Ray geometry from the live ionosphere along the chosen bearing: hop distance from takeoff angle on a spherical Earth, the F2 layer at its measured height along the path, and the skip zone set by the critical frequency. Dashed rays escape to space where the band is above the local MUF. Also drawn: daylight, darkness and the grayline crossing; land or sea under each reflection (sea is lower-loss); D-layer absorption; the auroral oval where the path crosses it; the E layer (~110 km); and ticks marking how far each mode still decodes.