In developing the equations of motion, the "flat earth assumption" limits the air vehicle speed to less than Mach 3 to 5.

In developing the equations of motion, the "flat earth assumption" limits the air vehicle speed to less than Mach 3 to 5. For a spherical earth, examine Mach numbers for straight and level flight equal 1, 3, 5, 10, 15, 20 and 25 to demonstrate the problem. Assume the air vehicle is at 100,000 ft. altitude where the speed of sound for a standard day is 1050 ft/sec and gravity is 31.566 ft/sec2 . Compare your result with respect to gravity. Anything unusual about Mach 25? Hint: spreadsheet table to compare data. Don't forget a Free-Body Diagram for the problem.