Contingency fuel

Why does a pilot who loads extra fuel for safety guarantee that the flight burns more of it?

A captain looks at the forecast, does not much like it, and asks for an extra tonne beyond the computed plan. Nothing about the route has changed. The aircraft will fly the same distance at the same speed. And yet the flight will now burn more fuel than it would have without the tonne — not because the crew flies differently, but because the tonne is aboard.

The fuel carried against trouble is partly consumed by the act of carrying it, which sounds like a margin that eats itself. Is safety fuel therefore self-defeating — and if not, what exactly does the extra tonne cost?

Start with what holds an aeroplane up. In level cruise the wing must generate lift equal to the aircraft's whole weight, fuel included. Fuel is not cargo riding along for free; it is part of the load the wing works against, and the only part that gets lighter as the flight proceeds.

Now ask what lift costs. A lifting wing leaves a disturbed wake, and the energy in that wake appears as a resisting force: induced drag, which rises with the square of the weight. Beside it sits parasite drag, the ordinary cost of pushing a shape through air, which does not care what the aircraft weighs.

Here is the step that makes the arithmetic tractable. An airliner cruises close to its best lift-to-drag ratio, and that condition has a tidy property — it is exactly where the induced and parasite contributions are equal. So take a one per cent increase in weight. Induced drag, going as the square, rises about two per cent; parasite drag does not move; if the two halves started equal, total drag rises about one per cent. Thrust must match drag and fuel flow tracks thrust, so fuel burn rises about one per cent too. Weight and fuel flow move together, near enough one for one.

Put a number on it. A widebody at around 200 tonnes carries an extra tonne: half a per cent more weight, so half a per cent more fuel flow. If it burns on the order of five tonnes an hour, that is about 25 kilograms an hour, and over ten hours roughly 250 kilograms — a quarter of the extra tonne, consumed purely in carrying the rest. That is two and a half per cent of the tankered fuel per hour, close to the three-to-four per cent rule of thumb I recall from flight planning. Derivation and recalled figure agree, which is mild reassurance that neither is nonsense.

Notice what that predicts, because it is the testable part. The penalty is not a fixed toll but a rate, proportional to time aloft: on a two-hour hop the same tonne costs about 50 kilograms, five per cent, and on a fifteen-hour sector a third or more.

So the margin only partly eats itself. Three-quarters of the extra tonne is still in the tanks at the destination, which is exactly where a safety margin belongs. What the crew bought was not a vanishing reserve but one that costs a few per cent per hour to hold.

Which is why the interesting decision is not the safety one. Regulators set the minima — taxi, trip, contingency, alternate, and a final reserve sized as a fixed holding time — and those are not the captain's to trade away. The genuinely discretionary case is tankering: loading cheap fuel at one airport to avoid buying dear fuel at the next. That is pure arithmetic, and it pays only when the price gap beats the fraction burned in carriage — so it pays on short sectors and stops paying on long ones.

One refinement, one correction, one limit.

Fuel burned carrying fuel must itself have been carried, so the true figure is a converging series rather than one multiplication — small at these percentages, but why planning software iterates. Weight has a second cost too: a heavier aircraft cannot reach its most efficient cruise altitude immediately.

Now the correction, to a popular story. It is often said that carriers squeeze pilots onto minimum fuel to save money, and that low-fuel emergencies are the result. The economics above are real, but the structure of the reserves is regulatory, not commercial, and low-fuel events are dominated by things fuel policy did not choose: weather that closed a destination, a blocked runway, holding that ran longer than forecast. A morality tale about cost pressure is doing work that arrival-rate variability actually did.

The limit: the one-for-one relationship between weight and fuel flow holds near best lift-to-drag ratio, and jets are usually flown a little faster than that, where parasite drag is the larger term — so the true sensitivity is a bit under one for one. The falsification test is direct. Fly one type at fixed altitude and Mach across a range of gross weights and log the fuel flow. If it rises roughly in proportion to weight, the mechanism stands; if it is flat, the whole account here is wrong.

• Why long flights climb in steps rather than settling at one altitude, and how that interacts with fuel weight.
• How regulators size a final reserve, and why it is stated as a holding time rather than a distance.

Every term the collection defines is gathered in the glossary.