Currently doing my CPL and in class we were shown a formula on how to calculate the true altitude, which as I understand it is the distance between the ground and the plane while taking into account non-standard temperature. Basically, what a radar altimeter would read back to you.

The formula I was given for this lesson was the following: $$ \begin{equation*} \frac{\tiny{(Indicated~Altitude-Airport~Elevation})}{1000}*\small{(STD~Temp.~at~Indicated~Altitude-Actual~Outside~Temp.)*4} \end{equation*} $$

I have a hard time wrapping my head around the logic of this equation. For instance, why is it that we would need the airport elevation to figure out how high we are relative to the ground below us?

Also, why is it that we can't simply use the part in the density altitude formula that derives the altitude change incurred because of the difference between OAT and standard temperature at a given altitude?

Let's take the following problem:

Airport Elevation: 500ft MSL

OAT: -10c

Mountain Height: 2000ft MSL

Indicated Altitude: 2500ft

QNH: 29.42

Given the following information, will the airplane clear the mountains?

The way I would personally calculate it is by converting indicated altitude into pressure altitude, then calculating the difference in temperature between OAT and standard temp. at pressure altitude, then multiplying that number by 117 (as you do to find density altitude). In that case the equation would be as follows:

$$ \begin{equation} Pressure~Altitude=(29.92-29.42)*1000+2500\\ Pressure~Altitude=3000ft\\ \Delta T=(15-\frac{2}{1000}3000)--10\\ \Delta T=19\\ True~Altitude=2500ft-\Delta T*117\\ True~Altitude=2500ft-19*117\\ True~Altitude=277ft \end{equation} $$

This answer however, turns out to be wrong according to my instructor though he was not able to give me an explanation on why that was beyond saying that I shouldn't think too much about it and just apply the formula that was given. That formula gives a true altitude of 2348ft for the plane, meaning that it will clear the mountains by about 300ft.

  • $\begingroup$ True altitude is the height above sea level, not the height above the ground. What you are describing is "Absolute Altitude" en.wikipedia.org/wiki/Altitude $\endgroup$ Apr 16 '18 at 17:41

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