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While some fuel volume sensors use ultrasonic measurements this answer to How is fuel mass measured in airliners? says:

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.

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

So in this case capacitive sensors (plus fixed tank shape) can determine the fuel volume, and a density measurement can convert that to a mass.

Question: How does a fuel density sensor work, being the "densitometer" or "cadensicon" mentioned in the block quote.

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    $\begingroup$ It reads a bit like you wouldn't need the densitometer in case of ultrasonic sensors, but you need them there as well. $\endgroup$
    – Arsenal
    Nov 5, 2021 at 12:02
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    $\begingroup$ I'm referring to your introduction - "While some fuel sensors use ultrasonic measurements this answer to How is fuel mass measured in airliners? says: ..." But yeah, the rest is fine. And for the topic: you can calculate density with a differential pressure sensor and a known height between them, but I have no idea what they use in aviation. $\endgroup$
    – Arsenal
    Nov 5, 2021 at 12:21
  • $\begingroup$ @Arsenal Oh, yes I see what you mean now, sorry my bad. I've edited to differentiate. Thanks! $\endgroup$
    – uhoh
    Nov 5, 2021 at 21:34

2 Answers 2

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I don't know what exact kind they are using in the A320 (from which the quote in the question is). @mins found a forum post about an Airbus A300-600 cadensicon:

The cadensicon measures fuel dielectric constant and density.

Unfortunately, that source does not describe how the density is measured.

However, I found a densitometer that is used for aviation fuel density measurements. It measures the change in resonance frequency of a spring, which is driven by a piezo. That frequency change depends on the fluid density, which allows calculating the density from the measured frequency and known calibration coefficients:

Densitometer

The densitometer uses a torsional mode natural frequency to determine density in real time, providing an accurate and reliable indication of fuel density over the temperature ranges typically encountered in aircraft fuel tank applications. It is designed to operate in all aircraft fuels encountered worldwide.

One end of a spring is driven torsionally to resonance using an oscillating electrical signal by a piezoelectric crystal, the other end of the spring is allowed to freely vibrate at its natural frequency. This end is “coupled” with the fluid media and natural frequency changes in response to the fluid density are measured on a second drive piezoelectric crystal.

The primary output is an AC voltage having a frequency that varies with density. Density is calculated from the output frequency via the equation: $ \rho = a + b / \text{frequency}^2 $, where a and b are constants determined during calibration. The standard method of acquiring the frequency in a microprocessor based system is with a timer/counter chip having a two-second gate time insuring high resolution.

(AMETEK Aerospace - Fluid Densitometer)

For more details, see the patent US4275585A.

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    $\begingroup$ Re A300: an A310's Cadensicon "utilizes a mass balance method" (.pdf; dtic.mil; pdf page 35) -- that's the most I could find, they're keeping it close to the chest :D $\endgroup$
    – user14897
    Nov 5, 2021 at 11:07
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Short answer

The two cadensicons used on A320 are float type, density is determined by measuring Archimedes force (buoyancy). A float is maintained by springs and the force on the springs is measured.

  • The force "is equal to the weight of the fluid that the float displaces".

  • This weight depends on different elements: volume, gravity field and density.

Volume is constant, gravity field is assumed constant, leaving only a dependency on density.


Details

A cadensicon, or capacitive density condensator, is a densitometer with a measure of fuel permittivity (dielectric constant), to calibrate the capacitive probes.

On the A320, there is a cadensicon for each tank (2 or 3 if there is a center tank), all float type. View of the A320 cadensicon:

A320 cadensicon (densitometer)

A320 cadensicon. Left: Boeing site, right: Airbus A320 documentation

From Airbus technical training manual for A320 fuel system:

Each cadensicon houses 2 sensors covered by fuel. A fixed capacitor covered by fuel is the primary source for dielectric constant of the fuel in each tank and a densitometer float measures fuel density. Both parameters are used for calculations of the fuel quantity. As density of the fuel grade in use changes with temperature, a fuel thermistor makes an allowance for temperature variations.

A partially immersed probe can be seen as the sum of two variables capacitors with different dielectrics (air and fuel) and which total capacity is a function of fuel level. Each tank has a probe fitted with a capacitance index compensator, which measures fuel permittivity at the bottom of the tank.

enter image description here

A320 fuel level probes, from Airbus A320 documentation

The location of the probes is chosen to ensure at least one probe cuts the fuel level in any aircraft attitude.

The FQI has two channels, one working to compute the mass, the other to monitor the first one. Mass is computed from the levels sensed by capacitive probes and:

  • Permitivity from cadensicon
  • Permitivity from capacitance index compensators
  • Density from cadensicon
  • Fuel temperature
  • Pitch and roll angles.

The conversion of levels to volume takes into account the attitude determined using the probes and a table in the computer memory containing the geometry of the tanks.

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