Vector Addition - Arctic Tern

 

Subject:  Physics

Date:

Teacher:

 

 

Title:  Vector addition – The impact of wind velocity on bird flight

Central Concept:   How to measure the impact of wind speed on the flight of birds.

Learning Standards (National Science Education Content Standards) :

B.4 - Motions and forces

A.1.4 - Formulate and revise scientific explanations and models using logic and evidence

A.1.1 - Identify questions and concepts that guide scientific investigations

 

Essential Questions:

What is airspeed, how is it different from ground speed?

How does wind speed impact ground speed: headwind and tailwind?

Representing wind as a vector quantity?

How to add vectors graphically?

 

Content and Skills:

Develop a mathematical understanding of distance and direction (B.4)

Characterization of motion, travel versus displacement (B.4)

Scientific inquiry and reading comprehension (A.1.4, A.1.1)

 

Learning Activities:

  1. Recap of previous lesson, discuss how the work done in the Arctic Tern Migration Project showed that the arctic tern, a bird which weighs a little more than 4 ounces, travels an average of  70000 kilometers (44000 miles) per year.
  2. The map of the Arctic Tern migration (show Arctic Tern migration map from the Arctic Tern Migration Project ) illustrates a migration route that is far from the shortest possible path.  Why would a animal choose this route?  It is clearly not random, as many animals take this route year after year.
  1. Discussion what are the possible factors that could help to shape animal migration routes?  Are migration the factors which shape the migration routes the same for all animals?
  1. Are flying animals affected differently from walking animals?
  1. How are bird migrations affected?  Food for thought, show the map of prevailing winds from Prevailing Winds Wikipedia page.  How do winds impact birds migrations?
  2. Introduce the concept of relative velocity.  The velocity of an object relative to the wind can be different than its velocity relative to the ground.  Sometimes, in windy conditions, birds like seagulls can hold a position that is almost stationary in relation to the ground.  In other words although the seagulls can have a ground speed near zero meters per second, their airspeed (due to high winds) is high enough form them to fly.
  1. Wind directly impacts birds’ ability to cover distances.  Like an escalator allows people at a shopping mall to go up and down while spending less energy, a favorable wind reduces the energy required for a bird to travel.  The inverse is also true, where a head wind increases the energy need by a bird to travel.
  1. Class examples of graphic vector addition:
  1. Vectors in the same direction
  2. Vector addition - Wind speed is not in the same direction as the bird flight
  1. A more complex classroom problem:  The Arctic Tern travels south at an average rate of 330 kilometers per day, while it travels north at an average rate of 520 kilometers per day.  If we are to assume that the birds are in the air the whole time and that the different in speed is due to more favorable winds during the northward route, how much faster are the winds (in the direction of travel) during the northward migration? (Give answers in meters per second)
  1. Answer:  Distance per day = average speed(m/s) x 3600(s/hour) x 24(hour/day) and speed = bird speed + wind speed

Using these equations we establish that the northward speed
v n is and
v s is
therefore the difference in wind speed is

v n - v s = 6m/s - 3.8m/s = 2.2 m/s

Note:  The migration of the Arctic Tern poses some questions which can foster classroom discussion.  

  1. Why is it that the Arctic Tern travels at a much faster rate during its northern migration then when it is going south?  
  2. Wind speed likely plays a role, but what other things might slow down a bird or make it go faster?  
  3. Availability of food in the Atlantic hot spot where they spend 25+ days on their way south is a factor, but what about factors such as competition among Arctic Terns (or other species)?
  4. What other questions can be posed about the information on the Arctic Tern Project website?

Equipment / Materials:

Internet access – projector or computer lab

Wikipedia page on the Arctic Tern - http://en.wikipedia.org/wiki/Arctic_Tern

Wikipedia page on Prevailing winds - http://en.wikipedia.org/wiki/Prevailing_winds

The Arctic Tern Migration Project - http://www.arctictern.info

Expected Outcomes:

Students should:

  1. Understand how vectors can be added
  2. Understand how to represent information about velocity as vectors
  3. Be able to add two vectors graphically.

 

Assessment / Assignment(s):

Homework:

Vector addition - add 2 vectors

  1. A bird is traveling west at 4 m/s and experiences a northward  wind at 4 m/s graphically represent the velocity vectors of the wind and the bird and add them graphically.

Extra credit - add 3 vectors

  1. what is the relative speed between a boat which is being dragged south at 3 m/s by a river current, and a bird who is flying north at 5 m/s while the wind is pushing it in a western direction at 8 m/s?