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This video is about European Air Transport flight 2939, a Boeing 737, which "lost all the instruments of the aircraft" shortly after takeoff.

BCS2939: We are flying heading now, and we don't have even altitude and anything, so if you can, give vectors back to the field, please.
Approach: Roger, Eurotrans 2939, turn right heading 360 and you can climb to 3000 feet.
BCS2939: Right turn 360, 3000 feet. -pause- We are almost in visual, we don't even have altimeters.

Despite the lack of instruments the pilots manage to fly the headings given by Shannon Approach and land safely.

It seems that the instrument panels of the 737 are entirely digital:

enter image description here

I understand what vectors are:

A vector is defined by a direction and magnitude. In aviation these represent your heading (the direction) and your speed (the magnitude). However, in normal aviation usage "vector" only refers to the heading and other nomenclature is used to assign/report speeds.

The 737's cockpit seems to lack an analog compass which would survive a power outage like this one:

enter image description here

How might the pilots have flown the headings given by ATC (as the visualisation shows they did) without a compass or altimeter?

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    $\begingroup$ You can't see it in the picture you have (only the bottom black part is visible), but it does have a liquid filled compass at the top of the center vertical column separating the two windows. $\endgroup$ – Ron Beyer Feb 28 '17 at 16:20
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    $\begingroup$ Sounds like they lost their pitot-static system, which would mean no altitude or airspeed, but they'd still have normal heading & attitude. Losing all the displays would be pretty bad, although if it was only the displays that were lost, they'd still have altitude, airspeed, and heading (and attitude) on the standby instruments. Since they were able to maintain control of the aircraft in IMC, they had some sort of attitude indication, so this sounds to me like a case of losing the pitot-static system. Which, while plenty bad, should be survivable. A very bad day at the office, though. $\endgroup$ – Ralph J Feb 28 '17 at 17:15
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    $\begingroup$ Even if there was no magnetic compass in the cockpit, they could use a smartphone which is able to provide both bearings and GPS speed and altitude, or even just a Tomtom. I'm sure everybody, including EASA and FAA, would agree a smartphone in receive mode is less dangerous than losing air data. $\endgroup$ – mins Feb 28 '17 at 18:32
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    $\begingroup$ @mins: Try using a handheld compass in a vehicle some time. It is wildly variable depending upon the exact millimetre of positioning relative to ferrous objects. When an aircraft compass is installed, it has to be bolted into final position and then "adjusted" which compensates for all the objects in the cockpit, engine, fuselage, etc. which modify the magnetic field sensed by the compass. A smartphone using GPS information only and ignoring its magnetic compass would work well though. $\endgroup$ – wallyk Feb 28 '17 at 23:57
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    $\begingroup$ @wallyk: That's true, but a handled GPS usually knows the North direction without using a magnetic sensor. It's also true that when one doesn't have visual references to perform a 30° right turn, an uncompensated compass is better than nothing. The B737 IRS can also be used in Track/GS or Heading mode to approximate the North. $\endgroup$ – mins Mar 1 '17 at 7:26
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14 CFR Part 25 describes the requirements for an airliner like the 737 to be certified by the FAA.

§25.1303 Flight and navigation instruments.

(a) The following flight and navigation instruments must be installed so that the instrument is visible from each pilot station:

...

(3) A direction indicator (nonstabilized magnetic compass).

Indeed the 737 has a magnetic compass, centrally located above the windshield. It's just hard to see in the picture you have, as it's hidden behind the overhead console controls. This is a very typical location for the compass in many large aircraft (but not all), as it's centrally located, allows both pilots to see it, and will have less interference from other instruments.

737 Compass

Even the newest version, the 737 MAX, has a compass.

737 MAX Compass

Images Source

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As fooot has described, the aircraft has a mechanical compass, which will work even if the electrical systems fail.

Though unlikely, it is possible to imagine a situation where the crew of an aircraft loses all heading indicators. In such a situation, ATC can still provide radar vectors. ATC will instruct the crew which turn rate to use, and when to start and stop their turn, based on observations on the ATC radar. The radio phraseology will sound like this:

Make all turns rate one (or [number] degrees per second), start and stop all turns on the command "now"

Turn left (or right) now

Stop turn now

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    $\begingroup$ It's nice to see that everything's been thought of :) $\endgroup$ – hobbs Feb 28 '17 at 17:50
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    $\begingroup$ @hobbs ATC can even figure out how to get somebody who "has only flown once before as a passenger" to make a successful landing, if they have to: bbc.co.uk/news/uk-england-humber-24450534. ("Successful" in the sense "that he could walk away from it" - touching down nose-wheel-first and bouncing the prop on the runway are just details!) $\endgroup$ – alephzero Feb 28 '17 at 18:56

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