An analysis of buckling in spherical shells and its design implications for hopper poppers

Abstract

The purpose of this project was to investigate a key design parameter of a hopper popper: the force it takes to "load," or invert, the popper. A hopper popper is an injection-molded rubber toy in the shape of a hemispherical shell that stores elastic potential energy when inverted. There is new interest for hopper poppers in projectile toys. However, the force it takes to invert the popper can easily exceed what child can produce. In the course of the study, tests were conducted on ten different hopper poppers to measure the force and displacement of loading. Theoretical equations for the buckling of spherical shells were then correlated to the data. It was found that the equations accurately predicted the main variables in buckling, which are the Young's modulus of the material, the radius of the popper, and the thickness of the shell. Furthermore, the ability of a hopper popper to be bi-stable (invert and stay inverted) was examined. It was found that the degree of curvature was the biggest factor in the stability of poppers; the closer the curvature was to 180 degrees, the more stable a popper was when inverted. Additionally, a more sophisticated brand of hopper poppers, known as Dropper Poppers, was examined to see what makes them more impressive than ordinary poppers. It was found that a hole of 0.14 inches in diameter helps these poppers stabilize when inverted even though their curvature is only 150 degrees. The lower angle was found to reduce inverting force because the normal force supplied to the bottom perimeter of the popper had a perpendicular component that helped stretch the popper out as it was being loaded. Finally, this thesis presents ideas for the future of hopper poppers. One is a mechanism designed for a blaster, which uses the mechanical advantage of a lever arm to invert a popper. Another is a design for new hopper poppers which could take less force to invert than a normal hopper popper, but store the same elastic potential energy.