Elastic centralizers are commonly used in radial drilling operations, and the support force of the centralizer in the wellbore is affected by the elasticity of the bow spring. There is no design method for bow springs in existing design manuals or standards. In view of this, a simple and practical bow spring design method has been studied. First, use the Clabelon's principle to derive the expression for the deformation energy of a single piece of bow spring. Using the Castigliano theorem again, take the partial derivative of the variable energy expression for the force in the displacement direction, simplify the integration term, and obtain a linear relationship between displacement and force. The coefficient of this relationship is the stiffness of a single piece of bow spring. Finally, through statistical regression analysis of sample test data, the stiffness calculation formula for multiple arched springs was obtained. Compared with the spring sample test and ANSYS finite element analysis results, it can be seen that the error rate between the calculation results of this method and the ANSYS finite element analysis results is about 2.29%, and the error rate between the method and the sample test results is about 1.99%. On the basis of previous research, this method further considers the influence of friction on the deformation of bow springs, and significantly reduces the error rate. Within the range of elastic deformation, the stiffness of a multi piece combination spring is approximately linearly positively correlated with the number of springs, with a correlation coefficient of ρxy = 0.98816. According to the experimental values, a correction coefficient fitting was performed on the stiffness of the combined spring, with a goodness of fit of R2 = 0.989, indicating a high degree of fitting. This method is simple, reliable, and has strong practicality, making it easy for relevant designers to use. This method is based on the basic principles and formulas of material mechanics and mathematical statistics, and has been proven to be highly reliable in practice. In situations where computational mechanics is not easy to implement, it provides good guidance for scientific research and production. This method fills the gap in the design cases of bow springs in relevant design manuals and industry standards.