1. A computer-implemented method for determining a safety factor formula for use in a braking model of at least one train, the method comprising: (a) for a specified scenario having specified train modeling constants, providing the specified train modeling constants and a plurality of train data inputs into a braking model programmed to determine a predicted braking distance; (b) for a plurality of subsequent specified scenarios having the same specified train modeling constants, modifying a plurality of the train data inputs, and providing the specified train modeling constants and the modified train inputs into the braking model to determine a plurality of subsequent predicted braking distances; (c) determine at least one safety factor based at least in part on the distribution of the predicted braking distance and the subsequent predicted braking distances for the specified scenarios; (d) repeating steps (a)-(c) for a plurality of different specified scenarios; (e) based at least partially on steps (a)-(d), determining a formula for, during train operation, calculating a safety factor based at least partially on (i) at least one operating train constant, and (ii) train speed, track grade, and train weight; (f) providing the formula to at least one on-board computer of at least one train for use in the determination, during train operation, of at least one safety factor based at least partially on (i) at least one operating train constant, and (ii) train speed, track grade, and train weight, to cause the at least one on-board computer of the at least one train to activate or cause the activation of an emergency braking system based at least partially on the at least one safety factor and a specified target location.