Relative Bearings (RB) refer to bearings taken relative to the position of the bow of the boat. These are not compass bearings but rather bearings taken from the pelorus.
The pelorus is a fixed protractor usually wrapped around the outside of the ships compass. The pelorus does not rotate like a compass. 0° (zero degrees) on a pelorus always aligns with the bow of the boat and 180° on a pelorus always aligns directly behind the stern.
Any object will be bear directly ahead (0° on the pelorus) or directly behind (180° on the pelorus) or off to the starboard or port side of the boat.
On the starboard side, relative bearings can range from 0° to 180°. Similarly, on the port side, bearings can range from 0° to 180°. To differentiate, the navigator would say an object lies at 45° off either the starboard or port side.
Using relative bearings is a great way to point out the proximate line of sighting of an approaching vessel, buoy or some other object of importance. “There is a power driven vessel approaching us 45° off our port.”
Converting Relative Bearings to Degrees Magnetic
Converting a relative bearing to degrees magnetic is a simple as adding or subtracting the pelorus bearing to the compass course of the boat. If the relative bearing is off the starboard side you add the pelorus bearing to the boat compass heading. Alternatively, if the relative bearing is off the port side you subtract the pelorus bearing from the compass heading.
In our example we are sailing on a course of 170°M. The tower is 45° off or port side. To covert our relative bearing to a compass bearing we would subtract 45 from 170 (170 – 45 = 125) to give us a compass bearing of 125°M. On our return course, compass heading of 350°M, the tower would now lie on or starboard side. When the tower is 45° off our starboard side our compass bearing would be 35°M (350 + 45 = 435 – 360, since our compass reverts to zero at 350°, gives us 35°).
Relative Bearings and Distance Off
Relative bearings are particularly useful in calculating distance off an object or shoreline by doubling your relative bearing taken on a specific point. You must hold your course, know your speed and the time elapsed from the first relative bearing until it is doubled.
The distance traveled from the time of the first relative bearing until it is doubled will equal your distance away from the point the bearings were taken from. Distance is determined by knowing your speed and how long you have been traveling. Effectively you are creating and isosceles triangle (a triangle that has two sides equal in length).
Most navigators will take a relative bearing of 45° and measure the time elapsed until the bearing doubles to 90°. In our example our vessel is traveling at 6Kts. and the time elapsed from our first relative bearing of 45° until our relative bearing has doubled to 90° is 30 minutes. We this information we can calculate that we have traveled a distance of 3NM until our relative bearing has doubled. We know that our distance traveled is equal to our distance off so that we are 3NM off the shoreline.
You can also use relative bearings in conjunction with the ship’s compass in order to determine distance off. We will assume that our vessel is on a compass heading of 100°. We see a tower 45° off our starboard side and wish to determine our distance off. Our compass bearing to the tower is 145° (100° heading plus 45° relative bearing off starboard = 145°). We can determine our distance off by doubling our relative bearing but how does this correlate to our ship’s compass? When our compass bearing to the tower is 190° we know that we have now doubled our relative bearing. (100° heading plus 90° relative bearing off starboard = 190°)
Factors Affecting Distance Off
Aside from human error, including failing to maintain course, speed or adequately record lapsed time, natural factors such as current and wind will also affect the accuracy of a distance off calculation.
If you are running with a current your distance traveled (or distance off) may be under estimated because the speed shown on the knot meter does not reflect your actual speed over ground (SOG). As an example, if you are adrift in a 1 Kt. current, your knot meter would read 0 when in effect your SOG is 1 Kt.
Can a Relative Bearing be used as a Danger Bearing?
It is very unwise to use a relative bearing as a danger bearing to avoid a hazard. Anyone who has sailed knows that the bow of the boat is always moving side to side with every wave. This means that your relative bearing is also increasing or decreasing with any movement of the bow.
On a matter of such importance, where any margin of error could have disastrous results, it is best to rely on the ship’s or handheld compass for a more accurate danger bearing.