# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Dip**

**From:**John Brenneise

**Date:**1998 Dec 10, 15:03 EST

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/ > > > > =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-= > =-= TO UNSUBSCRIBE, send this message to majordomo@XXX.XXX: > =-= > =-= unsubscribe navigation > =-= > =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-= =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-= =-= TO UNSUBSCRIBE, send this message to majordomo@XXX.XXX: =-= =-= unsubscribe navigation =-= =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=