8.1 — Physics of the Atmosphere

Introduction

Every aircraft flies within the Earth's atmosphere, and the behaviour of that atmosphere — its temperature, pressure, and density — has a direct and profound effect on aircraft performance, engine power output, instrument readings, and aerodynamic forces. An aircraft that produces 250 kN of thrust at sea level will produce significantly less at 35,000 ft because the air is thinner. An airspeed indicator calibrated for sea-level conditions will read differently at altitude unless corrections are applied. For these reasons, a thorough understanding of atmospheric physics is essential for every aircraft maintenance engineer.

Composition of the Atmosphere

The Earth's atmosphere is a mixture of gases held in place by gravity. By volume, dry air at sea level consists of:

Gas	Chemical Formula	Volume %
Nitrogen	N₂	78.08 %
Oxygen	O₂	20.95 %
Argon	Ar	0.93 %
Carbon dioxide	CO₂	0.04 %
Trace gases	Ne, He, CH₄, etc.	< 0.01 %

This composition remains remarkably constant up to about 80 km altitude. The two dominant gases — nitrogen and oxygen — together make up 99 % of the atmosphere. Although oxygen is the gas essential for both human life and combustion in aircraft engines, nitrogen plays an important role as an inert dilutant that moderates the chemical reactivity of pure oxygen.

In addition to these fixed gases, the atmosphere contains variable amounts of water vapour (0 – 4 % by volume). Water vapour is critically important for aviation because:

• Water vapour is less dense than dry air — the molecular weight of water (H₂O = 18) is lower than that of nitrogen (N₂ = 28) or oxygen (O₂ = 32). When water vapour displaces these heavier molecules, the resulting humid air is less dense than dry air at the same temperature and pressure.
• Lower density reduces performance — less dense air means less aerodynamic lift for a given airspeed and angle of attack, and less mass of air entering the engine per second, reducing thrust or power output.
• Water vapour causes weather — condensation of water vapour produces clouds, rain, snow, ice, and fog — all of which affect aviation operations.
• Water vapour can cause icing — when moisture in the atmosphere freezes on aircraft surfaces, it degrades aerodynamic performance and can block pitot tubes and engine intakes.

Regions (Layers) of the Atmosphere

The atmosphere is divided into distinct layers based on how temperature changes with altitude. The boundaries between layers are called pauses (tropopause, stratopause, mesopause). Understanding these layers is important because each has different characteristics that affect flight.

Troposphere (0 – ~11 km / 0 – ~36,000 ft)

The troposphere is the lowest and most important layer for aviation. It extends from the Earth's surface to the tropopause, which is at approximately 11 km (36,000 ft) altitude in the ISA. The word "troposphere" comes from the Greek tropos, meaning "turning" or "mixing," reflecting the turbulent, weather-producing nature of this layer.

Key characteristics of the troposphere:

• Contains approximately 75 % of the total mass of the atmosphere — the air is densest near the surface and becomes progressively thinner with altitude.
• Temperature decreases with altitude at an average rate of approximately 6.5 °C per 1,000 m (about 2 °C per 1,000 ft). This rate of temperature change is called the Environmental Lapse Rate (ELR). The reason temperature decreases is that the ground absorbs solar radiation and heats the air from below — the further you go from this heat source, the cooler it gets.
• All significant weather occurs in the troposphere — clouds, rain, snow, thunderstorms, turbulence, icing, and wind shear are all tropospheric phenomena. This is because the troposphere contains virtually all of the atmosphere's water vapour and has the vertical temperature profile that drives convective air currents.
• Virtually all commercial and general aviation takes place here — or in the very lowest part of the stratosphere. Turboprop aircraft typically cruise at 20,000–30,000 ft, while jet airliners cruise at 30,000–43,000 ft.
• Wind speed generally increases with altitude — surface friction slows winds near the ground. At higher levels, winds can be very strong, especially in the jet stream (narrow bands of very high-speed wind near the tropopause, often 100–200 knots).

Tropopause (~11 km / ~36,000 ft)

The tropopause is the boundary between the troposphere and the stratosphere. It is not a sharp line but rather a transition zone where the temperature lapse rate decreases to zero — temperature stops falling and either remains constant or begins to increase.

