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Landfall-Learning > Mathematics > Navigation Methods

Navigation Methods - How We Get From Here to There

In Navigation Tools we describe the charts, compass, sextant, and GPS and how they relate to the grid of latitude and longitude lines that cover the earth. These tools, together with an understanding of Universal time, help us determine exactly where we are. Once you have an understanding of the navigational tools, you can begin to learn about navigational methods, or how to use these tools.

In this section we more thoroughly discuss the various methods we can use to pinpoint a specific geographic location and plot our position. These methods include:

After reading these sections, test your mastery of these topics with the exercises!

Dead Reckoning

Often, we are sailing the boat within close sight of land. When doing so, we can see the features on land and identify those features on the chart. In this case, it is very easy to navigate.

If we want to be even more precise, or if we can see land but it is still a ways off, we can use our compass to help determine exactly where we are. With our boat's compass, or even better, a handheld compass, we can take the magnetic heading or "azimuth" from our location to a distinctive land feature near the shore. This feature could be a rocky point, a lighthouse, a mountain, a cove, or anything that is distinct in our sight and is shown on the chart. We then compute the "back azimuth" by adding 180 degrees (if the azimuth is less than 180) or subtracting 180 degrees (if the azimuth is greater than 180). We then draw the back azimuth on the chart from the feature on shore with a pencil. Now we know that we are somewhere on that line.

Then we identify a second object on the shore and repeat the process, drawing a second line on the chart. Where those two lines intersect is very accurately where we are located on the chart.

To verify our measurements, we will repeat the process a third time. The third line on the chart should intersect the first two lines at almost the same point. This is called a "triangulating position." Because the boat is always moving, the three lines will never really intersect at the exact same point, but they will be very close.

The three lines will form the sides of a small pyramid or triangle. We then mark a dot in the center of the triangle and measure the latitude and longitude of that center dot to identify our position. We always write the date and time down on the chart when we mark our position.

We can then steer the boat on a compass heading in a straight line to where we want to go from our present location, now that we know where we are on the chart. If we wait a while and triangulate our position again, we can measure the distance between the two marks and find out how far we have traveled. Since we know how long it took us to cover the distance, we can also calculate our average speed.

Parallel Rules on Chart

Unseen Currents and Dead Reckoning

Often we encounter unseen currents in the ocean. Also, while the wind pushes a sailboat forward, it can also push us off course. This is known as "set and drift." If this happens, our second position will show us that. If we have been traveling forward on a specific heading, our second position should show us on that same heading on the chart. But if our second position shows that we are not on that same heading, then we know that we are being pushed off our course by the wind or a current. Once we know we are being offset from our intended course, we can deliberately steer a course to counteract where the current and/or wind is pushing us. Depending on the amount of set and drift, or the strength and direction of the wind current, we may have to steer many degrees off our map heading to go in the direction we want to go!

There is another situation when we may intentionally steer off our course. If we are heading into port (into a harbor) and we are still too far from shore to identify features on land, we will intentionally steer slightly to the left or to the right of where we want to end up. This way, when we do come within sight of identifiable features on land, we know to look in the opposite direction for our destination. This is called a "deliberate offshoot" and it makes finding our destination a bit easier.

Calculating Speed with Dead Reckoning

Remember from Navigation Tools that each degree of latitude consists of 60 minutes. Each minute is equal to one nautical mile or one "knot". So if we traveled a total of 30 minutes of latitude in 5 hours, we are traveling at an average speed of 6 knots. While that may not seem very fast, it is actually the average speed for a boat Landfall's size!

The most dangerous time on a boat is when the boat is close to land. As you grow closer to shore, the water becomes shallower and the likelihood of hitting a reef or running aground increases. In many countries these near-shore hazards are marked with aids to navigation, such as buoys and lights. Unfortunately, unless you understand what all of the aids to navigation mean and how to use them, they offer no help. Many of these aids are unlit, so at night the very items placed to assist you become hazards themselves!

As you approach land you are also much more likely to encounter other boats. Just like on the highway in your car, there are "rules of the road" which must be understood and followed by everyone to avoid collisions. Also, boats and ships do not have brakes like cars do, so extra care must be taken to stay safe. Generally speaking, we prefer to approach land during the daylight to minimize these risks.

Global Positioning System (GPS)

Deck Mount GPS Handheld GPS

When navigating with a GPS there is not much need for dead reckoning. However, when we are near shore, we often use the dead reckoning method along with the GPS, just to stay in practice. Also, in the event that for any reason the GPS stops working (like a power failure or dead batteries), we can still navigate easily and safely. But GPS really shows its value when we cannot see land or any other navigational aids. This can happen when we are far offshore, but it can also happen when it is dark, rainy or foggy.

The GPS works on the same principle as the triangulation process we described above. The only difference is that instead of using a feature on the shore, the GPS uses signals from three or more satellites in "geosynchronous" orbit around the earths. In other words, the satellites maintain the same position in relation to the Earth's rotation in their orbit. There are twenty-four of these satellites in constant orbit around the earth. The GPS receiver on the boat takes the data from these satellites to triangulate its exact position on earth. Once the GPS has picked up the signal from at least three different satellites, the computer chip inside does all of the work for us! Our only task is to learn which buttons to push to make it work.

The GPS display then shows us our position in latitude and longitude, the direction we are traveling, and the speed we are moving. Even though this is done electronically, we still plot our position on the paper chart every couple of hours in case the GPS loses its memory or power.

In the days of the sextant, it was very difficult to get a good measurement on overcast days or in rough seas. The GPS works day or night, regardless of the weather. Because this tool is so valuable to our safe navigation, we always carry a handheld GPS as a backup.


Dead Reckoning Exercises

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GPS Exercises

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