I immediately remembered the posts on the other F800 site where a handfull of F800-S/ST riders described just such an event. It occurs when it's hot outside, the speed is relatively fast/sustained -and- the low fuel light has been on, but there is enough fuel left for at least another 15--20 minutes riding at speed. It logically points to either the fuel pump or it's finned electronic controller module reacting badly to heat buildup. With the low fuel light on for a while, the fuel level drops below the usually submerged fuel pump, completely canceling the liquid fuel's cooling effect. That may or may not be a cause, but it's an important factor.
Minutes after the flame-out I exited the divided highway and stopped at the first good gas station (Shell) to fill up. I removed the seat for a look-see at the fuel pump controller and wires. I knew immediately the small flannel rag neatly covering the fuel pump housing's outer circumference was a bad thing. What was I thinking? With the seat on, it cuts off major cooling airflow to the finned fuel pump controller. I have made this same type of a trip before, running perfect, with the low fuel lite on, but in much colder weather. After the gas-up and cleaning rag relocation to the left rear body panel side pocket, out on the road it ran perfect immediately. Just like it has for the previous 5,850 miles (9,415km). At the BMW open house, my intended destination, I spoke with the service dept manager about the flame-out event and got a surprised reaction from him. He said he'd "speak with the rep about it" relaying all the details (Low fuel lite, sustained speed, warm/hot weather). He said I could leave the bike for them to check it out, but it wouldn't be until Tuesday that it'd be looked at. I said no, it's running AOK after the gas up. The 50 minute fast ride home was totally flawless, assuring me the flame-out was NOT a preliminary symptom of component failure.
Lessons learned so far:
--Don't put anything in/on/over the fuel pump's rubber cover area that disrupts normal airflow.
--The F800 S/ST fuel pump controller is susceptible to malfunctioning if overheated.
--The oddly shaped rubber cover over the fuel pump appears to be a post production correction for a design error.
In my garage with the seat off again I looked at the odd protruding rubber tower where the pressurized fuel line exits the fuel pump housing. It is shaped like that to function as an air scoop, capturing the breeze blowing under the seat and forcing it out around the controller's Aluminum heat exchanger fins. My putting a rag there apparently caused an out-of-the-blue, new-2-me, potentially serious problem.
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