Tuesday, November 13, 2007

Why is Snow so Slippery?

Snow sports are a blast. I prefer snowboarding, but I would never miss out on a toboggan ride or a turn on one of those old fashioned snow saucers (What genius conceived of those anyway? Is there anything more insane that cruising down a hill on a disk with no obvious way to steer or stop? Of course, I love it anyway.) As embarrassing as it is, I've even been known to to ride an inner tube now and then.

The key to all those sports - as well as skiing, snowlerblades, ski bikes, and cafeteria lunch trays - is that things slide well on snow. You could leave it at that and simply go outside to have fun, but I just had to know a bit more.

If you hunt around, you'll see that there are at least two possible reasons why snow is slippery. One common explanation is that the melting point of ice rises as you squeeze it. Water ice is unusual in that way. This could explain why ice skates work. When you stand on skates, it creates very high pressures under the sharp blades. The pressure raises the melting point of the ice until it creates a thin layer of water, which is very slippery. (This is, however, not a universally accepted explanation.)

Pressure might work for ice skaters, but it's not much help for sleds, skis, snowboards, or any other device that slides on a large, flat surface. Because your weight is distributed over a big board, the pressures are very low. At best, you might raise the melting point of the ice by a degree or so, but if the temperature of the air and snow outside is more than a few degrees below freezing, you won't actually melt any snow with pressure.

Another possibility I've heard on occasion is that the friction of the board sliding on the snow creates heat, which melts some of the snow and creates a thin lubricating layer of water. Now, this explanation sounded just absurd to me. But I didn't want to dismiss it until a estimated just how much heating you might get from snowboarding down a hill.

You know what? I was stunned -- STUNNED -- to find out that cruising down a hill creates lots of heat. At a relatively modest 36 kilometers an hour (22 mph) down an equally modest hill (imagine a 15 degree slope or so), someone about my size (75 kilograms) creates about 300 watts of heat power due to friction between the snowboard and the snow. That's three times as much power as put out by a typical light bulb. If you've ever touched a lit incandescent bulb, you know that's hot. Theoretically, friction could heat the bottom of the board by nearly 40 degrees Celsius (about 100 degrees Fahrenheit)!

In the real world, the bottom of your board will never get that hot. It will only warm up to the point that it melts the snow. It takes energy to melt snow, and the melting ends up using the energy that would heat your board to any higher temperature than 0 degrees C (32 degrees Fahrenheit).

But suppose you were snowboarding on a day when temperatures went as low as at -40 degrees C, even moving slowly would generate enough heat from friction to melt the snow and provide a very thin layer of water for you to slide on. (Of course, -40 C is just about the lowest temperature ever recorded in Alaska, so you'd probably get an awful case of frostbite before you got to the top of the lift.)

So there you have it - it's friction, not pressure, that melts snow below your board and let's you whiz down the hill at a breakneck pace. Wacky.

For those of you who like the details, the math that led me to this conclusion is below.

The Math and Physics

You can change the parameters of the problem to model any sliding sport you like, but I'm using a snowboard in my analysis.

The first thing to do is figure out how much work is done when you slide on a snowboard. Work is defined as force times distance. Specifically, we're interested in the frictional force multiplied by the distance traveled.

The force of friction is just the force pushing the snowboard down onto the snow multiplied by the coefficient of friction (u).

Because the snowboard is moving downhill, the force pushing against the snow due to the mass of the snowboard and rider is reduced by the cosine of the hill slope.

Friction force = m g u cosine(theta)

= rider's mass (I'm using 75 kilograms)
g = acceleration due to gravity (0.8 meters per second squared)
u = coefficient of friction for a waxed board sliding on snow (about 0.04, according to Wikipedia)
theta = slope of the hill (I'm using a modest 15 degrees)

If you multiply this by the distance traveled on the hill, you get the total energy expended on the trip. If instead, you multiply the force by the velocity of the snowboard, you get the work per unit time. That's the same as the power (watts in SI units).

