Bearings and Lines of Position

Good dead reckoning (DR) techniques can result in fairly accurate positions. But, even when employing the very best techniques, the DR position becomes less accurate as time increases beyond the last known position. Small errors tend to accumulate into one total error, which is unacceptable. To minimize this error, the navigator must be able to establish an accurate position from which to restart DR. This accurate position is free of any DR errors and is called a fix. A fix is simply a point from which the navigator can restart DR, just as if it were the takeoff point. We begin our discussion of fixing with an explanation of lines of position (LOP).


Lines of Position (LOP)

It is possible to solve part of the fix problem without knowing an exact location. For example, assume you are in a strange town and you call a friend to meet you downtown. If you tell this person that you are somewhere on Park Street, your friend can limit any search for you to that particular street. In this case, Park Street is an LOP. An LOP is a series of possible positions or fixes. It can be a straight line, such as a city street, or a curved line, such as a river, but it gives a definite clue to position.

If you tell your friend that you are at Park Street where it crosses the Karuzas River, it would then establish your exact location. You have used two LOPs to determine your exact position. Thus, two intersecting LOPs identify a point that establishes a fix.

You can use the same procedure as a navigator. You may be flying along a railroad that you identify as the Jedicke Railroad on your chart. As you continue on this course, you notice the railroad crosses a river that is labeled the King River on your chart. When you fly over the point where these two visual LOPs cross, you know your exact location over the ground and on your chart. You now have a fix from which you can continue to DR.

Types of LOPs

A fix gives definite information as to both track and groundspeed (GS) of an aircraft since the last fix, but a single LOP can only define either the track or the GS—not both. And it may not clearly define either. The evidence obtained from an LOP depends upon the angle at which it intersects the track. LOPs are sometimes classified according to this angle.


Course Line

An LOP that is parallel or nearly parallel to the course is called a course line. [Figure 5-1] It gives information as to possible locations of the aircraft laterally in relation to the course; that is, whether it is to the right or left of course. Because it does not indicate how far the aircraft is along the track, no speed information is provided.

Figure 5-1. Line of position parallel to track is the course line.

Figure 5-1. Line of position parallel to track is the course line.

Speed Line

An LOP that is perpendicular, or nearly so, to the track is called a speed line because it indicates how far the aircraft has traveled along the track and, thus, is a measure of GS. [Figure 5-2] It does not indicate whether the aircraft is to the right or left of the course.

Figure 5-2. Line of position perpendicular to track is the speed line.

Figure 5-2. Line of position perpendicular to track is the speed line.

LOPs by Bearings

One method of determining an LOP is to establish the direction of the line of sight (LOS) to a known fixed object. The direction of the LOS is the bearing of the object from the aircraft. A line plotted in the direction of the bearing is an LOP. At the time of the observation, the aircraft was on the LOP.

Figure 5-3. True bearing equals relative bearing plus true heading.

Figure 5-3. True bearing equals relative bearing plus true heading.

Relative Bearings (RB)

An RB is the angle between the fore-and-aft axis of the aircraft and the LOS to the object, always measured clockwise from 000° at the nose of the aircraft through 360°. In Figure 5-3, the RB of the object is shown as 070°. Convert this to a true bearing (TB) before it can be plotted. To do this, simply add the RB to the true heading (TH) the aircraft was flying when the bearing was obtained. (Subtract 360° if the total exceeds this amount.) Thus:

RB + TH = TB (RuB THe TuB)

RB is the relative bearing, TH is the true heading, and TB is the true bearing.

Assuming the aircraft was on a TH of 210° when the bearing was taken, the corresponding TB of the object is 280°. (070° RB + 210° TH = 280° TB)


Plotting the LOP

As previously stated, two intersecting LOPs determine the position of the aircraft. The only other possible point from which to begin plotting the LOP is the object on which you took the bearing. The procedure is to use the reciprocal of the TB of the object, thus drawing an LOP toward the aircraft. In actual practice, it is not necessary to compute the reciprocal of the bearing; the TB is measured with the plotter, and the LOP is drawn toward the opposite end of the plotter. To establish an LOP by RB, the navigator must know:

  1. Position of the source (object) of the bearing,
  2. TH of the aircraft,
  3. RB of the object, and
  4. Exact time at which the TH and RBs were taken.