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The control tower of a certain airport with true altitude of 2000ft informs the pilot that QNH is 900hPa and the temperature at the airport is -10 degrees Celsius. The airplane is at FL300 (vertically above the airport) and the OAT measured by the airplane sensor is -30 degrees Celsius. What's the true altitude of the airplane?

The teacher gave us the following formula

$$Z_v=Z_{QNH}+(Z_{QNH}-Z_t)\frac{4(T_v-T_{Std})}{1000}$$

but the question is. We have the $Z_t$ (2000ft) and $T_v$ (-30 degrees Celsius), we can calculate the $Z_{QNH}$, but what is the $T_{Std}$ ? Is it the temperature at the flight level considering the ISA Atmosphere or do we need to start with -10 degrees Celsius and calculate the temperature at FL300?

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  • $\begingroup$ Look what ISA gives you for ground and air temperature and subtract the difference from the actual ground temperature. $\endgroup$
    – Peter Kämpf
    Apr 10, 2018 at 19:22
  • $\begingroup$ @PeterKämpf, just to confirm, are you saying that $T_{std}=T(ISA)_{Ground}-T(ISA)_{air}-T(Real)_{Ground}$? $\endgroup$
    – Emanuel Camacho
    Apr 10, 2018 at 20:06
  • $\begingroup$ No, $T_{std} = T(real)_{Ground}-T(ISA)_{Ground}+T(ISA)_{air}$ $\endgroup$
    – Peter Kämpf
    Apr 10, 2018 at 22:30

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Standard temperatures are based on the Standard atmosphere. A lapse rate, dry or wet depending on your environment, is used determine the standard temperature for a given altitude relative to the standard sea level temperature. The post, How does one calculate true altitude? may help you out here.

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