# NavList:

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

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Re: Snellius Construction questions
From: John Karl
Date: 2009 Jan 5, 19:44 -0800

```One way this Snellius construction can be understood is by first
understanding the case a single LOP that results from the horizontal
angle between two markers B & C (buoys, etc.).  If you measure a
horizontal angle A between the two markers, your ship is on a circular
LOP with radius R = a/(2sin A), where a is the distance between the
markers.  The three locations, B, C, and the ship, all lie on this
circular LOP.
You can can find the center of the LOP circle by striking arcs of
radius R from both markers; then draw the LOP with radius R centered
on this point.
Alternatively, as the website shows, the center of the LOP circle can
be found by the construction line they laid out at angle A from the B-
C connecting line. By drawing the special case where the line from one
marker (say B) to the ship passes through the center of the circle,
you can see that a right triangle is formed, B-ship-C, with the right
angle at C.  You'll also see that the perpendicular bisector of the B-
C line must passes through the center of the LOP circle.  By studing
the angles in this figure, you can understand their construction.

It's tough without graphics and hand waving,
John Karl

On Jan 5, 2:43�pm,  wrote:
> I have found an intriguing example of triangulation from a 16th century
mathematician, Willebrord
Snellius(http://www.sailingissues.com/navcourse4.html). I have searched other
web sources on the web and so far, have had no success in finding a straight
forward explanation of how this method of triangulation works. Have any of
you actually used the "Snellius Construction" technique, and could you help
me understand it as a practical navigation application?
>
> Thank you,
>
> Todd Frye
>
> -----------------------------------------------
> [Sent from archive by: fryefamily-AT-sisna.com]

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