Equations for version 2 of flight code

Problem with flight paths near the North or South Pole

As shown in the previous sections the bulk of the equations are performed in Mercator space. A drawback of this it that it cannot cope with a flight path exiting either through the North or South of this two-dimensinal space. Even though the North and South pole are only two points on the globe, in Mercator space they are the two longest sides and this appears to increase the difficulties they present. So that any flight path passing either over or close to the North or South pole cannot be solved with version 1 of the code. However, this can be avoided if rotations are applied so that the route falls along the equator in Mercator space, which is what is done for version 2 of the code.

Material covered here

These page document the flight path code and cover

• The important angles: deriving the equations for the α, β and the tilt.
• Equations in rotated space: how the code has been modified for use with the rotated coordinates
• Adding grid points around the poles: how imaginary levels have been added to the boundaries.