The atmosphere is a gaseous envelope surrounding the earth. Its characteristics are different throughout the world. For this reason, it is necessary to adopt an average set of conditions called the I**nternational Standard Atmosphere** (ISA).

The international reference is based on the following standard assumptions at sea level:

– A temperature of 15°C

– A pressure of 1013.25 hPa (29.92 in Hg)

– An air density of 1.225 kg/m3

**IMPORTANT:**

– Temperature decreases with altitude at a constant rate of –6.5°C/1000m or –1.98°C/1000ft up to the tropopause.

– The standard tropopause altitude is 11,000 m or 36,089 feet. From the tropopause upward, the temperature remains at a constant value of –56.5°C.

– The air, which is considered as a perfect gas in the ISA model, presents the following

characteristics:

a) ISA temperature = T = +15°C = 288.15 K (0°C = 273.15 K)

b) Above MSL and below the tropopause (36,089 feet):

ISA temperature (ºC) = T – 1.98 × Alt(feet)/1000

Let’s make a quick example:

If you want to know whats the STANDAR TEMPERATURE at a given altitude, use the formula, in most of the cases you can do an approximate calculation using the formula:

**ISA temperature (ºC) = T – 1.98 × Alt(feet)/1000**

ISA Temperature (ºC) = +15ºC – (2.0 x (given altitude in FT))

ISA Temperature (ºC) = +15ºC – (2.0 x (7000ft/1000)))

ISA Temperature (ºC) = +15ºC – (14ºC)

ISA Temperature (ºC) = 1ºC

“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 ± ΔISA at a given flight level.”

Example:

Let us consider a flight in the following conditions:

– Altitude = 35,000 feet

– Actual Temperature = –45ºC

The standard temperature at 35,000ft is:

Formula: ISA Temperature (ºC) = +15ºC – (2.0 x (given altitude in FT))

15 – (2 × 35) = –60ºC,

whereas the actual temperature is –45ºC,

i.e. 15ºC above the standard.

Conclusion:**The flight is operated in ISA + 15 conditions.**

**Pressure Modeling**

To calculate the standard pressure P at a given altitude, the following assumptions are made:

– Temperature is standard, versus altitude.

– Air is a perfect gas.

The altitude obtained from the measurement of the pressure is called Pressure Altitude (PA), and a standard (ISA) table can be set up.

Assuming a volume of air in static equilibrium, the aerostatics equation gives:

**dP = – ρgdh**

With

> ρ = air density

> g = gravity acceleration

> dh = height of the volume unit

> dP = pressure variation on dh

The perfect gas equation gives:**P / ρ = RT**

With

> R = universal gas constant

**Consequently:**

At Mean Sea Level (MSL): Po = 1013.25 hPa

Above MSL and below the tropopause (36,089 feet):

With

> Po = 1013.25 hPa (standard pressure at sea level)

> To = 288 .15 K (standard temperature at sea level)

> α = 0.0065 ºC/m (standard temperature gradient)

> go = 9.80665 m/s2 (gravity acceleration at sea level)

> R = 287.053 J/kg/K

> h = Altitude (m)

**NOTE:** For low altitudes, a reduction of 1 hPa in the pressure approximately corresponds to a Pressure Altitude increase of 28 feet.

Above the tropopause (36,089 feet):

With

> P1 = 226.32 hPa (standard pressure at 11,000 m)

> T1 = 216.65 K (standard temperature at 11,000 m)

> h1 = 11,000 m

> go = 9.80665 m/s2

> R = 287.053 J/kg/K

> h = Altitude (m)

**Density Modeling**

To calculate the standard density ρ at a given altitude, the air is assumed to be a perfect gas. Therefore, at a given altitude, the standard density ρ (kg/m3) can be obtained as follows:**ρ= P / RT**

With

> R = universal gas constant (287.053 J/kg/K)

> P in Pascal

> T in Kelvin

At Mean Sea Level (MSL): ρ0 = 1.225 kg/m3

**International Standard Atmosphere (ISA) Table**

The International Standard Atmosphere parameters (temperature, pressure, and density) can be provided as a function of the altitude under a tabulated form.

## Published by www.aviation-performance.org (Founder)

Senior Flight Operations and Performance EngineerView all posts by www.aviation-performance.org (Founder)

**Published**