Airspeed Types: IAS → CAS → EAS → TAS → GS

A jet at FL350 reading 280 kt on the airspeed indicator is moving through the air at roughly 478 kt, and — with a 60 kt tailwind — over the ground at 538 kt. Same aeroplane, same instant, three numbers more than 250 kt apart. None is wrong. The wing cares about one; the navigator cares about another; the Mach meter watches a third.

There is only one true airflow over the pitot tube. IAS, CAS, EAS, TAS, GS, and Mach are different stops along the cascade of corrections — from "what the needle reads" through "what the airframe is doing" to "what the ground is doing under us".

Formal definitions

Each of the five names below is read straight from Oxford ATPL Book 5, Instrumentation, Chapter 4 — the ASI — and Chapter 7 — the Machmeter.

Indicated Airspeed (IAS)

The ASI is calibrated to read true airspeed for the air density of 1225 grams per cubic metre which would be produced by the ISA MSL pressure of 1013.25 hPa and temperature +15°C. No allowance is made in the calibration for the change in density which occurs with change of altitude.

— Oxford ATPL Book 5, Instrumentation, Ch.4 §Calibration

In plain terms: IAS is whatever the needle says. It is the dynamic pressure on the pitot tube, displayed on a scale that would only be correct at sea-level ISA in still, dry air — and even then only after the instrument and the static port have been subtracted off.

Calibrated Airspeed (CAS)

CAS is IAS corrected for Instrument and Position (Pressure) Error.

— Oxford ATPL Book 5, Instrumentation, Ch.4 §CAS

In plain terms: CAS is the IAS the needle would have shown if the instrument were perfect and the static port were in clean air. On modern transport aircraft an Air Data Computer applies the correction automatically and the displayed value is effectively CAS already.

Equivalent Airspeed (EAS)

Equivalent Airspeed is CAS corrected for Compressibility Error only. EAS is the most accurate value of dynamic pressure. It has been corrected for Instrument, Pressure and Compressibility error, all of which are forms of measurement error.

— Oxford ATPL Book 5, Instrumentation, Ch.4 §EAS

In plain terms: EAS is the true dynamic pressure felt by the wing, expressed as a sea-level airspeed. Limit speeds (V_S, V_NE, gust limits) are derived from EAS and then re-clothed in IAS or CAS to display in the cockpit.

True Airspeed (TAS)

Unless the air round the aircraft is at the calibration density of 1225 grams per cubic metre, which can only occur near sea level, the ASI cannot correctly indicate TAS… EAS + Density Error = TAS.

— Oxford ATPL Book 5, Instrumentation, Ch.4 §TAS

In plain terms: TAS is the aircraft's speed through the airmass. It is the only one of the five that the wind triangle, ground speed, and fuel-flow planning actually care about.

Ground Speed (GS)

Ground speed is the speed of the aircraft over the ground. It is the vector sum of true airspeed and wind velocity.

— Oxford ATPL, General Navigation

In plain terms: GS is TAS plus wind. Headwind subtracts, tailwind adds, crosswind tilts the track via the wind triangle. Everything the navigator does — ETA, fuel planning, descent profile, time to next waypoint — uses GS, not TAS.

Mach number (M)

The speed of sound is not constant but varies with air temperature. A formula for calculating the local speed of sound (LSS) is LSS = 38.95 √T, where T is the absolute temperature. Mach Number = TAS / LSS.

— Oxford ATPL Book 5, Instrumentation, Ch.7

In plain terms: Mach is TAS expressed as a fraction of the local speed of sound. It branches off TAS rather than sitting in the serial cascade. Above the crossover altitude it replaces CAS as the high-speed limit, because compressibility effects depend on Mach number, not on dynamic pressure.

The cascade

Each step strips one error or applies one transformation:

1. Instrument & position error (IAS → CAS). ASI imperfections and disturbed static-port flow. Usually a few knots, handled by the calibration card or the ADC.
2. Compressibility (CAS → EAS). Pitot pressure exceeds ½ρV² at high speed; the ASI over-reads. Always subtractive. Negligible below ~10 000 ft or 200 KCAS; exceeds 20 kt near the speed of sound.
3. Density (EAS → TAS). Thin air produces less dynamic pressure for the same TAS, so the ASI under-reads. Correct by dividing by √σ (σ = ρ/ρ₀).
4. Wind (TAS → GS). Add the tailwind component, subtract the headwind. In no wind, GS = TAS exactly.

Mach branches off TAS separately: M = TAS / a, with a = 38.95 √T_K (kt).

Quick formulas worth remembering

• TAS = EAS / √σ
• M = TAS / a
• a (kt) = 38.95 √T_K — at ISA MSL (288 K) → 661 kt; at FL350 ISA (218 K) → 575 kt
• Below 10 000 ft (or below 200 KCAS), CAS ≈ EAS within a knot or two — compressibility is buried in the calibration
• Rule of thumb below 10 000 ft: TAS ≈ IAS × (1 + 0.02 × alt_kft) — a 240 IAS at 8 000 ft gives TAS ≈ 240 × 1.16 ≈ 278 kt

Worked example — the cascade in numbers

A B737 cruising at FL350, OAT −55 °C, with the pilot reading 280 kt on the airspeed indicator. Assume the ADC has already applied the instrument and position correction, so CAS = IAS = 280 kt.

Step 1 — temperature, density, speed of sound:

• T = −55 + 273.15 = 218.15 K
• Pressure ratio at FL350 ≈ 0.235
• Density ratio σ = 0.235 × (288.15 / 218.15) ≈ 0.311
• √σ ≈ 0.558
• a = 38.95 √218.15 ≈ 575 kt

Step 2 — compressibility correction (CAS → EAS):

At 280 KCAS and σ = 0.311 the correction is roughly 5 % of CAS, or about 15 kt. So EAS ≈ 265 kt.

Step 3 — density correction (EAS → TAS):

TAS = EAS / √σ = 265 / 0.558 ≈ 475 kt

Step 4 — Wind (TAS → GS):

Assume a 60 kt tailwind along track: GS = 475 + 60 = 535 kt.

Mach (from TAS):

M = TAS / a = 475 / 575 ≈ 0.83

One aircraft, one airflow, six numbers: 280 / 280 / 265 / 475 / 535 / M 0.83. The wing feels 265, the navigator plans to 535, the structural limit watches 0.83.

Common mistakes

1. Using TAS as a stall reference. Stall speed is fixed in EAS (because the wing only cares about dynamic pressure). The TAS at which an aircraft stalls at FL350 is far higher than the TAS at which it stalls at sea level — the EAS is the same.
2. Forgetting compressibility above 10 000 ft / 200 KCAS. Compressibility is the correction students are most likely to ignore in TAS calculations. Below 300 kt TAS it is small enough to skip; near the speed of sound it exceeds 20 kt.
3. Mixing Mach and TAS for V_MO / M_MO. The high-speed limit is V_MO in CAS at low altitude and M_MO in Mach at high altitude. The crossover is the altitude at which a constant CAS equals a constant Mach. Above it, only Mach matters; the same CAS now exceeds M_MO.

Why it matters

Every airspeed-related question on the ATPL syllabus hinges on knowing which speed is being asked for. Limit-speed tables, V-speeds, ground speed, time-to-station, navigation triangles, and high-speed buffet margins all live at different points in this cascade. Confuse two links in the chain and the answer is silently wrong by 10 %, 20 %, or in the worst case (TAS quoted where Mach was meant) it crosses the limit and you never see the warning.