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    Sextant Observation Errors
    From: Dan Hogan
    Date: 1995 May 22, 16:18 PDT

    The following courtesy of:
    	The Navigation Foundation  (Tel. 301-622-8448)
    	P.O. Box 1126, Rockville MD 20850
    	The Navigator's Newsletter, IssueTwenty-Four, Spring 1989
    Dan Hogan
        dhhogan@earthlink.net     dhhogan@delphi.com
    The Personal Equation, Variation in the Dip Correction, Random Error in
    Sextant Observations
    by John M. Luykx
    The two major sources of error in celestial observations are a) the
    observer's personal error in actually measuring the altitude of the
    celestial body with sextant and b) the variations in normal dip caused by
    changes in refraction due to sea/air surface temperature.
    Personal Error
    	It is known that the technique, quality and accuracy of observation
    will vary from observer to observer. Each individual observer, however, can
    determine the quality of his observations by conducting a comprehensive
    series of tests over, generally a long period of time and with several
    celestial bodies. Such tests will provide siginificant results when the
    observer is satisfied that:
    	a. the sextanr I.C. is correctly computed
    	b. the sextant was in correct adjustment
    	c. the observer's height of eye is accurately known
    	d. the sextant was not "canted" during observation
    	e. a "good" observation was made
    	f. the most accurate sight reduction method was employed
    	g. no computational errors were made
    A series of tests under the above conditions should be conducted by the
    	a. with different celestial bodies
    	b. at various altitudes
    	c. under various conditions of weather and sea
    	d. at different places
    	The altitudes obtianed during the tests should then be compared with
    computed values obtained by computer, sight reduction tables or mathematical
    computation. The difference between the two (observed and computed values)
    may be considered the personal error and applied with sign reversed to
    future observations as a personal correction.
    Dip Error
    	The dip correction (height of eye) tabulated on the inside front
    cover of the Nautical Almanac is based on the following formula which
    incorporates a standard value for atmospheric refraction;
    		D = 0.97 x SQRT h
    	Where D = minutes of arc
    	            h = hight of eye in feet
    	Significant variations in dip error caused by non-standard
    refraction may be experienced when large differences between sea and air
    temperatures at the surface occur. Because non-standard refraction is
    probably the single most important source of error in sextant observations,
    a considerable amount of research has been conducted to determine the mean
    values of refraction (used in the Dip tables), the conditions under which
    values differ from the mean and the value of such differences.
    	The results of this research indicate generally that:
    	a. When surface air temperature is less that the suface  water
    temperature, the value		of dip is greater than normal.
    	b. When surface air temperature is greater than the surface water
    temperature, the 		value of dip is less than normal.
    	When significant variation in sea/air surface temperature exists,
    corrections to the standard value of dip in the Nautical Almanac may be
    applied as follows (h. of e. 10'-30'):
    	1) For every ten degree decrease of thr surface air temperature
    below the value of the surface water temperature, the value of the tabulated
    dip is to be increased by 1 minute of arc.
    	2) For every ten degree increase in the surface air temperature
    above the value of the surface water temperature, the value of the dip is to
    be decreased by 1 minute of arc.
    	Dip meters of varing types have been developed during the past 100
    years to measure the actual value of dip for normal heights of eye and for
    any instant of time. These instruments are optical instruments which measure
    the vertical angle from a point on the horizion through the observers's
    zenith to the opposite point of the horizion. The angle subtracted from 180
    and divided by 2 is equal to the actual value of dip at the time of
    observation. An instrument of this type developed by Admiral Davies,
    President of the Foundation, is described on pages 7-8 of issue 18 of the
    Newsletter (Fall. 1987).
    Random Error
    	Individual observations by sextant taken on board a rolling, yawing,
    pitching vessel often contain large values of random observational error.
    	To improve the reliability of position lines from such sextant
    observations, it is often recommended that a series of observations be taken
    and the results averaged to reduce random error. The mean time of
    observation and the mean value of altitude  for the series of observations
    are then computed and used in sight reduction. Individual observations of
    the series may be plotted on cross section paper (altitude verses time) and
    a curve "faired" through a series of plotted points of observation. Unless
    the observations were made at or near the time of meridian passage, the
    faired curve would be nearly a straight line. Any point along the line may
    be used as an observation.The slope of the curve of observations when
    compared with the slope of a curve of altitude change, computed for the time
    of observation will further indicate the accuracy of individual observations
    in the series.
    	The average of a series of observations was standard practice for
    celestial observations taken from aircraft. Accurate and reliable mechanical
    averaging devices for aircraft sextants [were manufactured] especially
    during World War II by C. Plath in germany, Henry Hughes in England and by
    Bendix and Kollsman in the United States. During World War II the Japanese
    sextant manufacturer, Tamaya, developed a mechanical averger whic was
    installed as an intergal part (not removeable) of a marine sextant of the
    Gago-Coutinho type.

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