## Walking in A Winter Wonderland

The snow that was pelting Atlanta earlier has finally made it up here. It’s still at the “ooh, isn’t that pretty!” stage, rather than the “oh, no, not more goddamn snow” stage, so I went for a walk in it.

Yes, the world shrouded in snow and silence was beautiful. But what struck me is that I unconsciously started walking differently.

I usually walk differently in the snow; that part isn’t surprising. What I found surprising is that apparently I’ve internalized my snow gait to the point where I didn’t need to consciously turn it on. Huh.

Normally, when I walk on dry ground, my heel hits the ground first, followed by the ball. My legs don’t bend much.

But when I’m walking on snow, my whole foot hits the ground at the same time. I also bend my knees so that my foot comes down straight, rather than at an angle. It’s a bit like an elephant or a Star Wars AT-AT, where the thigh moves the most, and the shin hangs vertically down from there. As you can imagine, my steps are shorter and I don’t walk as quickly.

It all has to do with coefficients of friction. Plural. For those who have forgotten High School physics, there are two coefficients of friction between two given surfaces: the static one, and the dynamic one. Dynamic friction refers to how hard it is to rub the two surfaces against each other. Static friction refers to when the surfaces are motionless, and how hard it is to get one of them moving.

If you’ve ever received a box of equipment (say, a new computer) and tried pushing it across the floor, you may have noticed that pushing it along the floor is easier than getting it to move in the first place. That’s because when it’s just lying there, you have to overcome static friction to get it to move. When it’s already moving, and you want it to keep moving, you have to overcome dynamic friction. And the dynamic friction coefficient is typically lower than the static one.

Normally, when you’re walking, this doesn’t matter a lot: when your sole hits dry pavement, both the static and dynamic coefficients of friction are high enough that you can trust them to hold your foot in place and allow you to push against the ground for the next step. But on snow or ice, there’s a very real danger of slipping, falling into traffic, and having your head squished by a passing car.

In this light, I think my snow gait makes sense: hitting the ground with my entire foot at once means there’s more surface to take advantage of what little friction there is (though on the other hand (foot?), my body weight is distributed over a larger area, so there’s less friction per square centimeter; I don’t know how this affects things).

Putting my foot straight down means that it’s not moving with respect to the ground when it hits, which in turn means that I’m taking advantage of the static friction coefficient, which is higher than the dynamic one, to keep from slipping. And the “elephant walk” bit is just so that I can put my foot down vertically.

So now that you know how to safely walk on slippery surfaces, go out there and enjoy the snow.

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### 5 Responses to Walking in A Winter Wonderland

1. Eric Haas says:

In this light, I think my snow gait makes sense: hitting the ground with my entire foot at once means there’s more surface to take advantage of what little friction there is (though on the other hand (foot?), my body weight is distributed over a larger area, so there’s less friction per square centimeter; I don’t know how this affects things).

The decrease in pressure just about exactly compensates for the increase in surface area. I think the reason people walk flat-footed in the snow is, the larger surface area means they won’t sink into the snow as much (as they would if they put all their weight on their heels first), so they’ll burn less energy while walking.

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2. arensb says:

Eric Haas:

The decrease in pressure just about exactly compensates for the increase in surface area.

I dimly remember from High School physics that it exactly compensates; that the way the math works out, the total friction is proportional to your mass, and your footprint has nothing to do with it. If your mass is 100kg and you walk on stilts, you’re pushing very hard on a small area; and if you’re wearing snow shoes or clown shoes, you’re pushing lightly over a much larger area; but if you multiply mass/area × area, you get the same mass.

Having said that, I suspect that in the Real World, the area does matter. A car enthusiast friend of mine assures me that there are good reasons why race cars (e.g., dragsters) use wider tires than normal.

And yes, your point about not sinking into the snow is well-taken. But that’s a separate issue from slipping on snow or ice.

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3. Fez says:

Gads the physics is decades old but if my increasingly age-addled mind recalls correctly amongst other considerations are that the system you describe is, except for relatively small areas for finite periods of time, dynamic so you have to consider the relative angle of the forces in play and the kinetic coefficient of friction between said materials. At a guess TehPedia probably has some coverage of the topic (and may indeed demonstrate that I’m completely off base and I’m OK with that.)

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4. Eric Haas says:

Having said that, I suspect that in the Real World, the area does matter. A car enthusiast friend of mine assures me that there are good reasons why race cars (e.g., dragsters) use wider tires than normal.

It’s not the width of the tires that matters; it’s the compound that the tires are made of. A softer compound gives better traction, but a softer tire has to be wider in order to support the weight of the car. A wide, hard tire doesn’t provide better traction than a narrow, hard tire.

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5. Fez says:

Eric Haas Says:

It’s not the width of the tires that matters; it’s the compound that the tires are made of. A softer compound gives better traction, but a softer tire has to be wider in order to support the weight of the car. A wide, hard tire doesn’t provide better traction than a narrow, hard tire.

The tire tread compound actually has little to do with the bearing strength of the tire. The strength of the tire is mostly determined by the construction of the carcass – the layers of (typically) steel and nylon belts that make up the circumference and sidewall of the tire. To a first order the traction can be approximated by the classic friction equation Friction=u*Weight. In the example of a dragster, where the rubber meets the road (seewhatIdidthere) is where u gets complex.

The launch pad and track surface is not homogeneous – natural surface variances and debris reduce the available traction on any given square inch so a wider tire will have more surface area in contact with areas that have greater usable traction. u is also variant depending upon, as you pointed out, the tread compound as well as it’s temperature. All else equal, a skinny tire will heat more under acceleration than a wide tire causing the compound to shear away (which creates debris, which reduces u), and in a pathological case will liquefy and lead to a failure or create so much heat the tire ignites.

Dragster tires are also wide because of a huge variance in overall diameter when in service. If you’ve ever watched a top fuel dragster warming up the tires (attempting to maximize u by heating the tread and cleaning off debris) they narrow significantly while increasing in height. The sidewalls are designed with flex to allow this geometry change which has the effect on the vehicle of changing the final drive ratio allowing for greater top speed. This flex also comes into play during launch where the rear of the contact patch will dig in during the weight transfer thus increasing usable traction over that area.

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