Radius of earth is 3963 miles. Calculate 1/4 arc length by multiplying by 1.57 = 6222 miles. Diameter of earth is roughly 24,901miles, divided by 4 is 6225 miles so that match checks out.
Add 40,000 feet (7.58 miles) and recalculate gives a quarter arc of 6234 miles.
So you add roughly 12 miles (0.2%) to a trip a quarter of the way around the earth by travelling at 40,000 feet.
Low in the atmosphere you get lots of drag but also lots of lift. This is best for underpowered planes such as small prop planes.
Very high in the atmosphere has extremely low drag but also poor lift. This is best for aircraft designed to travel above the speed of sound.
Around 30-40 thousand feet is the sweet spot for commercial airliners. It strikes the right balance of drag to lift.
It’s also safer to fly above 20k feet. If anything goes wrong, you have more time to respond.
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