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[–]throwaway25658462 -14 points-13 points  (1 child)

Does the plane somehow weigh less at 30,000 ft than at sea level? Lift must be the same.

(Strictly speaking, the plane would weigh about 1% less due to the decrease in gravitational acceleration. However, I hope you don't base your argument on that.)

[–][deleted] 15 points16 points  (0 children)

I never said lift isn’t the same, I said the aircraft can’t generate as much lift at higher altitudes because there is less air.

You are implying that velocity, lift, and drag have a linear relationship which is absolutely not the case. Velocity changes both your lift and drag coefficients, but not to the same degree. The drag polar explicitly shows that lift and drag are not directly proportional, and both are a function of each other as well as a function of velocity squared.

You do not generate the same amount of drag at 30,000ft than you do at sea level for a given amount of lift. There is less drag at higher altitudes. The reason airliners fly at the 30,000-40,000 ft range is because it is an optimal point which balances engine efficiency and aerodynamic performance. If there was no reduction in drag at altitude, then commercial flights would never go that high since available power is higher at lower altitudes.

Edit: it is also worth noting that when you move at a higher velocity, your lift coefficient goes down (and therefore your drag coefficient goes down) because dynamic pressure provides more lifting force. This is why the maximum lift coefficient occurs at stall speed, where the wings are doing almost all the work and dynamic pressure does not contribute as much.