Foil is a program for the creation and display of airfoil cross-sections. Foil can generate NACA 4 and 5 digit airfoils, as well as accept coordinates as input. Output can be to the screen, printer, or disk, in numerical or graphical formats. A not-fully implemented option allows for the processing of scanned airfoil images to find the coordinates (Note: this is almost finished).
Foil is free, but not public domain. I retain all rights to the program. See the file "License/Warranty" for more information.
This is my first Mac program, and was written to teach myself how to program on the Macintosh. Foil was created using THINK C 5.0.4 and the THINK Class Library (1.1.2). Any questions, comments, or criticism may be sent to:
hulburt@leland.stanford.edu
-or-
Abrams 4F, Escondido Village
Stanford, CA 94305.
After August 10, 1994, I can be reached c/o:
1119 Bridle Drive
Richland, WA 99352
I will probably be on-line through the internet or AOL - look for me
in the aeronautics-type groups. (after June 1994)
2.0 A Note On File Formats
Foil will read files in the “NACA” and “Soartech” format. The first line of a file is the airfoil name. The second line must be “start”. The line following the last coordinate entry must be “end”. Any notes or comments may be placed after the “end” line. The NACA format starts at the leading edge (x = 0.0) and goes to the trailing edge (x=1.0), with x and y values in three or four columns (three columns implies x, y(upper), y(lower) and four columns implies x(upper), y(upper), x(lower), y(lower) ). An example of the NACA format is shown in Example 1. The Soartech format starts on the upper part of the trailing edge and moves towards the leading edge on the upper surface, then wraps around and continues back to the lower surface at the trailing edge. The Soartech format has two columns, x and y. The columns may be delimited by space(s), tabs, commas, or asterisks (a new feature). An example is shown in Example 2. Note: Internally, Foil uses the NACA format. This should be transparent to the user.
NACA 63A210
start
0 0 0 0
0.423 0.868 0.577 -0.756
0.664 1.058 0.836 -0.900
1.151 1.367 1.349 -1.125
---
90.050 1.519 89.950 -0.539
95.026 0.769 94.974 -0.279
100.000 0.021 100.000 -0.021
end
le radius = 0.742, te radius = 0.023, slope le = 0.095
Example 1: NACA Format.
NACA 63A210
start
1.00000 0.00021
0.95026 0.00769
0.90050 0.01519
0.85072 0.02254
---
0.00664 0.01058
0.00423 0.00868
0.00000 0.00000
0.00577 -0.00756
0.00836 -0.00900
---
0.84928 -0.00812
0.89950 -0.00539
0.94974 -0.00279
end
le radius = 0.742, te radius = 0.023, slope le = 0.095
Example 2: Soartech Format.
3.0 Commands
File:
Open: Presents the standard Macintosh file dialog and allows the user to select ‘TEXT’ and ‘PICT’ files. If a text file is selected, the file will be opened and the coordinates displayed in a table, while the airfoil is drawn in another window. If a picture file is opened, the PICT will be displayed in its own window and the Scan command will be enabled (see Airfoil:Scan).
Close: Closes the currently selected window. If there is no associated file or the it has been modified, the user will be given the option of saving it (see Save/Save As…).
Save/Save As…: Presents the standard file dialog and saves the information in the currently selected window. If the window contains a airfoil, the data will be saved in a ‘TEXT’ file, in the format selected in the File Preferences… dialog (see Edit: File Preferences…). The Save As… option allows the saving of the information under a different name.
Save As Pict…: Presents the standard file dialog and saves the currently selected airfoil window as a ‘PICT’ file. Note: windows of opened PICT files cannot be saved. (This needs some work and will be fixed in a later release.)
Page Setup…: Presents the page setup dialog for the currently selected printer.
Print: Displays the standard printing job dialog and then prints the contents of the currently selected window. If the “Print airfoils at highest resolution” (see Edit:Preferences) is checked, airfoils will be printed at the highest possible resolution supported by the printer.
Quit: Exits the program. If unsaved information exists, the user will be given the opportunity to save it before exiting.
Edit:
Note: The Cut, Copy, Paste, and Clear commands are not supported currently.
Cut: Removes the currently highlighted information and copies it to the clipboard.
Copy: Copies the currently highlighted information to the clipboard. Unlike the Cut command, the highlighted information is not removed.
Paste: Copies the information in the clipboard and inserts it at the current point.
Clear: Removes the currently highlighted information.
File Options…: Displays the file options dialog. The user can select the delimiter used for saving airfoil text files, and the format of those files (see A Note On File Formats).
Preferences…: Displays the user preferences dialog. If the OK button is pressed, the program is changed to reflect the preferences selected by the user. The Cancel button keeps the current set of preferences.
