


Miniature Missiles!
Developed by Rhonda Crawford, Oak Grove High School, Hattiesburg, Mississippi
2011 Naval Historical Foundation STEM teacher fellowship



Instructional Goal
The nuclear ballistic missiles have played a vital role in protecting our country against nuclear warfare. Even though we have not had to use them, potential enemies know that we have them and it serves as a deterrent to keep an enemy from attacking the U.S. In this unit of study students will create a 3D drawing of a missile and build a model to scale of the missile.
Types of Fleet Ballistic Missiles
A missile is a solidpropellant, inertially guided weapon. They have supporting system components such as navigation, launcher, targeting/guidance from the SSBN.
The purpose of this sequential generation of strategic weapons is to serve as a deterrent to prevent nuclear war. These missiles are a major contribution of the Navy and the submarines carry 24 nuclear tipped ballistic missiles. It assures a potential enemy that a nuclear attack on the US will be followed by a devastating nuclear blow.
Polaris
A1 Polaris:
 1st successful underwater missile launched in 1960 from the USS George Washington and was retired in 1965
 28' long, 54" diameter
 Weight: 28,000 lbs.
 Range of 1,380 miles
A2 Polaris:
 Launched in 1961 from the USS Ethan Allen and was retired in 1971
 31' long, 54" diameter
 Weight: 32,500 lbs.
 Range of 1,730 miles
A3 Polaris:
 Launched in 1963 from the USS Andrew Jackson and was retired in 1981
 32' long, 54" diameter
 Weight: 35,700 lbs.
 Range of 2,880 miles
Poseidon
C3 Poseidon:
 This was an improvement of the Polaris to maximize the effectiveness of the Navy's FBM weapon system
 It was a 2stage, solid propellant missile, capable of being launched from a submerged FBM submarine
 Launched in 1970 from USS James Madison and was terminated in 1992
 34' long, 74" diameter
 Weight: 64,600 lbs.
 Range of 2,880 miles
Trident The Trident program was established to develop an improved long range missile to expand the submarine operating area. This provides the US with a credible deterrent to nuclear war in the 1980s and beyond.
Trident I:
 3stage solid propellant, inertially guided that uses an extendible aerospike to increase its aerodynamics
 First launched from a submarine in 1979
 34' long, 74" diameter
 Weight: 73,000 lbs.
 Range of 4,600 miles
Trident II:
 3stage solid propellant, inertially guided, submarine launched that will be the US's strategic seaborne deterrent into the next century
 First deployed from a submarine in 1990
 44' long, 83" diameter
 Weight: 130,000 lbs.
 Range: > 4,600 miles
Teacher Help 
Download Teacher Help Guide in PDF format by clicking icon 

Download Lesson Plan Resource Kit by clicking icon 

Video Resources
Fleet Ballistic Missile Display: This is a video of the "Fleet Ballistic Missile" display in the Covert Submarine Operations exhibit in the Cold War Gallery.
Operation Dominic, 1962: The launch of a Polaris A1 submarine launched ballistic missile from the nuclear submarine USS ETHAN ALLEN, and the ensuing nuclear detonation of its warhead, are shown in this clip from the 1973 U.S. Navy film "Our Crucial Deterrent". Source: Naval History and Heritage Command, Photographic Section, UM23.
First Poseidon Missile Launch: The 1972 launch of a Poseidon submarine launched ballistic missile is shown in this clip from the 1973 U.S. Navy film "Our Crucial Deterrent". Source: Naval History and Heritage Command, Photographic Section, UM23.
Trident Missile Launch: Dual launch of Trident C4 missiles, the fifth type of ballistic missile, first launched in 1977 and retired in 2005. From the Chief of Naval Operations, Submarine Warfare Division.
Trident Missile Launch from the USS Nevada: Launch of a Trident D5 missile, the sixth type of ballistic missile, and the only ballistic missile still deployed on U.S. and U.K. ballistic missile submarines. USS Nevada was converted from Trident C4 to D5. From navy.mil

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Miniature Missiles
Directions:
This assignment includes 2 parts. Each person will design your assigned missile in 3D (using a program such as SolidWorks or Google SketchUp) or on graph paper. Your group will then create a scale model of your missile using modeling clay.
 Name of missile: ________________________________
 Dimensions of the missile: (Use the "Types of Missiles" tab)
___________Length ___________Width ___________Heigth
 To complete the drawing and the model, use a scale of 4 ft to 1 in. Convert the dimensions of the missile for the drawing and model.
___________Length ___________Width ___________Heigth
 Using the missile images in the "Types of Missiles" tab, create a model using modeling clay of the missile to scale.
Evaluation:
 Scale drawing (individual assignment)
 Model of missile (group assignment)
Types of Missiles