Power = m g u cosine(theta)* v

v = velocity (for this problem, I'm using 10 meters/second, which is about 36 kph, or 22.5 mph)

Plug all that in, and you find a power output of about 284 watts to slide down the hill.

The equation for heat conduction through a slab of material (such as a snowboard deck) is

Power = dQ/dt = k A (T2-T1)/L

k = thermal conductivity (about 0.25 Watts/(meters*degrees Kelvin))
A = area of board touching the ground (about .25 square meters for a typical board)
T2 = temperature on the hot side of the board (in Kelvin)
T1 = the temperature on the cold side of the board
L = the thickness of the board (I'm using one centimeter, 0.01 meters)

When I rearrange this to solve for the temperature difference between the two sides of the board (T2-T1) and plug in the numbers, I get temperature difference of about45 degrees.

As I mentioned above, that's the maximum temperature difference between the two sides, but the hot side should never get above the freezing point of water because the heat generated by friction would have to melt all the snow before it could lead to higher temperatures. That's because of the phase transition from ice to water that occurs at the freezing point (It's the same reason that water with any ice in it at all will have a temperature of exactly 0 degrees Celsius. You can confirm this by putting a pot of snow on the stove and turning up the heat. The temperature will rise to 0 degrees C and stay there until all the snow is melted.).

So, if you're out snowboarding when the air temperature (and top of your board) are at -5 degrees Celsius, the temperature of the bottom of your board be about 0 degrees Celsius when you're moving along at 10 meters/second. In fact, it will always be at about 0 degrees Celsius if you're moving at almost any reasonable speed, and there will be a very thin layer of water under it due to all the frictional energy you're generating by sliding down the mountain.

Read the rest of the post . . .

Saturday, November 3, 2007

eXtreme Sports Physics Gift List, Part 2

More holiday gift ideas for eXtreme sports addicts.

(In case you missed it, I posted five other ideas a little bit ago in eXtreme Sports Physics Gift List, Part 1.)

Hang Time!
When you catch air, you're in freefall. Another way to put it is that you're in a very low orbit that intersects with the ground. Either way, you're briefly weightless.

If you were to strap an accelerometer to your leg to measure the forces on your body, you would see it go to zero when you're in the air. If only there was some way to hook an accelerometer to a timer, you'd know how much hang time you pulled . . .

Actually, there are at least two companies making timers to record the duration of your monster airs. My favorite is the AirPod, but you might want to look into the slightly glossier (and pricier) HangTimer. Personally, I'm all about the data, bling means nothing to me. So I'll save a couple bucks and go with the AirPod.

I'm guessing a lot of folks will be disappointed to find out how little time they spend airborne. On the other hand, once you come to terms with the fact that humans really weren't meant to fly and you learn to appreciate the few precious seconds during each run that you get to enjoy free of our earthly bonds, you'll realize that devices like the AirPod and HangTimer are excellent tools for evaluating and perfecting your aerial skills.

AirPod - fly, be free, take data
$59 and up

In Search of a Fast Frame Rate

If you're a decent photographer, you'll always be a welcome addition in any eXtreme sports road trip. You might even get a free meal or two along the way.

As a rule, eXtreme sports junkies love to see themselves immortalized in high resolution action pics. One of the tricks to getting the shot is making sure you have a camera that can take lots of images very quickly. Pros spend multi-thousands for high frame rates. But you can do almost as well with a few cameras that slip in at just about a thousand bucks.

After using several digital cameras that deliver 2 to 3 frames a second, I found that I was going to need something faster, particularly in the skatepark and on the slopes. My budget limited me to the 5 frame per second and 8.2 megapixel Canon EOS 30D, which retails (with one lens included) at Amazon for $1025. Here's an example of one shot I captured of my son grinding the coping in a 10 foot deep pool at our local skatepark.

