One can only estimate the dynamic vertical impact loads under motion, since there are many effective parameters some of which are unrepresented in an equation and since the values of the considered parameters are not deterministic but estimations. Many empirical and semi-empirical equations in the literature correlate dynamic impact loads to train speed and measurable aspects of train and track components. These aspects frequently relate to track and train geometry and track stiffness. However, the development of these equations relies on load and deflection measurements from particular in-service tracks or especially set-up test tracks. The constants that frequently appear in these equations are particular to the conditions that generated them. Therefore, one lacks an explicit understanding of these equations unless one takes the time to investigate in detail the particular study and the particular set of data that generated these equations. Train speed limits also bound the applicability of these equations. This paper concentrates on the development of an explicit mathematical equation aimed to provide an explicit analytical estimate for the dynamic impact loads that develop on any railway track by the axles of a moving train. This paper introduces the concept of impact reduction factor and introduces a new equation that relies on the principle of conservation of energy and kinematic principles along with the impact reduction factor to estimate the impact loads generated by a moving train. The introduced equation analytically relates the dynamic impact load factor to train speed, track stiffness and vertical irregularity development along the track horizontal alignment. (C) 2017 The Authors. Published by Elsevier Ltd.