## Snow Removal: Is There a Better Way? [1]

### Deck

I’ve spent several hours recently clearing snow off my driveway, which left me some time to think about shoveling. Particularly, I’ve been wondering if I’m doing the job in the most efficient way.

Should I push snow from the garage and out to the street (like one of my neighbors, who, it seems, doesn’t care about the two-foot-high pile he leaves for other folks to drive around)? Do I work horizontally, and move snow onto the edges of my lawn? Or is there some geometric snow-removal magic I’m missing? Diagonal? Circular?

I looked online, but my Google search yielded only safe-shoveling techniques—like bending with your knees, using an ergonomically correct shovel, and taking frequent breaks to avoid overexertion. I found nothing about snow-removal efficiency, though.

To solve my shoveling conundrum, I emailed a professor in the University of Colorado at Denver’s mathematics department. Since I planned to share the information with readers, I asked about a generic driveway—in other words, a slab of concrete that can fit two cars if they’re side-by-side.

This is assistant professor Alexander Engau’s response:

“[M]athematically speaking, we would be interested to maximize or minimize some objective, in this case, probably time needed to shovel. It seems reasonable to assume that you would need to cover the whole area—mathematically, this has to do with Hamiltonian paths [5] or cycles—trying to not shovel anything twice. You could achieve this by walking right into the middle, and shoveling in rectangles or circles of increasing radius to finally dump everything onto your lawn. Of course, this only works if you don't have too much snow and can keep pushing it.

If you have a lot of snow, the question would become quite complicated: One could estimate shovel speeds that depend on the amount of snow on your shovel—fastest when walking an already shoveled area, slowest when pushing it all forward without dumping anything in between at the driveway edges—and then find a path that clears the driveway in the least amount of time. This will then depend on how strong the shoveler is, the width (and robustness) of the shovel (we don't want to break it), whether it is still snowing, etc.

So I am sorry, no 'final answer....'

In any case, I am quite optimistic that the human mind automatically finds a rather efficient way, by intuition and past experience. That's the good news.

Plus, if someone doubts their math skills, they can always send their kids! It effectively gets them some exercise and fresh air, and it efficiently gives the parents time for themselves or to prepare the next meal.”

Sadly, there isn’t a snow-shoveling silver bullet, which means I’m now left with another question: How many hours can my children last in the cold?

*—Image courtesy of Shutterstock [6]*