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The need to reduce computational burden in the preliminary design stage of switched reluctance machines is fostering the interest in design-oriented analytical modelling. To this end, this work proposes a novel design-oriented analytical model that comprises two main parts, each of them containing an original scientific contribution: 1) a new interpolation technique for the flux loci based on 2${\text{nd}}$-order Fröhlich-Kennelly equations, and 2) an analytical model that calculates flux linkage in partial overlap and saturated conditions. The model is validated against finite element analyses of four switched reluctance machines and the experimental results of a physical prototype. Finally, an in-depth discussion on the use, accuracy and limitations of proposed analytical model is provided.