A method is disclosed for reducing feed rate variations when unwinding a web material to transport the web material away from the parent roll at a web takeoff point where the feed rate variations are induced by parent roll geometry variations. The method utilizes calculated and/or measured data to make suitable adjustments in the driving speed for an out-of-round parent roll to get closer to a relatively constant feed rate. By dividing the parent roll into 1, 2, . . . n sectors, the data can be refined to a relatively high degree taking into account high speed data processing capabilities as well as operating system response times to make appropriate driving speed adjustments.