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WINGSECTIONS Description:

One-liner:  Prepares a wing surface as 2D sections in B-spline form
----------

Purpose:
--------

   WINGSECTIONS completes a simplified form of wing surface definition
   from previously-prepared chord/thickness data and associated defining
   sections.  The input sections are in B-spline form, and the results are
   output as an expanded file of B-spline sections along with a summary
   tabulation and an expanded file of XY coordinates for possible use by
   a flow solver.

Method:
-------

   The simplifying assumption here is that all sections can be represented
   adequately by B-spline curves with the SAME KNOTS. (See a version of the
   SMOOTH program for methods of determining such B-spline representations
   of related XY datasets.)

   As long as two sections have the same knots, lofting of intermediate
   sections can be achieved by lofting the control points.  This allows
   standard algebraic methods to produce a compact surface representation
   that is readily adapted by NURBS-based CAD/CAM systems as a full 3-D
   surface.  Ideally, the same procedure could provide an alternative
   input scheme for flow solver applications, although a CAD system is
   better suited to geometry refinements such as detailed wing tip design.

   Initially, WINGSECTIONS uses a slightly-modified version of the
   geometry summary table output by R22OPT for the thickness/chord data.
   For each station with "LOFT" = 1, a defining section in B-spline curve
   form is expected.  The defining sections may be normalized (or not).
   They should be concatenated as one input file.

   Sample thickness/chord data file:
   ---------------------------------

   OAW-1E Geometry (Squared-tip form)                          <Title>
   KG         Z       XLE       YLE     CHORD  ...    MAX T  ...  LOFT
    1 -203.4000  10.87916   0.00000  21.80275  ...  1.27510  ...     0
    2 -197.1225  10.34812   0.00000  23.46226  ...  1.57230  ...     0
    3 -190.8450   9.81707   0.00000  25.12178  ...  1.87720  ...     1
    4 -187.6130   9.54366   0.00000  25.97618  ...  2.06160  ...     0
    . .........   .......   .......  ........  ...  .......  ...     .
   43  -61.5653   0.03096   0.00000  55.70325  ...  8.88560  ...     0
   44  -58.3333   0.00000   0.00000  55.80000  ...  8.92800  ...     1
    . .........   .......   .......  ........  ...  .......  ...     .
   58   58.3333   0.00000   0.00000  55.80000  ...  8.92800  ...     1
   59   61.5653   0.03096   0.00000  55.70325  ...  8.90020  ...     0
    . .........   .......   .......  ........  ...  .......  ...     .
   98  187.6130   9.54366   0.00000  25.97618  ...  1.33900  ...     0
   99  190.8450   9.81707   0.00000  25.12178  ...  1.11590  ...     1
  100  197.1225  10.34812   0.00000  23.46226  ...  0.88500  ...     0
  101  203.4000  10.87916   0.00000  21.80275  ...  0.36720  ...     0

   Corresponding defining sections file:
   -------------------------------------

   OAW-1E-P2-MOD2 Tip-cap Section                                <Title>
     1.000000000000000       2.000000000000000       5.000000000000000
     21.00000000000000       21.00000000000000

   0.0000000000000000E+00  0.0000000000000000E+00  0.0000000000000000E+00
   0.0000000000000000E+00  0.0000000000000000E+00  9.1353959917732475E-02
   0.2411894763703840      0.4024486663234111      0.5634075800663552
   0.7232546095157547      0.8761017106844363      0.9779216600852452
   1.022438833587189       1.065594150116754       1.154251426767800
   1.286308448870403       1.428047814045446       1.568080209559026
   1.710104876249171       1.852958747840903       1.984070742665636
   2.067673456116899       2.067673456116899       2.067673456116899
   2.067673456116899       2.067673456116899

