The Strain Pattern Analysis (SPA) method was conceived at the RAE in the 1970s as a means of estimating the displacement shape of a helicopter rotor blade by using only strain gauge data, but no attempt was made to provide theoretical justification for the procedure. In this paper, the SPA method is placed on a firm mathematical basis by the use of vector space theory. It is shown that the natural norm which underlies the SPA projection is the strain energy functional of the structure under consideration. The natural norm is a weighted version of the original SPA norm. Numerical experiments on simple flexure and coupled flexure-torsion systems indicate that the use of the natural norm yields structural deflection estimates of significantly greater accuracy than those obtained from the original SPA procedure and that measurement error tolerance is also enhanced. Extensive numerical results are presented for an emulation of the SPA method as applied to existing mathematical models of the main rotor of the DRA Lynx ZD559 helicopter. The efficacy of SPA is demonstrated by using a quasi-linear rotor model in the frequency domain and a fully non-linear, kinematically exact model in the time domain: the procedure based on the natural (or weighted) norm is again found to be superior to that based on the original SPA method, both in respect of displacement estimates and measurement error tolerance.