Airspeed Calculator Formula
Understand the math behind the airspeed calculator. Each variable explained with a worked example.
Formulas Used
True Airspeed (TAS)
tas = ias / sqrt(density_ratio)True Airspeed
tas_ms = ias / sqrt(density_ratio) * 0.5144Density Ratio (sigma)
density_ratio_out = density_ratioVariables
| Variable | Description | Default |
|---|---|---|
ias | Indicated Airspeed (IAS)(knots) | 250 |
pressure_alt | Pressure Altitude(ft) | 10000 |
oat | Outside Air Temperature (OAT)(°C) | -5 |
isa_temp | Derived value= 15 - 0.001981 * pressure_alt | calculated |
density_ratio | Derived value= (288.15 / (oat + 273.15)) * pow(1 - 0.000006875 * pressure_alt, 4.2561) | calculated |
How It Works
Indicated vs True Airspeed
Indicated airspeed (IAS) is what the pitot-static system reads, calibrated for sea-level standard density. As altitude increases and air density decreases, the true airspeed (TAS) becomes higher than the indicated reading.
Simplified Relationship
TAS = IAS / sqrt(sigma)
where sigma is the density ratio (local density divided by sea-level standard density). This approximation is valid for low subsonic speeds where compressibility effects are negligible.
Worked Example
An aircraft reads 250 KIAS at 10,000 ft pressure altitude with OAT of -5°C.
ias = 250pressure_alt = 10000oat = -5
- 01ISA temperature at 10,000 ft = 15 - 1.981 × 10 = -4.81°C
- 02Temperature ratio component = 288.15 / 268.15 = 1.0746
- 03Pressure ratio component = (1 - 0.000006875 × 10000)^4.2561 = 0.6877
- 04Density ratio sigma = 1.0746 × 0.6877 = 0.7392
- 05TAS = 250 / sqrt(0.7392) = 250 / 0.8598 = 290.8 knots
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