    1.000000000000000      0.9766573616010096      0.9167987120914935
   0.8182593557168120      0.6759316525938030      0.5204441164611799
   0.3669437255341476      0.2052794078141187      0.1237065524658922
  -5.3327239734320598E-03 -1.3476529667296819E-03  7.8166813309687295E-02
   0.1828410957291661      0.2952688069166972      0.4437506124776002
   0.5805998573300908      0.7177141130728990      0.8390485132513349
   0.9283616157847692      0.9785103137567076       1.000000000000000

   4.7510568983852863E-03  4.2093382707367472E-03  5.6186343982026685E-03
  -5.3332570885323248E-04 -9.6907468475426527E-03 -1.7661125500254172E-02
  -3.1396893930427520E-02 -2.6467468887536488E-02 -2.1503660335958938E-02
  -1.7591147529822391E-02  1.5159539809190553E-02  4.0424128341521668E-02
   4.8592957581737368E-02  4.6747271055867917E-02  4.4292514180655268E-02
   4.6004845731045817E-02  3.6009187829119820E-02  2.3870693882375195E-02
   1.4528201781536322E-02  9.4037158124965926E-03  7.2510391473770142E-03
   OAW 60-085-16 (OAW-1 Cabin section)            <Next defining section>
   1.000000000000000       2.000000000000000       5.000000000000000
   21.00000000000000       21.00000000000000

   0.0000000000000000E+00  0.0000000000000000E+00  0.0000000000000000E+00
   0.0000000000000000E+00  0.0000000000000000E+00  9.1353959917732475E-02
   0.2411894763703840      0.4024486663234111      0.5634075800663552
   0.7232546095157547      0.8761017106844363      0.9779216600852452
   1.022438833587189       1.065594150116754       1.154251426767800
   1.286308448870403       1.428047814045446       1.568080209559026
   1.710104876249171       1.852958747840903       1.984070742665636
   2.067673456116899       2.067673456116899       2.067673456116899
   2.067673456116899       2.067673456116899                <Same knots>

   1.000000000000000       0.9766573684613700      0.9167986913545925
   0.8182593719759367      0.6759316192254129      0.5204440817792035
   0.3669437646467861      0.2052793407910668      0.1237065913369712
  -5.3327403303544115E-03 -1.3476487841357643E-03  7.8166807256873784E-02
   0.1828411143917873      0.2952687381718988      0.4437506889818151
   0.5805997456052916      0.7177141687293529      0.8390484488001356
   0.9283616554188250      0.9785102941149742       1.000000000000000

  -2.4999999441206455E-03 -1.5764163893617429E-03 -3.8547663530724645E-04
  -1.0803315819805590E-02 -3.8935721655883260E-02 -5.1152378185592381E-02
  -5.1869694038945192E-02 -5.0224055012760078E-02 -5.0413761744842232E-02
  -3.5318966792019309E-02  3.0945843199744209E-02  7.4389077816659148E-02
   9.5813309764173755E-02  0.1101315601432895      0.1102606125877267
   9.1098402348239831E-02  6.2800820726638147E-02  3.6244110229431285E-02
   1.8563923826951780E-02  8.3565019335236754E-03  2.4999999441206455E-03
   <The next section follows similarly.>

Points to note:
---------------

   > The 5-word header of each curve must be readable list-directed.
     It is offset for this reason.  The other blank lines are for
     human readability only.

   > A compact representation is the goal here.  (Otherwise, a vast
     collection of points defining the wing section could be supplied
     to the CAD system.)

History:
--------

   02/23/93  D.A.Saunders  Initial implementation.
   02/27/93    "     "     Added discretized output file for R22OPT, etc.
   03/07/93    "     "     Added more commentary; checked for mismatches.
   04/14/93    "     "     Allowed for 72 pts. per surface.
   06/16/93    "     "     Allowed for 75 control pts. per wing section.

Author:   David Saunders, Sterling Software/NASA Ames Research Center
-------                                     Moffett Field, CA
Source: README, updated 2013-10-31