Relationships between the optimal softening length ﹩{\delta }_{{\rm{opt}}}﹩ and impact parameter for the four softening prescriptions in simulations of Plummer clusters with N_c = 8192. Lines connect the ﹩{\delta }_{{\rm{opt}}}﹩ values, while the error bars indicate the ranges for those values. Each line represents results from simulations with different Q values. Panels (a)–(d) correspond to prescriptions 1, 2, 3, and 4, respectively. Softening lengths and impact parameters are scaled by the initial cluster radius R_c. Uncertainty ranges grow with impact parameter. For all but the smallest impact parameter cases, softening lengths of zero are reasonable.