At the end of roll-to-roll (R2R) manufacturing process machines, the web substrate must be wound into rolls. Winding is the only means known to store and protect vast lengths of very thin webs for subsequent processing. Web thickness variation in wound rolls is a root cause of large manufacturing loss due to residual stress-related defects. Minute thickness variations down the length and across the web width can induce large residual stress variations and defects within the roll. Winding models allow the exploration of winding residual stresses whose variation has been affected by web thickness or coating imperfections. Knowledge of these stresses is used to mitigate manufacturing defects. Spot web thickness sensors are employed in R2R process lines that scan over the web width while the web is moving downstream through the process machine. Spatially, this provides a measure of web thickness in a zig-zag pattern. During manufacturing, the thickness variation is used as a control feedback parameter to manipulate a forming or coating die lip to reduce the web or coated web thickness variation. The thickness variation acceptable in process may be very different than that which is acceptable based on the residual stresses in the wound roll. It will be determined whether the thickness test data captured spatially for process feedback are sufficient to characterize the residual stresses in the wound roll. A winding model will be developed and verified that is used to characterize these residual stresses.