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This question already has an answer here:

Does anyone know a good source for an expression of IAS as a funtion of TAS? I was hoping to find an accurate IAS equation that is only dependent upon TAS, static pressure and static temperature.

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marked as duplicate by fooot, Gerry, Ralph J, xxavier, bogl Dec 6 '18 at 8:47

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You might look at Ed William's aviation formulary.

http://www.edwilliams.org/avform.htm#Mach

From there:

> The airspeed indicator measures the differential pressure, DP, between
> the pitot tube and the static port, the resulting indicated airspeed
> (IAS), when corrected for calibration and installation error is called
> "calibrated airspeed" (CAS).
> 
> For low-speed (M<0.3) airplanes the true airspeed can be obtained from
> CAS and the density altitude, DA.
> 
>   TAS = CAS*(rho_0/rho)^0.5=CAS/(1-6.8755856*10^-6 * DA)^2.127940
> (DA<36,089.24ft)  Roughly, TAS increases by 1.5% per 1000ft.

Note that you can go from TAS to CAS, but you will need help getting to IAS, specifically the instrument error for that AS indicator in that aircraft.

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TAS : True Air Speeda

IAS : Indicated Air Speed

CAS: Calibrated Air Speed (reference airspeed based on an idealized Pitot tube)

IAS = CAS + Ki, where Ki is an error component specific of your instrument

The conversion between TAS and CAS (and IAS) needs also to take into account the variation of air density (i.e. altitude). So the conversion requires a bit more parameters.

A good answer is provided here: How do you convert true airspeed to indicated airspeed?

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