The Hill from Bryan Complex to Huntington Gym: Why Colgate Needs to Salt the Roads

As we’ve approached the beginning of Hamilton’s long winter, the roads are already covered in snow and ice. Last year, ice-covered hills were a source of distress for Colgate students. There were times in which rock salt was not immediately spread on the roads, sidewalks, and stairs. This can be highly dangerous, as many had wiped out on the ice. Nonetheless, it is important to look at why icy roads can pose a hazard, and the hill from Bryan Complex to Huntington Gym is an excellent example.

The coefficient of friction on icy roads ranges from 0.1-0.3 (1). However, when rock salt is spread on the roads, the coefficient of friction increases to 0.3-0.6.

The hill itself is at approximately a 30-degree incline or decline depending on how you look at it. Assuming the possibility of slipping and sliding down the hill (which happened to me!), you could gain a significant amount of velocity towards the end. The inclined portion of the hill is approximately 50m long before leveling out. Last year, the ice extended for the duration of the decline.

With this in mind, and assuming the mass of someone sliding down is 75kg and the coefficient of friction without salt is 0.2, we can find the velocity at the bottom of the hill. 

It is a reasonable assumption that losing balance and sliding at 22.5 m/s isn’t safe. However, with salt on the road, this can be avoided. Assuming a coefficient of friction for salted roads of 0.5, the amount of grip that the rubber bottoms of shoes can have is far greater than on icy roads. As a result, walking down the hill will not be as treacherous of a journey. 

1) A D Roberts and J D Lane 1983 J. Phys. D: Appl. Phys. 16 275