What is wrong about this interpretation of QFE and QNH?

Question

I'm a little confused about the QFE and QNH definitions, and its application on aviation. I learnt that:

$QFE$ = pressure measured by an altimeter which is adjusted to ground level (it gives a height of 0 when the airplane is on the ground).

$QNH$ = pressure measured by an altimeter which is adjusted to sea level (it gives the field elevation when the airplane is on the ground).

So, by those definitions we can say that on ground level $QFE=p_0=101325Pa$ and $QNH=p_{ISA}(h_e)$ where $p_0$ is the SSL pressure and $h_e$ is the field elevation. $p_{ISA}$ is the pressure on a standard atmosphere associated to the height $h$. For the troposphere we have:

$$p_{ISA}[Pa]=101325\left(1-\frac{0.0065 h[m]}{288.15}\right)^{5.25588}$$

So, pressure drops with an height increment. For example, if the field elevation is positive (i.e. it's above the sea level) and the airplane is above the field we have to have $QFE>QNH$, because the height measured by $QFE$ configuration is lesser that the height measured by $QNH$ ($h_{QHN}=h_{QFE}+h_e$ and $h_e>0$)configuration, and by the relation between $p$ and $h$ if $h_{QFE}<h_{QNH}$, then $p_{QFE}>p_{QNH}$.

What I have seen in many problems of QFE determination by QNH and vice versa, is that the definitions used for QFE, QNH were exchanged. See for example this question How can I calculate QNH from QFE?.

I've seen this type of resolution done in many exercises, and so I presume that I'm wrong! But I still didn't get it! What am I missing here?

I can even show you a figure that was used on the theoretical slides of my Aircraft Performance course:

As you can see this figure says that $h_{QFE}=h_{QNH}+h_e$ which should instead be $h_{QNH}=h_{QFE}+h_e$ (the opposite) according to the $QFE$ and $QNH$ definitions.

Answer 1

Your question is quite not clear, you are challenging definitions and use of definitions, but you may start with a misunderstanding:

QFE = pressure measured by an altimeter which is adjusted to ground level (it gives a height of 0 when the airplane is on the ground).

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Definitions

To ensure clarity, QFE/QNH:

• are reference pressures, not altitudes
• are not read/measured by the altimeter, but entered by the pilot in the setting window.
• when mentioned in an altitude would be mentioned like, for instance: "I'm flying at 1,000 ft referenced to QFE", and not "my QFE is 1,000 ft".

QFE and QNH are not what the needles of the altimeter indicate, they are only the pressures that are to be entered in the setting window to calibrate the altimeter for common low level flight references.

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How is QNH determined

While QFE is a direct measurement of the pressure, where the temperature is ignored, QNH is never measured, it is "retro-computed" from QFE:

• Determining QNH requires first to know the local pressure (QFE) at the relevant location (e.g. airfield reference point)
• The actual altitude of this location is then converted into a pressure difference, using the ISA model (+1 hPa per 27 ft at low altitude), without taking into consideration the temperature
• The offset (which is positive unless the airfield altitude is under sea level) is added to QFE, the result is QNH (hence QNH pressure is usually > QFE pressure)

Said otherwise: QNH is the theoretical pressure value at MSL. but as the temperature wasn't taken into account, and actual distance between isobaric surfaces vary with actual temperature, then the actual pressure at MSL (if it could be measured) would be likely different.

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Altimeter readings

After calibration with QFE or QNH value, any change in actual pressure -- that can be due to an actual altitude change, a local temperature change or a local pressure change -- will be sensed by the altimeter, the pressure change being indicated by an altitude change at the ISA rate of -27 ft for each added hPa.

By principle when the altimeter is on an isobaric surface equal to any pressure entered in the window, the value read is zero. As by definition the QFE is the pressure at the airfield level, then if the altimeter is at the airfield, set to QFE, and QFE has been just updated, then it indicates 0 altitude above ground level (AGL).

More generally (I hope this is accurate, else correct me):

Note that the pressure scale on the left has the higher value at the bottom, while the altitude scale on the right has it at the top.

As you can see this figure says that $h_{QFE}=h_{QNH}+h_e$ which should instead be $h_{QNH}=h_{QFE}+h_e$ (the opposite).

You or the book may be correct, depending on the sign of $h_e$. But it's not clear. If this quantity is positive, you are correct.

Remember that QFE and QNH are not altitudes, they are the altimeter reference values. For an airfield above MSL, QFE < QNH and an altimeter reading (h) referenced to QFE ($h_{QFE}$) will be approximately the height above the airfied (AGL) while when referenced to QNH ($h_{QNH}$) it will be approximately the altitude above MSL (AMSL).

Indeed altitude above sea level is larger than height above ground. Possibly in your example above, the author may have $h_e$ as a negative value.

Answer 2

Your question is a bit confusing since you seems to be already giving the definition for QNH and QFE. I'll just leave this example to see if it can clear things up for you:

Let's say you are at an airfield which is at 500 feet above sea level. The ATIS tells you that the QNH is 1020hpa. While on the ground, if you set your altimeter to 1020hpa it will read 500ft, which is you altitude AMSL. Now if you want to know the QFE, just set your altimeter to read 0ft and you'll see the QFE on the altimeter setting window.

To wrap it up, setting the QNH on your altimeter will give you your altitude AMSL and the QFE your altitude AGL.

I hope this helps.