All DR calculations take one of three different forms; (1) How long will it take to go a certain distance? (2) How far will I go in a certain amount of time? and (3) How fast should I go to travel a certain distance in a given amount of time? To answer any of these questions, a navigator needs to know three things: (1) the true course, (2) the boat's speed, and (3) the amount of time the boat has traveled at that course and speed. Thus, in addition to the need for a compass course, you will need a knowledge of boat speed, an accurate watch, and a chart on which to plot the information.
|"Measure distances using the latitude scales which run up and down the sides of the chart. Here, one minute of latitude equals one nautical mile."|
Time is always recorded in military format, i.e., using four digits in a 24 hour format. This means that each day starts at midnight with a time reading of (0000) proceeds to 0100, 0200, 0300 and so on to noon (1200). After noon (1200) the time is additive, 1300, 1400, 1500, continuing up to midnight, which is 2400. Remember that 1300 is 1:00 p.m. and 0100 is 1:00 a.m.
After knowing what direction you are going, the second part of DR calculations is the use of boat speed and time. In order to calculate (reckon) where you are, you must have all three pieces of the puzzle. For example, if you are on a compass course of 170 degrees, where will you be in one hour if your boat is making six knots through the water? Using a variation of 10 west and deviation of 0 degrees, first you will convert the compass course of 170 to a true course of 160 degrees. Then you will compute the distance traveled in one hour (60 minutes) at a speed of six knots. In this case, the computation is very easy since you will travel six nautical miles in one hour at six knots.
Remember that a knot is a unit of speed equal to one nautical mile per hour. So, in this example your DR position will be plotted six nautical miles (NM) in a true direction of 160 degrees on your chart.
In order to simplify things I deliberately used a speed and time that would make the calculations easy. If I had said that your average speed was 49 mph, the distance was 176 miles, and you needed to be there at 1145, you would have needed some extra time to do the calculations. For this reason, you can always use a boat speed of some multiple of six knots, i.e. three knots, six knots, 12 knots or 18 knots, for planning purposes. On a sailboat, the speed will vary greatly and inevitably complicate your calculations.
Fortunately, the actual formulas to make these calculations are easy. It is 60D = ST, where D is the distance in nautical miles, S is the boat speed, and T is the time in minutes. Many navigators have been taught to remember the mnemonic as the address 60 "D" Street. By algebraic manipulation, we can rewrite the main equation to determine the answers to the three navigational questions of distance, speed, and time.
|D =||S x T||solves for Distance|
|S =||60 x D||solves for Speed|
|T =||60 x D||solves for Time|
Here is an example for the more complex problem above where the speed was 49mph, the distance was 176 miles, and you needed to arrive at 1145. Since we are solving for time, the formula is:
|T =||60 x D|
Fill in the numbers as:
|T=||60 x 176||T=||10,560||T=||215.51 minutes, |
or 3 hours, 36 minutes
If you need to be at your destination by 1145, you will have to leave by 0809 to make it on time.
Practice your DR techniques every time you go out until it becomes second nature and you gain confidence in your navigational ability. The effort you expend on those sunny days will be returned tenfold on the foggy days. Your reward will be a safe voyage.
THE RULES OF DEAD RECKONINGKeep these fundamental rules in mind when plotting the vessel's DR position. You should plot:
1. At least every hour on the hour.
2. After every change of course or speed.
3. After every fix or running fix.
4. After plotting any line of position.
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