A CIESE Realtime Data Project

CIESE -Navigational Vectors - Lesson #1

Lesson Index

Lesson #1
Scalars and Vectors

Lesson #2


  1. What is your hometown? Obtain a map of your state. Locate your hometown on the map.
  2. What is your state capital? Locate your state capital (or another large city) on the map. On your map, draw a line between your hometown and your state capital.
  3. Suppose that there is an airport in both of these locations. You must plan a flight from your hometown to your state capital. Use a ruler and the scale on your map to determine how far the plane would travel. This value is the distance. Distance is a scalar value.
  4. If the distance you determined is not already in kilometers (km), convert it to km using a unit conversion calculators.


Can you fly your plane from your hometown to your state's capital knowing only the distance??? OF COURSE NOT .... as a pilot, you need to know direction.

  1. Using a compass rose or a protractor and your map, find the direction that a pilot would need to head the plane to go from your hometown to your state capital. Express your direction as a degree heading from North (0º).
  2. Now express the distance and direction together (example: 10 km at 37o). Distance and direction, together, is called displacement. Displacement is a vector.
  3. Check your answer on the How Far Is It? web site. What is that value for displacement?
  4. How did your values for displacement compare?
  5. Use your knowledge of vectors to describe the flight path of a plane between your hometown and state capital.

Scalars and Vectors

In the previous sections, you saw the difference between distance and displacement. As was mentioned, one is a scalar, and the other is a vector. But what are scalars and vectors?

A scalar is just a regular number. You've been using scalars for a long time now. Your height, how many dollars you have, and how much time has gone by in this class so far - all of these are scalars. No big deal, right? The only information a scalar gets across is the size of something, which we call magnitude. Scalars only have a magnitude, or size.

A vector is like an "enhanced" number. It also has a magnitude (size), but in addition, it contains a direction, which is usually given in degrees. Because of this, a vector is written differently than a scalar. The most common way of writing a vector is to draw it using an arrow. The length of the arrow represents the magnitude, and the direction the arrow is pointing in represents...well, the direction. Here's an example:

If you took out a ruler and measured the length of the arrow, that would be the vector's magnitude. And the direction is due East. (If we set North as 0º, which is what pilots do, then the vector above has a direction of 90º. Check out the tool that pilots use to measure direction - the compass rose.)

So, now do you see why distance is a scalar and displacement is a vector? Distance is simply how far you have moved, while displacement is where you are in relation to where you started out from.

For example, say I walk 10 feet North and then 8 feet South. What is the distance I have walked? What is my displacement? Let's see:

Get it?
, I have walked a distance of 18 feet. However, displacement is where you are in relation to where you started out from. In this case, my displacement is 2 feet at 0º (North). Get it?

  1. Draw a vector on your map from your hometown to your state capital. Is the tail or the head of the vector at the state capital?

Ready to Become a Pilot?

  1. The following information is important for pilots to know for any airplane flight. Which of these quantities are vectors and which are scalars? Why?

    • Number of passengers
    • Plane speed
    • Plane velocity
    • Distance traveled
    • Flight displacement
    • Flight duration
    • Plane Altitude
    • Acceleration of plane
    • Deceleration of plane
    • Amount of fuel needed
  2. Give examples of other vector and scalar quantities that you use or encounter every day.
  3. In what other areas other than flight would knowledge of vectors be useful?
  4. Imagine that you are a pilot ready to fly between two cities. You must first file a flight plan. What do you think should go in a flight plan? Choose any two cities, devise your own version of a flight plan for this trip, and share it with the rest of the class.