Why does the optimum cruise altitude depend on the weight of the airplane?

Question

In this answer, Bianfable notes:

[O]ptimum cruise altitude for a 777-200LR at a weight of 340 t is only FL285, but after burning 100 t of fuel it has increased to FL360

Why is that? Is it simply the momentum of the heavier plane is able to reduce the effect of drag? Is it linear, or stepped? And, does the plane rise at some point to the higher level (assuming on a long trip)?

FreeMan suggests in comments it may be the Angle of Attack (AoA) that makes a difference - higher AoA for heavier planes means more drag, so better off at higher altitudes.

As ymb1 notes in comments, from their earlier question, I wonder about this sentence:

At higher altitude the friction and pressure drag is lower but the induced drag is higher, so increasing the mass will cause a much higher jump in drag.

That makes me wonder if it's more related to the different components of drag, than the AoA (or just the AoA, maybe it's a combination of both?)

Answer 1

The lift equation:

Lift = wing area x Coefficient of Lift x air density x V$^2$

provides three variables to lift a given amount of weight: Angle of Attack, air density, and velocity.

Aircraft have the least amount of drag per unit lift at a specific AoA, so best to keep it there. Speeding up a little is a very good idea but there are 2 factors with the 777, drag from Mach effect (important at high subsonic speeds) and the ability to produce additional thrust in the thin air. So that leaves altitude (air density) as the best controlling factor for lift production.

Even though the indicated airspeed will be higher for the same True airspeed at FL285 compared with FL360, there is plenty of oxygen for the engines to push the plane along at its optimal AoA and matching airspeed.

True airspeed determines Mach effect

As fuel is burned off, less weight allows the plane to climb to a higher altitude because lower indicated airspeed is required, therefor less thrust, allowing the airliner to stay in its safe Mach "envelope".

does the momentum of the plane reduce the effect of drag?

No, more weight indirectly increases drag. The plane must fly faster, at a higher AoA, or in thicker air to generate the same amount of lift. All require more thrust, because there is more drag.

Answer 2

Because the density of the air decreases with increasing altitude. Thus to achieve the same net lift, to reach equilibrium with a given weight, the wing must have a higher angle of attack.

The higher angle of attack also increases drag which requires additional thrust to overcome.

Thrust available also decreases with increasing altitude due to decreasing air density. Thus for a given weight a given wing and given engines an optimum altitude is reached which provides some safety margins and optimizes fuel burn.