1 00 10 01 11 00 10 01 11 10 00 01 11 01 00 10 11 10 00 01 11 00 10 01 01 11 00 01 01 10 11 00 11 01 00 10 11 00 11 10 00 01 00 10

11 10 00 01 11 01 00 10 11 10 00 01 11 00 10 01 01 11 00 01 01 10 11 00 11 01 00 10 11 00 11 10 00 01 00 10 10 11 00 10 01 11 00

0 10 01 11 10 00 01 11 01 00 10 11 10 00 01 11 00 10 01 01 11 00 01 01 10 11 00 11 01 00 10 11 00 11 10 00 01 00 10 10 11 00 00 10

0 11 00 10 01 11 00 10 01 11 10 00 01 11 01 00 10 11 10 00 01 11 00 10 01 01 11 00 01 01 10 11 00 11 01 00 10 11 00 11 10 00 01 00

11 00 10 01 11 10 00 01 11 01 00 10 11 10 00 01 11 00 10 01 01 11 00 01 01 10 11 00 11 01 00 10 11 00 11 10 00 01 00 10 110 11 0

10 01 11 10 00 01 11 01 00 10 11 10 00 01 11 00 10 01 01 11 00 01 01 10 11 00 11 01 00 10 11 00 11 10 00 01 00 10 110 11 00 10 01 11

1 00 10 01 11 00 10 01 11 10 00 01 11 01 00 10 11

11 00 10 01 01 1

01 10 11 00 11 01 00 10 11 00 11 10 00 01 00 10

11 10 00 01 11 01 00 10 11 10 0000 01 11 00 10 01 01 11 00 01 01 10 11 00 11 01 00 10 11 00 11 10 00 01 00 10 10 11 00 10 01 11 00

0 10 01 11 10 00 01 11 01 00 10 11 10 00 01 11 00 10 01 01 11 00 01 01 10 11 00 11 01 00 10 11 00 11 10 00 01 00 10 10 11 00 00 10

0 11 00 10 01 11 00 10 01 11 10 00 01 11 01 00 10 110 00 01 11 00 10 01 01 1

01 01 10 11 00 11 01 00 10 11 00 11 10 00 01 00

11 00 10 01 11 10 00 01 11 01 00 10 11 10 00 01 11 00 10 01 01 11 00 01 01 10 11 00 11 01 00 10 11 00 11 10 00 01 00 10 110 11 0

10 01 11 10 00 01 11 01 00 10 11 10 00 01 11 00 10 01 01 11 00 01 01 10 11 00 11 01 00 10 11 00 11 10 00 01 00 10 110 11 00 10 01 11

10 00 01 11 00 10 01 01 11 00 01 0

1 10 00 01 11 00 0

0

48 AUGUST 2008

Visualization Analysis,and Selection of

Airfoils(Right on your computer)

Two of the primary goals in designing an air-foil are to produce the highest value of the maximum lift coefficient at stall angle of

attack and the lowest coefficient of drag at cruise conditions. Why then do we not have just one standard airfoil that accomplishes these goals? For airfoils in real life, such things as design Reynolds and Mach numbers, stall behavior, effect of flaps, and aircraft structure play important roles. Different Reynolds and Mach numbers also are important in the examination of the differences between various theoretical methods and experiments. (Figure 1)

Numerous programs are available for the pur-pose of determining how any particular airfoil will behave. Some are relatively simple and free of charge, while others are elaborate and expensive. The more design parameters that need to be consid-ered, the more complex and costly the program is likely to be. Some will allow you to study the effect of flaps and even the location of the hinge line.

I’ll start with the most simple and least expensive and work my way up to elaborate programs that you, as a private individual, might not want to use. In every case, the italicized website address will lead you to the pertinent websites. As far as I can tell, all of the programs will run on Windows machines, and some will work on Macintosh computers as well.

Just as there are a number of different pro-grams, there are several different theoretical ways to estimate airfoil behavior. Some time before he died in 1921, the Russian aerodynamicist Nikolai Egorovich Zhukovsky (or Joukowski) developed a mathematical method of relating the flow around a cylinder to that around other shapes. In the 1960s, Richard Eppler discovered a way to more accurately calculate (or estimate) pressure and velocity distributions on airfoils using a computer. Other related methods use more detailed and com-plicated approaches, but this is not the place to delve into that mysterious territory.

CHUCK BODEEN • EAA 709226

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EAA Sport Aviation 49

NASA Joukowski

A free, online java script, NASA Joukowski, www.GRC.NASA.gov/WWW/K-12/airplane/map.htm, was created by Tom Benson at NASA’s Glenn Research Center. By adjust-ing the parameters of the “transfor-mation” in this program, the shape could be made to look like an airfoil with variable thickness, camber, and angle of attack. The flow is inviscid (having zero viscosity); there is no flow separation when an actual air-foil would stall. (Figure 2)

FoilSim

Another free program from Tom Benson, FoilSim, www.GRC.NASA.gov/WWW/K-12/airplane/foil2.html(Figure 3), takes the Joukowski code several steps further. Using the dif-ferent plot options, absolute lift or lift coefficient can be plotted against a number of other variables. Using other options can specify speed, altitude, chord, and span. There is even a correction for aspect ratio. The optional “Stall Model” shows what might be the effects of a stall. However, if you look closely you will see “K-12” embedded in the web address of this program and that of NASA Joukowski. These two codes were developed as secondary educational tools.