In order to get this shot, I actually took 6 pictures, as you can see from this sequence. The one I wanted is number 4.

The high frame rate is good for more than just photos, it also helps me do a bit of physics calculating. For instance, from these shots I can tell that my son traveled about 2 meters in the second that it took to fire off 5 frames, which means he was moving at 2 meters a second. The pool curvature is about 2.5 meters in radius at this point, so he was experiencing a horizontal g-force of about 1/6 the force of gravity. That's what was pinning him to the board as he carved around the pool. Cool, isn't it?

The 30D's older brother, the EOS 20D, has the same frame rate and resolution, but a smaller buffer, so you can't shoot as many shots in a row before stopping to let the electronics catch up.

If you're made of money, you can step up to the 10 megapixel EOS 40D at 6.5 frames per second. (The last time I checked, the EOS Rebels were all limited to 3 frames per second, so they don't make my cut.)

As far as I know, the Canon EOS line offers the fastest frame rate among the $1k cameras. If I find anything faster, I'll let you know.

Canon EOS SLRs
Just hold the button down, chances are at least one of those dozens of shots is going to be a keeper
$974 and up

Eye Witness

There's nothing like watching a crash from the first person perspective, and the best way to do that is with a helmet cam. (I'll post my own favorite crash as soon as I can get it downloaded from my son's PC.)

You can spend a bundle for a high tech, waterproof, shock proof helmet camera, or you can save money the way I did.

I bought a $99 camera that records straight to flash memory. Then I sometimes tucked it under the strap for my snow goggles (be sure to loop the camera's wrist lanyard around your goggle straps), velcroed it to my leading leg, or duct taped it to my skate helmet.

It makes for cool, low budget follow shots and gives a realistic view of what it's like to cruise down a mountain or thread your way through a half pipe. The crashes are the most fun to watch, complete with brutal crunching sounds and groans of pain. Just don't show them to your parents or significant others until a season or two has passed. Otherwise they'll beg you to stay off the slopes, rails, ramps, tracks, or whatever else you ride.

Helmet Cams
- first person adventure and pain
$79 and up

First Aid - it's the best kind

Despite taking things to the edge, few extreme sports injuries involve compound fractures or head trauma. A few bumps, bruises and abrasions are the much more likely results of any given adventure. But the recent epidemic of coverage in the media of staph infections makes it clear that even minor scrapes need quick attention. Besides, you don't what your favorite eXtreme athlete staining his or her stylin' new jeans or jacket with unsightly blood stains.

I used to load up my backpack with a few Band-Aids and sterile pads, but it's a lot easier to just grab a prepackaged first aid kit and toss it in the trunk with the rest of my gear. REI offers a range of kits, from tiny sets that slip in the glove box to fairly comprehensive packs that include everything you need for most injuries, including a copy of "The Wilderness First Aid Manual."

First Aid Kits - 'cause your mom won't always be nearby to kiss the boo boo
$28 and up

Surfrider Gift Membership

As the nigh-invulnerable superhero "The Tick" once said after being asked if he could destroy the Earth "Ye Gods! I hope not! That's where I keep all my STUFF!"

The Earth is a fragile place, and even if the Tick is no threat, without the work of groups like the Surfrider Foundation, you're likely to eventually lose all your stuff - and a lot more. In their own words . . .

The Surfrider Foundation is a non-profit grassroots organization dedicated to the protection and enjoyment of our world’s oceans, waves and beaches. Founded in 1984 by a handful of visionary surfers in Malibu, California, the Surfrider Foundation now maintains over 50,000 members and 80 chapters worldwide.

Even if you're not into eXtreme water sports, remember that most of this precious planet is ocean, and you can't have a healthy Earth without clean water.

So join Surfrider this year or give someone a gift membership - your great grandkids will thank you for it, and you get a cool bumper sticker.

Surfrider Gift Membership

Read the rest of the post . . .