Airfoils:
NACA 4 Digit: Displays the NACA 4-digit airfoil dialog. The user can enter the complete designation (i.e. 4412) or enter the parameters individually (see Theory:NACA Airfoils). After the designation is entered, the coordinates are calculated and the airfoil is plotted on the screen in a new window according to the user’s preferences. If the “Display Airfoil Coordinates” option is checked (see Edit:Preferences), the coordinate data is displayed in another window.
NACA 5 Digit: Same as 4 Digit but creates NACA 5 Digit airfoils.
Joukowsky…: Displays the Joukowsky Airfoil dialog. For information on the parameters, see Equations:Joukowsky Airfoils.
Airfoil Options: Displays a dialog that allows the user to select the number of points on the airfoil, the distribution of the points, and the method/accuracy used to calculated them. The “Small Angle Approximation” checkbox turns on and off the sin approximation as discussed in the Equations section. A “Standard Distribution” is a prescribed set of x-values commonly used in NACA airfoils, with x = {0.0, 0.5, 0.75, 1.25, 2.5, 5.0, 7.5, 10.0, 15.0, 20.0, 25.0, 30.0, 40.0, 50.0, 60.0, 70.0, 80.0, 90.0, 95.0, 100.0 }. The “Specify Number of Points” places that number of equidistant x-points on the both the upper and lower surfaces. The “Cosine Distribution” clusters more points near the leading and trailing edges, which can be useful for some user.
Drawing Options: Displays a dialog that gives the options for displaying the airfoil on the screen and Printer. If the “LE Radius” checkbox is on, the leading edge circle representing the leading edge radius will be shown for generated NACA Airfoils. The “Camber Line” and “Thickness” options show these lines on the plot. The “Max Camber” and “Max Thickness” options show the maximum of these values on the plot. If the “X-Y Axes” option is on, an axis will be displayed. The X:Y ratio is the ratio of x to y (i.e. a value greater than one will expand the y-axis, and a value less than one will shrink it).
Scan: This command is implemented only for PICT files. The cursor will change to a small box with a tag on it. The first tag will be TE (for trailing edge). Place the cursor around the trailing edge and click the mouse button. The tag will change to LE (for leading edge). Place the cursor around the leading edge and click the mouse again. After the TE and LE have been entered, the program scans the airfoil, and displays the scanned airfoil in a new window. The scanned image must not be upside down. It should be scanned using the “Line Art” option. Make sure there the image is “cleaned up”, i.e. no extra lines or dots on the outside of the image, as these will adversely affect the scan. Currently the routine corrects for airfoils which are not scanned exactly (on a slant), and removes noise from the airfoil. It is probably about as far as I'm going to take this without a lot of requests.
Compare Airfoils: This command displays a dialog with three buttons labeled 'Select'. Pressing the select button causes the standard Macintosh file dialog to be displayed. Click on the airfoil you want to compare. At least two airfoils must be selected. After 'OK' is pressed, the airfoils are displayed in a new window, with three different colors (or line patterns). A legend detailing the airfoils is shown in the upper righthand corner.
4.0 Explanation of Terms
A NACA airfoil is composed of a thickness distribution added to a camber line. The camber line is the line equally distant from both the upper and lower surfaces. The camber line determines the "curvature". An airfoil with thickness but zero camber will be symmetric. The chord line is the line connecting the two furthest points on the airfoil, and generally airfoil sections are nondimensionalized by setting the length of the chord line (c) to 1. Therefore, the actual x-coordinate in the real world (say for a 5" chord) can be calculated by x(real-world) = x(section) * (chord length) and the y-coordinate can be scaled similarly. The small circle at the leading edge represents the leading edge radius, a measure of the curvature of the "nose" of the airfoil. An airfoil with a larger leading edge radius will have a blunt, more-rounded nose.
5.0 NACA Airfoils
The NACA 4- and 5-digit airfoils were part of a systematic attempt to understand wing theory by looking at airfoil sections. These allowed researchers to independently study the effects of camber and thickness. A NACA 4- or 5-digit airfoil (NACA airfoil) is composed of a camber line (also called mean line) and a thickness distribution. This allowed experimenters to separate the effects of camber and thickness. An advantage of the NACA airfoils is that the coordinates can easily be calculated given the designation, so if someone tells you that they are using a NACA 4412 airfoil, you can reproduce the same cross-section. Other airfoil families tend not to be so systematic in the designations (see Eppler, Reigels). In a NACA airfoil, the designation corresponds to geometric and/or aerodynamic properties of the section. Table 1 (Anderson) shows a partial list of planes that use NACA airfoils. In addition, many helicopters have used NACA 0012 or NACA 23012 airfoils (Eppler).
