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    Re: Averaging
    From: Bill B
    Date: 2004 Oct 23, 00:36 -0500

    Fred
    
    Thank you so much.  For me, a picture IS worth a thousand words.
    
    I took the liberty of expanding the y axis via PhotoShop to emphasize the
    relationships.
    
    If I am reading it correctly, the higher the altitude, the sooner it becomes
    linear. By default, the lower the altitude, the slower it becomes linear.
    
    Now I get into a fuzzy area for me.  The rate-of-change for Hc is
    substantially less for lower altitudes, so am guessing that error wise, the
    two variables (linearity vs. rate of change) come close to canceling each
    other out when averaging.  I leave that to the mathematicians to confirm or
    deny.
    
    From a practical standpoint, it is easier to get a good cut on a body with a
    low Hc rate-of-change than it is on one whipping along at 1d per four
    minutes/15' per minute/15" per second than one with a slower rate of change;
    especially on the water in a small craft.
    
    Bill
    
    
    
    > Here is a graph of altitude versus time for meridian altitudes that
    > vary from 15 to almost 90 degrees.
    >
    > The non-linearity is greatest in the graph for 75 degrees, and you can
    > see that it's a pretty straight line by 50-75 minutes after passage.
    > The non-linearity is less at 60 degrees but extends up to 100 minutes
    > after passage.  By 45 degrees, the curve is almost imperceptible, but
    > of course there (otherwise the sun could never rise or fall!).
    >
    > At meridian passages of 90 degrees you can see the sun goes straight
    > up, then straight down; my mistake the other day was looking at that
    > curve rather than one a bit lower, such as 75 degrees.
    
    
    
    
    

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