Dot Physics

A small version of the seasons

So, it snowed here (in Louisiana). Sure, it wasn’t a lot, but it was still a big deal. The following day, there was still some snow on the house roofs. I took some pictures. Here is a shot looking at the North side of a house.

i-e1a0f43b4605963923178117b385a8da-2009-12-06_north_roof.jpg

And here is a view of the South side of the same roof.

i-350500f8f1730beb662506577fd55274-2009-12-06_south_roof.jpg

What is so cool about that? All the houses were the same way. North side of roof = snow. South side = no snow. At first, I was going to use these pictures to talk about flux. Basically, since the Sun is lower in the South sky the southern side of the roof gets more solar energy flux. Then I realized my error. Not only does the southern side have a greater flux, it is also exposed to the Sun for a longer time (the northern side is in the shade from the south part of the roof for part of the time). What else depends on time and flux? The seasons. This roof is like a mini-Earth.

The South side of the roof gets more energy because it has sunlight for longer and a greater flux. First, let me show the longer time. Check out this diagram.

i-57653708e354bcc9fbc87b407c58ccad-2009-12-06_untitled_9.jpg

In the morning and evening, the sunlight doesn’t even hit the north side of the roof. But now let me talk about flux. Suppose the Sun is in a position to shine on both the south and north side of the roof. Here the lines represent light from the sun (which is far enough away that these lines would be parallel to each other)

i-0ef196693a5964da681054c7d32bfe09-2009-12-07_untitled_10.jpg

How many lines hit the south side of the roof? I count 5 lines, with only 2 hitting the north side of the roof. If both sides of the roof are the same size, then the south side is going to get a lot more energy from the solar radiation. Also, think of it from the perspective of the Sun. If you were the Sun, looking at the roof, which side would look bigger?

In general, flux is the amount of “something” interacting with an area (in this case sun light). It depends on:

  • The strength of the “something” (in this case light)
  • The size of the area (roof in this case)
  • The angle between the “something” and a line perpendicular to the surface.

This is the same flux that is seen in Gauss’ Law, but I am not sure it is the same as the flux in a flux capacitor. If the something is constant in direction and magnitude over the area, then the flux can be calculated as: (note the “something” has be a vector quantity)

i-8ee07683d5cd4251d576f5360b4d47df-2009-12-07_la_te_xi_t_1_6.jpg

Here, the vector S is the “something” and the vector A is a vector that has a magnitude equal to the area. The direction of vector A is perpendicular to the surface.

Back to the seasons and the roof. The time the sun hits each part combined with the flux is why one side has snow and the other doesn’t. Here is a graph I used when I previously talked about the seasons.

i-e2604963d77e69395bac6f29f9f08dee-2009-12-07_untitled_11.jpg

Let me end by just saying that the south side of the roof is clear and it is not closer to the sun than the north side.

Comments

  1. #1 george.w
    December 7, 2009

    Wonderful! I am really enjoying your explanations. I wish I’d had this post 20 years ago when trying to straighten out my kid’s teacher who told him that the Earth was warmer in Summer because it was closer to the sun.

    The other day on the way to breakfast my wife and I noticed differential evaporation of frost on everything, even telephone wires. Frost was changing to water vapor, and the humidity was high enough that the vapor immediately condensed into visible form. So it looked like everything was steaming, just on the east side.

  2. #2 david
    December 8, 2009

    Interesting. So it would seem to follow as a thought experiment that less moisture is evaporated from the north side of the trees around there as well? And so the moss is more likely to grow there on the north side?

  3. #4 Rhett Allain
    December 8, 2009

    @Bee,

    In Louisiana, this is called snow. Sometimes they call frost snow also.

  4. #5 Eric Lund
    December 8, 2009

    @Bee: Much depends on whether you are used to snow. Where I live (New Hampshire) I don’t bother checking whether we are shutting down for a snowstorm unless (1) the forecast calls for at least 6 in/15 cm or (2) it will be mixed with or changing over to freezing rain. (I don’t mind snow, but freezing rain I can do without.) Where my mother lives in Seattle, an inch or two of lowland snow will paralyze the city, especially if it doesn’t melt right away. I have heard anecdotally that the DC metro region cannot deal with even a half inch of snow, and southern England also cannot deal with accumulating snow.

  5. #6 TGAP Dad
    December 8, 2009

    I went to school at Northern Michigan University, in Marquette, MI. In the dead of Winter, we wouldn’t even have noticed six more inches of snow. In my time there, one storm dropped 54 inches during a three-day period spanning Valentine’s day. I’ve even seen it snow in August. (In an unsurprising corollary, I’m in shorts and t-shirts at 55 degrees, turn on the A/C when it hits 80, and have trouble tolerating temperatures over 90.)

    Where I live now, in the Southern lower peninsula, we haven’t even gotten as much snow, so far this fall, as pictured in this post. So I was surprised to hear that Southern Louisiana has gotten any snow at all.

  6. #7 Jim Thomerson
    December 8, 2009

    This is why vegetation on a north slope is different from the vegetation on the facing south slope.

  7. #8 wilburgall
    December 8, 2009

    Snow on the roof can be a tell-tale for poor insulation. The uniform snow coverage on your roof tells me you have uniform insulation. It does not tell how good the values are. The time it takes to melt can give a clue for that. Fun stuff.

  8. #9 Tom
    December 9, 2009

    @Eric-

    Yes, a half-inch can shut down DC, under the right circumstances; it requires that the snow stick immediately. (Otherwise it takes a little more.) I can recall an afternoon commute taking 4x as long as normal because of one such dusting that hit at about 2 PM.

    The first line of defense for snow removal after a storm is solar. If we get several days below freezing after a snowstorm it’s bad news.

    All in all a far cry from my younger days in upstate NY.

  9. #10 Lydia
    December 9, 2009

    Very cool. I’m a biology student with a distaste for physics but this blog applies physics concepts to easy everyday questions. Keep it up. You’re like the “physics” verions of the TV show “Numbers.”

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