Airplane Airfoil
---------- --------
Beechcraft Sundowner NACA 63A415
Beechcraft Bonanza NACA 23016.5 (at root)
NACA 23012 (at tip)
Cessna 150 NACA 2412
Fairchild A-10 NACA 6716 (at root)
NACA 6713 (at tip)
Gates Learjet 24D NACA 64A109
General Dynamics F-16 NACA 64A204
Lockheed C-5 Galaxy NACA 0012 (modified)
Table 1. Aircraft Using NACA Airfoils.
In a 4-digit airfoil, the first digit is the value of the maximum camber (in percent of the chord), the second digit is the position of the maximum camber from the leading edge in tenths of the chord, and the last two digits denote the maximum thickness of the airfoil in percent. For the NACA 2415 airfoil, the maximum camber is 2%, the position of the maximum camber is 0.4c, and the thickness is 15%. This example is displayed in Example 3.
NACA 2415
NACA 24 mean line (24)
15
NACA 2 maximum camber, % (2%)
4 10 * position of maximum camber (0.4c)
15 thickness, % (15%)
Example 3. Breakdown of NACA 4-Digit Designation
See Abbott for the equations of the NACA airfoils, or look in the MSW manual.
The NACA 5-digit airfoils are set up in a similar manner to the 4-digit airfoils. The primary difference is the use of a different camber line. In a 5-digit airfoil, 1.5 times the first digit is the design lift coefficient in tenths, the second and third digits are one-half the distance from the leading edge to the location of maximum camber in percent of the chord, and the fourth and fifth digits are the thickness in percent of the chord. For example, a NACA 23015 airfoil has a design lift coefficient of 0.3, has the maximum camber at 0.15c, and is 15% thick. Additionally, the first three digits indicate the mean line used. In this case, the mean line designation is 230. The 5-digit airfoils use the same thickness distribution as the 4-digit airfoils. This example is displayed in Example 4.
The Joukowsky airfoils are not an airfoil family per se: they are created by conformally mapping a circle into an airfoil. The subject of conformal mapping and the mathematics behind it can be found in a number of textbooks (see Jones, Abbott). The routine used by this program follows the methods and programs in Jones. The Joukowsky Airfoils… dialog has six parameters that can be adjusted to produce reasonable airfoil cross-sections (currently the angle of attack is not used but may be in the future). However, these are not necessarily practical as compared to NACA or other airfoil series (these airfoils are attractive for mathematical reasons, not aerodynamics). The airfoil produced is dependent on the location of the center of the original circle, its radius, and angle of zero-lift. The center of the original circle is at (xc, yc). The angle of zero-lift is defined by the line connecting a point on the circle and the center (from point t to point c). The following general rules can be applied to produce cross-sections:
• Flat plate: center at (0,0) and place point t at (1,0).
• Symmetrical Airfoil (no camber ): the center must be shift away from the y-axis. i.e. make the center at (0.02, 0).
• Cambered Airfoil (no thickness): the center must be shifted away from the x-axis. i.e. make the center at (0, 0.02).
• Airfoil with Camber and Thickness: the circle is shifted away from both the x- and y-axes. i.e. (-0.02, 0.05).
Generally, xt>xc should be used. This section of the program does very little error checking on the user's input and can produce strange results. The parameter Δ denotes the "shift in origin in the preliminary transformation" and "can vary between 0 and 0.8" (Jones).
Comments: This is the “classic” book on airfoil design and data. Approximately half of the book is devoted to data (coordinates, wind-tunnel tests, etc) of NACA airfoils. The first half is an introduction to airfoil design, covering such topics as: simple flows, 2-d wing theory, viscosity, high-lift devices, etc. A chapter is devoted to airfoil families, and describes the NACA airfoils. It’s a good book to buy, loaded with information, and only $12.95.
Comments: A good beginning book on basic aerodynamics. This is not the most recent edition, and the newer one has more pictures and text. Has some good background information on famous people in aero. history, as well as some information on NACA/NASA airfoil history.
Comments: A more recent book on airfoils by noted airfoil designer Eppler. Like the others, it starts off with theory and includes an airfoil catalog. The catalog includes a large number of airfoils designed by Eppler for a variety of uses. Also discusses an inverse airfoil design method developed by the author and used in several computer programs (ie, see NASA TM-80210).
Comments: Covers wing theory from the ground up, sections to swept wings. Easy to read and in a more comfortable format as compared to other books. Has a good sense of the history behind the developments.
Comments: I found this book in the Stanford University library and I don’t know how available it is elsewhere. It is similar in format to Abbot and von Doenhoff, in that the first half is mostly theory, with the last containing results of various airfoils tested in numerous wind tunnels. It has a little more detail on the NACA 4 and 5 digit airfoil construction than does Abbott and von Doenhoff, and information on non-NACA airfoils.
