In this paper formulae are derived for the surface area of a right cylindrical screw having as cross-section edge straight lines and/or circular segments. These formulae involve the non-elementary functions of the incomplete elliptic integral of the first, second and third kinds. These integrals are tabulated in the literature. ยง 1. Introduction. In the design of rocket motors and the propulsion units for guided missiles and similar devices, where storage and simplicity of servicing are necessary, solid propellants are frequently required. The problem of casting propellant grains free of flaws to large size and complex cross-section has proved difficult and slow. A reasonable solution to this problem has been to use continuously extruded grains from an extrusion press. The extrusion of propellants and explosives, however, involves problems of its own. In particular these materials are extremely sensitive to heat and are likely to explode within the press. Since the heat generated during extrusion is proportional to the surface area of the feed screw, it is important that this term be known. In this paper the surface area of a right cylindrical feed screw having a cross-section composed of straight line segments and/or arcs of circles is derived. This calculation enables the design engineers to keep careful control of temperatures to be generated inside extrusion presses with feed screws of this type. Thus, designs can be computed and temperature estimates made without actual construction of the screws.
These formulae require tables of three non-elementary functions, F(d?, k), E(ยข, k) and a(dp, o~2, k), the incomplete elliptic integrals of the first, second and third kinds respectively. Tables of the first two are --377 --