## Friday, September 26, 2008

### Lesson 12: Cross Bearing Fix

Using NOAA Chart 12221 TR, Variation 9W, and the deviation table from Lesson 10 -

Relative Bearings, Lines of Position and Cross Bearing Fix

You may determine the position of your boat by many methods of piloting. The line of position is common to all methods. For example, if you observe a charted standpipe and a charted flag pole in range (lined up), you are somewhere on the line drawn from the standpipe to your boat through the flagstaff. This line is called a range line and is a line of position (LOP). Although a single visual observation can provide a line of position, it does not establish a position. You are located somewhere along this LOP. If an LOP is obtained by magnetic compass, the compass bearing must be corrected to true degrees by apply variation and deviation for the compass heading at the time the bearing was obtained.

Remember a single line of bearing gives you a LOP. Your boat is somewhere along that LOP. You also know that you cannot accurately fix your position by a single LOP. You must plot two (2) or more intersecting LOP’s to obtain a Cross Bearing Fix. The greater number of lines of position intersecting at the same point the greater the confidence in the fix. For a fix to be most accurate, LOP’s must be derived from simultaneous observations or bearings time corrected. In the normal practice of small-boat navigation, you may take two (2) or more bearings, one after the other, and these are considered to meet accuracy requirements.

Bearings can be taken by sighting across a compass, using a hand bearing compass, relative bearings or by RADAR. The direction to the object sighted is recorded. When using cross bearings the fix is obtained by taking bearings on two (2) well defined – charted objects and plotting the observed bearings onto a chart. A more accurate fix may be obtained by taking a third bearing on another well defined object. There should be a separation of at least sixty (60) degrees between lines of position.

Need to Know

A line of position or relative bearing is where the observer and sighted object is assumed to be located somewhere in the same visual “range”.

Two intersecting lines of position taken on two separate sighted objects (objects with known, charted positions) can provide the position of the observer.

Three lines of position on three separate objects (all with known positions), provide a far more accurate fix than using two lines of position.

Only a ship’s heading has a deviation value, relative bearings obtained from lines of position never have deviation values.

Relative bearings are expressed in relation to the ship’s steering compass.

Always work relative bearings up from magnetic steering compass readings to true direction before plotting on a chart.

Always plot bearings values in the correct direction and in true degrees “back” towards the respective sighted object used for that specific bearing or line of position.

Learning Exercise: Cross Bearing Fix

In the following problem set, you will be given the vessel’s heading per steering compass plus three relative bearings. Find Lat/Lon using this information. Remember that deviation is taken from the ship’s heading (SH), not relative bearing(s).

Remember !

Using only the ship’s heading to determine deviation value and use the same value for each “D” in table below. Remember, remember, and remember….bearings never have deviation values! Bearings never deviate, only a ship’s head deviates.

Work each relative bearing reading up to True degrees (- W + E).

On the chart, plot each reading in True degrees, in the correct direction, towards its respective sighted object.

At the point which the lines of position intersect indicate the vessel’s position at the time when the compass bearings were taken.

Drop the pencil in the geometric center of the triangle or cocked hat.

Determine LATITUDE AND LONGITUDE

Learning Exercise:

1. You are on a course of 027º PMC when you take the following bearings PMC:

New Point Comfort Light “2” – 253º
Horn Harbor Entrance Light “HH” – 282º
Wolf Trap Light – 348º

What is the position of the fix?

A. LAT 37º 19.4’ N LON 076º 09.8’ W
B. LAT 37º 19.7’ N LON 076º 09.9’ W
C. LAT 37º 19.4’ N LON 076º 09.5’ W
D. LAT 37º 19.7’ N LON 076º 10.3’ W

2. You are on a course of 089º PMC when you take the following bearings on your vessel magnetic steering compass:

Great Machipongo Light “5” – 004º
Cape Charles Light – 253º
Sand Shoal Inlet South Light – 334º

What is the position of the fix?

A. LAT 37º 11.95’ N LON 075º 41.5’ N
B. LAT 37º 12.0’ N LON 075º 40.9’ W
C. LAT 37º 11.6’ N LON 075º 43.0’ W
D. LAT 37º 11.9’ N LON 075º 41.6’ W

3.You are on a course of 035º PMC when you take the following bearings per magnetic compass:
Cape Charles Light – 343º
Chesapeake Light – 131º
Cape Henry Light – 261º

What is the position of the fix?

A. LAT 36º 58.4’ N LON 075º 49.1’ W
B. LAT 36º 58.1’ N LON 075º 50.0’ W
C. LAT 36º 57.8’ N LON 075º 49.2’ W
D. LAT 36º 57.6’ N LON 75º 049.8’ W
4. You are on a course of 153º PMC when you take the following bearings on your ship’s compass:

Cape Charles Light – 345º
Chesapeake Light – 148º
Cape Henry Light – 241º

What is the position of the fix?

A. LAT 37º 01.6’ N LON 075º 50.9’ W
B. LAT 37º 11.5’ N LON 075º 50.1’ W
C. LAT 36º 57.6’ N LON 075º 51.6’ W
D. LAT 36º 57.9’ N LON 075º 50.8’ W

5. You are on a course of 060º PMC when you take the following bearings PMC:

Horn Harbor Entrance Light “HH” – 285º
New Point Comfort Spit Light “2” – 256º
Wolf Trap Light – 348º

What is the position of the fix?

A. LAT 37º 19.4’ N LON 076º 09.8’ W
B. LAT 37º 19.4’ N LON 076º 09.5’ W
C. LAT 37º 19.7’ N LON 076º 09.9’ W
D. LAT 37º 19.7’ N LON 076º 10.3’ W