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Warning: Use these tables and
methods at your own risk. They have been tested however we aren't
responsible for their misuse or any errors that might cause an accident.
Results checked against Ed Williams
Great
Circle Calculator.
If you like these
tools and find them useful, feel free Tools There are some basic measurements you need to make to track your position.
Rules for DR
Trick for Speed Measurements If your instruments have failed, use the following formula and something that floats. Speed (kts) = 0.6 * Distance * t For example, say your boat is 30 feet long from bow to stern. Drop a small piece of wood (yes, this is like a Dutchmans Log) in the water at the bow. Start a stopwatch. When the wood passes the stern stop the watch. The elapsed time is "t" and the "Distance" is 30 ft. From this you can approximate your speed. Try this several times in different conditions and compare to your instruments and refine your technique before you need it. Using The DR Tables Assuming you're familiar with the basics of DR, we'll jump into the meat of the tables. The goal is to covert the distance you've traveled on a course to Latitude and Longitude. The tables are quite simple, but you'll need a calculator. The procedure will be explained in detail, however these are the basic steps:
Let's take a closer look at the tables as they are used in the above procedure. The first set of tables will convert your course into two factors, a Lat Factor and a Lon Factor. Look at the following except:
How you use this table is by finding your heading and noting the Lat Factor or Lon Factor. For example, say your heading (once corrected to true) is 8°. Lat Fact=0.99 and Lon Fact=-0.14. If your heading is 188, just reverse the signs on the factors. The next step is to scale the distance you've traveled according to the Latitude of your last Fix. This can be done with the second table as shown in the following excerpt:
Using the degrees of latitude from your Fix, you can move across the table to the last two columns to get the scale factor to convert your distance traveled to minutes of Latitude and Longitude. (The NM per 1° of Lat or Long is just for your reference.) Finally, you compute your change in Latitude and Longitude by multiplying the respective portions together as follows: Change Lat = Distance Traveled *
Lat Fact * Lat Scale Example FIX: 34º44.6' N
118º23.3' W SOLUTION Remember you're working in degrees and minutes! For example 1º30' - 0º45' has be calculated like 0º90' - 0º45'. Likewise adding 1º30' + 0º45' = 2º15' and NOT 1º75'. Explanation of How the Tables Were Made The first set of tables are generated by using a normalized right triangle of 1 nm at a true heading of θ degrees. The angle is varied through the four quadrants (360 degrees) and the resulting Latitude and Longitude distances are computed with the proper sign applied depending on the heading. This allows the theoretical distance traveled in Latitude and Longitude to be computed for any distance, just by multiplying by each factor by the real distance traveled. The theoretical distance then needs to be mapped onto the curved Earth's surface. This is where the second table is used. The second table scales the theoretical distance to fit the curved distance of the Earth at the appropriate Latitude. The following formulas were used (from American Practical Navigator Java Scripts): Distance of 1degree Latitude at
Distance of 1degree Longitude at
(NOTE THAT PI()=3.14159265358... and LAT=latitude in degrees) Then to compute the scale factor of minutes per nm, the above equations were divided into 60 to generate minutes per nm which are the last two columns in the tables used for the DR calculation. So by just knowing your speed and distance and multiplying through the two tables the change in Latitude and Longitude can be computed in minutes, then added to the last fix. |
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