How to solve engineering problems involving turbulent drag: Exact, asymptotic analytical and numerical techniques

The movement of a body subjected to a drag force proportional to the square of the velocity is of great importance in the field of mechanical engineering, since it is a realistic model in the regime of high velocity of the flow. In this paper, the trajectory of a projectile in quasi-vertical launch with quadratic drag is analyzed using the technique of matched asymptotic expansions. Through the asymptotic analysis, approximate analytical expressions for the projectile movement are found. The asymptotic solutions are compared with exact numerical results.