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U.S. Navy Museum Cold War Gallery Lesson Plan
Missiles on Target with Geometry
Developed by Alan Skripsky, Tremper High School, Kenosha, Wisconsin
2011 Naval Historical Foundation STEM teacher fellowship
  Instructional Goal

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Geometry teachers who are looking for a short application activity to generate curiosity and interest in 3-dimensional geometry can guide
their students through a quick look at the U. S. Navy's fleet ballistic missiles (FBMs). Not only will the students learn a bit of history of applied technology used to win the Cold War, they will quickly recognize how cylinder volume is important in estimating solid propellant rocket motor capacity of the various stages of a submarine ballistic missile.

In this lesson students will make simple scale models of large, 3-dimensional shapes to make estimates of surface area and volume. Students will discuss space limitations, and buoyancy considerations aboard a modern nuclear-powered ballistic missile submarine. Teachers are free to expand or shorten the lesson as needed.

Lesson Activities
  1. View the US Navy YouTube Video "SSBN History", which looks at the history of the fleet ballistic submarine nuclear deterrence mission.
  2. Recognize 3-dimensional geometric shapes, associated formulas, and model problem solving in the Activities below.
  3. Verify the accuracy of estimations.
  4. Discuss space limitations that impact the design of a modern U.S. Navy ballistic missile submarine.

Trident II (D5) Missile is the sixth generation of the U. S. Navy's Fleet Ballistic Missile (FBM) program which started in 1955 and is still being used today. These missiles carry multiple nuclear warheads and are launched from U.S. Navy nuclear-powered submarines.

The length of the Trident II (D5) Missile is 44 ft.

The Trident II (D5) Missile consists of:
  • a first stage (FS) motor section
  • an interstage (IS) section
  • a second stage (SS) motor section
  • an equipment section (ES)
  • a nose fairing (NF) section that contains the third stage
  • a nose cap at the top of the NF deploys an aerospike after launch
Video Resources

play videoAll Hands TV: SSBN History:  This 2009 All Hands TV looks at the history of the fleet ballistic submarine (SSBN) nuclear deterrence mission. SSBNs have been providing the US with security for many, many years.

Click icon to download Activity in PDF format
Geometric Shapes

Question:  What three-dimensional geometric shape does the first stage of the Trident II look like?

Discuss the second stage, third stage, and nose fairing also.

The first stage section includes the first stage rocket motor, Thrust Vector Control (TVC) system, and the components to initiate the first stage ignition.

Question:  If you had to cover the lateral surface area of the first stage with 3 x 5 index cards, what formula would you use to determine how many cards to use?

Class Discussion:  If you had a cylinder the same size as the first stage of a Trident II that were made of paper, and you cut it down the side and unfolded it, what would it look like?


Class Discussion:  Discuss the unfolded shape of the second stage, and third stage also. The height of the second stage is 7 feet with a radius of 42 inches. The height of the third stage is 8 feet with a radius one-third the size of the first stage. Note:  the third stage is inside the nose fairing.


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