Is this something found in the POH? I know there is a IAS and CAS chart.

  • $\begingroup$ Did you perhaps mean the other way around: IAS to TAS? I'm not sure why you would want to calculate what your airspeed indicator is showing you directly. $\endgroup$ – Pondlife Mar 4 '16 at 3:35
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    $\begingroup$ This seems to be an odd question... You would normally do the calculation the other way round, since IAS is generally a known quantity and TAS is generally not. Of course, mathematically you can use the same formula to do the calculation either way. $\endgroup$ – J Walters Mar 4 '16 at 3:36
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    $\begingroup$ Related, also by @User, possibly duplicate: How do you calculate indicated airspeed on a flight plan?. $\endgroup$ – J Walters Mar 4 '16 at 3:38
  • $\begingroup$ @Pondlife Well I wanted to go from TAS to CAS to IAS, for planning my cross country. $\endgroup$ – User Mar 4 '16 at 4:46
  • $\begingroup$ I think this answer to the other question you asked covers this. Your POH usually lists a bunch of power settings and the TAS and fuel burn for each one. You pick the power setting (RPM) that gives you the range/performance you want, then you set the throttle to that setting in flight. Now you can read the IAS off the airspeed indicator and convert it to TAS, then compare your calculated TAS to the POH TAS. If there's a significant difference you can replan your time, fuel etc. You never need to calculate IAS because it's right in front of you. $\endgroup$ – Pondlife Mar 4 '16 at 13:48

Short Answer

Getting to grips with Aircraft Performance and Calibrated Airspeed are two good places to start!

The short answer:

From TAS to IAS $IAS=f(TAS)$:

$$IAS = a_0 \sqrt{5\left[\left(\frac{\frac{1}{2} \rho {TAS}^2}{P_0} + 1 \right)^{\frac{2}{7}}-1\right]} + K_i $$

From IAS to TAS $TAS=f(IAS)$:

$$TAS = \sqrt{\frac{2 P_0}{\rho}\left[\left( \frac{ (\frac{IAS - K_i}{a_0})^2 + 1}{5} \right)^{\frac{7}{2}} + 1 \right]} $$

WARNING: the units should be taken as SI, ($\frac{m}{s},\frac{kg}{m^3},Pa$).

In particular:

  • $a_0$: speed of soundat sea level in ISA condition = $290. 07 \; \frac{m}{s}$
  • $P_0$: static pressure at sea level in ISA condition = $1013.25 \; Pa$
  • $\rho$: density of the air in which you are flying $\frac{kg}{m^3}$
  • $IAS$: indicated Air Speed $\frac{m}{s}$
  • $K_i$: is a correction factor typical of your aircraft. You should find it in the POH.

How to get to this formula, see the long answer below.

Long Answer

From the definition of dynamic pressure:

$$ q_c = \frac{1}{2} \rho v^2 $$

Where $v = TAS$, I am assuming you are interesting in subsonic speeds (cross-country flight), so we don't consider compressibility effects for the CAS:

$$CAS = a_0 \sqrt{5\left[\left(\frac{q_c}{P_0} + 1 \right)^{\frac{2}{7}}-1\right]} $$

Substituting the dynamic pressure definition in the $CAS$ as a function of $TAS$

$$CAS = a_0 \sqrt{5\left[\left(\frac{\frac{1}{2} \rho {TAS}^2}{P_0} + 1 \right)^{\frac{2}{7}}-1\right]} $$

Where $a_0$ is $295.070 \; \frac{m}{s}$ and $P_0$ is $101325 \; Pa$. the density $\rho $ is the density at your altitude that day, you can get it from International Standard Atmosphere calculator or table/formulas. If you measure it from your aircraft instruments $\rho = \frac{P}{RT}$, with $R=287.058 J kg ^{-1} K^{-1}$. You should give in Pressure in Pascal (not $hPa$) and most important temperature in Kelvin $K$. Reverting the formula above (double proof is appreciated):

$$TAS = \sqrt{\frac{2 P_0}{\rho}\left[\left( \frac{ (\frac{CAS}{a_0})^2 + 1}{5} \right)^{\frac{7}{2}} + 1 \right]} $$

Being $$ IAS = CAS + K_i \\ CAS = IAS - K_i $$

Where $K_i$ is a correction factor typical of your aircraft. You should find it in the POH.

Finally we get TAS as a function of IAS $TAS=f(IAS)$

So: $$TAS = \sqrt{\frac{2 P_0}{\rho}\left[\left( \frac{ (\frac{IAS - K_i}{a_0})^2 + 1}{5} \right)^{\frac{7}{2}} + 1 \right]} $$

  • $\begingroup$ @Federico Thanks! I edited that! $\endgroup$ – GHB Mar 4 '16 at 14:45

I just dial in the OAT, look for the TAS in the white window, and read the IAS on the black scale.

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  • $\begingroup$ Does that instrument have an aneroid cell built into it? $\endgroup$ – quiet flyer May 13 at 5:00

Complementing GHB’s answer, an exact formula for converting CAS to TAS that takes compressibility effects, indicated altitude, and static air temperature into account is $$ \text{TAS} = \sqrt{ \frac{7 R T}{M} \left[ \left( \left( 1 - \frac{L h}{T_{0}} \right)^{- \frac{g M}{R L}} \left[ \left( \frac{\text{CAS}^{2}}{5 a_{0}^{2}} + 1 \right)^{\frac{7}{2}} - 1 \right] + 1 \right)^{\frac{2}{7}} - 1 \right] }. $$ In this formula (which is valid only for subsonic speeds), the inputs are

  • $ \text{CAS} $ — the calibrated airspeed ($ \text{m}/\text{s} $),
  • $ h $ — the indicated altitude ($ \text{m} $) up to $ 11,000 ~ \text{m} $,
  • $ T $ — the static air temperature ($ \text{K} $);

the output is

  • $ \text{TAS} $ — the true airspeed ($ \text{m}/\text{s} $);

and the various physical constants are

  • $ a_{0} = 340.3 ~ \text{m}/\text{s} $ is the speed of sound at sea level in the ISA,
  • $ g = 9.80665 ~ \text{m}/\text{s}^{2} $ is the standard acceleration due to gravity,
  • $ L = 0.0065 ~ \text{K}/\text{m} $ is the standard ISA temperature lapse rate,
  • $ M = 0.0289644 ~ \text{kg}/\text{mol} $ is the molar mass of dry air,
  • $ R = 8.3144598 ~ \text{J}/(\text{mol} \cdot \text{K}) $ is the universal gas constant,
  • $ T_{0} = 288.15 ~ \text{K} $ is the static air temperature at sea level in the ISA.

You read your TAS from your POH. Then you get to your CAS by using a flight computer, such as the E6-B. Then you use your POH to convert from CAS to IAS.

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    $\begingroup$ This makes no sense. Why would you ever start a calculation with TAS? $\endgroup$ – Simon Mar 4 '16 at 7:11
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    $\begingroup$ @Simon, well, that's what the question asks. So it should have been comment on the question rather than the answer. $\endgroup$ – Jan Hudec Mar 4 '16 at 9:59

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