(Science: wind-chill temperature) How cold is it outside?...

(Science: wind-chill temperature) How cold is it outside? The temperature alone is not enough to provide the answer. Other factors including wind speed, relative humidity, and sunshine play important roles in determining coldness outside. In $2001,$ the National Weather Service (NWS) implemented the new wind-chill temperature to measure the coldness using temperature and wind speed. The formula is given as follows: \[ t_{w c}=35.74+0.6215 t_{a}-35.75 v^{0.16}+0.4275 t_{a} v^{0.16} \] where $t_{a}$ is the outside temperature measured in degrees Fahrenheit and $v$ is the speed measured in miles per hour. $t_{\mathrm{w} c}$ is the wind-chill temperature. The formula cannot be used for wind speeds below 2 mph or for temperatures below $-58^{\circ} \mathrm{F}$ or above $41^{\circ} \mathrm{F}$. Write a program that prompts the user to enter a temperature between $-58^{\circ} \mathrm{F}$ and $41^{\circ} \mathrm{F}$ and a wind speed greater than or equal to 2 and displays the wind-chill temperature. Here is a sample run: Enter the temperature in Fahrenheit between -58 and 41: 5.3 Enter the wind speed in miles per hour: 6 The wind chill index is -5.56707

(Science: wind-chill temperature) How cold is it outside? The temperature alone is not enough to provide the answer. Other factors including wind speed, relative humidity, and sunshine play important roles in determining coldness outside. In $2001,$ the National Weather Service (NWS) implemented the new wind-chill temperature to measure the coldness using temperature and wind speed. The formula is given as follows:
\[
t_{w c}=35.74+0.6215 t_{a}-35.75 v^{0.16}+0.4275 t_{a} v^{0.16}
\]
where $t_{a}$ is the outside temperature measured in degrees Fahrenheit and $v$ is the speed measured in miles per hour. $t_{\mathrm{w} c}$ is the wind-chill temperature. The formula cannot be used for wind speeds below 2 mph or for temperatures below $-58^{\circ} \mathrm{F}$ or above $41^{\circ} \mathrm{F}$.
Write a program that prompts the user to enter a temperature between $-58^{\circ} \mathrm{F}$ and $41^{\circ} \mathrm{F}$ and a wind speed greater than or equal to 2 and displays the wind-chill temperature. Here is a sample run:
Enter the temperature in Fahrenheit between -58 and 41: 5.3
Enter the wind speed in miles per hour: 6
The wind chill index is -5.56707

Key Concepts

Input Constraints and Validation

Because the wind chill formula is only valid within certain ranges of ambient temperature and wind speed, it is essential to enforce input constraints. Validating these inputs ensures that the computed wind chill index is both physically meaningful and consistent with meteorological standards.

Wind Speed

Wind speed is a critical factor in determining the wind chill temperature. Higher wind speeds can increase the rate of heat loss from the body by removing the warm air layer that surrounds it, thus accentuating the perception of cold.

Empirical Formula Application

The wind chill temperature is computed using an empirical formula that incorporates both ambient temperature and wind speed. This formula uses coefficients and an exponent on the wind speed term to capture the nonlinear relationship between wind speed and perceived coldness.

Wind Chill Index

The wind chill index is a measure that combines air temperature and wind speed to determine the perceived decrease in air temperature felt on exposed skin. It represents the rate at which heat is lost from the body and provides a more accurate sense of how cold it really feels in windy conditions.

Ambient Temperature

Ambient temperature refers to the actual air temperature as measured in the environment. It is a key component in calculating the wind chill index because it serves as the base temperature upon which the effects of wind are superimposed.

Transcript

00:03 Okay, looks like they want us to measure perceived coldness.

00:08 You may have seen this problem in multivariable calculus.

00:12 Maybe you will see it soon in the future.

00:14 Let's see.

00:18 So they want us to calculate a measure of coldness, calculate coldness as our, let's see, in the chill index, going to using, let's see, we're going to take in temperature, and wind speed.

00:49 What do we need to do? we need to prompt the user for temperature.

00:56 We're going to need to calculate in the chill index using the formula they give us.

01:03 Then we're going to need to display to the user.

01:08 This is definitely all we need because they even give us a sample and they tell us specifically how the program should run, what we should say.

01:15 So let's see.

01:17 When we get the temperature from the user, first off, we should remember that, when we get input, we're going to get strings.

01:28 So i need to turn string input from the console into numbers.

01:33 So what we're going to do is call e -vile on any input.

01:37 And how are we going to ask for the input? let's see.

01:39 They specifically say, enter the temperature in fahrenheit.

01:44 So they tell the user that they need to have already computed it as fahrenheit.

01:50 And they tell us it only work.