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    Re: Raw data for bubble
    From: Bill B
    Date: 2007 Mar 09, 19:05 -0500

    > Bill wrote:
    >> The second paragraph is what I mean. Take the Hc (calculated elevation, not
    >> Ho--observed elevation) from your AP every 4 to 5 minutes and plot that
    >> slope. Fit that slope to the observations.  Then you are working against a
    >> known and can more easily detect outliers.
    Peter responded:
    > This is a new method for me. I calculate the 'Change of Altitude in 5
    > Minutes of Time' as a function of azimuth and latitude. The main thing
    > is to end up with the actual (apparent) rise or fall as a line, used
    > to compare the sights made against. They are plotted on graph paper,
    > altitude vertically, time horizontally. If the sights were perfect
    > their slope would be parallel to the calculated slope. The extent that
    > they do not fit that slope is an indication of error, but only of
    > random error.
    Perhaps slightly different methods, but I think we are doing the same thing.
    Calculating and plotting theoretical rise or fall against time, then fitting
    our observations to that slope instead of letting all the observations drive
    the slope.
    >> Exactly. I have used Excel to compare the the slopes of calculated altitude
    >> (Hc) versus  Ho (observed altitude).  When comparing the observations to the
    >> Hc slope, the stray sheep often stick out like a sore thumb.  They are much
    >> harder to identify compared to the linear regression slope for obvious
    >> reasons.  The two slopes can be significantly different.
    Peter Responded
    > Do you mean that you use Excel to draw a graph?
    Yes. I will enter my observation altitudes (generally Ho as opposed to Hs or
    H) in a spread sheet column and times of observations a second column. Then
    I will enter calculated altitude (Hc) at 4 minute intervals in a third
    column, along with time of Hc calculation in a forth column.
    Using chart wizard I'll plot Ho vs. column-two time, then Hc vs. column-four
    time on the same chart/graph.  You can graphically connect the Hc dots and
    move the slope line up or down to observation data to spot outliers.
    I also like to have Excel add a linear regression slope to the observations
    and compare that to the actual slope (Hc vs. time).  Often quite different.
    Of course this all requires a computing device.  If I understand David Burch
    of Starpath correctly, on the water he may plot raw sextant data (Hs) from a
    4-minute period, reduce one observation at before the beginning time and one
    at or past the end and use that *real* slope, sliding it up to the
    observations. Then, as you suggested pick one observation on the line, or an
    arbitrary point on the line to reduce. I imagine unless the declination of
    the body has changed dramatically over the 4 minute period it should be
    close enough.
    I am not clear the PDF explaining Burch's methods is still available on his
    site << http://www.starpath.com/celestial/celestial_title.htm>> (including
    tabular methods--move up 1d in LHA = 4 minutes time and if the d correction
    factor has not changed, you can pluck the new Hc directly +1d page).
    If it is no longer available I have it archived and would be happy to send
    off list to anyone interested.
    Peter wrote:
     > ...An example of how this can be useful is
    > when you are trying to make an observation at prime vertical - unlike
    > a meridian passage the body just zooms past this due east or west
    > point of azimuth. It is the only way I know of being sure to be able
    > to adopt that precise moment.
    Would you please go into more detail on the above paragraph?
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