HQ U S Air Force Academy Integrity Service

HQ U. S. Air Force Academy Integrity - Service - Excellence Automating Recycling Sorting Mike Grieg Erik Mc. Millan Alex Yantis

The Problem SIMIODE 2018 Problem A: Cardboard and paper are falling down a tube from a great height. A fan will blow air across the stream of falling material. Determine the minimal height and wind speed that can be used to separate 30%-40% of the paper that is in the falling column of material. Assume the distribution of the cardboard and paper items are relatively uniform. State assumptions. Establish feasibility. Integrity - Service - Excellence

Constants, Initial Values, and Nomenclature Density of Air Cross-Sectional Area Density of Paper Horizontal Velocity U, m/s Density of Cardboard Vertical Velocity V, m/s V(0) = 0 Paper Thickness Horizontal displacement x, meters x(0) = 0 Cardboard Thickness Vertical displacement y, meters y(0) = 0 Integrity - Service - Excellence

Free Body Diagram Integrity - Service - Excellence

The Fan and the Tube X Y Integrity - Service - Excellence

Assumptions n Integrity - Service - Excellence

Theory n Integrity - Service - Excellence

Theory n Integrity - Service - Excellence

Theory n Integrity - Service - Excellence

Results Height Times Aloft Fan Speed Required Paper Cardboard L = 5 meters L = 10 meters 2 stories 7. 03 2. 99 0. 4952 0. 9904 4 stories 13. 99 5. 82 0. 2477 0. 4895 8 stories 27. 93 11. 49 0. 1217 0. 2433 Integrity - Service - Excellence

Problem Update Which aspect of your model results in the largest difference in sorting quality if that aspect undergoes a small change. For example, does a small change in height of the drop make a bigger difference in the final results as compared to a small change in the wind speed? Integrity - Service - Excellence

Model Sensitivity Study n Integrity - Service - Excellence

Nominal Case Unperturbed Value Density of Air 0. 204 Density of Paper -0. 324 Density of Cardboard 0. 120 Paper Thickness -0. 324 Cardboard Thickness 0. 120 Acceleration due to Gravity -0. 200 Length of recycling pile -0. 785 Height 0. 404 Fan speed 0. 400 Accuracy 1. 000 Integrity - Service - Excellence

Nominal Case Unperturbed Value Density of Air 0. 204 Density of Paper -0. 324 Density of Cardboard 0. 120 Paper Thickness -0. 324 Cardboard Thickness 0. 120 Acceleration due to Gravity -0. 200 Length of recycling pile -0. 785 Height 0. 404 Fan speed 0. 400 Accuracy 1. 000 Integrity - Service - Excellence

Fan Control System Case Unperturbed Value Density of Air -0. 110 Density of Paper 0. 175 Density of Cardboard -0. 065 Paper Thickness 0. 175 Cardboard Thickness -0. 065 Acceleration due to Gravity 0. 108 Length of recycling pile 0. 217 Height -0. 219 Fan Speed 1. 000 Integrity - Service - Excellence

Fan Control System Case Unperturbed Value Density of Air -0. 110 Density of Paper 0. 175 Density of Cardboard -0. 065 Paper Thickness 0. 175 Cardboard Thickness -0. 065 Acceleration due to Gravity 0. 108 Length of recycling pile 0. 217 Height -0. 219 Fan Speed 1. 000 Integrity - Service - Excellence

Conclusion n This proof of concept test validates the methodology of using a sorting column to process recyclables autonomously. n n Our recommendation is to pursue this strategy of recycling sorting, using the highest column heights and smallest lengths possible. n Fan power consumption is roughly proportional to the velocity squared, the lower operating speeds required for these towers will offset the higher up-front cost. Integrity - Service - Excellence