TheAiry projection properties of the Airy projection as an ideal projection according to the Airy criterion for a region bounded by an almucantar are examined. It is shown that the Airy projection constructed for the entire globe is not one-to-one; two points on the ellipsoid’s surface correspond to a single point in the projection. Two versions of the projection with the one-to-one property have been developed: the first version covers 98.5% of the globe, and the second version covers 93%. The first version has the drawback that the minimum length scale near the boundary of the region approaches zero. Therefore, the second version is preferable. The first ideal projectionIdeal projection known to mankind according to the Airy criterionAiry criterion is the azimuthal projectionAzimuthal projection proposed by the Royal Astronomer G.B. AiryAiry (Airy (1861) Explanation of a projection by balance of errors for maps applying to a very large extent of the Earth’s surface and comparison of this projection with other projections. London, Edinburgh, and Dublin Philosophical Magazine 4, 22(149):409–421. 10.1080/14786446108643179). This projection is ideal for areas limited by almucantarAlmucantar. The polar distance of this projection \(\rho\) is determined by the minimum condition of the Airy criterion (Lapaine (2016) George Biddell Airy and his Contribution to Map Projections Theory. Paper presented at the 6th International Conference on Cartography and GIS, 13–17 June 2016, Albena, Bulgaria ISSN: 1314-0604).