This assignment is to be done in teams of 2 each. The first order of business is for you to decide who your team is. Use the e-mail list on the course web page.

Each team will pick 2 aircraft, and do a comparison. The purpose of the comparison is NOT to declare which aircraft is "better": it is to study the design, and try to explain why things were done as they were done. Assume that the designers of each of these aircraft did the best that could have been done at the time, for the specifications and constraints which guided them.

The results will be posted on your web page(s). You can post identical reports on both team members' web pages, but don't feel constrained by this: feel free to add what you want to your own web page. Be proud of what you post on your web pages: people all over the world see those pages....

In each Case Study below, you will  calculate the lift/drag ratio of the aircraft at two flight conditions:
    - supersonic flight, Mach 2 at 15000 meters standard altitude
    - subsonic flight, Mach 0.7 at 10000 meters

There are several Validation Problems which you must complete, to show that your methods are correct.

1. Find the Cp distribution for a circular arc airfoil at Mach 2, at 3 degrees angle of attack. The airfoil is constructed with the upper and lower surfaces being circular-arc sections: not a symmetric airfoil. The chord is 3 meters. The upper surface max-thickness point is 0.025 chords above the chord; the corresponding lower-surface point is 0.015 chords below the chord.

From the Cp distribution, find the lift and wave drag, and make sure that the lift corresponds to the theoretical lift coefficient value.

Do this problem by two methods: 1) using analytical expressions for the slope.  2) using whatever program (Matlab, Excel, FORTRAN..) which you use to do the calculation on the actual wing sections for your aircraft. Compare the answers and show that your calculation method is correct and accurate.

2. Use a flat-plate boundary layer computation for the boundary layer characteristics over the wing surface. You will have some conceptual difficulty with the flow over the leading edge of these thin wings. Use Thwaites' method to figure out boundary layer characteristics for a flat plate, and compute skin friction. Extend this to calculate heat transfer to an aluminum surface in the supersonic flow case. Predict where boundary layer transition will occur, and sketch this line out along the wing planform. Use turbulent boundary layer relations to calculate the skin friction for the turbulent boundary layer. Speculate how the answer will change because the flow over a swept wing includes a substantial spanwise component.

3. Use slender-body theory to predict pressure distribution over the forebody of the aircraft at, say, 5 degrees angle of attack. Lets see is we can also compute supersonic drag for the fuselage.

4. Plot the cross-sectional area of the aircraft along the longitudinal axis of the aircraft, and hence predict where the strongest shock might occur in transonic flight.

5. Find the lift of a simple wing planform like a delta wing at Mach 2.
 

Note: Beyond this point, this is an "Open-Ended Assignment"

1. This is still to be done by simple means,  where you do not have access to the Great Full-Physics Infinite-Grid Full Configuration CFD codes. You will use the "theory" learned in school to calculate loads, piece by piece, and add everything up. In the process, we will have to guess at the effects of interactions between components, etc., but that's what makes it fun. Use your ingenuity and judgement.

2. The professor does not know the answers: He is doing this at least in part to learn. In some cases, we will "luck out" and find published data on exactly what we seek. In this case, the report should include these data as confirmation / questions on our own calculations; we still have to do the calculations.

3. Do not wait until all the exact data fall onto your head magically from heaven. You are operating under time and resource constraints, but you WILL find the answers (note the presentation deadline of the 11th of April). If you feel resentment, panic, lack of guidance, insufficient resources, extreme workload, "bosses" who don't understand the reality of your existence, great ! Welcome to "The Club": these are good signs that you are beginning the long process of coming around to face reality and do something constructive.  The next stage is to get real angry, instead of sitting around feeling sorry for yourself, and start improvising where you do not have data. An answer which is 95% accurate is a lot better than no answer at all. Use reason and "common sense".  Feel free to take a pencil and paper and sketch out approximate versions of what you need. Measure off diagrams. Do back-of-the envelope calculations. Make empirical expressions out of data as needed. Then check to see how much error you may be making. Use the "validation problems" wherever possible to keep a hold on reality.  Keep moving.
 

Here are the aircraft:

1. Boeing Joint Strike Fighter.
2. Lockheed-Martin F-22
3. NASA / Boeing HSCT (any configuration)
4. Rockwell B1-B
5. British Aerospace / Aerospatiale Concorde
6. Lockheed SR-71
7. Eurofighter
8.  Saab Viggen.
9. McDonnell Douglas / Boeing F-15
10. McDonnell Douglas / Boeing F/A-18
11. General Dynamics/ Lockheed F-16

Pick any two of them, but remember that you are going to compare their aerodynamics.

A. Beginning steps:

1. Find data on these aircraft. Look for starters at the "AE1350, Fall 1999" web page off the "Design-Centered Introduction" of ADL.

2. Especially, note things like wing geometry, tail geometry, fuselage cross-section area, gross weight, fuel load..

3. Find quantitites like Wing Loading, Aspect Ratio.

4. Find data on how the wing is twisted or cambered; find the airfoil sections used. Until you can find the real airfoil section, improvise! Find airfoil sections that are close, or construct the geometry yourself.

5. Figure out the leading edge sweep.

B. Initial Aerodynamics calculations

For each flight condition,

1. From the wing loading, find the lift coefficient at each flight condition.
2. Estimate the induced drag coefficient if any.
3. Look for drag data and estimate the fuselage / profile drag coefficient.
4. Look up the section on transformations, and see how to transform the given wing shape to either an incompressible-flow geometry, or appropriate geometry for a reference condition in supersonic flow.
5. Find the pressure distribution on the wing airfoil section at the flight condition: this may involve transformation in the subsonic case, and a detailed geometry-based calculation (find surface slope everywhere) in the supersonic case.
6. From these, estimate the lift on the wing, and the lift distribution.
7. Estimate the location of the center of pressure.
8. Use the methods for bodies of revolution to get estimates of what the fuselage does.
9. Estimate Reynolds number per meter, at each flight condition.
10. Estimate boundary layer transition locations.
11. Estimate skin friction drag.
12. Estimate surface heating rates.

If you get this far, you may want to go on and analyze what the tails do, and keep going until you know a great deal more about the aerodynamics. Describe what you find out. We'll keep refining the project as we go along, and we find out the problems. :-)