A precise parametric equation for the trajectory of a point projectile in the air with quadratic drag and longitudinal or side wind

By using the projective-dual variables were received highly precise power like formulas for absolute coordinates and time as functions of current inclination of relative trajectory i.e. connected with longitudinal or side wind. The formulas use as key parameters the initial slope, the top point radius of curvature and squared dimensionless speed in the point. As an indicator of accuracy served the discrepancies between these approximate formulas and exact integral expressions. For the starting drag forces up to 1.2 of weight at initial speeds of about 100 mps and at that of wind up to 40 mps, and in the direct fire range of throwing angles θ0 <; 15° an absolute error accounted for the order of decimeters, and relative one did not exceed some decimals of percent. Because of the “almost” algebraic type of the formulas received they can be implemented in a simple ballistic calculator.