Plan Geometry of Headland-Bay Beaches

A "headland-bay" beach is denned 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, $$r = e^{\theta cot\alpha}$$, 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 41.26° 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 suggested as a continuation of this preliminary study.