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Rolling the Black Pearl Over: Analyzing the Physics of a Movie Clip
5.A. Biran, Ship Hydrostatics and Stability (Butterworth-Heinemann Elsevier, Burlington, MA, 2003).
6.J. Mégel and J. Kliava, “Metacenter and ship stability,” Am. J. Phys. 78, 738–747 (July 2010).
7.A. Cromer, “Stable solutions using the Euler approximation,” Am. J. Phys. 49, 455–459 (May 1981).
7.Also see T. Timberlakeand J. E. Hasbun, “Computation in classical mechanics,” Am. J. Phys. 76, 334–339 (April/May 2008).
8.S. F. Hoerner, Fluid-Dynamic Drag, 2nd ed. (Hoerner Fluid Dynamics, Midland Park, NJ, 1965). Also see W. F. Hughes and J. A. Brighton, Schaum's Outline of Fluid Dynamics, 3rd ed. (McGraw-Hill, New York, 1999).
9.J. W. Brasher, W. L. Christensen, and V. W. Rinehart, 1986 Annual Report of the National Shipbuilding Research Program, online at www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA454077.
10.Use the formula in Eq. (11) for air resistance with ρ= 1.2kg/m3 (for moist air at sea level) and C = 1.2 for a square plate at high Reynolds number. Many of the sails are oriented perpendicular to the length of the ship and thus do not contribute to the rolling drag. From the movie we estimate a net lateral area for contributing surfaces of about A = 200 m2 at a mean height above the water of about d = 15 m so that β = 5×105 N⋅m⋅s2, comparable to what we calculated for the keel.
11.M. Denny, Float Your Boat! (Johns Hopkins University Press, Baltimore, 2009).
12.The Vasa Museum, online at www.pkvirtual.com/virtual/prace/vasa1.pdf.
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