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U.S. Navy Museum Cold War Gallery Lesson Plan
Sailing Blind: The Challenges of a Submarine's Navigator
Developed by John Clark, Physics Teacher and Military Historian, Deltona High School, Deltona, FL
2012 Naval Historical Foundation STEM-H Teacher Fellowship

  Instructional Goal

How does a submariner navigate when submerged? Let your students find out as they explore the concept of vector addition as used in the Navy to combine dead reckoning calculations and inertial navigation data to determine the ships position after many hours under the sea. Can the students navigate through the Strait of Gibraltar to reach a safe port?

Students will complete activities applying the concept of vector addition to a real world application - a submariner calculating the ship's position in the water while submerged.


In the early days of sailing, navigating by the stars or celestial navigation kept ships on course. A tool called a sextant allowed a sailor to calculate the ship's position with a fair degree of accuracy. A sextant allowed the navigator to determine the angle between a selected star and the horizon. The sextant measured the angle from the horizon up to the star. Using simple trigonometry a possible range of positions could be determined. By determining the angle to other stars, an accurate position can be found.

When sailing under the water getting a star fix is difficult as submarines have no windows and when it surfaces it is highly vulnerable to detection. Avoiding detection remains a submarine's greatest protection. Still, a submarine navigator must have a good sense of where the ship is even when underwater and underway.

With advances in technology it has become easier for a submarine to know its current location with high precision. Often, only putting up the periscope a few feet above the water line is enough to get a location "fix" in today's world. Ironically, while the math is automated and the data transfer lighting fast, the concept of today's state of the art GPS tracking is still based on the same "triangulation" principles used with the sextant.

So how do you navigate a submarine underwater? The answer is a combination of two systems that can calculate a ship's position - dead reckoning and inertial navigation. Dead reckoning uses a fixed starting point and then adds the speed and direction of ship to determine the current position. However going in a straight line in the ocean is difficult in comparison to dry land. Currents and tides in the water are also moving the ship around while it sails along and if these factors are not accounted for it is very likely that the navigator is not where he thinks he is.

To account for the factors of current, tides, and not steering straight, the navigator uses additional information collected from the inertial guidance system which collects data on forces acting on the ship. If a current is pushing the ship, or there is a change in speed, or there are small course changes, the inertial guidance system will collect that data for the navigator to use in adjusting the position calculation predicted by dead reckoning. The inertial guidance system uses gyroscopes and accelerometers to detect a ships movement. In a sense, the two devises sit in the middle of the ship and the ship moves around it.

Teacher Help
Download Teacher Help Guide in PDF format by clicking icon
Download Lesson Plan Resource Kit by clicking icon

Inertial Navigation systems - overview:  www.usnavymuseum.org/Ex2_Navigation.asp.

Inertial Navigation systems - how they work:  en.wikipedia.org/wiki/Inertial_navigation_system.

Gyroscopes explained:  en.wikipedia.org/wiki/Gyroscopes.

Accelerometers explained:  en.wikipedia.org/wiki/Accelerometer.

Background on Celestial Navigation:  en.wikipedia.org/wiki/Celestial_navigation.

play videoNavy Satellite Navigation Video:  This 1967 Navy film explains the highly successful Navy Navigation Satellite System (NAVSAT), which was built during the 1960's, and operated through 1996. It includes a detailed explanation of the computing equipment used to operate the system in the 1960's.

play videoReading Navy Charts:  Nautical Charts - "Reading Charts" 1999 US Navy Navigation Training.

Click icon to download Activity in PDF format
Finding the Strait of Gibraltar


Approximately 9 miles (14 km) wide at its narrowest point, the Strait of Gibraltar is the entry point into the Mediterranean Sea from the Atlantic Ocean. It's bordered by the continents of Africa and Europe, and the countries of Morocco, Spain, the British colony of Gibraltar, and the Spanish exclave of Ceuta. It is the only way for a submarine assigned to patrol the Mediterranean Sea to transit from the Atlantic Ocean. For a submerged submarine a 9 mile opening is considered very narrow and dangerous to transit submerged due to the turbulent currents. However due to the rough surface waters and extensive shipping traffic, the transit is commonly done submerged. The satellite photo to the right shows the compressed water flow as the forces of the Atlantic are pushed through a very narrow opening.


Use vector addition to adjust your dead reckoning location from where you think you are to where you really are.


Activity worksheet (basic): Click Here

Activity worksheet (advanced): Click Here


Students will work with two scenarios of data to calculate a final position. One is for a basic class and one is for a more challenging assignment.



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