Tag Archives: Breguet range equation

The cost of flying low

Last 12th October, I came from Amsterdam to Madrid by plane. That day there was an air controllers strike in France. While flying, the pilot commented that the company had tried to re-route the flight in order not to lose the slot it had, this proved almost impossible so what they did was to fly at a lower level. The pilot explained that this was very “costly as the engines consume much more” at that lower level.

How much more? How costly was this measure? I wanted to check it out, and some weeks later I have made the numbers that I show here.

We flew in an Airbus A321. Since it was the early flight in the morning I assume it carried maximum fuel and the weight was limited by Maximum Landing Weight (75.5 tonnes, MLW), so the takeoff weight would be the MLW plus the fuel weight we would consume in the flight, in the order of 5,500 kg (an average of 2,400 kg/hour according to some operators). Thus I used a takeoff weight of ~81,000 kg.

When flying at a lower level, the air density is higher and this increases drag. Normally, planes in this route fly at ~ 33,000 ft or ~ 10,000 m. What flight level did we use? This I don’t know, so I took the worst situation: say we flew at FL210, or 21,000 ft (~ 6,400 m). We can find at the chart the Standard Atmosphere and see the difference in density at both altitudes (~ 0.53ρ0 compared to ~ 0.33ρ0).

 

Flight levels, image from Wikipedia.

 

 

Standard Atmosphere, image from Wikipedia.

 

Using the Breguet range equation, all other things being equal (same distance, same aircraft, same weight at the departure…), we can relate the weights and densities of the initial flight plan the company had and the one used after trying to re-route.

 

Breguet range equation.

 

The result I got is that by flying at FL210 instead of FL330 the aircraft would have consumed over 1,400 kg of fuel more, a whole 26% more.

I checked the prices for fuel at IATA (International Air Transport Association) and at the moment is 746$/mt. The 1,400 kg of extra fuel would cost about 1,050$ (~ 760€), or about 4.2€ more per passenger (assuming we were around 180 passengers).

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