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Numerical-analytical integrating the equations of a point mass projectile motion at the velocities close to sonic peak of air drag exponent V.V. Chistyakov Yaroslavl’ State Academy of Agriculture, 58 Tutaevskoe shosse, Yaroslavl’, 150042, Russia Abstract. — It is shown that the relative air drag force for many different ballistic profiles obeys the law as follows   ( ) ( ) T n V V R V w W  with V being the velocity, WT — some threshold velocity close to that of sound, w equals to ( ) T R W and n(V) is the exponent in broken power Gȃvre formula. Using the Legendre transformation and in frames of perturbation approach received was the expression for addition ( ) bb a b   to resolvent function ( ) bb a b  , where a(b) is an intercept and b=tg θ , θ — inclination angle .