The atmosphere and partial pressure
The Earth's atmosphere in its lower layers (troposphere, up to ~36 000 ft) is a roughly constant gas mixture:
| Gas | Volume fraction |
|---|---|
| Nitrogen (N₂) | ~78% |
| Oxygen (O₂) | ~21% |
| Argon (Ar) | ~0.9% |
| Carbon dioxide (CO₂) | ~0.04% |
| Others (water, noble gases) | < 0.1% |
This percentage composition is constant in the troposphere — what changes with altitude is the total pressure, and therefore the partial pressure of each gas.
Dalton's Law
Dalton's law: in a gas mixture the total pressure equals the sum of the partial pressures of each component:
P_total = P_N₂ + P_O₂ + P_Ar + P_CO₂ + …
The partial pressure of a gas is the product of its volume fraction and the total pressure:
P_x = X_x × P_total
Example — oxygen at sea level:
- Total pressure P_total = 1 013 hPa (≈ 760 mmHg).
- O₂ fraction 21% → P_O₂ = 0.21 × 1 013 = 212.7 hPa (≈ 160 mmHg).
How partial pressure changes with altitude
Total pressure decreases with altitude approximately by the barometric height formula — every 5 500 m (18 000 ft) the pressure halves.
Because the percentage of O₂ remains constant, the O₂ partial pressure decreases in the same ratio as total pressure:
| Altitude | Total pressure | P_O₂ | Hb saturation |
|---|---|---|---|
| Sea level (0 ft) | 1 013 hPa | 212.7 hPa | 98% |
| 5 000 ft (1 500 m) | 843 hPa | 177 hPa | 95% |
| 8 000 ft (2 440 m) | 753 hPa | 158 hPa | 93% |
| 10 000 ft (3 000 m) | 697 hPa | 146 hPa | 87% — first symptoms |
| 12 500 ft (3 800 m) | 624 hPa | 131 hPa | 82% — crew oxygen required |
| 15 000 ft (4 600 m) | 572 hPa | 120 hPa | 80% |
| 18 000 ft (5 500 m) | 506 hPa | 106 hPa | 72% — half sea-level pressure |
| 25 000 ft (7 600 m) | 376 hPa | 79 hPa | < 50% |
| 40 000 ft (12 000 m) | 188 hPa | 39 hPa | TUC seconds |
Consequences for the body
Oxygen transport
- Haemoglobin (Hb) only binds O₂ when the alveolar partial pressure is sufficiently high.
- Below pO₂ ~140 hPa (corresponding to ~10 000 ft) saturation drops noticeably → hypoxia symptoms.
CO₂ elimination
- CO₂ is exhaled regardless of ambient partial pressure (diffusion from blood into alveoli).
- At altitude a stressed pilot may hyperventilate → pCO₂ in blood drops → respiratory alkalosis (see Hyperventilation).
Gas expansion (Boyle's law)
- Boyle: P × V = const → with decreasing outside pressure gases expand.
- Trapped gases (middle ear, sinuses, GI tract) expand → pain, eardrum pressure.
- See Decompression sickness (the "bends") for N₂ issues.
Water vapour pressure (Armstrong line)
- At about 63 000 ft (19 200 m) outside pressure equals the human body's vapour pressure (47 mmHg at 37 °C).
- Above this altitude body water boils at body temperature — pressurised cabin or pressure suit required.
Regulatory thresholds
EASA Part-NCO.OP.190 and FAA FAR §91.211:
- Above 10 000 ft cabin altitude for more than 30 minutes: oxygen recommended for crew.
- Above 13 000 ft (FAA) / 12 500 ft (Part-NCO): oxygen required for crew (immediately).
- Above 15 000 ft: oxygen required for all passengers.
PPL(A) without pressurised cabin should therefore operate below 10 000 ft cabin altitude — almost always the case in general VFR flying.