geometry - Does the rotation of the earth dramatically affect airplane flight time?

Say I'm flying from Sydney, to Los Angeles (S2LA), back to Sydney (LA2S).

During S2LA, travelling with the rotation of the earth, would the flight time be longer than LA2S on account of Los Angeles turning/moving away from our position?

Or, in the opposite direction, would the flight to Sydney be faster since the Earth turns underneath us and moves Sydney closer?

===

• 
  

  Please ignore jet stream effects and all other variables; this is a control case in an ideal environment.

  
  


• 
  

  By "dramatically" I suppose I mean a delay of 1 hour or more.

  
  

Answer

During the flight, you need to get up to use the restroom. There's one 10 rows in front of you, and another 10 rows behind you. Does it take longer to walk to the one that's moving away from you at 600 mph than the one that's moving towards you at 600 mph?

No, because you're moving at 600 mph right along with it -- in the ground-based frame of reference. In the frame of reference of the airplane, everything is stationary.

Similarly, the airplane is already moving along with the surface of the Earth before it takes off. The rotation of the Earth has no direct significant effect on flight times in either direction.

That's to a first order approximation. As others have already said, since the Earth's surface is (very nearly) spherical and is rotating rather than moving linearly, Coriolis effects can be significant. But prevailing winds (which themselves are caused by Coriolis and other effects) are more significant that any direct Coriolis effect on the airplane.