The hypothesized sail of Becklespinax would have had a very similar function to other sails that existed during the Mesozoic (and the Permian as well). Sails have become somewhat less evolutionarily vogue in extant taxa, though there are examples dotted throughout nature of sail-like structures. These are not sails in the way we think of ancient sails as membranous structures stretched over vertebral spines except in some fish. Regardless of the presence of sails on extant taxa, the sails of fossil animals are hypothesized to have served one or more of five distinct purposes: sexual selection, thermoregulation, sound display, camouflage, and/or food storage. Food storage is more likely to result in a fatty hump, something Becklespinax has not been hypothesized to possess (the evidence for various structures of the sail are all based on fragmentary evidence so a fat hump could be a viable possibility though it has not been explored to my knowledge). Sound display properties of sails have only been discussed by Gregory Paul in respect to Armagasaurus and its double row of sails. The most likely uses for the sail of Becklespinax was in the use of camouflage, sexual display, and thermoregulation. Thermoregulation in sails has been exploredin a few papers and is fairly well understood. The general idea is that the blood flow and positioning of the sail in relation to the sun and wind helped to regulate body temperature of ectothermic or partially endothermic animals. Sexual display is a fairly straight forward use of the sail. Blood flow and pigmentation controls of the sail would have influenced the display structure of the sail. Camouflage properties may have been controlled in the same manner, or it may have been a static pigmentation pattern on the sail structure.