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

[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.

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?)

• I looked at this question and its linked questions; I don't think any of them answer this, but it's well possible I misunderstand something here, so please point me to the right one if I missed the duplicate. Thanks!
– Joe
Sep 24 at 16:42
• IIRC (and I'm not sure of all the specifics), the heavier the plane, the higher the AoA is going to be to maintain level flight at a given altitude. If the plane is 340t at FL360, the AoA is going to be so high that it will be very inefficient (too much drag) which will reduce range. At FL285 and 340t, though, AoA will be sufficiently low to be at max efficiency in cruise. Sep 24 at 16:57
• In case someone asks, my source for that claim is the Boeing 777 FCOM vol. 1 (PI.31.1 Performance Inflight - All Engine). Here is a screenshot of the relevant table. Sep 24 at 17:01
• First of all, +1 for researching it. I asked a very related question, and I think the answer here will help, but the terms used may be too technical. If they are, as a suggestion, you can edit your question to include the additional points being discussed about. But I don't think it's a duplicate of yours.
– ymb1
Sep 24 at 17:03
• I was thinking something along the lines of, "I found this, but what does "lower lift coefficient" mean and how does it relate to it." Very optional, but may help make the answers more to the point.
– ymb1
Sep 24 at 19:39

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.

• Airliners also increase wing area and Lift Coefficient with slats and flaps for lower speed takeoff and landing. Sep 24 at 21:05
• @ymb1 that is correct and edited, thanks. Sep 25 at 3:23

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.

• By "net lift," do you mean lift - weight? Sep 25 at 2:47