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    Re: Sun, distances and self-confidence
    From: Bill B
    Date: 2005 Jun 10, 13:23 -0500

    > Thanks! You mentioned a serious problem indeed.
    > The local joke is
    > "If you don't like the weather in Kiel, just wait 10 minutes".
    > And this is literally true.
    > I've never seen a place where clouds come and go so fast.
    > In the limited time that Sun is visible from my window,
    > it is very hard to catch it in a hole between the clouds.
    Very much like my experience on Lake Michigan last weekend.  The marine
    forecasts should have been done for every ten-mile stretch, and even then
    would have changed almost hourly.  Clouds sweeping in from the southwest.
    The plot of hourly barometric pressure looked like a sine wave, and the
    horizon was hazy enough that it was nearly impossible to get a good IE check
    (air and water temp maybe 20 F apart).  Out of five tries, two IE checks
    were in the right neighborhood at 0.6' on the arc (usual O.7'), one was 0.2'
    off the arc, one at 1.0' on the arc, and the last 1.2' on the arc.  Tried
    every trick I have read, including sweeping the horizon once set and looking
    for a traveling "hump," all to no avail.  Winds had started about 17 kn out
    of Michigan City Saturday, dropped to 7 kn an hour or two later, and then
    picked up to 32 kn with heavy rain and lightning about three hours into the
    sail to Chicago (about 30 minutes after my observations). Off and on.
    (Talked to some of the racers in the Chicago/Michigan City race after the
    fact and they saw breezes in the lower 40 kn range--as forecast in the storm
    warnings. Tornadoes were reported in Michigan.)  Quite an interesting day
    weather wise.
    Despite my disappointment at the lack of a crisp horizon, I was not going to
    lose the opportunity to shoot on the water, and reckoned I was not the first
    sailor to encounter the horizon obstacle. (Remembered tales of  tropical
    navigators with clear skies but a hazy horizon, but did not have a dish of
    mercury with me ;-) Seas were calm with 1-3 ft swells, so I had a go at it.
    Picked the closest to a sharp line I could find and used it.
    Besides the horizon, yaw was the biggest obstacle to overcome.  Adjusting
    for pitch and heel/roll was relatively easy, but yaw with an inexperienced
    guest helmsman was difficult. Sort of "set and wait, adjust, set and wait."
    Before departing I took measurements from the waterline to the cockpit sole,
    coachroof by the mast, and foredeck at the anchor locker for use in
    calculating dip.  Then it was a simple matter of measuring my height of eye
    from the surface, and adjusting for heel by noting the difference between
    resting waterline and boot-topping/water under sail.  I had a mate hold my
    GPS and mark down the time and coordinates at my mark.  Then I averaged the
    times, Ho's, and position and did a single reduction with the averages on a
    pocket calculator.  Results were 1.9' Away.
    Monday on the return trip the same "spot weather" but milder.  When we left
    for Michigan City small-craft warnings were forecast there for the
    afternoon.  We actually wound up motor sailing in due to lack of wind. It
    was hot and humid (and when the wind died we got a boatload of those nasty
    little biting flies that can't read the insect-repellant label that states
    it repels them--I prefer the Canadian Wren-sized flies you can hunt with a
    410 shotgun/birdshot).  2-3 foot swells, wind still out of the southwest.
    The horizon was like a line of loose cotton between the water and sky with
    no discernable line, except to the northwest where it resembled Saturday's
    horizon.  We were about 9 nm off, and with the haze against the sand dunes
    it seemed like a lost cause. I tried one shot, and decided to give it up.
    Then I thought there might be something to be learned about accuracy and
    repeatability under the conditions, so did three shots and recorded them.
    The three averaged out to 0.8' Away.  Better lucky than good.
    When I returned home I ran all the individual observations through Omar
    Reis's site (http://www.tecepe.com.br/scripts/AlmanacPagesISAPI.isa) for
    Hc's , calculated individual errors and averaged them, and used Excel to
    plot the Hc's vs. Ho's, and established a linear-regression trend line for
    the Ho's.
    Saturday, June 4, approx. 13:36:48 EST
    On-board calculation of averages: 1.9' Away
    Error by Omar (Ho - Hc)
    Mean of errors:  -1.7 (Away)
    The slope of the Excel-generated linear-regression trend line for Ho was
    parallel to the Hc slope plot but below.  I would love to discard the -3.2
    as an outlier and improve the results significantly, but in all fairness
    would also have to discard the -0.3 when compared to the Hc slope if
    plotting by hand on a boat, so little would change.
    Sunday, June 6, approx. 14:33:45 EST
    On-board calculation of averages: 0.8 Away
    Error by Omar (Ho - Hc)
    Mean -0.9 (Away)
    As you can imagine, this Excel plot was a mess.  The slope of the Hc line
    was much steeper than the slope of the Ho trend line.  By chance I guess
    (being mathematically challenged), the lines intersected each other in their
    middles, so luck won out?  Fitting to the Hc slope would have given similar
    results.  Somehow, founded or not, my gut tells me I am better to fit the
    data points to the Hc slope then picking an arbitrary time/elevation than
    doing the same on the linear-regression slope.
    The difference in Hc calculations from my averages and Omar's site Hc's I
    regard as rounding errors.  Often my calculations from the Nautical Almanac
    data vs. Omar's are 0.1' off.
    Also played with position with my hockey-puck compass and sextant using the
    Sears Tower and John Hancock buildings around Chicago, and position from an
    object (Sears Tower and Michigan City power-plant smokestack using the
    sextant and trig with mixed results.  All in all, a great learning
    Looking forward to your comments and results with a natural horizon and/or
    small craft.  Did you pack that magnificent Soviet three-armed protractor to
    play with?

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