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Landfall-Learning > Mathematics > Navigation Tools

Navigation Tools - Getting Us From Here to There

Unlike when driving a car, there are no roads or highways marked on maps of the seas and oceans. So how do we know where we are and where we're going, especially when we can't see land? Well, we have to navigate. Navigation is the science of working out the position of a vessel (or airplane or missile, for that matter) and charting a course for guiding the vessel safely from one point to another. A navigator usually tries to find the shortest route between two points. The initial planning and the end results of navigation are plotted on charts. Most of the navigable waters of the world have been surveyed accurately by the hydrographic services of the maritime nations and reliable charts of the waters are usually available.

In addition to charts, here are other tools we can use to help us navigate. Landfall's navigation tools include:

After reading these sections, test your mastery of these topics with the exercises! Once you have an understanding of the navigational tools, you can begin to learn about navigational methods, or how to use these tools.


On a vessel we carry special maps called "nautical charts." These provide a "to scale" representation of the navigable waters, landmasses, and "aids to navigation". Aids to navigation are the buoys, lights and radio beacons placed along the coastal waterways to make navigation easier in confusing or dangerous waters. These charts also show the "relief", or the elevation of landmasses and the depth of oceans and waterways. This clues us in to the terrain on shore as well as on the sea bottom. Latitude and longitude lines are also shown on the chart. This allows us to relate what we see around us to our specific coordinates. Once we know how to use our navigational tools, the latitude and longitude lines, together with our charts, serve as our sea "street signs".

Compass Navigation

The compass rose similar to the simple one above has appeared on charts since the 1300's. The term "rose" comes from the figure's compass points resembling the petals of the well-known flower. Originally, this device was used to indicate the directions of the winds (and it was then known as a wind rose). This compass rose shows the directions of the eight major winds. (There are 32 points of wind shown on a full compass rose.)

Our ship's compass shows us this information about our direction in relation to "magnetic north". The compass is divided into the same basic points, but a magnetic compass tells us which direction is magnetic north and from that we can tell which direction we are going. Because the compass is mounted in the cockpit directly in line with the bow of the boat, when we are standing at the helm, we can look down at the compass and know exactly in which direction the boat is headed. (In the picture below, the compass is headed "due north".)

A compass is a circle made up of 360 degrees. Every 90 degrees represents a different cardinal direction. North is 0 degrees, and no matter which direction you are going, the compass always points to magnetic north. Going clockwise from north, East is 90 degrees, south is 180 degrees, and west is 270 degrees. So just by looking at the compass, we can tell which direction we are going. But that doesn't help much unless we know where we are in the first place. And a good chart really helps, too, but in the middle of the ocean with no land anywhere to be seen, a map and compass are not enough. What else do we need?

Latitude and Longitude

Any location on Earth can be described by two numbers: its latitude and its longitude. If you look at a map or globe of the earth, you will see that the planet is divided by equally spaced horizontal lines that run around the earth like a series of parallel belts, and another set of lines the run vertically, up and down from the two poles. If an airplane pilot or a ship's captain wants to specify position on a map, latitude and longitude are the "coordinates" they use. Actually, these are two angles, measured in "degrees," "minutes" and "seconds." These are denoted by the symbols (,',") .

The horizontal lines on the map mark "latitude" and are marked both north and south of the equator. The equator itself is considered 0, or zero degrees of latitude. As you travel north, the numbers increase and the corresponding number is designated as "X degrees latitude North". As you travel south of the equator, the numbers also increase and the corresponding number is designated as "X degrees latitude South."

Each degree of latitude measures 60 nautical miles. So if you travel 600 nautical miles north of the Equator, your position would be 10 degrees North latitude. Within each degree of latitude, each nautical mile is designated in "minutes." So, if you traveled 615 miles north of the equator, your position would be 10 degrees, 15 minutes North latitude. Each minute of latitude is divided into seconds.

Looking at the globe again, you will also see lines running north and south from the earth's two poles. These lines mark "longitude". While these lines are equally spaced at the equator, they come closer together as they approach the poles. Unlike with latitude, which uses the equator as its baseline, the baseline for longitude runs directly through Greenwich, England. This line of longitude is designated as "zero degrees longitude".

As you travel west from Greenwich, the degrees of longitude grow larger and are designated as West longitude. The same is true as you travel east from Greenwich, marking East longitude. West and East longitude meet at 180 degrees of longitude, in the middle of the Pacific ocean, and this line of longitude designates what is commonly called the "International Date Line".

Knowing the degrees, minutes and seconds of latitude and longitude, we can very accurately state our geographic position anywhere on earth using the intersection of the latitude and longitude lines. In fact, we can precisely pinpoint a position anywhere on the globe. But how do we find those lines when they aren't drawn anywhere on the real earth?

Well, this part gets a little complicated, and some of it just has to be taken on faith (unless you want to take some advanced astronomy and trigonometry classes!). Since the earth maintains a very regular position in relation to the sun, if we can measure the altitude and direction of the sun at a specific time and date, we can translate that into a very accurate position in longitude and latitude. In the olden days, sailors needed a watch, a compass and a sextant to take these measurements. Some sailors, including us, still use a sextant, but mostly today, thanks to modern technology, the sextant is only used as a back up. Primarily, sailors use the "Global Positioning System" or "GPS" to locate their position on the planet.

