Introduction:

In this homework assignment you implement and utilize a standard atmosphere model $($in this case the $1959$ ARDC Model Atmosphere$).$ The end result of this project should be a function that accepts an input altitude and then outputs the pressure, temperature, and density at that altitude as well a script using that function to plot those values for the entire atmosphere.

Assignment:

The $1959$ ARDC Model Atmosphere has the following parameters:

Sea level temperature $288\mathrm{.}16$ K

Sea level pressure $101\mathrm{.}325$ kPa

Sea level density $1\mathrm{.}2250$ kg$/$m$^3$

Gradient layer $-0\mathrm{.}0065$ K$/$m up to $11$ km

Isothermal layer $11$ km to $25$ km

Gradient layer $0\mathrm{.}0030$ K$/$m up to $47$ km

Isothermal layer $47$ km to $53$ km

Gradient layer $-0\mathrm{.}0045$ K$/$m up to $79$ km

Isothermal layer $79$ km to $90$ km

Gradient layer $0\mathrm{.}0040$ K$/$m up to $100$ km

$1)$ Create a sketch $($by hand or any drawing tool$)$ of the atmosphere pressure, temperature, and density with altitude up to $100$ km$.$ Please use altitude for the vertical axis; the temperature, pressure, and density do not have to be to scale.

Annotate the sketch with the approximate height of a tall mountain and the cruise altitude of a commercial airliner.

$2)$ Use equations for the standard atmosphere derived in class to calculate temperature, density, and pressure at the following altitudes. Do these calculations by hand and show your work.

$8,500$ ft

$34,000$ ft

$41,000$ ft

$75,000$ ft

$3)$ Write a MATLAB function that calculates the air properties at a given altitude using the $1959$ ARDC standard atmosphere model. The function should not output any variables to the Command Window $($suppress with semi$-$colon$).$

The function should have the first line:

function $[$T$,$ P$,$ rho$]=$ stdatm$\_$lastnameFirstname$($h$)$;

$4)$ Test your function at each of the altitudes in Part $2.$

Make a table including the values of your hand calculations from Part $2$ and the output of your MATLAB code at those altitudes. Add another column with the values given an external reference at those same altitudes $($you can enter "standard atmosphere calculator" or just "standard atmosphere" into your favorite search engine; you don't have to use the $1959$ ARDC model as the reference$).$

Comment on any differences$/$similarities you notice across the three sets of data; why do you think there are differences, if any?

$5)$ Write a MATLAB script to call your function with a variable altitude.

Name your script lastnameFirstname$\_$A$215\_$hw$1.$m$.$

Use comments for the first lines in the script to give your name, class, assignment, and date. Your first code line should be:

close all; clear all; clc

Comment all major lines of code $($creating and setting variables, with units; calling the function$).$

Using control flow in the script, call your function multiple times to create data and plots depicting the properties of the standard atmosphere up to $100$ km$.$ Plot temperature, pressure, and density on a subplot with altitude as the y$-$axis.

Submit the files for all the parts above $($Parts $3$ & $5$ must be submitted as $.$m files$)$ within a zip file file to Canvas with the file name:

lastnameFirstname$\_$a$215\_$hw$1.$zip