Engine Instrumentation — Page 534, Lesson 634

Let’s start with the capacitance fuel quantity system. This is how we measure how much fuel is in the tank, and it works on a very elegant electrical principle. The whole idea is built on a capacitor. A capacitor is two conductive plates, parallel to each other, with something between them. That something is called the dielectric. In our fuel tank, the dielectric is a mixture of fuel and air. The key point is that the capacitance — the ability of that capacitor to store an electrical charge — depends on what’s between the plates. Now, the principle of operation: we use fuel and air as the dielectric between parallel-plate capacitors of fixed area and fixed distance between the plates. So the plates don’t move, and their size doesn’t change. The only variable is the ratio of fuel to air between them. And that ratio is determined by the quantity of fuel in the tank. More fuel, more fuel in the dielectric; less fuel, more air. So capacitance becomes a direct measure of fuel quantity. Let’s talk units. Capacitance is measured in farads. But a farad is a huge unit, so in practice we use the picofarad, which is 10⁻¹² farads — that’s one millionth of a millionth of a farad. That’s the standard unit we work with here. Now, the capacitance depends on a formula. Let me read it to you exactly as it appears: Capacitance = Relative Permittivity × (Area of plates ÷ Distance between plates) Or, in symbols: C = Er × A/D. Let’s unpack each symbol. C is capacitance. Er is the relative permittivity. A is the area of the plates. 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, divided by the capacitance of the same capacitor with a vacuum — or air — as its dielectric. So it tells you how much better a material is at storing charge compared to a vacuum. Vacuum has a relative permittivity of 1.0. Air is very close, at 1.0006. In an aircraft fuel system, the area of the plates and their distance apart remain constant. So A and D don’t change. That means the capacitance of the tank units will vary only depending on the level of fuel within the tanks. The only thing that changes is Er, because the dielectric changes as fuel level changes. Now, here’s a useful way to think about the total capacitance of a tank. We can consider it as two components. There’s Ca, which is the capacitance due to air, and Cf, which is the capacitance due to fuel. At any instant, the tank capacitance, Ct, equals Ca plus Cf. So Ct = Ca + Cf. The fuel component and the air component add together to give you the total. Let me give you the typical dielectric values, because these matter for understanding why the system works. Impure water has a relative permittivity of 0 — interesting, that’s why we don’t want water in our fuel, it messes up the reading. Vacuum is 1.0. Air is 1.0006. Gasolene — that’s gasoline — is 1.95. Kerosene is 2.10. And distilled water is 81.00. Notice the huge jump for distilled water. That’s why water contamination is such a problem for this system — a little water changes the capacitance dramatically. So the key takeaway: the capacitance system measures fuel quantity by using fuel and air as the dielectric between fixed parallel plates. The only variable is the fuel-to-air ratio, which reflects fuel level. And we read that as capacitance, in picofarads, using the formula C = Er × A/D, with the tank capacitance being the sum of the air component and the fuel component. That figure shows the capacitance tank unit — the corrugated circular metal discs secured in place, which form the plates of the capacitor inside the tank.