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Aerospace
Calibrated airspeed from subsonic impact pressure
Speed read from the airspeed indicator scale after correcting for instrument and position error, calibrated to standard sea-level pressure p0 and sound speed a0.
- Ref
- AER-15
- Rev
- v1
- Field
- Aerospace
- Result
- VC [m/s]
The airspeed indicator is a pressure gauge for qc, scaled with standard sea-level values. Inverting the impact pressure formula at sea level gives calibrated airspeed VC = a₀√{2[(1 + qc/p₀)^((γ−1)/γ) − 1]/(γ − 1)}. In the subsonic range it equals true airspeed only at sea level in standard conditions, and the correction for position and instrument error must be applied to qc first.
Speed read from the airspeed indicator scale after correcting for instrument and position error, calibrated to standard sea-level pressure p0 and sound speed a0. It is the subsonic sea-level calibration branch and needs qc ≥ 0.
Calculator
- Calibrated Mach number, VC/a₀0.5
- Impact pressure ratio qc/p₀0.1862
- Dynamic pressure at standard sea level, ½ρ₀VC²17,730 Pa
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- An impact pressure of 18.868 kPa corresponds to a calibrated airspeed of 170.15 m/s, or Mach 0.5 at standard sea level.
- The incompressible formula √(2qc/ρ₀) would give 175.51 m/s, 5.37 m/s too high, which shows the compressibility correction.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m/s) | Local step | Change in result |
|---|---|---|---|---|---|---|
| qc Corrected impact pressure | 0 to 60,000 Pa | 0 | 286.9 | 286.9 | +10% | +4.58 % |
| γ Heat-capacity ratio | 1.1 to 1.67 | 156.6 | 190.4 | 33.79 | +10% | −4.39 % |
| a0 Sea-level speed of sound | 330 to 345 m/s | 165 | 172.5 | 7.5 | +10% | +10 % |
| p0 Sea-level pressure | 101,000 to 101,500 Pa | 170 | 170.4 | 0.3958 | +10% | −4.4 % |
Sweep of Corrected impact pressure
| Corrected impact pressure (Pa) | Calibrated airspeed (m/s) |
|---|---|
| 0 | 0 |
| 7,500 | 109.2 |
| 15,000 | 152.6 |
| 22,500 | 184.8 |
| 30,000 | 211 |
| 37,500 | 233.5 |
| 45,000 | 253.2 |
| 52,500 | 270.8 |
| 60,000 | 286.9 |
Sweep one variable
Variables and how each one contributes
Calibrated airspeed
What the equation gives you. Everything else feeds it.
Sea-level speed of sound
The standard sea-level speed of sound, in m/s. Scales the speed in direct proportion. Raising it by 10 % (to 374.3) moves the result by +10 %, from 170.1 to 187.2 m/s.
Heat-capacity ratio
The heat-capacity ratio cp/cv of the gas, about 1.4 for air. A lower γ (hotter, more complex gas) changes the compressible-flow exponents and the sizes of the shock and expansion effects. Raising it by 10 % (to 1.54) moves the result by −4.39 %, from 170.1 to 162.7 m/s.
Sea-level pressure
The standard sea-level pressure, in Pa. A higher reference pressure lowers the calibrated speed for the same qc. Raising it by 10 % (to 111,500) moves the result by −4.4 %, from 170.1 to 162.7 m/s.
Corrected impact pressure
The impact pressure corrected for instrument and position error, in Pa. Raises the calibrated speed, roughly with its square root. Raising it by 10 % (to 20,750) moves the result by +4.58 %, from 170.1 to 177.9 m/s.
Worked example with the values above
- Pressure ratio: 1 + qc/p₀ = 1 + 18,870 / 101,300 = 1.186213.
- Power: (…)^((γ−1)/γ) − 1 = 0.05.
- VC = 340.3 × √(2 × 0.05 / 0.4) = 170.147 m/s.
Assumptions and limits
- Calorically perfect gas with a constant heat-capacity ratio, and isentropic deceleration to the pitot tube.
- Subsonic flow for the pitot and calibrated-airspeed formulas; a shock forms ahead of the probe above Mach 1.
Common mistakes
- Using the incompressible ½ρV² formula at high Mach number, where it underestimates impact pressure.
- Confusing true, equivalent and calibrated airspeed.
- Treating a recovery temperature as a static temperature.
Statistics and uncertainty
Air-data conversions are exact for the stated models, so errors come from the instrument: pitot and static ports carry position errors of 1 % to 2 % in speed, and a poorly designed temperature probe can have a recovery factor that differs from 0.9 by several per cent.
Where it is used
- Converting instrument readings to speed, Mach number and static temperature.
- Understanding what the airspeed indicator and temperature probes really measure.
Maths you need
- Stagnation point: where the flow is brought to rest
- Dynamic pressure: q = ½ρV²
- Speed of sound: a = √(γRT)