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Modern automotive microprocessor control systems provide a characterisation of the spark timing to control knock. This representation is normally provided in the form of look-up tables and in this study is referred to as Borderline Spark. Five and six factor augmented Box-Behnken response surface experiments have been designed to characterise Borderline spark as a function of the relevant control system input variables. Least squares regression techniques were used to generate a Borderline Spark response surface model. Confirmation experiments on two different engines showed that the response surface model provided an accurate prediction over most of the operating range. Symbolic integrals together with Sequential Quadratic Programming have been used to achieve the optimal fit of the model to the look-up tables using MATLAB.