Evaluation of Aerodynamic Drag and Torque for External Tanks in Low Earth Orbit

A numerical procedure is described in which the aerodynamic drag and torque in low Earth orbit are calculated for a prototype Space Shuttle external tank and its components, the “LO2” and “LH2” tanks, carrying liquid oxygen and hydrogen, respectively, for any given angle of attack. Calculations assume the hypersonic limit of free molecular flow theory. Each shell of revolution is assumed to be described by a series of parametric equations for their respective contours. It is discretized into circular cross sections perpendicular to the axis of revolution, which yield a series of ellipses when projected according to the given angle of attack. The drag profile, that is, the projection of the entire shell is approximated by the convex envelope of those ellipses. The area of the drag profile, that is, the drag area, and its center of area moment, that is, the drag center, are then calculated and permit determination of the drag vector and the eccentricity vector from the center of gravity of the shell to the drag center. The aerodynamic torque is obtained as the cross product of those vectors. The tanks are assumed to be either evacuated or pressurized with a uniform internal gas distribution: dynamic shifting of the tank center of mass due to residual propellant sloshing is not considered.