Wayfinding and waves

27 April 2009

I once had a brief discussion with a much smarter fellow than myself wherein he argued that four was an arbitrary number for cardinal geographic directions. While I concede (now, as I didn’t then) that he is correct from a geometric point of view, there seems to be at least one evident physical reason for the choice: one direction each for sunrise, sunset, and halfway from each to the other.

While Guy Ottewell gives a potential (if esoteric) thesis for why A is the first letter of a couple of different alphabets, I have nothing like the speculative erudition to say whether my guess holds any water. I do know, though, that while useful direction finding tools can be simple, they can also be arbitrary. Polynesian navigators use celestial coordinate systems shaped from the rising and setting of the Sun and other stars, and these coordinate systems are sometimes symmetrical and even, but not always. Navigators also shape their course based upon other information including clouds, wind, sea critters, birds, and other factors.

One of these other factors was brought into sharper focus for me as I flew from Minneapolis to Cleveland last week, passing over Lakes Michigan and Erie on the way. As far as I’ve been able to figure, this trip was at a similar altitude to those from Hilo to Honolulu, flying at approximately 30,000 feet. What struck me as different, though, was that while I was used to seeing the Pacific Ocean with increasing complexity as more and different sets of waves gradually revealed themselves crossing and rolling on its slightly rough skin, I didn’t see any texture of swells on the two Great Lakes.

Having grown up about six blocks from the edge of Lake Superior, and spent time tagging along on boats with my father from a tender age, I can attest that the Great Lakes do possess waves of sufficient size as to be seen from the air. Those waves might not be the sixty-foot seas of the northern Pacific that cause the weather announcers to doubt their script in the middle of reading it, or even the massive rollers that create the fantastic offshore breaks at Peahi near Maui or Mavericks off California, but Great Lakes waves have sunk ships and otherwise imposed their presence in plenty of ways. In short, I was surprised that I couldn’t see anything from the air, even on a relatively calm day.

My guess as to the cause is something called fetch. In this case a noun, fetch refers to the distance across the water that a wind blowing in that direction has to build up waves. While modeling the problem quantitatively is by nature more complicated, fetch can have an effect equal to that of the speed of the wind. It is the biggest reason why small lakes don’t have big waves. Wind speed and fetch can also affect the rate at which waves come in, their period, a characteristic well known and scrutinized by surfers everywhere.

I’ll do some checking with other resources, but I would guess that the tapestry of overlaid swells that help Polynesian navigators orient themselves on the Pacific was also present on Lake Michigan a week ago, and that the chief difference in appearance wasn’t caused by a difference in height of the waves, but rather in their frequency. Lake Michigan is long and thin, perhaps 85 miles wide from Milwaukee, WI on the west side to Grand Haven, MI on the east, but 280 miles north to south from rural Summer Island on the UP to industrial Gary, Indiana. Thus, when the wind is blowing most directions, there is fairly little water to build up long distances between waves. Only if the wind blows due north or due south (winds being named for the direction they are blowing _from_, in most cases) is their enough fetch to produce swells wide enough to be seen from the air.

Any kindly contributors with more knowledge are invited to comment, particularly if you have done some calculations. I am halfway through building a KML file for the trip, and will post it to the comments when it’s finished.

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One Response to “Wayfinding and waves”

  1. Ben Berkey Says:

    With out looking up/researching this fetch concept. I hazard a guess that it has a bit to do with refraction and straight up wave physics. The pacific is HUGE with a pseudo constant wind direction, so you set up classic first year physics (spherical cows, ignore friction, etc) waves. And these waves all go the same direction with the same speed. The great lakes are big but I think they are small enough that the edges matter. (DAM Boundary conditions now we have to solve annoying differential equations).

    But then again the summit can cloud ones thoughts a bit…. Anyway happy forth.

    -Ben


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