CHAPTER 13 PROJECT
Many mathematical equations-or models, as they are sometimes referred to-involve radical expressions. In this project, we will investigate one of these models. The model helps us understand the calculation of windchill factors. We will investigate the model using English and the metric systems of measurement.
Part I
The term "windchill" was first used by an Antarctic explorer, Paul Siple, in 1939. He described the chilling effect of the wind when combined with a low air temperature on the human skin. Siple and Charles Passel were responsible for the first wind chill formulas, which were used until the winter of 2001. At that time, the United States and Canada revised the formulas after extensive experimentation revealed some of their shortcomings.
One form of the Siple-Passel wind chill formula is
where t is the actual temperature in Fahrenheit degrees and v is the wind velocity in miles per hour.
One form of the revised wind chill formula is
where t is the actual temperature in Fahrenheit degrees and v is the wind velocity in miles per hour.
1. Write both formulas for the windchill factor, given the air temperature of 32°F.
2. Complete the following table, which calculates the windchill factor for both formulas if the temperature measures 32°F and the wind velocity, miles per hour, is that shown in the table.
|
Wind speed, v,
mph |
10 |
15 |
20 |
25 |
30 |
35 |
40 |
|
Siple-Passel wind chill factor, T, °F |
|
|
|
|
|
|
|
|
Revised wind chill factor, T, °F |
|
|
|
|
|
|
|
3. Describe what is happening to the measured temperature of 32°F as the wind speed increases. That is,
what do you "feel" is happening to the temperature?
4. Graph both equations in step 1 on the same coordinate plane.
5. Describe the difference in the windchill factor obtained by the two equations.
6. Repeat the first five steps for a measured air temperature 0°F.
7. Compare the tables and graphs you have produced, and describe what happens
when the wind speed is held constant and the temperature is dropping.
Part II
One form of the Siple-Passel windchill formula is given by the equation
where t is the actual temperature in Celsius degrees and v is the wind velocity in kilometers per hour.
One form of the revised windchill formula is given by the equation
where t is the actual temperature in Celsius degrees and v is the wind velocity in kilometers per hour.
Repeat steps 1 through 7, using 0°C and -10°C as the air temperature. Compare your findings from Part I and part II.
Part III
Additional adjustments are being proposed to the revised Siple-Passel formulas fin order to take account of factors that reflect one's comfort level with the temperature and humidity. Find a reference that discusses one of these concepts, and write a short summary of your findings. Be sure to document your reference source.