Plan Geometry of Headland-Bay Beaches

Abstract

A beach is defined as a beach lying in the lee of a headland subjected to a predominant direction of wave attack. Such beaches characteristically have a seaward-concave plan shape resulting from erosion caused by refraction, diffraction, and reflection of waves into the shadow zone behind the headland. Tide-induced currents have no direct effect on the plan shape of headland-bay beaches. Increasing radius of plan curvature with distance from the headland suggested testing the logarithmic spiral, r = ecot , as an approximation to the shape of headland-bay beaches. Four natural beaches were selected for testing goodness of fit to the log-spiral approximation: Spiral Beach, Sandy Hook, New Jersey; Halfmoon Bay Beach, California; Drakes Beach and Limantour Spit Beach lying along the Drakes Bay shoreline to the north of San Francisco, California. Published maps were used as a source of data on shoreline shape except for Spiral Beach which was mapped by the writer using engineer's transit in a longitudinal-survey technique. An IBM 7090 computer was programmed to generate a best fitting log-spiral to each shoreline curve. Results ranged from excellent to good with the best fit being to Spiral Beach curvature, for which mean squared error in length of the log-spiral radius vector was only 0.82 feet squared. Constant spiral angle, a, ranged between 41.260 and 85.64°. Centers for three of the best fitting log-spirals lay in close proximity to the shoreward portion of each headland. Many hundreds of headland-bay beaches exist along the coast line of the United States, but their presence is not unique to this shoreline. Measurements on aerial photographs, field mapping, and model studies are