The tropopause is not at the same altitude everywhere:

• At the poles: approximately 8 km (26,000 ft) — lower because polar air is colder and denser, so it compresses the troposphere
• At the equator: approximately 16–18 km (52,000–59,000 ft) — higher because tropical air is warmer and expands the troposphere upward
• At mid-latitudes (ISA standard): approximately 11 km (36,089 ft)
• The tropopause also varies with season (higher in summer, lower in winter) and with weather systems (higher in high-pressure systems, lower in low-pressure systems)

The tropopause is significant for aviation because it often marks the upper boundary of weather — flying above the tropopause generally means smooth, clear air. The jet stream is found near the tropopause, particularly where there are sharp breaks or discontinuities in its height.

Stratosphere (~11 – 50 km)

The stratosphere extends from the tropopause to the stratopause at about 50 km. The name comes from the Latin stratum, meaning "layer," because the air here forms stable, horizontal layers with very little vertical mixing.

• Temperature increases with altitude in the stratosphere. In the lower stratosphere (from 11 km to about 20 km), temperature remains approximately constant at −56.5 °C (in the ISA). Above 20 km, it begins to rise, reaching about 0 °C at the stratopause (50 km).
• The reason for this temperature increase is the ozone layer — a region of high ozone (O₃) concentration centred at about 25 km altitude. Ozone absorbs ultraviolet (UV) radiation from the sun, converting it to heat. This heating warms the upper stratosphere.
• Very little weather — because temperature increases with altitude (a temperature inversion), the stratosphere is extremely stable. Warm air over cold air suppresses vertical motion, so there is virtually no convection, no clouds (except rare nacreous/polar stratospheric clouds), and no turbulence.
• Some high-altitude aircraft operate here — Concorde cruised at about 60,000 ft (18 km), and military reconnaissance aircraft like the U-2 and SR-71 routinely flew in the stratosphere.

Mesosphere (~50 – 85 km)

The mesosphere extends from the stratopause to the mesopause at about 85 km. Temperature decreases again with altitude in this layer, reaching the coldest temperatures in the entire atmosphere — as low as −90 °C at the mesopause. Meteors burn up in the mesosphere due to friction with the (still present but very thin) air molecules. This layer is above the operating altitude of all aircraft but below orbital altitude, making it difficult to study directly — it is sometimes called the "ignorosphere."

Thermosphere (~85 – 600 km)

The thermosphere is the outermost significant layer. Temperature increases rapidly due to absorption of extremely energetic solar radiation by the sparse gas molecules. Temperatures can reach 1,000 °C or more, but because the air is so thin, these temperatures would not feel "hot" in the conventional sense — there are simply too few molecules to transfer significant heat. The International Space Station orbits within the thermosphere at about 400 km altitude. The aurora borealis (northern lights) and aurora australis (southern lights) occur in this layer.

International Standard Atmosphere (ISA)

The real atmosphere is constantly changing — it varies with geographic location, time of day, season, and weather patterns. On a hot summer day in Dubai, sea-level conditions are radically different from those on a cold winter day in Tromsø, Norway. This variability creates a problem: how can we compare aircraft performance data, calibrate instruments, or design aircraft when the atmospheric conditions keep changing?

The solution is the International Standard Atmosphere (ISA) — a fixed, internationally agreed reference model of the atmosphere. The ISA was originally defined by ICAO (International Civil Aviation Organization) and is also published in ISO 2533. It does not represent the actual atmosphere at any particular place or time — it is a theoretical model used as a common reference baseline.

ISA Sea-Level Conditions

The ISA defines the following values at mean sea level (MSL):

Property	ISA Value	Equivalent Values
Temperature	15 °C	288.15 K / 59 °F
Pressure	1013.25 hPa (mb)	29.92 inHg / 760 mmHg / 14.696 psi / 101,325 Pa / 1 atm
Density	1.225 kg/m³	0.002377 slugs/ft³
Temperature lapse rate	−6.5 °C per 1,000 m	≈ −1.98 °C per 1,000 ft
Tropopause altitude	11,000 m	36,089 ft
Tropopause temperature	−56.5 °C	216.65 K
Speed of sound at MSL	340.3 m/s	661.5 knots / 1,116 ft/s
Gravitational acceleration	9.80665 m/s²	32.174 ft/s²

ISA Temperature Lapse Rate

The ISA assumes a constant temperature lapse rate of 6.5 °C per 1,000 metres (approximately 2 °C per 1,000 feet) throughout the troposphere. This means that for every 1,000 m you climb, the temperature drops by 6.5 °C. The lapse rate continues until the tropopause is reached at 11,000 m (36,089 ft), where the temperature has fallen to −56.5 °C. Above the tropopause, in the ISA, the temperature remains constant at −56.5 °C throughout the lower stratosphere (up to 20 km).

