Correctly and quickly identifying disease patterns and clusters is a vital aspect of public health and epidemiology so that disease outbreaks can be mitigated as effectively as possible. The circular scan method is one of the most commonly used methods for detecting disease outbreaks and clusters in retrospective and prospective disease surveillance. The circular scan method requires a population upper bound in order to construct the set of candidate zones to be scanned, which is usually set to 50% of the total population. The performance of the circular scan method is affected by the choice of the population upper bound, and choosing an upper bound different from the default value can improve the method's performance. Recently, the Gini coefficient and Lorenz curve, which were originally used in economics, were proposed to determine a better population upper bound. We present the elbow method, a new method for choosing the population upper bound, which seeks to address some of the the limitations of the Gini-based method while improving the performance of the circular scan method over the default value.