Dead Reckoning Calculations
Any sailor who has ever used dead reckoning
(DR) knows that it's a simple system which
allows you to determine your present position
by plotting the course and speed from a known
past position. A navigator can also determine
the boat's future position by projecting the
present course and speed from the present
position. Of course it's important to remember
that a DR position is only approximate because
it does not allow for the effect of leeway, Dead reckoning begins at a known
current, or steering error. point, like this red nun above.
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.
To measure courses, use the compass rose nearest to the chart section currently in use.
Transfer course lines to and from the compass rose using parallel rulers, rolling rulers, or
triangles. You can also measure direction at any convenient place on a Mercator chart
because the meridians are parallel to each other, and a line making an angle with any one
makes the same angle with all others. Compass roses give both true and magnetic
directions. However, for consistency, and by convention, use only true directions on the
chart.
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. Since the Mercator's latitude scale "Measure
expands as latitude increases, measure distances on the distances using
latitude scale closest to the mid-area of the course line. On the latitude scales
large-scale charts, such as harbor charts, use the distance scale which run up and
provided in the margin. To measure long distances on small- down the sides of
scale charts, break the distance into a number of segments and
the chart. Here,
measure each segment at its mid-latitude to insure accuracy.
one minute of
Time is always recorded in military format, i.e., using four latitude equals
digits in a 24 hour format. This means that each day starts at one nautical mile."
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.
For DR work, always use the boat's
speed through the water, which is
taken from the knot meter. Do not use
the boat's Speed Over Ground (SOG)
which you can get from the GPS or
Loran. I will cover this difference in
more detail in later articles.
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 Sailors can use the latitude scale on the chart
variation of 10 west and deviation of (never the longitude scale) for measuring
0 degrees, first you will convert the distance. One degree of latitude equals 60
compass course of 170 to a true nautical miles. One minute equals one nautical
course of 160 degrees. Then you will mile. The distance between the 30 and 35
compute the distance traveled in one above is five nautical miles.
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.
A handbearing compass is a useful tool
to check the accuracy of where you think
you should be, and where you end up--
While this may sound complicated, it is which further enables calculations of set
really quite simple. In fact, you make these and drift.
types of calculations mentally every time
you drive your automobile. If you need to be at a place 180 miles away from your house
at 1200 (noon), and you expect to average 60 mph, you almost automatically calculate
that you need to depart home at 0900 (9:00 a.m.). First you deduce that it will take three
hours to travel 180 miles at 60 mph, and then you subtract the three hours from 1200 to
arrive at that 0900 departure time. If you have been on the road for two hours at an
average speed of 60 mph, how far have you traveled? The answer is easily figured out to
be 120 miles and you know that you have 60 miles left to travel on your 180 mile trip. If
the distance remaining is 60 miles and you need to be there in one hour, how fast should
you drive? The answer, of course, is 60 mph.
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.
SxT
D= solves for Distance
60
60 x D
S= solves for Speed
T
60 x D
T= solves for Time
S
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:
60 x D
T=
S
Fill in the numbers as:
60 x 176 10,560 215.51 minutes,
T= T= T=
49 49 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.
Draw a line from each DR position
and extend this line from the DR or
fix position in the direction of the
course steered. Above the course
line, place a capital C followed by
the true course in degrees to the
nearest whole degree (do not use
tenths or fractions of a degree).
Below the course line, place a
capital S followed by the speed
through the water in knots to the
nearest knot (do not use tenths of a
knot). Enclose a fix from two or
more Lines Of Position (LOPs) or With a proper grasp of dead-reckoning
GPS by a small circle and label it fundamentals, a crew can expect a safe and
with the time to the nearest minute. enjoyable nautical adventure.
Mark a DR position with a
semicircle and the time. Express the time using four digits without punctuation (military
format). Use either zone time or Greenwich Mean Time (more on time in future articles).
By convention label the fix time horizontally and the DR time diagonally in relation to
the bottom of the chart, at that position. Make sure that you write all of these labels
neatly, succinctly, and clearly so that you can read them later.
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 RECKONING
Keep 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.
