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    3-armed protractor
    From: Jeremy C
    Date: 2009 Jul 26, 10:14 EDT
    A while back there was some discussion about the use of a three-armed protractor for navigation.  Here is a case where it was used in the real world.
    We are currently anchored in the lagoon of the island of Diego Garcia.  The captain is not happy with reliance on electronic navigation so is requiring the mates on watch to provide visual bearings as well as GPS/ECDIS fixes and RADAR.
    There are two ways to use the 3 armed protractor for anchor position.  Since we are equipped with Alidades and gyro repeaters, I find it easier to shoot three bearing with good spread on the gyro compass and calculate the differences in gyro degrees between the three.  To this end  I set the main arm of the protractor to the first object (a point on East Island) with the highest numeric bearing (in this case about 340 degrees).  Next I shot another bearing of the main water tower on the island (about 278 deg) , and finally the tangent of a Point Marianne at about 203 degrees.  I set the main leg of the protractor at East island and set that at 0 degrees.  I rotated the second leg so that it read about 62 degrees relative and counterclockwise from the first leg and finally the third leg was adjusted to 136.5 degrees on the scale.  When the three legs are set on the charted objects, the ship's position lies where the center of the protractor and can be fixed by marking the chart through the hole at the center.  If the three relative bearing change appreciatively, you will know that the ship is dragging anchor, a fact confirmed by Radar and GPS information. 
    To use the sextant to obtain the relative angles in this case, I'd first superimpose the water tower on top of the tangent point of East island and read the scale.  I would then have to compare the water tower with point Marianne since the angular distance between East Island and Point Marianne exceeds the sextant arc.  Given these two bearing differences, i could set the scales (after summing the two observed angles to get the angular distance between East Island and Point Marianne) of the protractor and proceed with the plot. 
    I did not opt for the sextant in this case because it is faster to quickly shoot the three bearings on the repeater than break out the sextant and shoot the horizontal bearings.  Also, since the angle between the first and third bearings exceed the arc of the sextant, I wouldn't be saving much time in calculations.
    The true advantage to the sextant method is not precision (the sextant can give you 0.1' of arc precision as opposed to a fraction of a degree on the Alidade), but that it gives you direct readings of the angles which allows you to skip the computation step, but only if the three objects are within 120 or so degrees from each other.  Once you exceed the sextant arc, you are back to calculating and the method becomes slower because superimposing objects takes more time than simple visual bearings.  The goal of using the 3-armed protractor is to determine a fix as quickly as possible.  The 3-armed protractor is much faster than plotting three bearings with other plotting tools, and much less messy on the chart over time as well.
    A word on precision in this particular case.  The main reason that we don't need sextant precision is that we don't really need to know the angular distance between the fixed objects any finer than a couple tenths of a  degree.  The protractor itself is only marked in whole degrees and while you can easily interpolate visually both the compass rose and the protractor to within a couple tenths of a degree, the added precision of a sextant is certainly overkill that will not improve the realistic plot of the ship on the chart.
    Today i found a variaition of about 1 degree in the bearings over time which did little to affect the position obtained by the visual bearings and told me that we were swinging in our set anchor watch circle. 
    Attached is a photograph of the protractor on the chart.

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