Mathematical Umbrellas
Angela Chuang
University Transition
Floor Location : M 039 D

This project is about mathematically analyzing the efficiency of the two umbrellas: the birdcage umbrella, which has a dome-like shape, and the standard umbrella, which most of the people on the streets use. Before analyzing the efficiency, first, the equation of the parabola of both the umbrellas were found using calculations for finding the arc length of a parabola. The rib lengths of both umbrellas were set to be the same to ensure that the amount of material used in the making of both umbrellas are equal. The radius of both umbrellas were also set, using measurements from a personal standard umbrella and measurements of the birdcage umbrella obtained online. Next, the efficiency of the umbrellas were analyzed using two ways. The first was analyzing the area coverage of both umbrellas when the person holding the umbrella is either just standing or walking. The area was calculated using the vertical and horizontal cross-sectional area. The second way was comparing the amount of wind force that is exerted on both the birdcage and the standard umbrella when held at 0, 45, and 90 degrees. The wind force was calculated using the cross-sectional area that goes against the wind and the density and velocity of the wind.