Are those numbers correct? In the worst case, the chord would be the diameter and the great circle would be half the circumference, so the ratio would be (pi.d

Are those numbers correct? In the worst case, the chord would be the diameter and the great circle would be half the circumference, so the ratio would be (pi.d/2)/d = pi/2 = 1.57. For fun the cos rule can be used to derive a general formula for the ratio of great circle to chord, given the angle (theta) in radians subtended at the centre of the Earth: theta / sqrt( 2-2.cos(theta) ) where: theta = (great circle distance) / radius (Assuming I haven't mucked up my algebra.) -- Not sure why my comment is rendering in italics. No emphasis is meant. Figured it out, it was the asterisk I used for a multiplication symbol.