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The float valve position and the rotation rate of the bucket wheel were converted to an analog indication via a drive magnet. As you'll be able to imagine, this was a very delicate arrangement.
When Aircraft Digital Instruments fuel flowed through a pipe, it could be accurately measured via the Aircraft Electronic Data Management Systems (EDMS). The output could either be displayed as a bar graph or as a number (depending on the pilot preference). Modern EDMS not only indicated fuel levels and fuel flow levels with a high degree of accuracy, they could provide other valuable information too such as, distance-to-empty and with a GPS plugged in, they could even indicate whether the plane had enough fuel to make it to a show destination.
In days gone by, an aircraft fuel flow indicator was basically an adaption of the vehicle fuel flow indicator. It had an analog system (i.e. mechanical) via a micro float valve and a tiny bucket wheel. As the fuel flowed, the bucket wheel rotated inside the fuel pipe and provided a fairly accurate fuel flow rate. Meanwhile the float valve gave an actual indication of who much fuel was left in the tanks. The fuel balance indicator and fuel flow indicator looked a little more complex than your average car fuel indicator but the a should-have functionality was the same.
Some 20 years ago, the humble fuel indicator and fuel flow indicators were upgraded to electrically powered indicator. This brought in a level of accuracy to the fuel indicator and fuel flow indicators. The system no longer relied on metal wires or cables connecting the float valve or bucket wheel to the actual fuel indicator and fuel flow indicators. These metal cables were prone to get tangled and during a turbulent flight, were known to get tangled making them highly unreliable. Which is why in WWII struggle movies, you often saw pilots tapping at the fuel flow indicator to make sure nothing were stuck.
Aircrafts have two wings and a fuel tank in each of them. Some aircraft are adopted for long duration flights and may have more than two fuel tanks. Having one fuel flow indicator for one tank is easy to understand but ever wonder how a single fuel flow indicator can provide details about fuel levels in two or more tanks? Read on.
The electrical system did away with the cables and as an alternative worked by calculating the capacitance. Basically, the electrical fuel indicator and fuel flow indicators used a capacitor to do the calculation. Heres the way it worked the capacitor stored an electric charge. How much of this electric charge it stored depended on the level of the fuel in the aircraft.
In the United States, J.P. Instruments are the premier manufacturers of modern day fuel indicator and fuel flow indicators. More information here: https://www.jpinstruments.com/ Error margin would indicate a fuel leak and trigger an alarm.
More the fuel, higher the stored charge very straightforward whilst you think about it. In turn, the capacitance charge level is converted by the Airplane Gauges into an analog or digital read-out.