A new regularity in blast fragmentation called the fragmentation-energy fan was recently discovered. When plotting distribution free percentile passing P fragment sizes x_(P )for blasted rock versus specific charge q in a log(x_P )vs.log⁡(q) diagram, then the regression lines for different P-values tend to be straight with slopes -α(P) and to converge on a common focal point. A consequence is that if α(P) is known then the mathematical form of P(x,q) is known and the Swebrec distribution incorporates the fan behavior. This fan is an important component in new prediction equations for blast fragmentation that have error levels of half of those of the Kuz-Ram or CZM models. The fan concept is also applied to drop weight testing data used to assess the crushability of ores in comminution. A closed form solution for the t_10 vs. drop weight energy E_cs (kWh⁄tonne) for arbitrary fragment sizes D is derived, t_10=f(E_cs,D) without a priori assuming the form of the function.