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I know this is an almost impossible situation, but... Imagine that a pilot is kidnapped and placed inside a Cessna plane. At a certain point the kidnapper jumps out of the plane, destroying the radio and taking all the aeronautical charts with him.
My question is: what should the pilot do, since he does not know where he is (he does not even know which country), there are no signs of civilization where he's flying, and he has no aeronautical charts?
The first thing you should do during a lost com's situation is fly the plane (that is really the first thing you should always do).
The second thing you should do is use visual reference points to figure out where you may be and get some situational awareness. Even in a foreign land a pilot may be able to identify known land marks like city skylines or prominent geological features. Even something like a coast line can be identifying. If the pilot becomes concerned about fuel (which any good pilot will at some point) then they should be on the look out for an airfield or a nice area to put the aircraft down.
The third order of business is to squawk 7600 on your transponder. This will alert any ATC facilities pinging you on radar, that you are unable to transmit and/or hear them.
This falls in line with the FAA's general advice of "Aviate, Navigate, Communicate".
Just a bit of an applicable side note: In the US under the FAA, and in other jurisdictions there are lots of areas that full under "uncontrolled" airspace where no radio or charts are required to be onboard anyway and many pilots are proficient flying in such a situation. Id even go so far as to say that a solid chunk of Piper Cubs are still flown this way.
You are right, this is a pretty improbable situation. But, I will give it a whack.
Aviate - Fly the plane. Fly it at as high of an altitude possible while still keeping visual contact with the ground. Just in case you lose an engine. Fly it in a wide circle or holding pattern until you get your bearings. Slow down your airspeed and lean your mixture for max endurance. You want to conserve fuel as well as ground position. No use in getting more lost quicker.
Navigate - Look for something identifiable. Or at least something that will lead you to civilization and suitable landing areas. Think of it like being lost on the ground. Look for your North direction using the sun or stars. Evaluate the ground for:
Find water. In the US water towers (not all) are marked with location names. If you find a river, you will usually find civilization close by. If you find a shoreline, you may be able to find a flat area suitable for landing.
Fly downhill. Fly towards the lowering terrain. You are more likely to find a landing area.
If all else fails go IFR (I Fly Roads).
Communicate - If the transponder works, squawk 7600. If you have a cell phone, try it. You May have to descend to get it to work. Only do so if you have established where you are and if the aircraft is safe to continue flight. Turn on all of your exterior lights. If you see an airport, circle directly above the field at 2000 to 4000 feet AGL and look for light gun signals.
Land as far away from the kidnappers/highjackers as possible.
Aviate, navigate, communicate.
First, make sure flight is stable. Figure out how long you can do that, and set up flight to maximize that.
Now try to figure out where you can go. From the Question, it sounds like there are no easy answers: no airport in sight, no giant concrete arrows pointing the way, etc. in that case, pick a best direction taking into account terrain, weather, light and wind and start looking for a place to put down. Climb a bit for a wider view if you’re low and can afford it.
Take the first acceptable place, as you’ll want to preserve your passengers (if any), your plane, and even perhaps your remaining fuel.
What about communicate? Well, the problem statement seems to rule that out in flight, but after down SERE training becomes relevant. But that’s another Question...
I think the other answers miss a few points. I think we can assume the pilot knows where he was when he was kidnapped, no? So the first thing to do, after making sure the plane is in stable flight, is to check the fuel gauges. Assuming the Cessna is a 172 with standard tanks, it has 40 gallons usable fuel, enough for about 4.5 hours of flying. So check the fuel gauges, and see how much you have left. If the tanks are half full*, then given the 140 mph cruise speed, you can guess that you're within about 300 miles of where you started. Then start looking for familiar features like mountains, lakes, roads &c, which should be identifiable unless you're over the Amazon Basin or Canadian north. That will get you oriented, and you can probably find an airport, or some other good place to land.
*If they're close to empty, disregard the rest, and look for a spot to land, or do a survivable crash.
