True Airspeed from CAS and Density Altitude

True airspeed from calibrated airspeed: the airspeed indicator senses dynamic pressure, so in thinner air the same calibrated airspeed is a faster true speed. TAS = CAS / sqrt(sigma), with the ISA density ratio sigma = (1 - 6.87535e-6 h)^4.2559 at the density altitude h (ft): 1.000 at sea level, 0.862 at 5,000 ft (TAS 7.7% over CAS), 0.739 at 10,000 ft (16.4% over). A 120 KCAS climb at 8,000 ft density altitude is really 135 KTAS. The field rule of thumb (+2% per 1,000 ft of density altitude) is shown for comparison; it tracks within a few knots to about 10,000 ft. Treats CAS as equivalent airspeed (the low-speed assumption); TAS is still airspeed -- add the wind for ground speed. Per the FAA Pilot's Handbook / ICAO Standard Atmosphere. A planning estimate; the aircraft flight manual and the pilot in command govern.

sigma = (1 - 6.87535e-6 h)^4.2559 (h = density altitude in ft, troposphere); TAS = CAS / sqrt(sigma). Rule of thumb: TAS ~ CAS (1 + 0.02 h/1000).

True airspeed from calibrated airspeed and the ISA density ratio, per the FAA Pilot's Handbook of Aeronautical Knowledge and the ICAO Standard Atmosphere, by name; first-principles.

The TAS = CAS/sqrt(sigma) relation and the ISA density-ratio formula are public FAA/ICAO standard-atmosphere physics; the CAS and density altitude are the user's inputs.

Estimate. AHJ and licensed professional govern.

Field names used by the API: cas_kt, density_altitude_ft, tas_kt, density_ratio

• TAS relation TAS = CAS / sqrt(sigma), sigma the ISA density ratio at the density altitudeFAA PHAK / ICAO ISA
• Density ratio sigma = (1 - 6.87535e-6 h)^4.2559, h in ft (troposphere, <= 36,089 ft)ICAO Standard Atmosphere
• Low-speed CAS ~ EAS assumed; the compressibility correction matters only at high speed/altitude; TAS is not ground speedscope of this tile