Abstract— Wall climbing robots require adhesion methods which are suited to the climbing surface material and roughness. In this paper, an optimum design of a magnetic adhesion mechanism has been developed for ferrous surfaces that maximises the magnetic adhesion force. This in turn maximises the payload that can be carried by the climbing robot. Experiments have been designed using the Response Surface Methodology (RSM) to study the effect of identified independent parameters (namely the distance between magnets, air gap and yoke thickness) that affect the response variable i.e. the magnetic adhesion force. A quadratic regression model has been developed to represent an empirical relationship between the response variable and the independent variables. Statistical analysis of the predicted model has been investigated using analysis of variance (ANOVA). To inspect the adequacy of the predicted quadratic model, validating experiments have been carried out at different conditions where the experimental results showed similar response values to the predicted model responses. Numerical optimisation has been applied to predict the optimum variable conditions for maximum adhesion force and air gap, resulting in an adhesion force of 240.3 N at 20 mm distance between magnets, 18.5 mm air gap and 8.3 mm yoke thickness. The optimum conditions have been numerically validated using a commercial finite element simulator. The numerically optimised design parameters have been used to design and construct a prototype wall climbing robot.