Yes, indeed they tell them how to get from one place to another in the flight school, and they wouldn't get lost if the earth
was a flat circle and they were taught accordingly. But they are told to navigate on a sphere because it is a sphere. The Earth doesn't change its shape according to the belief of the pilot.
You may have heard of Flat Earther, and YouTuber, Darryle Marble, who took a spirit level onto an aircraft, in an attempt to prove that the earth is indeed flat. His case was based on the fact that the pilot – throughout the flight – did not have to drop the aircraft’s nose to compensate for the curve.
Marble recorded a 23 minute and 45 second time-lapse; and figured out that, during his experiment, the aircraft had travelled a little over 203 miles. According to Marble, this meant that the pilot ought to have compensated for some five miles of curvature.
Marble’s error is basic. He is assuming that 203 miles is a lot of distance. It’s not!
That the earth seems flat to us is due entirely to relative size; a concept known as ‘local flatness’ That is why – even at sea – the horizon always appears flat. It’s a matter of scale. You know this, of course.
For localised flights it is perfectly adequate to assume a flat earth. However, for trans-global navigation (and for trans-atmospheric flight) a spherical co-ordinate system is preferred (for a far more comprehensive explanation see ‘Flight Dynamics Principles’ by Michael V. Cook).
Aircraft fly by interacting, not with the ground, but with the atmosphere.
Charlie Page, a Boeing 787 Dreamliner pilot, reminds us that:
‘The important factor here is that this is very much dependent on the air pressure. As weather systems move around the world, the pressure of the air changes above a certain location on the ground. These pressure changes are like the air in an inflatable mattress. Imagine placing a model aircraft on top of your mattress and treat the floor as sea level. As you pump air into the mattress, increasing the air pressure, the aircraft rises higher than the sea. When you let air out, lowering the pressure, the aircraft sinks closer to the sea.
‘As a result, pilots have to be aware of the air pressure for their location in the world. To make sure they are flying the correct altitude, they have to update their altimeter accordingly.
‘By flying at a Flight Level (FL), aircraft can fly for thousands of miles without having to reset their pressure setting. When climbing away from an airfield, ATC will instruct the pilots to climb to a certain Flight Level. Take the last two 0’s from the altitude and you have the FL — i.e. 23,000 feet becomes FL230. The pilots will change the pressure setting to 1,013 HPA and the aircraft is now flying at a Flight Level. When approaching the destination airfield, ATC will instruct them to set the local pressure setting, the QNH, and from then on, they are flying at altitudes.’ (‘How Do Pilots Decide How High They Fly?’).
The aircraft’s Flight Management System, by following the air pressure gradient, ensures that the aircraft is flown at an altitude that maintains constant ambient pressure.
This done, the aircraft will follow the earth’s curvature, simply because the atmosphere – attached to a spherical planet, and affected by the Earth's gravity – is also spherical, and not (as the FE’s insist) a ‘plane’.
No adjustments are needed, except where there are natural changes in barometric pressure (as you know, air pressure varies according to a number of factors, but the principal factor is distance above sea level); or when there are local changes (provided by air traffic control). In such cases, the aircraft’s altimeter is recalibrated.
An aircraft’s every movement – both laterally and vertically — is planned and coordinated with extreme precision; and aircraft are always separated by a minimum of 1,000 feet vertically.
Eastbound traffic fly at odd levels of altitude; and westbound traffic, at even levels. Using this rule (called the ‘semicircular rule’) ensures that aircraft flying toward each other don’t end up at the same level.
Flights that operate north/south routes are subject to country specific rules; but the end purpose is, of course, the same.