Short Notes 04: Air Density

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Basic Definitions

• Density (ρ): Mass per unit volume of air.
• Pressure Altitude (PA): Altitude in ISA where the observed pressure exists.
• Density Altitude (DA): Altitude in ISA where the observed air density exists.
• Key relationship: Aircraft performance depends on density, not pressure alone.

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Gas Law Relationship

• ρ ∝ P / T
• Density:
  • Increases with higher pressure.
  • Decreases with higher temperature.
  • Decreases with higher humidity (moist air is lighter).

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Effect of Temperature

• Warm air → expands → lower density.
• Cold air → contracts → higher density.
• Warmer than ISA: DA greater than PA.
• Colder than ISA: DA less than PA.

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Effect of Pressure (Altitude)

• Pressure decreases rapidly with height.
• Although temperature also decreases with height, pressure decrease dominates.
• Therefore, density always decreases with altitude.
• At ~18,000 ft, density ≈ 50% of sea-level value.

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Effect of Humidity

• Moist air is less dense than dry air.
• Reason:
  • Water vapour (H₂O) is lighter than N₂ and O₂.
  • Water vapour density ≈ 5/8 of dry air.
• High humidity → higher Density Altitude → poorer performance.

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Density Altitude Formula (Exam Use)

DA = PA + {ISA Deviation X times 120 }

• ISA Deviation = OAT − ISA Temperature
• +1°C (warmer than ISA) → DA increases by 120 ft.
• −1°C (colder than ISA) → DA decreases by 120 ft.
• When OAT = ISA: DA = PA.

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ISA Temperature Reference

• ISA lapse rate (for exams): 2°C / 1000 ft up to 36,090 ft.
• Above 36,090 ft to 65,617 ft: Isothermal at −56.5°C.

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Performance Implications

• High Density Altitude (Low Density):
  • Reduced lift.
  • Reduced engine power/thrust.
  • Longer take-off distance.
  • Poor climb performance.
• Low Density Altitude (High Density):
  • Improved aircraft and engine performance.

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Lowest Density Conditions (Worst Performance)

• Low pressure (high altitude)
• High temperature
• High humidity
• Common phrase: “Hot, High, and Humid”

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Highest Density Conditions (Best Performance)

• High pressure
• Low temperature
• Low humidity

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Moist vs Dry Air

• At same P and T:
  • Dry air → higher density
  • Moist air → lower density

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Latitude & Density (Important Concept)

• At the surface:
  • Equator → warm → low density
  • Poles → cold → high density
• Around ~26,000 ft: Density nearly uniform globally.
• Above ~26,000 ft:
  • Density becomes lower at the poles than at the equator.
  • Reason: Cold polar air columns cause pressure to fall more rapidly with height.
• Remember: Reversal of temperature–pressure–density relationship above ~8 km.

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Seasonal Tropopause Note

• Summer tropopause: Higher, colder.
• Winter tropopause: Lower, warmer (relative comparison).

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One-Line Exam Facts

• Density Altitude = performance altitude.
• DA equals PA only at ISA temperature.
• Pressure change affects density more than temperature change vertically.
• Anticyclonic (high pressure) air is denser than cyclonic air at same temperature.
• Moist air is lighter, not heavier.

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