Prediction of a rigid body falling through water column with a high speed (such as Mk-84 bomb) needs formulas for drag/lift and torque coefficients, which depend on various physical processes such as free surface penetration and bubbles. A semi-empirical method is developed in this study to determine the drag/lift and torque coefficients for a fast-moving rigid body in a water column. The theoretical part is to derive the relationships (called diagnostic relationships) between (drag, lift, and torque) coefficients and (position and orientation) of the rigid body from the three momentum equations and the three moment of momentum equations. The empirical part is to collect data of trajectory and orientation of a fast-moving rigid body using multiple high-speed video cameras (10,000 Hz). Substitution of the digital photographic data into the theoretical relationships leads to semi-empirical formulas of drag/lift and torque coefficients, which are functions of the Reynolds number, attack angle, and rotation rate. This method was verified by 1/12th Mk-84 bomb strike experiment with various tail configurations (tail section with four fins, two fins, and no fin and no-tail section) conducted at the SRI test site. The cost of this method is much lower than the traditional method using the wind tunnel. Various trajectory patterns are found for different tail configurations.
Diagnostic-Photographic Determination of Drag/Lift/Torque Coefficients of a High Speed Rigid Body in a Water Column
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Chu, P. C., Fan, C., and Gefken, P. R. (October 5, 2009). "Diagnostic-Photographic Determination of Drag/Lift/Torque Coefficients of a High Speed Rigid Body in a Water Column." ASME. J. Appl. Mech. January 2010; 77(1): 011015. https://doi.org/10.1115/1.3173767
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