Density and temperature

Air density and temperature

Air density (ρ) is the mass of air per volume. It is a key quantity for aerodynamics (lift, thrust, drag).

Source: ICAO Doc 7488 ISA; WMO; FAA-H-8083-25B.

Factors affecting air density

Air density mainly depends on air temperature and air pressure. It increases when air pressure increases and air temperature decreases:

Humidity and density — detail

When atmospheric pressure and temperature remains constant, but the relative humidity increases, air density decreases:

• Water molecules (H₂O, mol mass 18) are lighter than nitrogen (N₂, 28) or oxygen (O₂, 32).
• For equal molecule count per volume (same P and T), water vapour replaces heavier gases → density drops.
• Consequence: humid hot air = lowest density = worst aircraft performance.

Density altitude (DA)

Density altitude is the ISA altitude where ISA density matches actual density. Combines pressure and temperature effects into one quantity for performance:

• DA = pressure altitude + temperature correction.
• Rule: DA ≈ pressure altitude + 120 × (OAT − ISA temp at PA) [ft].
• Example: PA 3000 ft, OAT 25 °C (ISA at 3000 ft = 9 °C), Δ +16 °C → DA = 3000 + 120 × 16 = 4920 ft.

→ On a hot day at 3000 ft, the aircraft "feels" like 5000 ft.

Why density altitude matters for PPL

• Take-off distance rises with DA → longer runway needed.
• Climb performance falls with DA → worse climb.
• Cruise TAS rises with DA (for same IAS) — slightly positive.
• Engine power falls with DA (lower density = less O₂ = less combustion).

→ Pilot computes DA before every flight and compares performance against available runway.

Diurnal temperature variation

The energy and radiation balance of the surface of the Earth is also the cause for the diurnal variation of air temperature in the layers of air close to the ground:

• By day: ground absorbs solar radiation → warms → warms the lower air → T rises.
• At night: ground radiates heat as IR → cools → cools the lower air → T falls.

Radiation balance

In the evening, at night and in the early morning just after sunrise the radiation balance of the surface of the Earth is negative, with the effect that it cools:

• Incoming solar = 0 (night) or low (morning).
• Outgoing IR > incoming → net loss → cooling.
• Result: surface inversion in the morning, radiation fog in calm conditions.

Radiation processes affect the temperature of layers of air close to the ground at all times of the day and night.

Heating of the lower air layers

Heating of the lower air layers mainly happens by ascent (convection) of air heated directly at the surface:

• Air is NOT heated directly by solar radiation (air is transparent to visible light).
• Instead: ground heats → ground-contact air warms by conduction → convection lifts warm air.

Advection vs convection

• Convection: vertical motion of air (warm rising / cold sinking).
• Advection: horizontal motion of air. Advection processes can cause a change of temperature and moisture without vertical movement of air.
• Advection processes in the atmosphere can occur at all heights.

Advection example: The supply of mild ocean air from the Atlantic to Central Europe in winter with westerly winds is an advection process.

Besides radiation, advection processes — where air masses are transported horizontally — cause temperature changes in the atmosphere by bringing warmer or colder air to a region.

The supply of warmer air in a certain atmospheric layer is called warm air advection.

Guide to Meteorological Instruments and Methods of Observation*; FAA-H-8083-25B PHAK Ch. 12.*