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I hear it stated quite often that aircraft like to fly high because there's less drag at higher altitudes.

$$ \text{Range} = \frac{V}{g} \frac{1}{\text{SFC}} \frac{L}{D} \ln \left( \frac{W_\text{initial}}{W_\text{final}} \right) \; . $$

Aside from SFC, it seems that none of the components of the range equation are altitude dependent. Lift/Drag should remain constant assuming the lift and drag coefficients remain constant. Therefore, is it incorrect to say that there is a benefit to range flying at a higher altitude due to decreased drag?

Another question is, does the lift/drag ratio of an aircraft increase somehow at higher altitudes?

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There's less drag at the same speed (and other things being equal, aside from altitude).

This is due to lower air density at higher altitude, which linearly affects drag. But just the same, it affects lift! You get less drag, but less lift too. If you want to fly level, you can't afford that: lift must be equal weight.

So what do you do to restore lift? You either fly faster, or increase angle of attack (AoA), or both. Either way, drag will roughly be the same.

Flying faster with the same drag is the benefit. However, sooner or later you'll hit the speed limit. (Most commonly for jets, this will be the Mach limit). From then on, you can only increase AoA.

Changing the AoA affects the L/D ratio. It may increase or decrease, depending on how the wing was designed. There is a certain AoA which will be the 'best'. If the jet was optimised for cruise, it will fly close to that angle.

Does it make any sense to fly even higher, where you have to increase AoA past the best L/D angle? It might, but not much. Primarily because you might squeeze a little better fuel consumption in colder air (that SFC component), so the optimum may be slightly higher. But flying at a higher-than-optimal AoA may be unstable by speed. (Which is manageable, but is another difficulty you don't want).

At some point, you will exhaust either the AoA, getting dangerously close to stall (while, remember, being at the speed limit at the same time - the so called 'coffin corner'), or thrust: it will keep reducing in thinner air, until it becomes lower than drag. That's your ceiling.

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  • $\begingroup$ Ah yes, this all makes sense. To clarify, will an altitude be reached where the optimal cruise Mach for an aircraft will no longer provide enough lift at maximum L/D? Can this altitude be above the troposphere, and can flight planning put the plane above the troposphere to extend range? Thanks, this question has been on my mind. $\endgroup$
    – Rory McDonald
    Commented Nov 18, 2020 at 1:14
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    $\begingroup$ @MichaelHall don't you mean less drag at the same TAS? The drag at the same indicated a/s should be the same, the dynamic pressure being the same. $\endgroup$
    – John K
    Commented Nov 18, 2020 at 1:33
  • $\begingroup$ @RoryMcDonald most airliners already cruise above the troposphere except in the tropical lats where the trop is closer to 40000 ft. At mid latitudes it's in the low-mid 30s, and in the north in the 20s, and as low as the teens in the arctic in winter. $\endgroup$
    – John K
    Commented Nov 18, 2020 at 1:38
  • $\begingroup$ @MichaelHall, I'm not sure it would be a clarification, because it requires to introduce the concept of IAS. It doesn't normally appear in aerodynamic formulae: it exists for pilots. $\endgroup$
    – Zeus
    Commented Nov 18, 2020 at 23:24
  • $\begingroup$ @Rory, it depends on what you mean by "optimal cruise Mach". If you are climbing at the best AoA (L/D), you'll be flying faster and faster (in terms of 'normal' airspeed, TAS). Mach may be increasing still faster, because the air gets colder (thus the speed of sound drops). So eventually, as I said, one of two things will happen: you'll hit the Mach limit, or you'll run out of thrust. (You'll be increasing your thrust setting in the process, even though the absolute thrust and fuel consumption (per hour) won't be significantly changing). $\endgroup$
    – Zeus
    Commented Nov 18, 2020 at 23:41

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