Exercises 11–17 involve the notion of windchill temperature— see Example 7 in §...

Exercises 11–17 involve the notion of windchill temperature— see Example 7 in § 2.1, and refer to the table of windchill values on page 85

Windchill tables are constructed from empirically derived formulas for heat loss from an exposed surface. Early experimental work of P. A. Siple and C. F. Passel,⁴ resulted in the following formula:

Here W denotes windchill temperature (in degrees Fahrenheit), t the air temperature (for t < 9.14^oF), and s the windspeed in miles per hour (for s ≥ 4 mph).⁵

(a) Compare your answers in Exercises 11 and 12 with those computed directly from the Siple formula just mentioned.

(b) Discuss any differences you observe between your answers to Exercises 11 and 12 and your answers to part (a).

(c) Why is it necessary to take t < 91.4^oF and s ≥ 4 mph in the Siple formula? (Don’t look for a purely mathematical reason; think about the model.)