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The International Standard Atmosphere (ISA)
Mustafa Cavcar* Anadolu University, 26470 Eskisehir, Turkey
Nomenclature a = speed of sound, m/sec g = acceleration of gravity, m/sec2 h = altitude, m or ft p = pressure, N/m2 or hPa R = real gas constant for air, 287.04 m2/°Ksec2
T = temperature, °K or °C ρ = density, kg/m3 Subscripts 0 = standard sea level conditions 11 = tropopause caonditions Abbreviations ICAO = International Civil Aviation Organization ISA = International Standard Atmosphere MSL = Mean Sea Level PA = Pressure Altitude
1. Standard Atmosphere Modeling For purposes of pressure altimeter calibrations, aircraft and rocket performance and their design, and ...view middle of the document...
294 m/sec Acceleration of gravity =0g 9.80665 m/sec2
1.1. Temperature Modeling
The following diagram (Figure 1) illustrates the temperature variations in the standard atmosphere:
Figure 1 International Standard Atmosphere temperature variation [2].
Temperature decreases with altitude at a constant rate of -6.5°C/1000m (-1.98°C/1000ft) up to the tropopause. The standard tropopause altitude is 11,000 m (36,089 ft). Therefore, the air which is considered as a perfect gas in the ISA model presents the following characteristics within the troposphere:
1000
(m)5.60 hTT −= (1)
or
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1000
(ft)98.10 hTT −= (2)
For simple estimations, Equation (2) can be assumed
1000
(ft)20 hTT −= (3)
The temperature remains at a constant value of -56.5°C (216.65°K) from the tropopause up to 20,000 m (65,600 ft). This ISA model is used as a reference to compare real atmospheric conditions and the corresponding engine/aircraft performance. The atmospheric conditions will therefore be expressed as ISA +/- ∆ISA at a given flight level [2]. Example: Let's consider a flight in the following conditions:
Altitude = 31,000 feet Actual Temperature = -37ºC
The standard temperature at 31,000 feet is: 4731215 −=×−=T ºC, whereas the actual temperature is -37ºC, i.e. 10ºC above the standard. Conclusion: The flight is operated in ISA+10 conditions
1.2. Pressure Modeling To calculate the standard pressure p at a given altitude, the temperature is assumed standard, and the air is assumed as a perfect gas. The altitude obtained from the measurement of the pressure is called pressure altitude (PA). Both Table 2 and Figure 2 show variation of the pressure altitude as a function of the pressure. The last column of Table 2 shows corresponding flight levels for the given pressure altitudes. The flight level is the altitude expressed in hundreds of feet.
Table 2 Pressure altitude versus pressure [2].
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Figure 2 Pressure altitude versus pressure [2].
The pressure variations for the International Standard Atmosphere can be calculated by using ...
