The Panknin Twist Formula
We met Dr. Walter Panknin at the 1989 Madison Area RC Society
Symposium. His presentation at the MARCS Symposium, entitled "Flying
Rainbows," included all of the fundamental information required to
design and build a high performance swept wing tailless sailplane.
Copies of the 1989 Symposium Proceedings are no longer available
through the Madison Area Radio Control Society. High resolution GIF and
JPG images of the "Flying Rainbows" portion of the Proceedings are
available from this link.
The formula presented below is important in that it provides, early in
the design process, a well tested method of determining the geometric
wing twist required for stable flight.
There are six variables which influence the amount of required geometric wing twist:
The greater the taper ratio, the more twist will be required. This is
due to the loss of airfoil efficiency as the wing tip chord gets
The greater the aspect ratio, the less twist is required. However, as
aspect ratio increases, and the wing chord gets proportionally smaller,
it becomes more difficult to build a strong stiff wing.
sweep back angle:
The greater the sweep back angle, the less twist will be required.
However, angles of sweep back in excess of 20 degrees adversely affect
air flow over the wing and may lead to control problems.
airfoil moment coefficients:
The moment coefficient of the whole aircraft must be positive for
stability. While some of this moment is derived from the downforce
generated by the wing tips, it is also greatly influenced by the
pitching moments of the airfoils used. Sections used on contemporary
swept wing tailless aircraft have near zero pitching moments.
desired static stability value:
Increased static stability (CG further ahead of the neutral point) dictates increased wing twist.
design coefficient of lift:
The greater the design coefficient of lift, the more wing twist will be
required. The design coefficient of lift should be the coefficient of
lift at cruise speed so that trim drag is minimized. Some amount of up
trim is expected to be necessary for thermalling.
airfoil zero lift angles:
The zero lift angles of the root and tip airfoils influence the geometric wing twist required.
Calculation of required wing twist using the above formulae can be
easily accomplished on a hand-held calculator. If you have a computer
and Microsoft QuickBASIC, you might want to download the documentation
and programs from the links below.
A sample planform, and computation of required geometric wing twist...
= 120 inches; root chord = 13 inches; tip chord = 11 inches; sweep
angle = 17 degrees, as measured at the quarter chord line.
section E 222, zero lift angle = -3.65 degrees, pitching moment =
-0.097. Tip section E 230, zero lift angle = +1.73, pitching moment =
Design lift coefficient = 0.6; stability = 0.05
The taper ratio is 11/13 = 0.85; the average (mean) chord is (13 + 11)/2 = 12; the aspect ratio is 120/12 = 10.
K1 turns out to be 0.52; K2 equals 0.48.
main formula shows that a total of -8.6 degrees is required for this
planform. Once aerodynamic twist (due to the zero lift angles of the
two sections) is accounted for, it is found that roughly 3.2 degrees of
geometric washout is required.
Applications and spreadsheets
MAC; the Panknin twist program, the disk files creator application, and documentation for the Macintosh.
With the assistance of Alan Halleck, we've written QuickBASIC
applications for both the Macintosh and IBM-compatible operating
systems. The text files identified by the links below each contain
documentation and two programs, one for saving section aerodynamic data
to disk and the other for computing the wing twist, CG location, and
other variables. Set your web browser to save the appropriate link as a
text file. You can then open the saved text file with a text editor.
The coding for the two programs needs to be extracted and resaved
within separate files. After you've read the documentation and know how
the two programs work, use QuickBASIC to read and run the individual
IBM-compatible; the Panknin twist program, the disk files creator application, and documentation for IBM compatibles.
twist2.xls.zip; the twist2 template for Excel.
- Joa Harrison has written an Excel/Appleworks spreadsheet template
which includes all of the computations performed by the QuickBASIC
twist2.cwk.sit; the twist2 template for Appleworks.
twist3.xls.zip; the twist3 template for Excel.
- Glyn Fonteneau modified Joa's spreadsheet to include winglet
dimensions, based on information in Nickel and Wohlfahrt's "Tailless
Aircraft in Theory and Practice."
twist3.cwk.sit; the twist3 template for Appleworks.
No matter the resulting planform of your design, always keep the following five rules in mind:
Understand what you do
Build stiff, not just strong
There can be NO play in the linkages
Be sure of the precise location of the CG
Have confidence that it will fly
The complete text of Dr. Panknin's address, along with the full complement of diagrams, is available within the Proceedings of the 1989 MARCS Symposium. Contact Al Scidmore, 5013 Dorset Drive, Madison WI 53711 USA for ordering information.
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