Abstract: By using the space vector method, the equation of great ellipse on ellipsoidal surface only related to the geographical coordinates of the starting and ending points was derived, the parameter equations of great ellipse routes on various projection planes were obtained from the great ellipse equation and the positive solution formulas of the four kinds of common projection. And then the curvature and radius of curvature of great ellipse routes on the four kinds of projection planes were derived. The great ellipse route from London to New York was taken as an example, by drawing the great ellipse route on different projection planes and analyzing the curve of curvature and curvature radius, the conclusion is drawn that the representation of great ellipse route on gnomonic projection plane is straight line, while which of great ellipse route on the other projection planes are curves with curvature changing slightly. The formulas of curvature radius derived in this paper can be used to calculate the "substitution distance" of great ellipse routes, which is convenient to measure and draw the great ellipse routes on the nautical chart with any scale, and improve the efficiency of nautical drawing.

Key words: great ellipse route, nautical chart projection, curvature, radius of curvature, substitution distance