Estimating and calculating air density for wind turbine

The air density, ρ, changes slightly with air temperature and with elevation. The ratings for wind turbines are based on standard conditions of 59° F (15° C) at sea level. A density correction should be made for higher elevations as shown in the Air Density Change with Elevation graph. A correction for temperature is typically not needed for predicting the long-term performance of a wind turbine

Temperature and pressure

The density of dry air can be calculated using the ideal gas law, expressed as a function of temperature and pressure:

where ρ is the air density, p is absolute pressure, R is the specific gas constant for dry air, and T is absolute temperature.

The specific gas constant for dry air is 287.058 J/(kg·K) in SI units, and 53.35 (ft·lb_f)/(lb_m·R) in United States customary and Imperial units.

Therefore:

• At IUPAC standard temperature and pressure (0 °C and 100 kPa), dry air has a density of 1.2754 kg/m³.
• At 20 °C and 101.325 kPa, dry air has a density of 1.2041 kg/m³.
• At 70 °F and 14.696 psia, dry air has a density of 0.074887 lb_m/ft³.

Other Method

While air temperature data is not too hard to come by (and is relatively cheap to
measure even if you don't have data already), air pressure data can be tougher to find. If air
pressure data for your region is unobtainable, you can estimate density as just a function of site
elevation and temperature with the following expression.
ρ = (Po / RT) exp(-g*z/RT) (kg/m3)
where Po = standard sea level atmospheric pressure (101,325 Pascals) [or you can use a sealevel
adjusted pressure reading from a nearby weather station];
g = the gravitational constant (9.8 m/s2); and
z = the region's elevation above sea level (in meters)

Altitude

Standard Atmosphere: p₀=101325 Pa, T₀=288.15 K, ρ₀=1.225 kg/m³

To calculate the density of air as a function of altitude, one requires additional parameters. They are listed below, along with their values according to the International Standard Atmosphere, using theuniversal gas constant instead of the specific one:

• sea level standard atmospheric pressure p₀ = 101325 Pa
• sea level standard temperature T₀ = 288.15 K
• Earth-surface gravitational acceleration g = 9.80665 m/s².
• temperature lapse rate L = 0.0065 K/m
• universal gas constant R = 8.31447 J/(mol·K)
• molar mass of dry air M = 0.0289644 kg/mol

Temperature at altitude h meters above sea level is given by the following formula (only valid inside thetroposphere):

The pressure at altitude h is given by:

Density can then be calculated according to a molar form of the original formula:

Detail About estimating and calculating air density can be found in PDF tutorial by Oklahoma University, Just Download Here

those tutorial provide 3 different methods to calculate air density, although the best methods is using elevation or altitude theory