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Massive Missile Insides
The figure below shows the dimensions of the 6 Fleet Ballistic Missiles.
 Diameter for the Polaris A1, A2 and A3 is 54 inches
 Diameter for the Poseidon and Trident I is 74 inches
 Diameter for the Trident II is 84 inches
The volumes of the ballistic missiles are calculated using the lengths of the motors and the radius. The motor of the 3rd stages of the 3 latest missiles is about onethird of the diameter, so in order to find the volume of the 3rd stage divide the diameter by 3, then calculate radius and the volume of the 3rd stage. The volume of each motor is then added to get a total volume for each missile.
Use the formula for the volume of a cylinder to find the volumes of each missile motor section. The formula for the volume of a cylinder is V=Πr^{2}h, where V is the volume, r is the radius of the cylinder and h is the height of the cylinder.
Using the information above calculate the volume of each missile.
Calculations for Missile Volumes
Using the formula for the volume of a cylinder V=Πr^{2}h, these calculations were made:
Polaris A1^{ } 
volume of stages 1 and 2 combined. V=Π(2.25)^{2}(14) = 70.875Π 
Polaris A2^{ } 
volume of stages 1 and 2 combined. V=Π(2.25)^{2} (17) = 86.0625Π 
Polaris A3^{ } 
volume of stages 1 and 2 combined. V=Π(2.25)^{2}(18) = 91.125Π 
Poseidon C3^{ } 
volume of stages 1 and 2 combined. V=Π(3.08)^{2}(20) = 189.728Π
volume of stage 3. V=Π(2.06)^{2}(8) = 33.9488Π
volume of stages 1, 2 and 3 combined. V=189.728Π+33.9488Π = 223.6768Π 
Trident I C4^{ } 
volume of stages 1 and 2 combined. V=Π(3.08)^{2}(20) = 189.728Π
volume of stage 3. V=Π(2.06)^{2}(8) = 33.9488Π
volume of stages 1, 2 and 3 combined. V=189.728Π+33.9488Π = 223.6768Π 
Trident II D5^{ } 
volume of stages 1 and 2 combined. V=Π(3.5)^{2}(29) = 355.25Π
volume of stage 3. V=Π(2.33)^{2}(8) = 43.4312Π
volume of stages 1, 2 and 3 combined. V=355.25Π+43.4312Π = 398.6812Π 
** Remember that in order to find the 3rd stage radius, first divide the diameters by 3, then by 2. 

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How Far will a Missile Go?
What does the volume of a submarine missile have to do with the distance it travels?
Below is a table showing the total missile volumes and their ranges for the six U.S. Navy Fleet Ballistic Missiles.
Use the table above to complete the questions below:
 Using Grid paper make a scatter plot to display the relationship between total missile volume and the range of the missile. Describe the relationship you see.
 Draw a "best fit" line through the points on the graph. Use the line to find the equation for the line of fit. Write the equation for the line in slopeintercept form.
y = 4.921x + 592.652 (This is the calculator generated equation. The equations that are configured by hand may be close but probably not exact.)
 Use the graph of the line and the equation of the line to identify the slope and the yintercept. Explain what these values tell about the volume and the range of the missiles.
The slope is 4.921 and the yintercept is 592.652. The slope tells me how much the volume changes with the addition of each mile. The yintercept tells me what the range would be if the volume of the missile is 0, which does not make sense in this real world situation.
 Use your equation to find the range of the missile that has a volume of 500 cubic feet.
~3053 miles
 Use your equation to find the range of the missile that has a volume of 1500 cubic feet.
~7973.8 miles
 Use your equation to find the volume of a missile that traveles a range of 3500 miles.
~591 cubic feet
 Use your equation to find the volume of a missile that traveles a range of 800 miles.
~43 cubic feet
 Using Technology: Using the graphing calculator, enter the data points into the list menu.
 Use the calculator to determine the equation that will best describe your data. Compare it to the equation you developed in question #2.
 Using the table set and table key options on the calculator, find the range for a volume 500 cubic feet and 1500 cubic feet.
 Using the table key option on the calculator, find the volume of a missile that traveles 3500 miles; and 800 miles.



