I am excited that winter has arrived in New England. Last winter, my nephew taught me how to snowboard. I figured that I would be able to pick up the sport rather quickly. After all, I was an avid skateboarder when I was in college. However, the learning curve turned out to be much steeper than I had anticipated.
When my nephew asked me why I at first struggled on a snowboard, I explained to him that the equations that I use to design transfer chutes can also be applied to skateboarding and snowboarding. My speed down a hill is given by:
v = √(2as)
where v is my velocity, a is my acceleration, and s is the distance I have traveled. Acceleration is given by:
a = g cos α (tan α – tan φ’)
where g is the gravitational constant, α is the slope from horizontal, and φ’ is the angle of sliding friction between my snowboard and the snow. The angle of friction is the inverse tangent of the friction coefficient. Therefore, a high friction angle signifies high friction and vice versa.
When I was on a skateboard, the slope of the street was rather shallow and the friction between the wheels and the road was high. Therefore, my acceleration was low and my speeds were manageable.
When I was on a snowboard, however, the angle of friction between my board and the snow was low and the ski slope was high. As a consequence, my acceleration was very high, and my velocity increased dramatically. Fortunately or unfortunately, the friction between the snow and the seat of my pants was high, and therefore I would decelerate and come to a complete stop whenever I fell.
The same fundamentals hold for the design of transfer chutes. For chutes, the results of the velocity calculations are used to determine the cross-sectional area of a chute required to provide the desired capacity and layouts that ensure that the powder will continue to flow. The analysis also allows us to develop designs that control dust generation and minimize particle attrition. We also are able to use our proprietary DEM (Discrete Element Method) modeling ability to improve our designs. In addition to identifying segments where blockages or build-up may occur, DEM allows us to predict wear due to abrasion, which allows us to design transfer systems that are both reliable and low maintenance.
My nephew now knows better than to ask me questions.