity 75 %  
Table 1: Standard conditions for performance comparisons

 

Last modification of this page: 21.05.18

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