Airspeeds: IAS, CAS, EAS and TAS

Why it matters

A pilot reads one number off the airspeed indicator, but stall speed, structural limits, navigation and engine matching each need a different "airspeed". Mixing them up gives wrong stall margins, wrong fuel plans and wrong performance predictions. Every performance calculation in this subject — drag, thrust required, range, V-n diagram — quietly assumes you know which airspeed you are working with.

Key ideas

What the instrument actually measures. The pitot tube senses total (stagnation) pressure p₀ and the static port senses static pressure p. The airspeed indicator converts the difference, the impact pressure q_c = p₀ − p, into a speed using sea-level ISA values of pressure and density and the compressible-flow relation. It cannot know the real density, so the number it shows is not the true speed through the air.

The chain IAS → CAS → EAS → TAS.

• Indicated airspeed (IAS): the raw reading of the instrument.
• Calibrated airspeed (CAS): IAS corrected for instrument error (mechanical and dial errors) and position error (the static port does not sense true free-stream static pressure because of the local flow around the fuselage; it changes with angle of attack, flap setting and speed). Position error comes from flight-test calibration charts.
• Equivalent airspeed (EAS): CAS corrected for compressibility. The indicator is calibrated for sea-level pressure; at high altitude and high Mach number the impact pressure is larger than ½ρV², so CAS over-reads. The correction is negative, so EAS ≤ CAS, and it is negligible below roughly Mach 0.3 at low altitude.
• True airspeed (TAS): the actual speed of the aircraft relative to the air mass. It follows from EAS and the density ratio.

Why EAS is the aerodynamicist's speed. EAS is defined so that the dynamic pressure is the same as at TAS in the actual air: ½·ρ₀·V_E² = ½·ρ·V². Lift, drag and loads depend on dynamic pressure, so an aircraft stalls at (very nearly) the same EAS at every altitude, and structural speed limits on a V-n diagram are drawn in EAS. A pilot flying at constant IAS in a climb is approximately flying at constant EAS, while TAS rises.

Why TAS is the navigator's speed. Distance over the ground depends on TAS and wind: ground speed = TAS ± wind component. Range, endurance and Mach number calculations use TAS. Mach number is M = V/a, with V the TAS and a the local speed of sound.

At sea level on an ISA day σ = 1 and compressibility is small, so (with no instrument or position errors) IAS ≈ CAS ≈ EAS ≈ TAS. They separate with altitude and speed.

Connections. σ comes from the ISA topic. In the drag-polar and level-flight topics, writing speeds in EAS removes altitude from many results — for example, the minimum-drag speed in EAS is independent of altitude.

Formulas

V_E = V·√σ, where σ = ρ / ρ₀

V = V_E / √σ

q = ½·ρ·V² = ½·ρ₀·V_E² (dynamic pressure)

V = √(2·(p₀ − p) / ρ) (incompressible pitot relation, low Mach number only)

p₀ / p = [1 + (γ − 1)/2 · M²]^(γ/(γ − 1)) (isentropic, subsonic)

V_C = √{ [2γ/(γ − 1)] · (p_s/ρ_s) · [ (q_c/p_s + 1)^((γ − 1)/γ) − 1 ] } (CAS from impact pressure)

M = V / a, a = √(γ·R·T)

Symbols: V true airspeed (m/s); V_E equivalent airspeed (m/s); V_C calibrated airspeed (m/s); ρ local density, ρ₀ = 1.225 kg/m³ sea-level ISA density; σ density ratio; p static pressure, p₀ total pressure, q_c = p₀ − p impact pressure (Pa); p_s = 101 325 Pa and ρ_s = 1.225 kg/m³ sea-level ISA values used in the calibration; γ = 1.4; a speed of sound (m/s); T static temperature (K); R = 287.05 J/(kg·K). The incompressible pitot relation is acceptable for M below about 0.3; above that use the isentropic relation.

Worked examples

Example 1 (standard): TAS from EAS at altitude. Given: an aircraft flies at V_E = 100 m/s at 5000 m in ISA, where ρ = 0.7361 kg/m³.

1. Density ratio: σ = ρ/ρ₀ = 0.7361/1.225 = 0.6009.
2. V = V_E/√σ = 100/√0.6009 = 100/0.7752 = 129.0 m/s. The aircraft moves 29 % faster through the air than its equivalent airspeed suggests.

Example 2 (GATE level): TAS, EAS and CAS at cruise. Given: cruise at Mach 0.8 at 11 km in ISA: p = 22 632 Pa, T = 216.65 K. Take γ = 1.4, R = 287.05 J/(kg·K), sea-level p_s = 101 325 Pa, ρ_s = 1.225 kg/m³.

1. Density: ρ = p/(R·T) = 22 632/(287.05 × 216.65) = 0.3639 kg/m³; σ = 0.2971.
2. Speed of sound: a = √(γRT) = √(1.4 × 287.05 × 216.65) = 295.1 m/s.
3. TAS: V = M·a = 0.8 × 295.1 = 236.1 m/s.
4. EAS: V_E = V·√σ = 236.1 × 0.5450 = 128.7 m/s.
5. Impact pressure: q_c = p·{[1 + 0.2·M²]^3.5 − 1} = 22 632 × (1.128^3.5 − 1) = 22 632 × 0.5243 = 11 867 Pa.
6. CAS: V_C = √{7 · (101 325/1.225) · [(11 867/101 325 + 1)^(1/3.5) − 1]} = √(579 000 × 0.03215) = 136.4 m/s. So CAS exceeds EAS by about 8 m/s here: that is the compressibility correction. Note also that q_c = 11 867 Pa is 17 % larger than the dynamic pressure ½ρV² = 10 139 Pa.

Common mistakes

• Converting CAS to EAS with √σ. The step from CAS to EAS is a compressibility correction; √σ links EAS and TAS.
• Writing V_E = V/√σ (upside down). EAS is always the smaller of the two above sea level.
• Using the incompressible pitot formula at high subsonic Mach numbers.
• Taking Mach number from EAS or CAS. Mach number uses TAS and the local speed of sound.
• Using knots and m/s in the same equation (1 kn = 0.5144 m/s).
• Thinking stall speed rises with altitude in all forms. Stall EAS is nearly constant; stall TAS rises as 1/√σ.

For GATE AE

Expect one-step conversions between EAS and TAS using σ from the ISA, pitot-static questions asking for a speed from a measured pressure difference (incompressible or isentropic), and conceptual questions on which airspeed governs stall, structural limits and navigation. Practise combining this topic with ISA (finding σ first) and with the Mach-number relation for high-altitude cruise.

Quick check

1. Which airspeed gives the same dynamic pressure as the true speed in the actual air, but evaluated with sea-level density?
2. An aircraft holds constant EAS while climbing. What happens to its TAS?
3. Which correction converts CAS to EAS?
4. At σ = 0.25, what is TAS if EAS = 120 m/s?

Answers: 1. Equivalent airspeed (EAS). 2. TAS increases, as 1/√σ. 3. The compressibility correction. 4. 240 m/s.