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    Re: Measuring (and Calculating) Dip
    From: Brad Morris
    Date: 2013 Mar 19, 11:34 -0700

    To: All Concerned

    This past weekend, Alex Eremenko and I got together to measure some dip. Alex is in possession of a Soviet Dip Meter ( http://sextantbook.com/?s=Russian+dip+meter ). I am in possession of a Prismatic Circle of Reflection ( www.fer3.com/arc/imgx/Prismatic-Circle-of-Reflecti.ppt ). Both of these instruments are capable of measuring the angle between two horizons. Yet the optical principle in each is remarkably different.

    The Soviet Dip Meter (SDM) provides a direct reading of the average dip between Dip A and Dip B.

    The Prismatic Circle of Reflection (PCR)requires mathematical manipulation to provide the dip result.

    The calculation of dip is by the best fit to the Nautical Almanac or dip=0.02977*sqrt(h), where h is the height of eye, in meters. The result is in degrees

    The wave height correction is by atan((wvht/2)/(3860*sqrt(h))), where h is the height of eye, meters, and wvht is the peak to trough predominant wave height from the corresponding buoy.

    On 14 March 2013, Alex and I journeyed to Montauk Point. The height of eye was estimated to be 13 feet and the waves were reported at 5.9 feet. Thus, the calculated dip-wave height correction = 3' 8.95" (3minutes 8.95 seconds).
    PCR Measured 3' 22.5"
    Error Term 0' 13.55"

    SDM Measured 5' 09.00"
    Error Term 2' 00.05"

    SDM Measured 4' 39.00"
    Error Term 1' 30.05"

    SDM Measured 5' 00.00"
    Error Term 1' 51.05"

    On 16 March 2013, Alex and I journeyed to Orient Point. The height of eye was estimated at 13 feet and the wave height was 1 foot. The calculated nominal dip should have been 3' 28.97" Distinctly visible were mirages and as a result we expected anomalous refraction and dip.
    PCR Measured 10'05.50"
    Error Term 6' 36.03"

    We then hopped on the Orient Point -> New London Ferry to see Frank Reed. Height of eye was estimated to be 36 feet and the wave height continues at 1 foot. Since the ferry is quite large and long, the wave height correction continues as before. Calculated Dip is 5' 52.09". Mirages continued to be visible.

    PCR Measured 8' 12.50"
    Error Term 2' 20.41"

    PCR Measured 9' 17.50"
    Error Term 3' 25.41"

    PCR Measured 9' 40.00"
    Error Term 3' 47.91"

    SDM Measured 7' 12.00"
    Error Term 1' 19.91"

    After a wonderful visit with Frank, we returned on the New London -> Orient Point ferry. The same height of eye and wave conditions yields the same calculated dip 5' 52.91". No apparent mirages were visible

    PCR measured 5' 50.00"
    Error Term 0' 02.91"

    PCR Measured 6' 30.00"
    Error Term 0' 37.91"


    Frank - in http://fer3.com/arc/m2.aspx/Biruni-radius-Earth-dip-FrankReed-jan-2011-g15188 You wrote:

    beta = alpha0*Q*Re/s
    and the equivalent "refracted radius" for the Earth is
    R = Re/(1-beta)
    where alpha0 is the the index of refraction of air minus one equal to 0.000281, Q is just the usual temperature/pressure factor (=(P/1010mb)/(T/283K)), Re is the true radius of the Earth, and s is the scale height of the atmosphere.

    I believe this to fit into an equation of dip
    dip = arcos((R/(1-beta))/(h+(r/(1-beta)))
    where we have non-standard pressure and temperature.

    I would like to be sure that s is supposed to be 9000 meters.


    Alex has graciously permitted me to retain the Soviet Dip Meter for a period of time, such that comparative measurements can be evaluated. Thank you Alex.

    Best Regards

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