# Why might a passenger jet fly at altitudes in a strong headwind when the winds are more favorable at a different altitude?

I was a passenger on an east to west flight recently. During the flight I was playing with Garmin Pilot's new "Flight profile" feature that nicely shows the wind speeds at various altitudes, and I noticed that we were flying against an 80+ knot headwind at FL320, but if we'd dropped to FL220 we'd shave about 40 knots of headwind. That seems pretty significant. A 1,000 NM flight with 355 knot ground speed (which we were cruising at) would save 17 minutes of cruise time with 40 knots less headwind. That's a 10% increase in efficiency.

So the question is, did we stay (or even plan in the first place) to fly at FL 320 the entire cruise portion of the flight simply due to ATC needing to keep us there for traffic routing purposes, Is there an even larger increase in fuel efficiency between FL320 and FL220 than 10%, or is the difference negligible enough that it's not worth asking for a different altitude from ATC, or some other factor not considered here?

• winds are quite volatile so you can't rely on them staying the same for several hours – ratchet freak Apr 30 '16 at 13:22
• Pretty good answers below working through the math, but it must be stressed that the airlines optimize for minimum fuel cost much more strongly than for minimum flight time. While there are some other costs that go up with flight time (crew pay, aircraft maintenance), fuel is a big, big component and they fly to make money. I also find it useful to keep in mind the very approximate rule of thumb that true airspeed increases around 2% per 1,000 feet of altitude. (The real equation is far from linear so this a crude estimate, but useful.) – RobP May 7 '16 at 23:46

You assessment is flawed in that it does not take different air density in account. You state the following conditions:

• FL320
• 80 kt headwind
• 355 kt groundspeed
• 1000 nm distance

and you are proposing descending to the following conditions:

• FL220
• 40 kt headwind

At 32,000 ft, standard conditions are around 275 hPa, 225 K and density of 0.43 kg m$^{-3}$. If your 80 kt wind is a pure headwind, a 355 kt groundspeed translates into a 435 kt TAS. If we correct this TAS for the ambient conditions we get an indicated airspeed of about 255 KIAS. This is the airspeed that really matters because it is what the airplane experiences as it interacts with the atmosphere.

If we descend to FL220, where standard conditions are 430 hPa, 244 K and 0.61 m$^{-3}$, an airspeed of 255 KIAS yields a TAS of 363 kt TAS. If we have a headwind of 40 its, this yields a groundspeed of 323 kt. This is about 30 kt slower than you were flying at FL320. A flight of 1000 nm will take about 15 minutes longer to complete.

However, it is most likely possible that the airplane you were in is capable of flying faster than 255 KIAS at FL220 and in fact is probably capable of somewhere around 310 KIAS. Flying at 310 KIAS at FL220 will have true airspeed or 440 KTAS and with the 40 kt headwind a ground speed of 400 kt. This will get you to your destination faster, but at the expense of a much higher fuel burn.

It is also likely that you could have been flying faster at FL320 (not sure what max mach number would have been for you), but also at the expense of burning more fuel. If the airplane wasn't dispatched for the additional fuel burn to go faster at FL220, then after descending you would probably not have enough fuel to go fast enough to make up the difference in true airspeeds.

• Great answer. I don't agree with your first statement that my assessment was flawed, as one of the options I presented indirectly acknowledged that density altitude would be a factor, but otherwise, very instructive. I'm a little surprised by the magnitude of difference the density altitude makes in this example, without doing the math, it didn't seem like it would be that big. – Greg Taylor Apr 30 '16 at 22:04
• @GregTaylor I'm getting .74 mach. Perry slow for an airliner. What kind of plane were you in? – TomMcW May 1 '16 at 6:14
• It was an MD-80, technically S80. – Greg Taylor May 1 '16 at 12:25