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 so forth, knowledge of the vertical distribution of such quantities as pressure, temperature, density, and speed of sound is required. Since the real atmosphere never remains constant at any particular time or place, a hypothetical model must be employed as an approximation to what may be expected. This model is known as the standard atmosphere. The air in the model is assumed to be devoid of dust, moisture, and water vapor and to be at rest with respect to the Earth (that is, no winds or turbulence).  The first standard atmospheric models were developed in the 1920's in both Europe and the United States. The slight differences between the models were reconciled and an internationally accepted model was introduced in 1952 by the International Civil Aviation Organization (ICAO).  The International Standard Atmosphere is defined in ICAO Document 7488/2. The ISA assumes the mean sea level (MSL) conditions as given in Table 1.
* Professor, School of Civil Aviation; firstname.lastname@example.org.
Table 1 International Standard Atmosphere, Mean Sea Level Conditions
Pressure =0p 101 325 N/m2 = 1013.25 hPa Density =0ρ 1.225 kg/m3 Temperature =0T 288.15°K (15°C) Speed of sound =0a 340.294 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 .
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:
(m)5.60 hTT −= (1)
(ft)98.10 hTT −= (2)
For simple estimations, Equation (2) can be assumed
(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 . Example: Let's consider a...