How do you convert true airspeed to indicated airspeed?

Question

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

Answer 1

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.

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

Answer 2

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

Answer 3

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.

Answer 4

It's a common questions...you get a TAS from your POH based on an RPM setting in your cruise performance chart. Some Navlogs have a TAS/IAS box. If you can determine the IAS then you can look at the Air Speed Indicator to insure everything is correct (from an airspeed perspective). You still need to do a ground speed check because the TAS/IAS question doesn't help you with Navigation and confirming the forecasted winds. But this is a commonly asked question.

And yes, using your E6B and working backwards to your CAS and the chart in the POH for you IAS is how you do it. It's faster with an electronic E6B for sure.

PS - thanks for the math above, which will be way more accurate than the E6B, but I doubt I'll be doing the math! haha

Answer 5

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.