Library / Aerospace / AER-13
Aerospace
Equivalent airspeed
Speed at standard sea-level density that gives the same dynamic pressure as the true airspeed VT at local density ρ.
- Ref
- AER-13
- Rev
- v1
- Field
- Aerospace
- Result
- VE [m/s]
Dynamic pressure q = ½ρV² sets the aerodynamic forces. Equivalent airspeed VE is the speed at sea-level density that would give the same q: VE = VT√(ρ/ρ₀). At altitude it is lower than true airspeed, so a plane flying at a given VE has the same loads and stall behaviour wherever it is, which is why design speeds are quoted in equivalent airspeed.
Speed at standard sea-level density that gives the same dynamic pressure as the true airspeed VT at local density ρ. It is the quantity that fixes aerodynamic loads and stall at low Mach number. Use the same speed units on input and output.
Calculator
- Density ratio σ = ρ/ρ₀0.64
- Dynamic pressure, ½ρVT²3,920 Pa
- Equivalent airspeed as a fraction of VT0.8
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.
- At this density the equivalent airspeed is 80 m/s, 80 % of the true airspeed of 100 m/s.
- Both speeds give the same dynamic pressure of 3,920 Pa, so lift and drag are the same as at 80 m/s at sea level.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m/s) | Local step | Change in result |
|---|---|---|---|---|---|---|
| VT True airspeed | 10 to 400 m/s | 8 | 320 | 312 | +10% | +10 % |
| ρ Local air density | 0.1 to 1.3 kg/m³ | 28.57 | 103 | 74.44 | +10% | +4.88 % |
| ρ0 Sea-level standard density | 1.2 to 1.25 kg/m³ | 79.2 | 80.83 | 1.633 | +10% | −4.65 % |
Sweep of Local air density
| Local air density (kg/m³) | Equivalent airspeed (m/s) |
|---|---|
| 0.1 | 28.57 |
| 0.25 | 45.18 |
| 0.4 | 57.14 |
| 0.55 | 67.01 |
| 0.7 | 75.59 |
| 0.85 | 83.3 |
| 1 | 90.35 |
| 1.15 | 96.89 |
| 1.3 | 103 |
Sweep one variable
Variables and how each one contributes
Equivalent airspeed
What the equation gives you. Everything else feeds it.
True airspeed
The true airspeed, in m/s. Scales the equivalent airspeed in direct proportion. Raising it by 10 % (to 110) moves the result by +10 %, from 80 to 88 m/s.
Local air density
The local air density, in kg/m³. A lower density lowers the equivalent speed as its square root. Raising it by 10 % (to 0.8624) moves the result by +4.88 %, from 80 to 83.9 m/s.
Sea-level standard density
The standard sea-level density, in kg/m³. A larger reference density lowers VE as the square root of its inverse. Raising it by 10 % (to 1.348) moves the result by −4.65 %, from 80 to 76.28 m/s.
Worked example with the values above
- Density ratio: ρ/ρ₀ = 0.784 / 1.225 = 0.64.
- Square root: √(ρ/ρ₀) = 0.8.
- VE = 100 × 0.8 = 80 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)