Aircraft Designs Inc.

Aircraf t Des igns Inc . , www.AircraftDesigns.com , takes you to a company owned by Martin Hollmann (EAA 77760), where you can click on “Free Software,” fill out an information form, and then download Airfoil.exe (Figure 4), which Hollmann and Rick McWilliams (EAA 809597) put together in the year 2000. This program is based upon the Joukowski theory, and although CLmax is calculated, CL is linear with respect to angle of attack and can exceed CLmax. There is no documentation, so interpretation of the results is up to the user.

Oshkosh Airfoil

Jens Kristensen used the previous work of Hollmann and McWilliams to produce a version of the program named Oshkosh Airfoil, www.FFU.dk/airfoil.htm (Figure 5), that allows the parameters to be changed with a set of sliders rather than by typ-ing numbers. The program output

2. The NASA Joukowski

program shows the cylinder

on the left. By adjusting the

sliders on the left with your

mouse, you can change the

shape of the resultant airfoil

on the right. By adjusting

the sliders on the right you

can see the change in the

cylinder.

3. FoilSim bears considerable resemblance to the NASA Joukowski program—both are

from the Glenn Research Center. The flow separation at 10 degrees angle of attack is

purely artificial and not the result of calculation.

1. The Reynolds number (Re) makes little difference where the lift coefficient is linear

with respect to angle of attack. The drag coefficient is more strongly affected by Re as

is lift in the stall regime.

50 AUGUST 2008

Interactive Airfoil Design

An abbreviated version of PANDA (Program for Analy-sis and Design of Airfoils) is available free from this Stanford University site, http://ADG.Stanford.edu/aa241/airfoils/panda.html (Figure 6). You can input Reynolds and Mach numbers, thickness, and information about transition from laminar to turbulent flow. Output is the pressure distribution and coefficients of lift, drag, and moment. The maximum CL can be found by varying the angle of attack, although you may wonder about some of the very large values. The full version of PANDA is avail-able from Desktop Aeronautics, www.DesktopAero.com.

Kevin Jones’ Panel Code

As a member of the faculty at the Naval Postgraduate School, Kevin Jones has developed experimental and numerical methods for the analysis of micro air vehicles. His Panel Code, www.AA.NPS.Navy.mil/~jones/online_tools/panel2 (Figure 7), can be used to predict the low-speed flow about NACA 4- and 5-digit airfoils as well as the additional 1,550 examples contained in the University of Illinois at Urbana-Champaign (UIUC) Airfoil Coordinates Database. The program is based on potential-flow theory, which assumes the flow is incompressible, inviscid, and

5. Left: The coordinates of the upper and lower surfaces, the camber line, and the thickness are presented numerically on the

Oshkosh Airfoil screen. Right: The pressure distributions are shown. The parametric sliders that are moved by the mouse are shown in

the inset. The angle of attack can be changed over a limited range by clicking on the arrows in the lower left corner.

6. With the PANDA program, from Interactive Airfoil Design, you

can use your mouse drag points on the profile to reshape the

airfoil section.

4. Left: The airfoil.exe input screen where you set thickness, camber, and angle of attack. Center: Streamline output. Right: Pressure

distribution where you can read CL, CD, CM, and CLmax.

shows the coordinates, pressure distribution, as well as CLI (the lift coefficient at zero angle of attack) and α0 (the angle of attack for zero lift).

52 AUGUST 2008

irrotational. These assumptions limit the solutions to low-speed flows and low angles of attack. Flow separation cannot be predicted by this approach, so you won’t be able to use it to study stall behavior. A nice feature is that you can see the pressure distribution and the streamlines on the same plot. This program runs online and, like all programs I’ve mentioned, is free.

Xfoil

Mark Drela developed Xfoil, http://Web.MIT.edu/drela/Public/web/xfoil, at the Massachusetts Institute of Tech-nology in 1986 for the design and analysis of subsonic isolated airfoils (Figure 8). It consists of a collection of interactive, menu-driven routines that perform a wide variety of useful functions. Scientifically, this is a wonderful approach and it is free, but from the user’s point of view it is cumbersome since commands must be typed in one at a time to define the problem and specify the desired results. Google “Xfoil tutorial” and you will find some help if you care to try Xfoil in its basic form. Otherwise, use Profili2, which has a user-friendlier interface than Xfoil.

Profili2

To overcome the burden of entering literal commands one at a time, Stefano Duranti has created an interac-tive interface for Xfoil called Profili2, www.Profili2.com/eng/default.htm. This program (Figure 9) will cost you 10 euro (about $16), but it is well worth the invest-ment. Profili2 has many input and output options, a library of 2,387 airfoils, and a built-in Reynolds num-ber calculator.

