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Draw a picture of a cross section of the earth.
Draw in a line perpendicular to the surface of the earth, with a length
to
represent the observer's height.  Then, draw a tangent line to the earth
that
passes through the observer's eyes (the end of the line that represents
his height).
Draw a line from the center of the earth to the point of tangency.  This
point
is the horizon.  Now draw a line from the center of the earth to the
point where
the observer is standing.  The angle between these two lines (call it
theta)  is the
angular distance away from the horizon.
If the observer's height is H, and the radius of the earth is R then
cos(theta) = R/(R+H)
Go find a freshman physics student and look up R in the front cover of
his
textbook (almost all physics textbooks have such information in the
cover).
compute cos(theta) as above and take the inverse cos to get theta, then
convert
from radians or degrees, depending on the mode of your calculator, to
minutes.
Now draw a line tangent to the earth at the point of the observer's
feet.  Then observe
the angular difference between the this tangent line and the previous
line.   This angle is
the dip angle, and your freshmen physics student will be able to
complete the drawing and
show that , phi, (the dip angle, or angle between the two tangents) , is
equal to theta.
The difference is likely to be related to refraction, which is left to
your freshmen physics
student as an exercise.
John Brenneise
Navigatorus Rubus Goldbergitus.emeritus...
> -----Original Message-----
> From:	Millard Kirk [SMTP:mkirk@XXX.XXX]
> Sent:	Wednesday, December 09, 1998 9:27 PM
> To:	Navigation
> Subject:	[Nml] Dip
>
> 	I have always wanted to know the relationship between these two
> formulas,
> or are they related.
>
> Distance to visible horizon in nautical miles:
> D = 1.17 times the square root of the Height,
>
>  and
>
> Dip of the visible horizon in minutes of arc:
> D = 0.97 times the square root of the Height.
>
> 	One factor gives distance and the other gives degrees.  It has
> been a long
> time since I done any proof on formulas.
>
> 	Bowditch give the factor of 1.17 for the distance to visible
> horizon, and
> "The Calculator Afloat" uses 1.14 for its factor for the same formula.
> 	Although Bowditch does state that its formula is to the visible
> horizon,
> while "The Calculator Afloat" state only to the horizon.  Not
> visible?????
>
> Still...............
>
> Learning the Hard Way!!
>
> Millard Kirk KB8YQO 	Email - mkirk@XXX.XXX
> 116 Lewis Ave	     	Homepage- http://webpages.marshall.edu/~mkirk/
> Barboursville, WV       A West Virginia Blue Water Sailor
> 25504                   (304) 736-6544
> First United Methodist Church, Barboursville, WV
> Homepage  http://www.gbgm-umc.org/bfumcwv/
>
>
>
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