ISA Deviation

In the real world, the actual atmospheric temperature rarely matches the ISA exactly. The difference between the actual (observed) temperature and the ISA temperature at the same altitude is called the ISA deviation, expressed as ISA ± X °C.

ISA deviation is important because aircraft performance data (take-off distances, climb rates, engine thrust ratings) are published for ISA conditions. When the actual conditions differ, corrections must be applied. A positive ISA deviation (warmer than standard) means reduced performance — lower air density, less engine thrust, longer take-off distances, and reduced climb rates.

Application of ISA to Aerodynamics

The ISA is not just a theoretical curiosity — it is the practical foundation upon which aircraft are designed, certified, and operated. Here are the major applications:

1. Aircraft Performance Calculations

All performance data in the Aircraft Flight Manual (AFM) — take-off distances, landing distances, climb gradients, cruise performance, ceiling — are calculated and published for ISA conditions. When the actual conditions differ, the pilot (or performance engineer) must apply corrections. For example:

• On a hot day (ISA+20), the air density is significantly lower than standard. An aircraft that needs 1,800 m of runway at ISA conditions might need 2,200 m or more at ISA+20.
• At a high-altitude airport (e.g., Addis Ababa at 7,625 ft), the lower pressure means lower density, requiring longer take-off runs and reducing climb performance.
• When both high temperature AND high altitude combine (e.g., a hot day at a high-altitude airport), the performance penalties are compounded, potentially making operations unsafe if not properly accounted for.

2. Altimeter Calibration and Pressure Altitude

A pressure altimeter is essentially a calibrated barometer — it measures atmospheric pressure and converts it to an altitude reading using the ISA pressure-altitude relationship. If the actual atmospheric conditions match the ISA exactly, the altimeter reads correctly. In reality, they never match exactly, so corrections are needed:

• QNH setting — the altimeter is adjusted to show altitude above mean sea level by setting the actual sea-level pressure on the altimeter's subscale. This corrects for the difference between the actual sea-level pressure and the ISA standard of 1013.25 hPa.
• QFE setting — the altimeter is adjusted to show zero on the ground at the airfield (height above the airfield).
• Standard pressure setting (1013.25 hPa) — above the transition altitude, all aircraft set their altimeters to 1013.25 hPa. The resulting reading is called pressure altitude or flight level. This ensures vertical separation between aircraft regardless of local pressure variations.
• Temperature error — the altimeter corrects for pressure but not for temperature. In cold air (ISA−), the aircraft is lower than the altimeter indicates (because cold, dense air compresses the pressure levels closer together). This is summarised by the rule: "From high to low (temperature), look out below."

3. Airspeed Indicator Calibration

The airspeed indicator (ASI) measures the difference between total pressure (from the pitot tube) and static pressure (from the static port). This difference is called dynamic pressure, and it is related to airspeed by:

The ASI is calibrated assuming ISA sea-level density (1.225 kg/m³). The speed it displays is called Indicated Airspeed (IAS). At sea level in ISA conditions, IAS equals True Airspeed (TAS). At altitude, where the actual density is lower than 1.225 kg/m³, the IAS under-reads compared to TAS. The various airspeed definitions are:

Airspeed	Abbreviation	Definition
Indicated Airspeed	IAS	The reading on the airspeed indicator (uncorrected)
Calibrated Airspeed	CAS	IAS corrected for instrument and position errors
Equivalent Airspeed	EAS	CAS corrected for compressibility effects (significant above ~250 kt and at high altitude)
True Airspeed	TAS	EAS corrected for density — the actual speed of the aircraft through the air mass. TAS is always higher than IAS at altitude.

4. Engine Performance

Both jet engines and piston engines depend on the mass of air they can ingest per unit time. This mass flow rate depends directly on air density. Since density decreases with altitude (and with increasing temperature), engine performance degrades at altitude and in hot conditions:

• Jet engines — thrust decreases approximately in proportion to the decrease in density. A turbofan engine producing 100 kN at sea level ISA might produce only about 25 kN at 35,000 ft.
• Piston engines — power output decreases with altitude unless the engine is supercharged or turbocharged. A naturally aspirated piston engine loses approximately 3–4 % of its power for every 1,000 ft of altitude gain.
• All engine ratings in the Type Certificate Data Sheet (TCDS) are referenced to ISA conditions. When testing engines during maintenance, the measured performance must be corrected to ISA conditions for comparison with the published limits.

