Mathematical Model of the Hail Formation Mechanics in the Atmosphere and Estimation of the Hail Impact Damage to Aircraft Structural Element

The mathematical model of the hail formation mechanics in the atmosphere is proposed to be described as a two-dimensional boundary value problem for the heat equation with boundary conditions of the third kind under the condition of convective heat exchange of the hail outer surface with the environment in the form of the mathematical expectation of a functional of a diffusion random process. To obtain a solution using the numerical method, a large number of the random process paths were simulated and then a probabilistic estimate of the boundary value problem solution was determined. The steady rate of hail falling was determined in turbulent flow of a viscous medium using the proposed equation. The impact effects of hail on the structural elements of the airframe were evaluated. The results of residual deformation accumulation while the number of hail impacts increased, were obtained.