This assignment is designed to introduce you to several computing packages that we will use throughout the semester as well as give you an opportunity to recall how to use MATLAB.

Please keep a log of the time spent on this homework assignment (consider it your work time card). Turn this log in with the assignment.
 

1) Purchase the Abbott and von Doenhoff book if you haven't done so

2) Find the CAD lab (on the third floor of 110 Cummington) if you are not familiar with it

3) Get an account on the unix machine -- conductor-am.bu.edu

log into your account on acs

type      telnet conductor-am.bu.edu     at a terminal prompt

login as   new    (use new as the password a couple of times if necessary)

go through the new program (you are familiar with this from when you first signed up for an account on campus)

use your kerberose password but do not reset your email to this account

when the program is finished, type    logout

Take your student ID to the AME front office (110 Cummington) and ask for access to the computer lab on the fourth floor.  They will give you card access.  You will then be able to use the unix computers in room 410 of 110 Cummington.

NOTE that you can also access conductor-am from the xterminals located in the basement of IT.

If you are not already familiar with the basics of UNIX, I recommend that you take the two hour "Intro to UNIX" course that is offered at IT.  This course will help put you at ease when using your acs account or your new conductor-am account.  The earliest date is the 17th, but you have to pre-register, so do so today!  ( I have not factored this two hours into the predicted time for completing this assignment -- however if you take the class, you will be able to complete the tasks more quickly.  Hopefully, you can fit this into your schedule during the first couple weeks of this semester. )

You now have access to MATLAB and Maple on acs.bu.edu, conductor-am.bu.edu, and the PC's in the CAD lab.
In addition, you have access to the programs XFOIL and SOUSSA on conductor-am.bu.edu

TOTAL: 1/2 hour.
___________________________________________________________________________________________

4) MATLAB problem  ( you can do this on a PC or unix version of MATLAB)

Write a program that:

prompts the user for two constants:   a₁ and a₂

plots   y vs. x    where  y = a₁ x³ - a₂ x + 3   for the domain  x = [-10,10] and with the specifications that the

title is "MY GRAPH"

x-label is  "x-location"

y-label is "height"

y range is free

line is a thick and dashed

Save the figure as a gif file called  fig1.gif

Make sure that the comment lines at the top of the program have your name and homework assignment number as well as a short description of what the code does.  Print out the program and turn it in.

Open the fig1.gif using a web browser, and print it out from the browser and submit it with the program print out.

TOTAL: 1 hour
______________________________________________________________________________________________

5) MAPLE introduction

You will repeat the MATLAB assignment with minor alterations using MAPLE
It is MAPLE5 on the PC's that you want to run.  On a unix station you want to type  xmaple.

MAPLE is an algebraic manipulation package (as opposed to MATLAB which is a programming language)

So, in MAPLE:

set up the function   y = a₁ x³ - a₂ x + 3  by typing at the prompt :  y :=  a₁ * x^³ - a₂ * x + 3;    and hitting enter.

use the substitution command to insert values of a₁ and a₂     y2 := subs(a1 = #, a2 = #, y);  and hit enter.

create a plot with the same specifications as given above.   The basic command is  plot(y2, x=-10..10);

you must add things to the plot command  such as  plot(y2, x=-10..10,title='MY GRAPH') in order to adhere to the given specifications.  Use the help files to find the appropriate commands.

To provide program comments, insert text input instead of maple input (see the options bar at the top of the MAPLE interface) and simply type your comments.

Print out the maple script with the graph showing and turn it in.

While you are playing with MAPLE check out the results of  the commands:    dy:= diff(y,x);     and iy :=  int(y,x);  Pretty nice don't you think?

TOTAL: 1 hour
____________________________________________________________________________________________

6)  AIRFOIL/ WING calculation validation

Choose a NACA 4 or 5-digit series airfoil from Abbott and von Doenhoff's book.  (i.e. look in the section where you find the plots of coefficient of lift, drag, and moment and choose your favorite).

You will now use one airfoil lift calculation code called XFOIL to see how closely it predicts the results found in Abbott and von Doenhoff.

Then you will use a wing lift calculation code SOUSSA to explore the effect of using the airfoil in a finite wing.

a) XFOIL airfoil aerodynamics calculator

You must run this code on conductor-am.  You can do this by sitting at one of the unix terminals in room 411 or by accessing it through the x-terms at IT (see above for these directions).

Once logged in to a 411 cluster terminal or to conductor from IT, at a unix window prompt type  xfoil.

For further instructions on using xfoil see the PDF  quick reference linked here.

For this assignment you will use only the inviscid calculation capability of xfoil (this is its default mode).  Recall what this means in terms of the type of lift curve you will get (i.e. inviscid = no stall).  Later in the semester we will use xfoil again and invoke the viscous calculation mode.

Choose your airfoil and then have xfoil calculate the coefficient of lift at several angles of attack between -20 and 20.  Keep note of these values.

b)  SOUSSA wing aerodynamics calculator

You must run this code on conductor-am.  You can do this by sitting at one of the unix terminals in room 410 or by accessing it through the x-terms at IT (see above for these directions).
This code runs through matlab version 531.  To find out how to run this code see the associated web site (in particular the bullet running the code).

SOUSSA can only calculate the aerodynamics of inviscid flow past a wing.  Currently, the user interface only allows you to choose rectangular wings (although the code has the capability to run for wings with sweep, taper, and dihedral).
 

• First, choose your airfoil section and use it in a moderate aspect ratio wing (4-7).  Use the default values of number of points in the chord and span directions (note that it is really the number of points along the half span).  Choose a subsonic Mach number.
• Run only steady simulations and leave Lwake and nwake at their default values.  You can leave size, nose, flap. ang, bcmode, etc. at their default value as well.
• Run the code for several angles of attack from -20 to 20 and note the values of coefficient of lift and induced drag.
• (REMEMBER to delete and add the wing/AOA characteristics in between each run -- you should always be modeling just one wing element).   Note the value of the surface area.
• Do the same for one other aspect ratio.  Use the same Mach number. (Again note the value of the surface area.)
• Now, go back to the first aspect ratio, change the number of points in the two directions and compute the coefficients at a couple of different angles of attack.  You should note that as you increase the number of points the coefficient values converge.  (This is because the approximations used in the code are dependent on the size of the chunks along the wing -- you can see these chunks on the graph of the wing.)

c)  Analyze the results.
 

1) Plot the airfoil coefficient of lift (from Xfoil) and the experimental values from Abbott and von Doenhoff versus angle of attack.  (You can plot them using MATLAB or EXCEL).  Comment.

2)  Plot the airfoil coeffient of lift and the wing coeffient of lift (for the two different aspect ratios) versus angle of attack.  Note from the web page how to change CL_A to CL.

3)  Plot the wing coeffient of induced drag for the two wings analyzed versus angle of attack.  Comment.

4)   Compute the slopes of the 3 curves in #2.   Use the correction that you were given in AM201 to compare the wing lift curve slopes to the airfoil lift curve slope.  (i.e. recall that if you have the airfoil lift curve slope (in 1/radians), the Mach number, sweep angle (0 in this assignment), and the aspect ratio, you can determine a lift curve slope that would be valid for the given aspect ratio wing) .  Compare and comment.
 

TO TURN IN for section 6:

Please note which airfoil section you chose to analyze.
Attach the plots from part c above with the appropriate commentary.

TOTAL:  3.5 hours