How is fuel mass measured in airliners?

Question

Large airliners display the amount of fuel in each tank as a mass (usually in kg or lbs) and not as a volume. This makes sense since mass is important for weight&balance considerations and the fuel mass is proportional to the amount of available energy.

Based on a discussion in the comments under this answer, I am wondering: how is the fuel mass measured?

Answer 1

On the Airbus A320 family, the fuel volume is measured via capacitance probes and then converted to mass by also measuring the fuel density:

The FQI [Fuel Quantity Indication] system calculates the fuel quantity based on values taken from probes in the tanks. The probes measure the level of the fuel in the tank, as a consequence of changing capacitance due to the amount the probe is immersed. This allows the determination of the fuel volume in the tank.

Yet the information that is needed by pilots is the quantity of fuel on board expressed as a weight. The translation of fuel volume into fuel weight is performed by the FQIC using the fuel density measured by specific devices in each wing tank [...]

^{(Airbus Safety First - Fuel monitoring on A320 Family aircraft)}

The FCOM lists the sensors involved in this measurement:

The FQI system comprises : [...]

• A set of capacitance probes in each tank to measure fuel level and temperature.
• one densitometer (cadensicon) sensor in each wing inner tank permitting the calculation of the fuel quantity.
• one Capacitance Index Compensator (CIC) in each inner tank giving the dielectric constant of the fuel in case of cadensicon failure.

^{(Airbus A320 FCOM - Fuel Description - Fuel Quantity Indication and Level Sensing)}

Using the densitometer (or the backup CIC), the conversion from volume to mass is performed by the FQIC. The ECAM can then display fuel temperature and mass as calculated by the FQIC.

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Additionally, there is an independent system sensing low fuel level, which would alert the pilots even if something goes wrong with the normal FQIS:

In addition to the sensors and probes feeding the FQI system, each wing tank is equipped with three independent dedicated low level sensors. These sensors are located in such a way that they become dry when the remaining fuel in the tank is approximately 750 kg. If two sensors in the same tank remain dry for more than 30 seconds, a low level alert triggers in the cockpit (fig.2).

The low level sensors are fully independent from the Fuel Quantity Indication, and are different in that they:

• Do not provide pilots with a continuous indication of the fuel quantity in the wing tanks, but only the signal that the fuel level has reached below 750 kg (threshold crossed).
• The information provided to pilots in the form of the low level alert results from a physical measure (sensors dry or wet) rather than from a calculation.

^{(Airbus Safety First - Fuel monitoring on A320 Family aircraft)}

Answer 2

The 737 is the same as the A320 in principle (sensing filled volume then converting to kg or lbs for the crew).

From a 737 maintenance training manual:

Tank Units are hollow coaxial cylindrical capacitors mounted vertically to ribs inside each fuel tank. Fuel is used as the dielectric. The inner tube is profiled to correspond to the irregular shape of the inside of the fuel tank. The tank units are located throughout the tanks so an accurate reading is provided whatever the attitude of the airplane.

Here's an FAA drawing for such unit:

And indeed this sensor would be affected by temperature as Ralph has noticed, but it has nothing to do with directly sensing the mass or weight:

The use of tank unit capacitors, a reference capacitor, and a microchip bridge circuit in the fuel quantity indicators is complicated by the fact that temperature affects the dielectric constant of the fuel. [FAA; emphasis mine]

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_{FAA source: FAA-H-8083-31A, Aviation Maintenance Technician Handbook-Airframe Volume 2 (via faa.gov's Aviation Handbooks & Manuals)}