# If Earth is curve and spinning, why plane flying in high altitude does not delayed?

If earth is spinning globe then the layer of athmosphere have a different tangential velocity for different altitude. For near the ground (solid surface of the earth) then the velocity of the air just 465 m/s as usual. But for higher altitude this velocity makes the layer of athmosphere in this altitude will left behind than those the nearer ground layer.

This is because the farther from the the ground then the larger tangential velocity its needed to catch up with the same angle of rotation. It is like a wheel, more farther from the center makes its more faster in tangential velocity. But for athmosphere, its tangential velocity are the same with those on the ground, because it is not a rigid body.

So when a plane flying with different altitude, then its tangential velocity during circular motion around the earth will affected by different velocity of athmosphere layer. But why during a flight I never meet a correction of schedule because of this?

A plane travels at an altitude of about 8-10 km. The earth's radius is 6350 km - so you may reach a maximum distance of 6360 km from the center of the earth. Here's what that relative change looks like:

Tangential velocity is $v_T = \omega r$

At the surface of the earth:

$$v_{surface} = \omega \cdot 6350$$

At cruising altitude

$$v_{flight} = \omega \cdot 6360$$

So the difference in tangential velocity $$1 - \left | \frac{6360}{6350} \right | \approx 0.15\%$$

The maximum tangential velocity of the earth is around 1500km near the equator - so the largest difference would be on the order of 2-3 km/h.

• I should add this is a very simplified model. The key observation is that the largest possible effect from air not being a 'rigid body' can be neglected when compared to jet stream speeds (often 100 times larger) – Señor O Oct 18 '17 at 15:22