Temperature Variation with Altitude — Detailed

The decrease in temperature with altitude in the troposphere occurs because the primary heat source for the lower atmosphere is the Earth's surface, not direct solar radiation. The sun's energy passes through the atmosphere relatively freely and warms the ground. The ground then re-radiates this energy as infrared (heat) radiation and also heats the air in direct contact with it through conduction. This warm surface air then rises by convection, carrying heat upward. However, as air rises, it expands (because atmospheric pressure decreases with altitude), and this expansion causes the air to cool (adiabatic cooling). The net result is that the further from the ground, the cooler the air — this is the temperature lapse rate.

The actual (environmental) lapse rate varies with location and conditions — it can be greater than, equal to, or less than the ISA standard of 6.5 °C/km. In some situations, a temperature inversion occurs where temperature actually increases with altitude over a limited height band. Inversions are significant because they suppress vertical air movement, trapping pollutants and moisture below them, and can cause wind shear at their boundaries.

Pressure Variation with Altitude — Detailed

Atmospheric pressure at any point is caused by the weight of all the air above that point. As you climb higher, there is less air above you, so the pressure decreases. The key points about pressure variation are:

• Pressure decrease is NOT linear — it is exponential. Pressure drops rapidly at low altitudes (where the air is dense and heavy) and more slowly at high altitudes (where the air is thin and light). Near sea level, pressure drops by about 1 hPa for every 27 feet of altitude gain. At 18,000 ft, the same 1 hPa drop requires about 50 feet of altitude change.
• The pressure halving rule — a useful approximation: pressure halves approximately every 18,000 ft (5.5 km). Starting from 1013 hPa at sea level: ~500 hPa at 18,000 ft, ~250 hPa at 36,000 ft, ~125 hPa at 54,000 ft.

Altitude	ISA Pressure (hPa)	% of Sea Level	Flight Level
Sea level (0 ft)	1013.25	100 %	—
5,000 ft (1,524 m)	843	83 %	FL050
10,000 ft (3,048 m)	697	69 %	FL100
18,000 ft (5,486 m)	507	50 %	FL180
25,000 ft (7,620 m)	376	37 %	FL250
30,000 ft (9,144 m)	301	30 %	FL300
35,000 ft (10,668 m)	238	24 %	FL350
36,089 ft (11,000 m)	227	22 %	FL360
40,000 ft (12,192 m)	188	19 %	FL400

Density Variation with Altitude — Detailed

Air density is the mass of air per unit volume, measured in kg/m³. It is the single most important atmospheric property for aerodynamics, because both the lift equation and the drag equation contain density as a direct multiplier. If density halves, lift halves (for the same speed and angle of attack).

Density depends on both pressure and temperature, related by the equation of state (ideal gas law):

From this equation, we can see three fundamental relationships:

Factor	Change	Effect on Density	Reason
Pressure	Decreases (higher altitude)	Density decreases	Fewer molecules per unit volume (P is in the numerator)
Temperature	Increases (hotter day)	Density decreases	Molecules move faster and spread apart (T is in the denominator)
Humidity	Increases (more moisture)	Density decreases	Water vapour molecules (mass 18) replace heavier N₂ (28) and O₂ (32) molecules

All three factors that reduce density — high altitude, high temperature, and high humidity — have the same effect on aircraft performance: degraded performance. Specifically:

• Less lift for a given airspeed and angle of attack → the aircraft must fly faster or at a higher angle of attack to maintain level flight
• Less engine thrust/power → less mass of air flows through the engine per second
• Longer take-off and landing distances → less acceleration from engines, less aerodynamic braking
• Reduced rate of climb → less excess thrust available for climbing
• Lower service ceiling → the altitude at which the aircraft can barely maintain level flight

Density Altitude

Density altitude is a concept that combines the effects of altitude, temperature, and (to a lesser extent) humidity into a single, easy-to-use number. It is defined as:

The altitude in the ISA at which the actual air density would be found.

In other words, density altitude answers the question: "Given the current air density, what altitude in the ISA would have this same density?"