Using the results of the WKBI method, two hypothetical gases are introduced, whose graphs in the pressure-density plane and that of the polytropic gas have contact of order 4 and 5 at the sonic point. This is in contrast to the fact that such graphs for the Tricomi gas and the generalized Tricomi gas have contact of order 2 and 3, respectively, to that of the polytropic gas there. Various relations for these gases are derived and compared to those of the air, the Tricomi gas and the generalized Tricomi gas. Applicable range of the approximations to the airflow are 0.65 > M > 1.4 0.65 > M > 1.4 for the first approximation, and 0.5 > M > 1.5 0.5 > M > 1.5 for the second approximation, M M being the local Mach number. This is compared to such ranges as 0.9 > M > 1.2 0.9 > M > 1.2 for the Tricomi gas, and 0.75 > M > 1.3 0.75 > M > 1.3 for the generalized Tricomi gas. Flow solutions for the hypothetical gases are expressed by the Airy functions.