Do not down the three arm protractor, we used them on the boat when you needed to find your position FAST and RELIABLY. You set the THREE bearings you get from your instruments and just line them up with the objects on the map. You take RELATIVE bearings, not compass bearings. So the protractor center shows your boats position and direction with one step, no compass needed.
That's dangerously wrong on three counts.
Firstly it is not safe to sail without a compass, or to ignore it when taking bearings. It provides a valuable check on the bearings that you take for no extra effort.
Secondly if you take three magnetic bearings of navigational marks with a compass, a gross error will immediately be obvious when you plot them, because you won't get anything like a reasonable 'cocked hat'. There is redundancy in the measurements, because if you use a compass (and assuming you're awake) you really only need two bearings to get a position. If you take three bearings relative to the ship's heading then (a) the heading may have been different for each bearing, and more importantly (b) a gross error may not be obvious. If the boat's heading is unknown and the navigational marks are not widely separated then there may be no redundancy in the measurements at all (and you probably haven't been doing what any prudent navigator should do anyway).
Thirdly even if the heading is constant for the measurements of the bearings, the use of bearings relative to the ship's heading gives you the ship's heading at the instant of measurement, not its course. Tidal streams and perhaps leeway mean that the course over the ground will differ, sometimes very substantially, from the heading.
Finally you don't use a map when sailing, you use a chart. Hopefully one that's been corrected up to date.
