737NG AFM says :
The use of VNAV or LNAV with QFE selected is prohibited.
But what's the reason of this limitation?
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When you set your altimeter to the airport or runway QFE value, the altimeter shows your altitude above the airport or runway threshold:
(source: SKYbrary - Altimeter Pressure Settings)
The altitude limitations on an instrument approach are however specified in altitude above mean sea level (AMSL), which requires setting QNH. When setting QFE you are unable to follow the altitude limitations.
Since you tagged rnp, I guess you are asking about the different ways of flying an RNP approach. This is an example of 3 different minima for an RNP approach:
You can fly this approach in 3 ways:
LNAV: You get lateral guidance from GPS and no vertical guidance. You would start a 3° descent from ODIDO by looking at your ground speed and dialing in the vertical speed from the table:
This is not possible with QFE because you cannot know if you are at 4000 ft AMSL at ODIDO. You also cannot cross check your altitude of 1160 ft AMSL at 3.0 NM to RW07L.
LNAV/VNAV: You get lateral guidance from GPS and vertical guidance is provided by the Baro-VNAV system. This system required the altitude to be in AMSL to provide correct guidance, which is not possible with QFE.
The chart further says:
Baro-VNAV operations not authorized below -15°C.
This is because even with correct QNH set, the altimeter is still not showing true altitude AMSL due to temperature effects. Colder temperatures mean you are actually lower than indicated, which could potentially be dangerous.
LPV: You get lateral and vertical guidance from GPS using corrections from an SBAS. In this example, the correction signal is coming from EGNOS. Since the vertical guidance is now unrelated to the altimeter, this type of RNP approach can be flown with QFE set.