Engine Instrumentation — Page 534, Lesson 634

Let’s start with the big picture. We’re looking at how a capacitance fuel quantity system works — this is the system that tells the pilot how much fuel is in the tank, measured by electrical capacitance rather than a float or a mechanical gauge. The core principle is this: the system uses fuel and air as the dielectric between parallel-plate capacitors. Let me unpack that. A capacitor is two conductive plates separated by an insulating material — that insulating material is the dielectric. In this system, the plates have a fixed area and a fixed distance between them. So the only thing that can change is the dielectric itself — the material between the plates. And that material is a mixture of fuel and air. The ratio of fuel to air is determined by the quantity of fuel in the tank. More fuel means more fuel in the dielectric; less fuel means more air. Now, capacitance is measured in farads. The standard unit used here is the picofarad, which is 10⁻¹² farads — that’s one trillionth of a farad. So we’re talking about very small capacitance values. The capacitance depends on a formula. Let me read it exactly as it’s given: Capacitance equals Relative Permittivity times Area of plates divided by Distance between plates. Or, in symbols, C = Er × A / D. So C is capacitance, Er is relative permittivity, A is the area of the plates, and D is the distance between the plates. Now, what is Relative Permittivity? It’s a number given as a ratio — the capacitance of a capacitor having a certain material as a dielectric, compared to the capacitance of the same capacitor with a vacuum, or air, as its dielectric. So it’s a dimensionless number that tells you how much better a material is at storing electrical energy than a vacuum or air. Here’s the key point for an aircraft fuel system: the area of the plates and their distance apart remain constant. They don’t change. But the capacitance of the tank units will vary depending upon the level of fuel within the tanks. Because the dielectric changes — more fuel, higher permittivity, higher capacitance. Now, the value of capacitance of a tank can be considered as two components. There’s Ca, which is the capacitance due to air, and Cf, which is the capacitance due to fuel. And at any instant, the tank capacitance, Ct, equals Ca plus Cf. So Ct = Ca + Cf. That’s the total capacitance you measure, and it’s the sum of the air component and the fuel component. Let me give you the typical dielectric values from the table, because these are the numbers you’ll work with. Impure water has a relative permittivity of 0. Vacuum is 1.0. Air is 1.0006. Gasolene — that’s aviation gasoline — is 1.95. Kerosene is 2.10. And distilled water is 81.00. Notice the contrast here. Air is just slightly above vacuum at 1.0006. Kerosene at 2.10 is more than double that. And distilled water at 81 is enormous by comparison. So the fuel — kerosene or gasolene — has a much higher permittivity than air. That’s what makes the system work: as fuel level rises, more of the dielectric is fuel, so the capacitance rises measurably. One thing to note: impure water is listed at 0. That’s a striking value — it means impure water, as a dielectric, contributes nothing to capacitance in this context. That’s a real-world consideration for fuel contamination, but the key takeaway is the contrast between the fuel values and the air value. So, to tie it together: the tank unit is a capacitor with fixed plates. The dielectric is the fuel-air mixture. The capacitance you measure is the sum of the air component and the fuel component. And because fuel has a much higher relative permittivity than air, the capacitance tells you how much fuel is in the tank. That’s the whole principle of the capacitance fuel quantity system.