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Activity: Navigating with Nautical Charts
NGSS Science and Engineering Practices
NGSS Crosscutting Concepts
NGSS Disciplinary Core Ideas


  • Figs. 8.29–8.31
  • 3 x 5-inch index card or similarly-sized heavyweight cardboard
  • Ruler
  • Pencil
  • Scissors
  • Drawing or drafting compass (optional)


Image caption

Fig. 8.29. An example of how to make navigation triangles used to plot a course.

Image copyright and source

Image by Byron Inouye


Image caption

Fig. 8.30. Use your navigation triangles to transfer compass bearings between reference points and the compass rose. Note that the two longer X-marked edges always remain parallel and opposite from each other.

Image copyright and source

Image by Byron Inouye


Image caption

Fig. 8.31. Nautical chart of Kāne‘ohe Bay, O‘ahu, that shows Mokoli‘i, Kualoa Point, and He‘eia Kea Boat Harbor, as well as the major boat channel, nautical features, and islands within the bay.

Image copyright and source

Image adapted from NOAA Chart 19359 courtesy of National Oceanic and Atmospheric Administration (NOAA) and modified by Narrissa Spies


A. Construct navigation triangles

  1. Navigation triangles are tools used by navigators to plot courses and transfer compass bearings within a nautical chart (Fig. 8.29).
  2. Construct a pair of navigation triangles from a single index card.
    1. On the blank side of the index card, mark the two longer (5-inch-long) edges with “X” marks (Fig. 8.29).
    2. Mark the two shorter edges of the index card with “O” marks (Fig. 8.29).
    3. Draw a diagonal line using a ruler across the index card from the bottom-left corner to the top-right corner.
    4. Mark the two halves of the index card (now two right triangles) “#1” and “#2” (Fig. 8.29).
    5. Carefully cut the index card along the diagonal line to separate triangle #1 and triangle #2.


B. Triangulation

Imagine that you are lost and floating in the middle of Kāne‘ohe Bay, Hawai‘i. You are trying to reach He‘eia Kea Harbor safely without striking any coral reefs.


  1. In order to navigate safely, you will first need to determine your current location or position on the nautical chart (Fig. 8.31). This can be accomplished through triangulation. Triangulation is a technique used to determine the location of one unknown point by using the locations of two or more known points around it.
  2. You can see two distinct landmarks around you:
    1. The peak of Mokoli‘i (Chinaman’s Hat) is at bearing 20° on your compass.
    2. Kualoa Point is at bearing 340°.
  3. Where are you in Kāne‘ohe Bay? Use the navigation triangles to transfer or shift the landmarks’ compass bearings to the nautical chart.
    1. Align the X-marked edge of triangle #1 to the 20° mark on the compass rose. The edge must pass directly through the cross in the center of the compass rose (Fig. 8.30 A).
    2. Press down firmly on triangle #1 to maintain this original compass bearing.
    3. Place triangle #2 next to triangle #1 with their unmarked diagonal edges touching. The two X-marked edges should remain parallel to each other (Fig. 8.30 B).
    4. Carefully slide triangle #2 along the diagonal edge until the X-marked edge reaches the map symbol for the peak of Mokoliʻi (Fig. 8.30 C). Take caution not to move triangle #1 while sliding triangle #2. Always keep the two X-marked edges parallel and opposite from each other.
    5. Use the X-marked edge of triangle #2 to draw a straight line through the map symbol for Mokoli‘i (Fig. 8.30 D). If needed, you can use a ruler to extend the X-marked edge of triangle #2. Use a ruler to lengthen this straight line across the entire nautical chart. Label this line with the compass bearing “20°”.
    6. You have now used the navigation triangles to transfer the compass bearing from the compass rose to the map symbol or reference point (e.g., Mokoli‘i). Your ship’s position is somewhere along this line.
  4. Repeat steps 3a through 3e for the tip of Kualoa Point, spotted at bearing 340° on your magnetic compass.
  5. Locate the point on the nautical chart where your two drawn lines intersect. Label this point as “A”. This point marks your ship’s current location.


C. Plotting a course

  1. On the nautical chart, locate the boat channel closest to point A. Boat channels should have deeper water (indicated by white color) and are located between two dotted lines on the nautical chart.
  2. Mark the closest point of the near boat channel as point “B”.
  3. Use a ruler to draw a straight line between point A and point B.
  4. Determine the compass bearing for the course now plotted between point A (your current position or location) and point B (the nearest boat channel).
    1. Line up the X-marked edge of one of the navigation triangles to the A-to-B course line.
    2. Use the second navigational triangle to transfer the compass bearing of the A-to-B course line to the compass rose on the nautical chart (this technique is the reverse of the procedure described in Part B above).
    3. Write the compass bearing above the A-to-B course line.


D. Determining course distance

  1. Determine the distance of the course plotted above from your current position (point A) to the nearest boat channel (point B).
    1. Use a ruler to measure the length of the A-to-B course line. A drawing compass could also be used for this technique.
    2. Align the ruler or drawing compass with the scale at the edge of the nautical chart.
    3. Determine the distance of the A-to-B course in nautical miles.
    4. Write the distance below the A-to-B course line.


E. Sailing in to safe harbor

  1. Repeat the steps in Part C and Part D to plot course lines into He‘eia Kea boat harbor.
  2. Be sure to stay within the boat channel or at least in waters deeper than 5 feet.
  3. Record all course compass bearings and distances on the nautical chart.


Activity Questions
  1. List all the kinds of navigation information and aids shown on the nautical chart (Fig. 8.31).
  2. Where is the deepest part of the bay shown on the nautical chart?
  3. What environmental factors could affect the accuracy of navigation?
  4. Imagine that you have discovered sunken pirate treasure inside a deep shipwreck that is not marked on any nautical chart.
    1. Describe how you would you use the navigational tools in this activity to locate this shipwreck a second time on a nautical chart.
    2. Describe how you would plot a course to this hidden shipwreck from your home harbor.
  5. Assume that the peak of Mokoli‘i is exactly 0.3 nautical miles away from Kualoa Point. Use trigonometry to calculate the following distances:
    1. Distance from point A (determined in procedure b, step 5) to the peak of Chinaman’s Hat.
    2. Distance from point A to Kualoa Point.
    3. Use the scale in the nautical chart to estimate the distances described in questions 5b and 5c above. How do these chart estimates compare to your calculations?
  6. Assume that you are sailing at a constant speed of 10 knots (nautical miles per hour).
    1. How much time will it take to sail from point A to point B?
    2. How much time will it take to sail from point A to the final destination at He‘eia Kea boat harbor using the course you plotted?
    3. How does this total course time compare to course times calculated by your classmates?
Exploring Our Fluid Earth, a product of the Curriculum Research & Development Group (CRDG), College of Education. University of Hawaii, 2011. This document may be freely reproduced and distributed for non-profit educational purposes.