mike-wsm
I just thought of something. The earth is not a perfect sphere, it's diameter and circumference across the equator is larger than the poles which has to do with the earth's rotation.
Regardless to compute the differences of altitude you'd take the planet's circumference, which is pretty easy to compute (πD); you'd take the planet's circumference at altitude ([D+2(Altitude)]π); then divide the circumference of the planet at altitude by the circumference of the planet at sea-level.
At that point you multiple that number by the length of your trip.
Circumference of Earth at Sea Level (Across Equator) = 40,075 kilometers
Altitude of 35,000 feet = 11,000 meters
Altitude of 60,000 feet = 18,288 meters
Circumference of Earth at 11 kilometers = 40,144 kilometers
Difference in Circumference @ 11 kilometers = 69 km
Circumference of Earth at 18.288 km = 40,187 kilometers
Difference in Circumference @ 18,288 meters = 112 km
So theoretically, for a flight that would traverse 10,000 km on the ground right along the equator, you would travel about 10,017.22 kilometers by air if you were flying at 35,000 feet; and 10,027.95 kilometers if you were at 60,000 feet. Of course this is theoretical because you'd have to take off, climb to altitude, then descend; you would also have to fly right along the equator with no deviation (no northwest/northeast/southwest/southeast); to make it even more complex many airports are not at sea-level, and flights usually don't involve a constant climb and descent rate.