Strip thickness h2 on the delivery side of the rolls is equal to the work-roll gap under load if the elastic deformation of the material is excluded. As given by Eq. 1, h2 is the sum of S0 and S, S0 being the work roll gap without load and S the amount of deformation of the rolling mill under load. The S is given by rolling force P divided by mill modulus M, so the delivery side strip thickness is dependent upon the rolling force. The S, which is of the order of millimeters, cannot be neglected when calculating the delivery side strip thickness. Equation 1 is shown by curve (a) in the figure, which is called the elastic deformation curve of the mill. Rolling force P, which can also be determined by deformation theory, is expressed in Eq. 2 as a function of material factors and rolling conditions. Mean deformation resistance km is a function of the rolling reduction, rolling speed, rolling temperature, and material chemistry. In terms of geometrical relationships, the contact arc length L is related to both the roll radius and rolling reduction, as shown in Eq. 3. Equations 2 and 3 indicate that the rolling force increases as the mean deformation resistance of the material, entry side strip thickness, and amount of rolling reduction increase. This relationship is represented by curve (b) in the figure. This curve is called the plastic deformation curve of the material in rolling. The delivery side strip thickness is determined by solving Eqs. 1, 2, and 3, and corresponds to the point of intersection of the two curves in the figure. During rolling, the rolling force and the delivery side strip thickness change if some variation occurs in the roll gap, the mean deformation resistance caused by a variation in speed and temperature, or the entry side strip thickness. In other words, a change in the delivery side strip thickness can be instantaneously detected by monitoring the rolling force. When the rolling force changes, the delivery strip thickness can always be kept constant by adjusting So in Eq. 1 by the amount required to compensate for the rolling force difference. This is the principle of automatic gauge control (AGC).