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    Re: Measuring (and Calculating) Dip
    From: Bruce J. Pennino
    Date: 2013 Mar 19, 18:20 -0400
    Frank ,maybe we agree....maybe not.  If I'm  on a boat that goes up and down with waves, seems to me I want to try to measure sight with a sextant at the top of my wave to the top of the distant wave.  But this is probably impractical. What really happens, I guess, is that I'm somewhere moving up or down  in a wave sighting on a wavy surface/horizon. Hopefully  measurement errors cancel....but probably not. Consequently CN on a moving vessel has a combination of errors that leads to a band width of location. I believe it is common wisdom/experience that true location is within a band  at best 2 -3 miles total width.
    Now I move to shore with my total station (in the next couple of days I'll post  data showing all of my instrument measurement and observation errors focusing on near (2.5 miles) and far (12.5 miles) objects).   I'm thinking I'll measure 10 discrete vertical  angles always focusing on the highest part of a passing wave, but keeping the horizontal angle fixed. As the wave goes up and down I'll measure a vertical angle (dip). If the waves have a long time period, maybe I need to make more measurements or space them out.  When I average all of the data I have a mean vertical  angle. Right?   If I measure my height of eye above the mean waterline on beach , haven't  I measured the mean dip angle with refraction and everything included.  Then when you do the sight reduction, the refraction correction is incorporated into the final result. 
    Now if I'm 100,200,300, 500 ft above MSL when I measure a dip angle, waves become less significant as long as I know my elevation in relation to MSL and I know the tide level. Of course the tidal variation also becomes less significant as height of eye is increased.
    Based on the errors (scatter in my data with total station), I want my height of eye to be at least 8 or 10 ft because of measurement errors that can creep in, not including waves.  Incremental dip angle measurements should be made with at least  60 seconds of difference in dip.  For example, if my height of eye was 8 ft , I should measure about 2.7 minutes of dip ( by standard formula). For next data point (sight), I want my height of eye to be at least 15 or 17 ft (dip about 4 minutes) etc.  I don't think it is easy to refine dip very closely/precisely/accurately, even with a "so called" 3 second total station.
    ----- Original Message -----
    From: Frank Reed
    Sent: Tuesday, March 19, 2013 3:26 PM
    Subject: [NavList] Re: Measuring (and Calculating) Dip

    Brad Morris, you wrote:
    "The wave height correction is by atan((wvht/2)/(3860*sqrt(h))"

    Oh my, oh my... Brad, this equation is bullshit. I should have been more blunt in my previous explanations. I really thought that if I spelled it out to you carefully and slowly, you would see the issues yourself without the need for blunt language. I guess not.

    The correction for wave height is simple: your height of eye should be measured from the tops of the waves as nearly as possible. If you're on a vessel on open water, you can look over the side and see those wave tops. If you're at some protected location, either on shore or in a cove or some other protected waters, you should count your height of eye from your best estimate of the wave tops at the horizon. NO OTHER CALCULATION IS REQUIRED.

    Here we see another problem with mathematics in celestial navigation. Sometimes folks get hooked on the "appearance" of accuracy and mathematical sophistication that comes with a "complicated" equation when the real solution is both "seat of the pants" practical and mathematically elegant.


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