. Analytical solutions of the one-line model of shoreline change. Coast changes; Beach erosion; Shore protection. In the limit N + °° the polygon coincides with a semicircle. The solution (N = 101) is illustrated in Figure 17 which shows the shoreline evolution as a function of time for an initially semicircular-shaped beach. t1 = o. 1 2 ALONGSHORE DISTANCE (x/a) Figure 17. Shoreline evolution of an initially semicircular beach 49. If the beach is formed as a circular segment, the solution may be derived by superimposing Equation 41 with the appropriate summation limits and Equation 16
. Analytical solutions of the one-line model of shoreline change. Coast changes; Beach erosion; Shore protection. In the limit N + °° the polygon coincides with a semicircle. The solution (N = 101) is illustrated in Figure 17 which shows the shoreline evolution as a function of time for an initially semicircular-shaped beach. t1 = o. 1 2 ALONGSHORE DISTANCE (x/a) Figure 17. Shoreline evolution of an initially semicircular beach 49. If the beach is formed as a circular segment, the solution may be derived by superimposing Equation 41 with the appropriate summation limits and Equation 16 with reversed sign. In Figure 18 a definition sketch is shown. If the pitch height is denoted by p , then the width of the circle segment becomes 2v'p(2a - p) . Furthermore, the height of the rectangular fill is a - p , and the angle a (see Figure 18) is arc sin (1 - p/a) . Conse- quently, the summation of the solutions for the polygon stretches should start at angle a in the semicircle and end at angle it - a . The solution is 32. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Larson, Magnus; Hanson, Hans; Kraus, Nicholas C; U. S. Army Engineer Waterways Experiment Station; Coastal Engineering Research Center (U. S. ); United States. Army. Corps of Engineers. [Vicksburg, Miss. : U. S. Army Engineer Waterways Experiment Station ; Springfield, Va. : available from National Technical Information Service]
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