FORCE & MOTION • NAUTICAL CALCULATIONS

Title: By Land Or By Sea

(Nautical Calculations — Depth, Speed and Distance)

Grade Level (s): 6-8

Introduction: Did you ever wonder why a mile is 5,280 feet but a nautical mile is 6.080 feet? The difference is a result of the curvature of the earth. The nautical mile is an international unit equal to one minute (one sixtieth of a degree) of arc at the equator. A nautical mile works out to be about 1.15 of a mile. A nautical “knot” is a measure of speed, equal to one nautical mile per hour. To determine this speed, sailors would throw lines over the sides of the ships. Each line was divided into 47 ft. 3 in. sections called “knots”. The line was run over the ship’s side while a 28-second glass was emptying itself. The length of the knot was derived from the proportion that one hour (3600 seconds) is to 28 seconds as one nautical mile (6080 feet) is to the length of one knot (47 ft. 3 in.).

A “fathom” is the measurement determined by the arm span of an average sized man — about 6 feet. Sailors would often use their own body measurements to determine the depth of the ocean.

A “league” is three nautical miles. Therefore, twenty thousand leagues traveled under the sea would measure about 69,000 miles traveled on land!

Learner Objectives:

• The student will be able to combine math and science by using oceanography facts.
  
  
• The student will be able to convert ocean measurements using nautical calculations. By allowing students to convert distance and speed measurements to nautical units, they will gain an understanding of knots and fathoms.

Florida Sunshine State Standards:: Math: MA.B.1.3.2, MA.B.2.3.2, MA.B.3.3.1

Competency-Based Curriculum: Math: M/J-3-II-10B, II-11-B, II-12-B, II-13-C, M/J-1-III-1-A-a. Science: M/J-1-I-B

Conversion Table:

Materials:

conversion table
paper
pencil

Activity Procedures:

1. Each student will be given a conversion table to be used in the calculation and conversion of distance and speed measurements.
   
   
2. Using the conversion table, the students will then be asked to calculate the following conversions:
   1. How many feet are in three miles? In three nautical miles?
      
      
   2. How many feet are in a league?
      
      
   3. The deepest point in the ocean is at the Marianas Trench, which has a depth of 35,802 feet. Convert this to fathoms and then to leagues.
      
      
   4. The bluefin tuna, which weighs 1.500 pounds, is the largest and fastest marine fish. It swims up to 55 miles per hour. How fast is this in knots?
      
      
   5. We discussed that twenty thousand leagues under the sea converts to about 69,000 miles. Is it possible for such a depth to occur in the ocean? Write a three-paragraph paper on why or why not.
      
      
   6. How many fathoms are in 6.35 cable lengths.
      
      
   7. Since 10 chains equals 201.17 metes, how many meters does one chain equal?
      
      
   8. Since 1 knot equals 1.15 mi/hr, how many miles per hour are you traveling if you are going 15 knots?
      
      
   9. How many feet are in a cable length?
      
      
   10. How many miles are in a league?
       
       ANSWERS
3. Students will then be asked to create their own conversion word problems to be used as problems of the day by the teacher or to be used to share with each other.

Student Assessment:

1. Allow students to answer critical thinking questions about conversion of measurements.
   
   
2. Allow students to create their own question about conversion
   
   
3. Allow students to look into the history of navigation and find out more about nautical measurements.

Activity Extensions:

1. Encourage students to find other nautical terms and learn about their origin. (Social Studies, Science)
   
   
2. Allow students to write a report on the different nautical terms found (Language Arts)
   
   
3. Allow students to use other conversion tables such as monetary conversions of different countries to change to the U.S. monetary system. (Social Studies, Math)
   
   
4. Allow students to create their own conversion tables, even if it contains nonsensical terms, to get used to conversion. (Language Arts, Math)

Home Learning Activity:
Student must create five conversion questions referring to the conversion table.

References/Related Links:

http://www.cln.org/themes/earlynavigation.html
www.aquanet.com
http://ils.unc.edu/maritime/home.html

Answer Key to Activity Procedure #2

1. There are 15,840 feet in three miles (5,280 X 3). There are 18,240 feet in three nautical miles (6080 X 3).
   
   
2. There are approximately 18,216 feet in a league (3 X 1.15 X 5,280).
   
   
3. There are 5,967 fathoms (35,802 _ 6). There are approximately 2.6 leagues (35802 –5280 X 1.15 – 3).
   
   
4. The bluefin tuna swims about 47.83 knots (55 ÷ 1.15).
   
   
5. No, this is not possible because we said that the Marianas Trench is the deepest point in the ocean and it is only 35,802 feet.
   
   
6. There are 635 fathoms (100 X 6.35).
   
   
7. There are 20.117 meters in one chain (201.17 –10)
   
   
8. You are traveling 17.25 miles per hour (15 X 1.15).
   
   
9. There are 600 feet in a cable length (100 X 6)
   
   
10. There are approximately 3.45 miles in a league (6080 X 3- 5280).