Date of Award
Master of Science in Mechanical Engineering - (M.S.)
Anthony D. Rosato
Denis L. Blackmore
Galton boards have been used for over a half-century as a tool to illustrate the formation of Gaussian shaped distributions as well as the Central Limit Theorem. Here, the Galton board was used to study the spontaneous percolation of a particle through an ordered array of rigid scatterers. The apparatus that was designed and fabricated provided a means to release 1/8" diameter spheres one at a time in a controlled and precise manner at any location on the board. The three experimental variables used in these experiments were the particle material, the release height, and the board tilt. angle. The data, consisting of residence time and exit location, were analyzed and the relationship between statistical values and parameter settings was found to be as follows: (1) standard deviation of the radial displacement increased with release height and was unaffected by board angle, (2) average residence time increased with release height and decreased with board angle, (3) standard deviation of the residence time increased with release height, (4) average axial velocity was unaffected by release height and increased with board angle, and (5) standard deviation of the axial velocity increased with a decrease of release height and increased with an increase in board angle. From an analysis of the data, it can be inferred that the motion of particles on the Galton board is governed by a diffusional mechanism.
Oshman, Christopher, "Experiments with a Galton board" (2002). Theses. 705.