AeroFoil Don Reid (EAA 215) has created the free program AeroFoil, http://AeroFoilEngineering.com (Figures 10 and 11). After 14 days it automatically converts to AeroFoil Lite. Although you’re able to perform all of the calculations of airfoil design and analysis, your choices are limited and you won’t be able to print or save any data. A single user license sells for between $20 and $150.

AeroFoil uses the vortex panel method and integral boundary layer equations to calculate drag, lift, and airfoil pitching moment at different angles of attack. Direct comparisons of up to three airfoils at a time

8. Xfoil has several output modes in

addition to this pressure distribution.

9. The input and output options of Profili2 take advantage of

the computational power of Xfoil. On the graph above, the solid

lines represent output from Xfoil for NACA 23012 at three

different Reynolds numbers. The dashed lines are data from

the 1949 NACA experiments of Abbott and Von Doenhoff. Both

Drela and Duranti say that differences are probably due to such

things as the variance in Mach number and the conditions of

the experiment.

10. The AeroFoil web page compares data on the NLF-0215F foil

at Re 9,000,000 (black), AeroFoil (green) and Xfoil (red).

7. The input and output for Kevin Jones’ Panel Code program

are in two windows. The solution window starts with written

instructions and may be hidden behind the input window.

54 AUGUST 2008

may be performed. You can display lift, drag, and moment coefficients, pressure distributions, and boundary layer thickness. You can even have three airfoils on the screen at one time, which allows for comparison or design of wings by working with root, mean chord, and tip. The purchased version comes with 1,200 airfoils plus about 2,000 more from UIUC.

X-PlaneThe X-Plane flight simulator, http://X-Plane.com, from Austin Meyer (EAA 485514) has a built-in program, Air-foil-Maker (Figure 12), which allows you to examine the coefficients for a list of airfoils or to modify certain parameters to create new airfoil files. You can change the zero angle of attack intercept and slope of the lift coefficient, the maximum CL, mini-

14. The primary screens in Airfoil Optimizer.

Top left describes the airplane and selects

base line and candidate airfoils. Top right

compares base line and candidate with

other airfoils. Bottom left compares power

required, rate of climb, and drag between

the two selected foils. Bottom right will

show you lift versus AOA and drag versus

lift for any airfoil in the library instantly.

11. The velocity distribution screen in

AeroFoil allows you to change airfoils,

Reynolds number, angle of attack, and

even the scale of the drawing.

12. Airfoil-Maker parameters are set

on the left side of the screen and the

resultant coefficients of lift, drag, and

moment appear on the right side as

functions of angle of attack.

13. X-Plane provides the lift (green) and

drag (red) distribution across the wingspan.

AlphaTrainer adds those up. In this shot the

lift on both wings is “in the green.”

For information about more complex (and expensive) programs, search the Internet for: DesignFoil (www.DreeseCode.com) Public Domain Aeronautical Software (www.PDAS.com) Hanley Innovations (www.HanleyInnovations.com) Analytical Methods Inc. (www.AM-Inc.com)

More Reading: Airfoil Selection by Bill Husa (www.OrionTechnologies.net/Documents/Airfoil.htm) Design and Analysis of Airfoils by Martin Hepperle (www.MH-Aerotools.de/airfoils/methods.htm) GA Airfoils by Harry Riblett (http://Shop.EAA.org/html/04_books_howto.html)

G O D I R E C T

EAA Sport Aviation 55

mum CD, angle of attack at minimum CD, width of drag bucket, and much more. As the flying program starts, it calculates three-dimensional wing corrections that include aspect ratio and Oswald efficiency.

When “flying,” you can hit the “/” key and see lift and drag on the wings. See AlphaTrainer (below) for an example. The X-Plane package of programs is for sale for $79, but the free demo is fully functional, with the only restriction being that the joystick cuts out after 10 minutes.

AlphaTrainerAlphaTrainer, www.AlphaTrainer.com (Figure 13), is an add-on for X-Plane. The lifting forces all along the wing-span are summed up on each side, and the result is displayed as an arrow (vec-tor) against a colored background so that angle of attack can be visualized interactively during “flight.” If you already have X-Plane, AlphaTrainer is available on CD for $39.95, but it will soon be available as a download for $29.95. The product is the brainchild of Tom Shefchunas (NAFI 8683).

Airfoil OptimizerAi r f o i l O p t i m i z e r , w w w .D a V i n c i T e c h n o l o g i e s . c o m /AirfoilOptimizer.htm (Figure 14), by Gi l Crouse of DaVinci Technologies Inc., helps to select the best airfoil from a library of more than 300 by bringing together a comprehensive and consistent ae r o d y n a m i c p e r f o r m a n c e database and a software tool for intelligently sorting and matching the predicted airfoil performance against the flight requirements for your design. Xfoil is used for the lift and drag calculations. The program sells for $69.

A related product, Airplane PDQ, delves into aircraft performance, han-dling, and stability and control, as well as a CAD component for develop-ing your aircraft drawings.

Chuck Bodeen in an engineer and computer programmer with BS, MS, and ME degrees from Caltech. A student pilot, his interest in flying has led to the publication of more than 70 articles on flight simulation and other aviation subjects. He is also a consultant for companies with a desire to simulate their aircraft designs.