Similarity methods have been widely employed in engineering design and analysis to model and scale complex systems. The Empirical Similitude Method (ESM) is one such method based on the use of experimental data. Using a variant of the similitude process involving experimental data, we present in this paper, the use of advanced numerical approximations, trigonometric functions in particular to model and predict the performance of design artifacts. Specifically, an airfoil design is modeled, and the values of the drag coefficient are estimated based on the advanced ESM. Intermediate test specimens are used to correlate experimental data to produce the required prediction parameters. Mathematical development and error analysis are also elaborated by delving into continuity and adaptivity features of numerical algorithms.