The hyperbolic tangent function is used almost exclusively for computer assisted curve fitting of Charpy impact test data. Unfortunately, there is no physical basis to justify the use of this function and it cannot be generalized to test data that exhibits asymmetry. Using simple physical arguments, a semi-empirical model is derived and identified as a special case of the so called hyper-logistic equation. Although one solution of this equation is the hyperbolic tangent, other more physically interpretable solutions are provided. From the mathematics of the family of functions derived from the hyper-logistic equation, several useful generalizations are made such that asymmetric and wavy Charpy data can be physically interpreted.