Introducing scale analysis by way of a pendulum. http://dx.doi.org/10.1088/0143-0807/28/2/014

Abstract

Empirical correlations are a practical means of providing approximate answers to problems in physics whose exact solution is otherwise difficult to obtain. The correlations relate quantities that are deemed to be important in the physical situation to which they apply, and can be derived from experimental data by means of dimensional and/or scale analysis. These techniques are discussed through two examples. The first example involves determining the period of a pendulum, for which a simple yet very accurate correlation at arbitrary amplitudes of oscillation is derived. The second example refers to a more practical application, that of obtaining a heat transfer coefficient. In an appendix, the proposed correlation for the period of the pendulum is compared with other approximate formulae in the literature.