How to Calculate Great Circle Distance

When you're planning a trip by boat, "planning" means doing your navigational homework. For short voyages, it is possible to lay out the course and distance to be traveled on a chart. For longer distances, the mathematical solutions known simply as "The Sailings" are used. One of the Sailings, Great Circle Sailing, is based on the premise that sailing along the line of a Great Circle is the shortest distance between two points on the surface of a sphere. Determining the distance to be traveled along that great circle is an important part of your navigational effort. These steps presume that you have some level of knowledge of navigational astronomy.

Things You'll Need

• Scientific calculator
• Hydrographic Office Publication No. 229 ("HO 229")
• Appropriate volume(s) of U.S. Coast Pilots and the Sailing Directions
• Sight Reduction Worksheets for HO 229

Instructions

1. Determine the latitude and longitude of the point of departure (starting point) and destination by referring to the appropriate chart, the U.S. Coast Pilots or the Sailing Directions (En Route, see Resources below).

2. 

   Find the table at the the bottom of the sight reduction worksheet headed "Calculation of Hc and Az." In the column headed "Value," enter the "Lat" as the latitude of the departure point. Enter the latitude of the destination point as "Dec" (the declination) and the difference of longitude as the "LHA" (local hour angle).

3. 

   Find the pages in Publication Number 229 for the "LHA" on the worksheet. Use the "Same As" tables if the latitude of the destination and the latitude of the point of departure are on the same side of the equator; use the "Contrary" tables if they are not. On that same page, find the latitude of the point of departure (the "Lat," from the worksheet) and "Dec," from the worksheet (which is the latitude of the destination).

4. Calculate the distance in degrees. If you use the "Same As" tables, the distance (in degrees) is 90 degrees minus the tabulated altitude ("Hc" on the tables). If you use the "Contrary" tables, the distance is 90 degrees plus the tabular altitude.

5. 

   Convert the resulting distance in degrees to nautical miles by multiplying the number of degrees by 60 and adding the number of minutes. For each second, add 0.0106 nautical miles to the total.

Tips & Warnings

• If your calculations require that you use the "Same As" tables, your initial Great Circle course equals the tabulated azimuth angle, the column of figures headed by the letter "Z" under the latitude. If you use the "Contrary" tables, the supplement of the tabulated azimuth angle (180 - Z) is the initial Great Circle course angle.

References

• NGA Marine Information Page, Including All Publications Referenced

Resources

• The American Practical Navigator
• The Sailings