As a 777 pilot I, like many others, have wondered how the 777 would perform in the scenario where the pilots were incapacitated and the aircraft ran out of fuel. I had my ideas but there is nothing like seeing it for "real" so we tried this in a 777-2 full motion zero flight time approved simulator.
We used a zero fuel weight of 175 tonnes. We let it run out of fuel at FL 250 in track hold and alt capture. However it would not make any difference what mode it was in as everything would drop out. In real life one engine uses fractionally more fuel per hour than the other and there is typically a difference between main tanks of a few hundred kilos, so we had a 300 kg difference between the contents of the left and right tank.
When the first engine failed TAC (Thrust asymmetry compensation) automatically applied rudder. The speed reduced from 320 knots indicated to 245 knots indicated. It was able to maintain 245 knots and FL250. When the second engine failed the rudder trim applied by TAC was taken out and the trim went to zero. The autopilot dropped out and the flight controls reverted to direct mode. The speed initially came back to 230 knots but then the nose started to lower. The nose continued to lower and the rate of descent increased to 4,000 feet per minute, the nose kept lowering and the descent rate increased to 7,500 feet per minute with a bank angle that increased to 25 degrees. The speed at this point had increased to 340 knots indicated, above VMO but there was no horn as it was on limited electrics. About this point the RAT (Ram air turbine) chipped in and the CDUs and copilot's PFD (Primary flight display) came alive. The flight controls stayed in direct mode.The eicas screen was full of messages like pitot heat, flight controls, APU fault (The APU had tried to autostart due double engine failure but failed due no fuel to start it) low fuel pressure etc.
Then with a max descent rate of almost 8,000 feet per minute the nose started to slowly rise and keep rising. We had dropped to about FL170 but the nose slowly rose up to 6 degrees pitch up and we started climbing at about 3000 feet per minute and the bank angle reduced to only 5 degrees. It climbed back up to FL210 at which point the speed had come back to 220 knots and then the nose dropped down again and we were soon back to descending at 8000 feet per minute. So basically a series of phugoid oscillations with bank angle between 5 and 25 degrees and pitch attitude between about 9 degrees nose down and 6 degrees pitch up. It was losing about 8000 feet and then gaining about 3 or 4000 feet with airspeed fluctuating between 220 and 340 knots.
We didn't watch it all the way down due time constraints and stopped the experiment at 10,000 feet but it was consistent all the way down. Having watched it I can say with certainty that if the pilots were incapacitated and it ran out of fuel there is no way it could have landed on the water with anything like a survivable impact. Just passing on the info.