A CIESE Realtime Data Project

CIESE -Navigational Vectors - Lesson #2


Lesson #1

Lesson #2
Graphical Addition of Vectors


Lesson #3

A) Your Mission: Plan a flight from your state capital to Chicago, Illinois with a stop over in St. Louis, Missouri.

  1. Locate a map of the U.S. (Try the Reference Material section for online maps.) Find your state capital on the map.
  2. Draw a vector from your state capital to St. Louis. Using a ruler, compass rose or protractor, and the map, determine the flight's:

    a) Distance (km)
    b) Directional heading in degrees (as measured from 0º North)
    c) Displacement 

  3. Draw another vector from St. Louis to Chicago. Again using a ruler, compass rose or protractor, and the map, determine this flight's:

    a) Distance (km)
    b) Directional heading in degrees (as measured from 0º North)
    c) Displacement 

  4. Check your displacements using the How Far Is It? web site for each leg of the flight.

    a) Displacement from state capital to St. Louis (km and degrees)
    b) Displacement from St. Louis to Chicago (km and degrees)

B) How far has the plane traveled?

  1. Find the total distance the plane traveled by adding the distance that each vector represents.

  2. Does this value indicate how far the final destination is from the origin?

C) How far is the plane from your state capital at the end of the trip?

The value that you are looking for is the total displacement which is the distance and direction from the point of origin to your final destination. To determine this you must add the vectors:

 

Vector Addition Instructions

  • Draw the first vector on your map (your state capital to St. Louis).
  • Draw the second vector on your map (St. Louis to Chicago) with the tail of this vector beginning at the head of the first vector.
  • Draw a third vector called the resultant from the tail of the first vector to the head of the second vector.
  • Measure the length of the resultant vector (km) and its directional heading (degrees) from your state capital. This resultant represents the total displacement of the plane. 


  1. What is the resultant displacement of the plane from your state capital to Chicago (as measured from your vector diagram)?

  2. How did your measured displacement compare with the displacement found using the How Far Is It? web site? 

  3. Do your results make sense? Why or why not?

D) Ready to become a Pilot?

  1. Think of a situation (other than flying) where it would be preferable to know displacement rather than distance traveled.

  2. Think of a situation (other than flying) where it would be preferable to know distance traveled rather than displacement.

  3. Demonstrate how a magnetic compass could be used to find the displacement of a hiker.

  4. Create a vector game or puzzle for your classmates to solve. It could be a board game, a maze, a riddle, a mystery, a treasure hunt or anything else that you wish. It should use 5 vectors. Trade games/puzzles with your classmates and see if they solve it correctly.