Crabwise · Library

Why is calibrated airspeed not automatically the indicated number on a dial?

At 10000 ft and 0°C, a CAS of 120 kt gives 140.63 kt TAS while 125 kt gives 146.46 kt, so a 5 kt calibration error grows to almost 6 kt.

What the TAS calculation expects

Crabwise converts calibrated airspeed to true airspeed with the compressible-flow relation. It first finds the impact-pressure ratio qc/P0 = (1 + 0.2 (CAS ÷ 661.4786)²)^3.5 − 1, divides it by the pressure ratio δ for the entered pressure altitude, solves Mach from M = √(5 ((qc/P + 1)^(2/7) − 1)) and multiplies by the speed of sound a = 38.967854 × √(OAT + 273.15).

The field is labelled calibrated airspeed. If you type an indicated value, the app says it is treated as calibrated and points you to the POH airspeed-calibration table. The difference between IAS and CAS depends on the aircraft, its flap setting and speed, so the app cannot supply it.

Worked example

With CAS explicitly set to 120 kt, 10000 ft pressure altitude and 0°C, this subsonic model gives about 140.628 kt TAS. The result does not supply the correction needed to turn an observed IAS into that CAS input.

Calculated true airspeed (kt): 140.627909
Calculated Mach number: 0.218356

Get from the dial to the field

Note the indicated airspeed and the aircraft configuration.
Look up the matching calibrated value in the aircraft's calibration table.
Enter that CAS with the pressure altitude and outside-air temperature of the same moment.
Read TAS and Mach together, and record whether the input was corrected or approximated.

How a 5 kt input difference propagates

Keep 10000 ft and 0°C fixed. With CAS 120 kt, qc/P0 is about 0.023227; dividing by δ ≈ 0.687704 gives qc/P ≈ 0.033775, Mach ≈ 0.218356 and TAS ≈ 140.627909 kt. With CAS 125 kt, qc/P0 is about 0.025221, Mach ≈ 0.227419 and TAS ≈ 146.46479 kt.

Speed of sound at 0°C (kt): 644.031474
TAS from CAS 120 kt (kt): 140.627909
TAS from CAS 125 kt (kt): 146.46479

A 5 kt calibration error at the input becomes about 5.84 kt at this altitude, and the gap widens as altitude rises.

Common mistakes

Assuming IAS equals CAS at every speed because the two are close in cruise.
Pairing a speed from one moment with a temperature read later at another level.
Comparing the computed TAS with ground speed; wind separates the two.

Scope

The result is a subsonic standard-atmosphere conversion; the Library worksheet refuses inputs that would reach Mach 1. The NASA isentropic-flow pages listed below give the pressure relations, and the aircraft's handbook gives the calibration.

Educational calculation only. Check current aircraft limits, weather, performance and reserve requirements with approved information.