描述轮胎接地印痕的新方程

New equations are proposed to describe the shapes and sizes of the contact areas between tire and ground（the contact areas） under the conditions of static load，slip，camber，and rolling.The equations are super ellipse and trigonometric function with four parameters.Results indicate that the contact areas under the conditions of static load，slip，camber can be well described by super ellipse，in the most complicated case，fourteen parameters are used.The rolling contact area can be reconstructed by the trigonometric function completely.Symmetrical and asymmetrical shapes can both be described perfectly.The suggested curves will make calculate sizes of the areas easily.The described shapes and sizes are in good agreement with the measured，the maximum deviation is only 2.88%.This work will provide an instrument for understanding the contact area and be helpful for analyzing tire and road.