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What's the formula to calculate external temperature (static temperature) of an aircraft, given that I have Mach, TAS and altitude?

Since I don't know the formula, I tried to search on Google. But I found that I need total air temperature, which must be know by a sensor (and I don't know). So, is there any other formular/way to calculate static air temperature using only mach/tas/altitude, or is not possible with only these data?

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  • $\begingroup$ welcome to aviation.se. what have you tried? $\endgroup$ – Federico Mar 12 at 7:12
  • $\begingroup$ Since I don't know the formula, i tried to find in google. But I found that I need total air temperature, which must be know by a sensor (and I don't know). So, is there any other formular/way to calculate static air temperature using only mach/tas/altitude, or is not possible with only these data? $\endgroup$ – Jonis Maurin Ceará Mar 12 at 11:10
  • $\begingroup$ thank you for the clarification, I've added the details to your question. $\endgroup$ – Federico Mar 12 at 11:19
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is there any other formular/way to calculate static air temperature using only mach/tas/altitude ?

No.

Mach (or TAS) can only give you the ratio between total and static air temperature, as seen also on Wikipedia:

$$ \frac{T_\mathrm{total}}{T_{s}}={1+\frac{\gamma -1}{2}M_a^2} $$

Knowing the Mach number will give you the quantity on the right hand side of the equation ($\gamma$ is constant and is about 1.4 for dry air). If you cannot measure one of the two quantities on the left hand side, you cannot derive the other.

You could in theory derive the temperature from a measurement of the static pressure, if somehow you could also measure the air density, but that's not using only "mach/tas/altitude" as you requested.

A final option is to derive the temperature from the standard atmosphere model using the altitude, but that might not be a number reliable enough for your purposes.

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