How plains should travel further according to PI

If we would go around the globe on te ground they say its about 42000 KM , so the more altitude a plane would gain the further distances would get according to Pi

If we would go around the globe on te ground they say its about 42000 KM , so the more altitude a plane would gain the further distances would get according to Pi

You are correct sir. Now for extra credit how much further?

For example, if the distance to be traveled is 500 miles at sea level, how much further apart would the same location be at 6 miles above sea level?

Thats a hard thing to calculate should I take the radius of earth plus 6 miles that amount twice and then x PI to get the circumference of the plain of it flies a whole circle and take approx 2% of that as 500 miles is 2% of the 25k miles circumference?

Thats a hard thing to calculate should I take the radius of earth plus 6 miles that amount twice and then x PI to get the circumference of the plain of it flies a whole circle and take approx 2% of that as 500 miles is 2% of the 25k miles circumference?

You could do that. But an easier technique is to divide the new altitude by the radius of the Earth. Then multiply 500 miles by the result. The ratio of an increase of radius to circumference remains the same. So a 10% increase in radius corresponds to a 10% increase in circumference. So 3966/3960= 1.0015. 500 miles x 1.0015= 500.75 miles.

So by choosing to fly at altitude, planes gain the benefits of straight line travel at considerably higher speeds in exchange for a very small increase in travel distance.