The International Standard Atmosphere (ISA)

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1 Nomenclature The International Standard Atmoshere (ISA) Mustafa Cavcar * Anadolu University, 2647 Eskisehir, Turkey a = seed of sound, m/sec g = acceleration of gravity, m/sec 2 h = altitude, m or ft = ressure, N/m 2 or hpa R = real gas constant for air, m 2 / Ksec 2 T = temerature, K or C ρ = density, kg/m 3 Subscrits = standard sea level conditions = trooause caonditions Abbreviations ICAO = International Civil Aviation Organization ISA = International Standard Atmoshere MSL = Mean Sea Level PA = Pressure Altitude 1. Standard Atmoshere Modeling For uroses of ressure altimeter calibrations, aircraft and rocket erformance and their design, and so forth, knowledge of the vertical distribution of such quantities as ressure, temerature, density, and seed of sound is required. Since the real atmoshere never remains constant at any articular time or lace, a hyothetical model must be emloyed as an aroximation to what may be exected. This model is known as the standard atmoshere. The air in the model is assumed to be devoid of dust, moisture, and water vaor and to be at rest with resect to the Earth (that is, no winds or turbulence). [1] The first standard atmosheric models were develoed in the 192's in both Euroe and the United States. The slight differences between the models were reconciled and an internationally acceted model was introduced in 1952 by the International Civil Aviation Organization (ICAO). [1] The International Standard Atmoshere 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; mcavcar@anadolu.edu.tr. 1

4 m 2 / Ksec 2 T = temerature, K or C ρ = density, kg/m 3 Subscrits = standard sea level conditions = trooause caonditions Abbreviations ICAO = International Civil Aviation Organization ISA =

2 Table 1 International Standard Atmoshere, Mean Sea Level Conditions Pressure = N/m 2 = hpa Density ρ = kg/m 3 Temerature T = K (15 C) Seed of sound a = m/sec Acceleration of gravity g = m/sec Temerature Modeling The following diagram (Figure 1) illustrates the temerature variations in the standard atmoshere: Figure 1 International Standard Atmoshere temerature variation [2]. Temerature decreases with altitude at a constant rate of -6.5 C/1m (-1.98 C/1ft) u to the trooause. The standard trooause altitude is, m (36,89 ft). Therefore, the air which is considered as a erfect gas in the ISA model resents the following characteristics within the trooshere: T h(m) = T 6.5 (1) 1 or 2

1. Temerature Modeling The following diagram (Figure 1) illustrates the temerature variations in the standard atmoshere: Figure 1 International Standard Atmoshere temerature

3 T h(ft) = T 1.98 (2) 1 For simle estimations, Equation (2) can be assumed T h(ft) = T 2 (3) 1 The temerature remains at a constant value of C ( K) from the trooause u to 2, m (65,6 ft). This ISA model is used as a reference to comare real atmosheric conditions and the corresonding engine/aircraft erformance. The atmosheric conditions will therefore be exressed as ISA +/- ISA at a given flight level [2]. Examle: Let s consider a flight in the following conditions: Altitude = 31, feet Actual Temerature = -37ºC The standard temerature at 31, feet is: T = = 47 ºC, whereas the actual temerature is -37ºC, i.e. 1ºC above the standard. Conclusion: The flight is oerated in ISA+1 conditions 1.2. Pressure Modeling To calculate the standard ressure at a given altitude, the temerature is assumed standard, and the air is assumed as a erfect gas. The altitude obtained from the measurement of the ressure is called ressure altitude (PA). Both Table 2 and Figure 2 show variation of the ressure altitude as a function of the ressure. The last column of Table 2 shows corresonding flight levels for the given ressure altitudes. The flight level is the altitude exressed in hundreds of feet. Table 2 Pressure altitude versus ressure [2]. 3

The atmosheric conditions will therefore be exressed as ISA +/- ISA at a given flight level [2].

4 Figure 2 Pressure altitude versus ressure [2]. The ressure variations for the International Standard Atmoshere can be calculated by using the hydrostatic equation, erfect gas law and the temerature lase rate equation. The hydrostatic equation for a column of air (Figure 3): d = ρgdh (4) Figure 3 A small atmoshere element. The equation of state for the erfect gas: 4

the hydrostatic equation, erfect gas law and the temerature lase rate equation.

5 = ρrt (5) where R is the real gas constant for the air. Dividing the hydrostatic equation by the equation of state gives: d ρgdh = = ρrt g RT dh (6) The relationshi between the ressure at a trooshere altitude and sea level ressure can be obtained by integrating equation (1) between h and h : Performing the above integration, we obtain: h = d g dh = R T h h= h = (7) T In equation (7), the unit of T is K, and h is in meters. Pressure above the trooause For the altitudes above the trooause, the temerature is constant, so that integrating equation (6) from the trooause to an altitude above the trooause: results in d = g RT h= h dh = e g ( h h) RT (8) where the arameters with subscrit corresond to the values at the trooause, and = hpa, T = K, and h =, m 1.3. Density Modeling Since the ressure and standard temerature are known for a given altitude, the standard density can easily be calculated from the erfect gas equation (5): 5

integrating equation (1) between h and h : Performing the above integration, we obtain: h = d g dh = R T h h=. 65 5.2561 h = 1. 65 (7) T In equation (7), the unit of T is K, and h is in meters.

6 ρ = (9) RT 2. International Standard Atmoshere (ISA) Table [2] The International Standard Atmoshere arameters (temerature, ressure, density) can be rovided as a function of the altitude under a tabulated form, as given in Table 3: Table 3 International Standard Atmoshere [2] 6

7 References [1] Talay, T.A., Introduction to the Aerodynamics of Flight, NASA SP-367, National Aeronautics and Sace Administration, Washington, D.C., 1975, [2] Airbus, Getting to Gris with Aircraft Performance, Airbus Industrie, Customer Services, Blagnac, 2,

Aeronautics and Sace Administration, Washington, D.C., 1975,. 6-9.

THE BAROMETRIC FALLACY

THE BAROMETRIC FALLACY It is often assumed that the atmosheric ressure at the surface is related to the atmosheric ressure at elevation by a recise mathematical relationshi. This relationshi is that given