Universal Time

Two important concepts related to latitude and (especially) longitude must be understood before navigating anywhere. These concepts are Local time (LT) and Universal time (UT). Local time is a measure of the position of the Sun relative to a locality. At 12 noon local time the sun is furthest from the horizon and marks the midpoint between when the sun is in the eastern half of the sky and when it is in the western half of the sky. Local time is what you and I use to regulate our lives locally, our school and work times, and meals and sleep times.

But suppose we wanted to time an astronomical event, for example, the time when the 1987 supernova was first detected. Or suppose you are listening to radio signals that have crossed multiple time zones or the international date line? A worldwide, universally agreed-on standard for time and date is needed, one that is not tied to our locality. That time is universal time (UT), which is defined as the number of hours, minutes, and seconds which have elapsed since midnight (when the sun is at a longitude of 180) in the Greenwich time zone. Another way of saying it is that Universal time (UT) is the local time in Greenwich, England, at the line of zero longitude. From this one locality, the globe is divided into many different time zones.

Going east from Greenwich, local times are later for 12 times zones, until you get halfway around the globe and arrive at the International dateline at 180 degrees. Going west from Greenwich, local times are earlier for 12 times zones, until you get halfway around the globe and arrive at the International dateline at 180 degrees. (Remember, the 180th line of longitude is the International dateline.) There, depending on whether you're eastbound or westbound, you can lose a whole day, or gain a whole day!


A sextant is an optical instrument used for the measurement of angular distance between any two objects. The sextant enables a navigator to measure the angular elevation of the sun and other celestial bodies, and from this information the navigator can work out his latitude and longitude.

Sun Sights - As a backup for the GPS when we are offshore we carry a sextant. The use of the sextant goes back for hundreds of years. The sextant is a tool that allows the user to align the sun with the horizon to measure the angle of the sun in the sky. Because astronomers have made very accurate tracks of the sun's path across the sky, if we know the exact time and date, and if we can measure the altitude and direction of the sun at a specific time, we can establish our position in Latitude and Longitude using special tables called "sight reduction tables" published for just this purpose.

Once the measurements are taken, we use the sight reduction tables to convert the data we collected to plot our current coordinates. While this is the least accurate of the navigational methods, we can use it when crossing long distances in the ocean, to help us get close enough to shore to begin our dead reckoning. Because these measurements musk be very precise, this method requires a lot of practice to get an accurate "fix" on our location. Also, we must have a clear view of the noon sun and the horizon to get an accurate reading. So if the sun is blocked by clouds or the horizon is obscured by fog or rain, this is difficult to accomplish. Also, the sextant must be held very steady to ensure accuracy. If the boat is heaving up and down due to large waves, getting an accurate fix is also difficult.

Star Sights - The sextant may also be used at night by aligning certain stars. This classic method, called "celestial navigation," is used most commonly in the open sea. In celestial navigation the navigator uses celestial bodies that have been identified and grouped into constellations since ancient times. Celestial navigation makes possible voyages across thousands of miles of unmarked water. However, it has its drawbacks: not only do you have all of the difficulties encountered during the daytime, such as pitching seas, clouds, fog, rain, snow, mist, or haze that may prevent the essential sightings of celestial bodies, you must also be able to identify the correct stars in the night sky.


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. GPS works by receiving signals from three or more satellites in "geosynchronous" orbit around the earth. 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. We always carry a handheld GPS as a backup.

For more information about using the GPS for navigation, see the navigation methods page.
For more information about how we use the GPS on Landfall, see the electronics page.



Compass Exercises

(Assuming each student or classroom is given a compass)

  1. TBD: diagram of map and Landfall with landmass locations. Which direction do we go to get to...
  2. Discussion question: Assume we want to get from point A to point B, and that point B is 100 miles away, on a direct 120 degree heading from where we are. However, there is a 1 mile long, half mile wide reef directly in our path, halfway between point A and point B. How do we get to point B safely, without hitting the reef?

Map Exercises

Looking at the globe in your classroom or a map with latitude and longitude:

  1. What country are you in at 20 degrees North Latitude/100 degrees West Longitude?
    (Answer: Mexico)
  2. What country and what major city are you in at 53 degrees North Latitude/0 degrees Longitude?
    (Answer: London, England)
  3. What country are you in at 20 degrees South Latitude/140 degrees East Latitude?
    (Answer: Australia) If you are in the state of Maine, what is your Latitude/Longitude? (Answer: 45 degrees North Latitude/70 degrees East Longitude)
  4. If you go directly west from Longitude 179 degrees West on Tuesday, what day is it when you reach Longitude 179 East?
    (Answer: Wednesday)

These sites may help in doing your calculations:

Time Exercises

If it is 9am on Friday in your classroom, what time and day is it in:

  1. Los Angeles, California?
  2. Honolulu, Hawaii?
  3. Hobart, Tasmania?
  4. Osaka, Japan?
  5. Bombay, India?
  6. Moscow, Russia?
  7. Harare, Zimbabwe?
  8. London, England?
  9. Rio de Janeiro, Brazil?
  10. Havana, Cuba?

Is it Daylight Savings Time where you are? Does that change any of your answers?
If you don't have a map or globe with time zones in your classroom, looking at this Time Zone Map might help.