mjhjmtu

Inspired by this story;

The pilot of a Flybe plane that dropped 500 ft (152m) in 18 seconds had
selected the wrong autopilot setting shortly after take-off, an
inquiry has found...

...The plane climbed to 1,500 ft, but then pitched and "descended
rapidly" because the autopilot was set with a target altitude of 0 ft.

Why is 0 ft a valid target value for the autopilot? Is there any practical use for being able to set it so low and are there safety features that would prevent the plane just hitting the deck?

Quite simply, it's because sometimes you fly below sea level. There's a couple stories out there of aircraft navigation systems acting a bit odd due to their flight below sea level. For example, there is this one, which involves a C-130 landing on an airfield that is 1,210 feet below sea level.

There are numerous areas in the world that are below sea level. For example, flying at sealevel above Laguna Salada, Mexico means you are still 30 feet above the ground! It's added as an additional option to cover a small set of scenarios. A pilot is certainly not expected to select the incorrect altitude setting, as this is something that you should always doublecheck. Beyond that, he should not have enabled his autopilot so soon after takeoff (unless 1,500 was his cruising altitude).

The answer is no you would never depart with the altitude preselect at 0. You would normally set the initial level off altitude provided in your departure clearance, or an initial level off altitude indicated in the SID, or you might set a level off altitude that you have decided to use as a level off for the single engine profile in the event of engine failure, based on the terrain around the airport. All would be at least a 1000 ft above the airport at minimum.

You dial up that altitude in the AP's altitude preselect window, usually during the configuration setup during or after the crew departure briefing. When you are airborne, you will normally select the autopilot's speed hold mode (on the -8 AP it's called IAS mode) which makes the flight director command a pitch attitude to hold bug speed, then when you pass 400 feet or above, you engage A/P in IAS mode and it will pitch the plane to hold the bug speed you select during the departure. In IAS mode, whether you climb or descend depends on the power setting, so when you are climbing and descending in IAS mode you regulate the climb/descent with power while the AP pitches to hold the speed. You can also use VS mode, or vertical speed mode, and the AP will now pitch to a preset vertical climb or descent rate.

With those two vertical modes, the incident description doesn't make a lot of sense as they would have had to have selected VS mode and dialed in a descent rate, or been in IAS mode and cut the power. However...

The -8 400 has coupled VNAV, which adds an extra wrinkle. With VNAV engaged, the autopilot will pitch to climb or descend to an altitude preselect independently of IAS or VS mode, instead of just hold an airspeed or vertical speed, until a preselect altitude is captured. Coupled VNAV can also follow step climbs in a SID or step descents in a STAR if that is programmed into the FMS.

So my guess here is that they forgot to set the altitude preselect for their planned departure level off altitude, then engaged the autopilot in VNAV mode during the climbout, which caused the plane to dive to the existing altitude preselect of 0 feet, upon which hilarity ensued.

Besides flying below sea level, a situation for low and negative altimeter readings is use of QFE altimetry. (see also What is wrong about this interpretation of QFE and QNH?)

QFE altimetry which was used by some airlines (gone by now), and is still in use in Russia (undergoing phase-out), is where you set the altimeter's reference pressure so that it reads zero at some ground reference point, typically the runway threshold.

So if the runway is above you, on terrain, you will fly at a negative height and your altimeters will show as such.