A rotational ellipsoid with small eccentricity (spheroid) approximates well the shape ofthegeoid thus can be used for various calculations. A curve that cuts all meridians of arotating surface, in this case ellipsoid of revolution, at the constant angle is called aloxodrome. A deeper hsight into the principles of navigation leads to the understanding ofspheroidal models and elliptic integrals. Differential equation of a loxodrome on thespheroid presented here aims to understand mathematical postulates of navigation. lnscientific and professional literature the difference in latitude parts is obtained byintegration of radius of curvature as a function of geographic (geodetic) latitude. A moreprecise solution for meridional distance is provided by an equation which is based ongeocentric or eccentric (reduced) latitude. This approach (eq. 38 ard 41, pp 47) is stillrequiring more research. Plane and Mercator sailings shall be based upon either thespherical or the spheroidal model. The error lies in the use of meridional parts for thespheroidal earth together with latitude differences for the spherical earth. For solutions onthe spheroid the difference in latitude parts which takes account of the ellipticity must bedetermined and used in place of difference in latitude while difference in meridional partson the spheroid is also computed from a formula that takes account of the ellipticity. Theunits used are also different in that the sphere invokes units of nautical miles whereas thespheroid invokes units of geographic miles. Equation 31, pp 40, illustrates a loxodrome asa logarithmic spiral on a stereographic polar projection of the rotational ellipsoid(spheroid). The results of comparative analysis point out the advantages of differentionalequation of a loxodrome as a frrnction of geocentric latitude. The great ellipse on aspheroid is defined as the line of intersection of the surface ofthe rotational ellipsoid withthe plane passing through its geometric centre and the deparhre and destination points.Great ellipse calculations are simpler than those on the geodesic and more accurate thanthe geat circle with a spherical earth model. Distance and course to steer along part of agreat ellipse can be readily determined with the use of the differential equation of aloxodrome on a spheroid. For passage planning it is beneficial to use single referentialspheroid (e.g. WGS-84) including mathematical model that calculates position(latitude/longitude) shift only.