Measuring speed - Arctic Tern

 

Subject :  Physics

Date:

Teacher:

 

 

Title:  Measuring speed - instantaneous speed,  average speed, measurement error

Central Concept:   How to measure speed.

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 instantaneous speed?

What is average speed?

How do we measure speed?

How does uncertainty impact our results?

 

Content and Skills:

Develop a mathematical understanding of average speed (B.4)

Understand methods for taking measurements of speed (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   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. How was the distance measured?  
  1. Show the measurement page on The Arctic Tern Migration Project website
  2. Show the Bird Migration tracking website
  3. Activity :  Give students time to read the websites and answer the following questions:
  1. How does the tracking device work?  
  2. Why was this method chosen over GPS?
  3. What is the accuracy of the light-level geolocators?
  1. The position accuracy for the light-level geolocators plus or minus 150km.  This means that if we measure the daily travel of a bird by getting its position in the morning and then measuring the distance between the two points we have a potential error of up to 300 km.  This potential error, or uncertainty, represents the uncertainty contained in the two measurements.
  1. The information published in the The Arctic Tern Migration Project website suggests that the Arctic Terns travel an average of 330 km per day on their southern migration and 520 km on their northward route.
  2. The measurement uncertainty  the tracking device is 300 km.  This means that if the bird flies 330 km in a single day the device could produce a measurement which ranges anywhere from 30 km to 630 km.  How can they then be certain average the distance travelled by a bird is a day is 330 km?   Discussion
  1. It should be clear by now that the light-level geolocators do not provide the accuracy necessary to measure the daily travel of the birds.  However, if we look at a longer travel distances the error might play a smaller role.
  1. As the image shows a position uncertainty of 150 km does not give enough accuracy to measure the distance traveled in a single day.  If we extend the distance traveled to 3300 km, the uncertainty plays a smaller role in the measurement.
  1. How to quantify uncertainty or error.  One of the best ways to characterize error is as a percentage of the amount being measured.  In other words an 150 km error might be good enough for a measurement of 5000 km, while if we are measuring shorter distances the same uncertainty might not be adequate.
  1. For the example shown above the error for a single day is 300 km while the distance traveled is 330 km which means that the error as percentage of the measurement is
  2. When we look at a distance traveled of 3300 km the measurement uncertainty is still 300 km because we are only interested in the end points.  With a traveled distance of 3300 km the error as percentage of the measurement is
  1. Introduce the concept of instantaneous speed. What device do people use on a regular basis which measures instantaneous speed?  The automobile speedometer
  2. In his paper on the research documenting the migration of the Arctic Tern, Egevang states that the flight speed of the Arctic Tern was measured to be 11.3 m/s which corresponds to a daily travel distance of 976 km.  However the maximum average daily speed did not exceed 520 km.  How can this be explained?
  1. The Arctic Tern is capable of flying thousands of miles without landing, but as the numbers show it does not fly at full speed the whole time.  Assuming that it travels at about 10 m/s for part of the day, and for the remainder of the day it glides without making significant progress, how many hours per day must it travel at 10 m/s?
  2. If we were to assume that the Arctic Tern travels at a constant speed, at what speed (in m/s) must it travel to cover 520 km per day?

Note:  The example given for 10 days of travel assumes that the bird travels in a straight line, this is not the usual case.  Classroom discussion:  In a more realist and less linear travel path would just having the end points be enough to calculate the distance traveled?  Using graph paper can students estimate the distance traveled of a more complex path?  What kind of assumptions must be made?

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 difference between instantaneous and average speed
  2. Understand how uncertainty plays a role in measuring quantities
  3. Understand the relationship between measurement uncertainty and scale of quantity measured
  4. Be able to question measurement assumptions.

 

Assessment / Assignment(s):

Homework:

Using graph paper draw the first five days of measurements from the graph shown above, but do not use the same assumed path.  Now plot a path where the each daily travel falls within the uncertainty circles.  Can you come up with a longer travelled distance?  Using a ruler estimate the value of the distance traveled.