and sticking friction models: (sliding) (sticking) where ω is the angular velocity of the tool, Rshoulder is the radius of the tool shoulder, and Rpin is that of the pin. Several other equations have been proposed to account for factors such as the pin, but the general approach remains the same. A major difficulty in applying these equations is determining suitable values for the friction coefficient or the interfacial shear stress. The conditions under the tool are both extreme and very difficult to measure. To date, these parameters have been used as "fitting parameters", where the model works back from measured thermal data to obtain a reasonable simulated thermal field. While this approach is useful for creating process models to predict, for example, residual stresses, it is less useful for providing insights into the process itself. Applications The FSW process has initially been patented by TWI in most industrialised countries and licensed for over 183 users. Friction stir welding and its variants friction stir spot welding and friction stir processing are used for the following industrial applications: shipbuilding and offshore, aerospace, automotive, rolling stock for railways, general fabrication, robotics, and computers. Shipbuilding and offshore Two Scandinavian aluminium extrusion companies were the first to apply FSW commercially to the manufacture of fish freezer panels at Sapa in 1996, as well as deck panels and helicopter landing platforms at Marine Aluminium Aanensen. Marine Aluminium Aanensen subsequently merged with Hydro Aluminium Maritime to become Hydro Marine Aluminium. Some of these freezer panels are now produced by Riftec and Bayards. In 1997 two-dimensional friction stir welds in the hydrodynamically flared bow section of the hull of the ocean viewer vessel The Boss were produced at Research Foundation Institute with the first portable FSW machine. The Super Liner Ogasawara at Mitsui Engineering and Shipbuilding is the largest friction stir welded ship so far. The Sea Fighter of Nichols Bros and the Freedom-class Littoral Combat Ships contain prefabricated panels by the FSW fabricators Advanced Technology and Friction Stir Link, Inc. respectively. The Houbei-class missile boat has friction stir welded rocket launch containers of China Friction Stir Centre. HMNZS Rotoiti in New Zealand has FSW panels made by Donovans in a converted milling machine. Various companies apply FSW to armor plating for amphibious assault ships. Aerospace United Launch Alliance applies FSW to the Delta II, Delta IV, Atlas V, and the new Vulcan expendable launch vehicles along