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      User's Guide for the Revised Wave Drag Analysis Program


                          6 April 1992

                        L. A. McCullers
                          ViGYAN, Inc.
                         Mail Stop 412
                  NASA Langley Research Center
                       Hampton, VA 23665
                         (804) 864-7631



                          INTRODUCTION


     Awave is a streamlined, modified version of the Harris
far-field wave drag program described in the reference.  It has
all of the capabilities and accuracy of the original program plus
the ability to include the approximate effects of angle of
attack.  It is an order of magnitude faster, and improvements to
the integration schemes have reduced numerical integration errors
by an order of magnitude.  A formatted input echo has been added
so that those not intimately familiar with the code can tell what
has been input.


REFERENCE: Harris, Roy V., Jr.  An Analysis and Correlation of
           Aircraft Wave Drag.  NASA TMX-947.  March 1964.



                       INPUT DESCRIPTION


     Input for the wave drag analysis program is in a formatted,
card-image form.  Consequently, each line of the input file will
be refered to as a card.  All values default to zero if not
input.  All configurations are assumed to be symmetric with
respect to the X-Z plane so that only the "positive y" half of the
vehicle is defined.  The option exists to stack input files (see
NCON on the Case Control Card) to reanalyze a configuration with
minor geometry changes.  For the second and successive
configurations, the control Jx for unchanged components may be set
to 2 to avoid repeating the input data for that component.



                    Problem Control Cards


Title Card: Format(A80)

  Any 80-column alphanumeric title.


Geometry Input Control Card: Format(24I3)  Integer input must be
  right justified in the indicated 3-column field.

 Variable   Columns    Description

  J0          1- 3     = 0, No reference area
                       = 1, Reference area will be input and used
                       = 2, Reference area from previous
                            configuration will be used

  J1          4- 6     = 0, No wing
                       = 1, Cambered wing data will be input
                       =-1, Uncambered wing data will be input
                       = 2, Wing data from previous configuration
                            will be used

  J2          7- 9     = 0, No fuselage
                       = 1, Arbitrarily shaped fuselage
                       =-1, Circular fuselage
                       = 2, Fuselage data from previous
                            configuration will be used

  J3         10-12     = 0, No pod
                       = 1, Pod data will be input
                       = 2, Pod data from previous configuration
                            will be used

  J4         13-15     = 0, No fin (Vertical tail)
                       = 1, Fin data will be input
                       = 2, Fin data from previous configuration
                            will be used

  J5         16-18     = 0, No canard (Horizontal tail)
                       = 1, Canard data will be input
                       = 2, Canard data from previous
                            configuration will be used

  J6         19-21     = 1, Complete configuration is symmetrical
                            with respect to the X-Y plane, implies
                            an uncambered circular fuselage if a
                            fuselage exists.
                       =-1, The circular fuselage is symmetrical
                            (uncambered)
                       = 0, No X-Y plane symmetry

  NWAF       22-24     Number of airfoil sections used to describe
                       the wing (minimum = 2, maximum = 20)

  NWAFOR     25-27     Number of stations at which ordinates are
                       input for each wing airfoil section
                       (minimum = 3, maximum = 30)
                       If given a negative sign, the program
                       will expect to read both upper and lower
                       ordinates.  If positive, the airfoil is
                       assumed to be symmetrical.

  NFUS       28-30     Number of fuselage segments
                       (minimum = 1, maximum = 4)

  NRADX(1)   31-33     Number of points per station used to
                       represent a half-section of the first
                       fuselage segment.  For circular fuselages,
                       NRADX y and z coordinates are computed
                       (minimum = 3, maximum = 30)

  NFORX(1)   34-36     Number of stations for first fuselage
                       segment (minimum = 4, maximum = 30)

  NRADX(2)   37-39     Same as NRADX(1) but for second segment

  NFORX(2)   40-42     Same as NFORX(1) but for second segment

  NRADX(3)   43-45     Same as NRADX(1) but for third segment

  NFORX(3)   46-48     Same as NFORX(1) but for third segment

  NRADX(4)   49-51     Same as NRADX(1) but for fourth segment

  NFORX(4)   52-54     Same as NFORX(1) but for fourth segment

  NP         55-57     Number of pods described (maximum = 9)

  NPODOR     58-60     Number of stations at which pod radii are
                       input (minimum = 4, maximum = 30)

  NF         61-63     Number of fins (vertical tails) described
                       (maximum = 6) If given a negative sign, the
                       program will expect to read ordinates for
                       both the outboard and inboard sides of the
                       fins.  If positive, the airfoils are
                       assumed to be symmetrical.

  NFINOR     64-66     Number of stations at which ordinates are
                       input for each fin airfoil
                       (minimum = 3, maximum = 10)

  NCAN       67-69     Number of canards (horizontal tails)
                       defined (maximum = 2).  If given a negative
                       sign, the program will expect to read
                       ordinates for both the root and tip.  If
                       positive, the root and tip airfoils are
                       assumed to be the same.

  NCANOR     70-72     Number of stations at which ordinates are
                       input for each canard airfoil
                       (minimum = 3, maximum = 10) 
                       If given a negative sign, the program
                       will expect to read both upper and lower
                       ordinates.  If positive, the airfoil is
                       assumed to be symmetrical.


Reference Area Card: Format(3F7.0)  Input only if J0 = 1

  REFA          Reference wing area used for drag coefficient
                computation

  CBAR          Wing reference chord for use in aerodynamic moment
                coefficients

  XMC           x coordinate of moment reference center

Note: CBAR and XMC are not used in AWAVE but may be used in other
      programs which use this type of geometry deck.



                    Configuration Data Cards 


     Data describing the configuration are input in seven column
fields with a decimal point, with up to ten fields per card.  If
more than ten fields are required, additional cards are used.

     Columns 73 and up are used for identification.  This usually
consists of a key word and a number or combination of numbers
identifying that card within the group.  For example, "WAFORG 3"
would be the card specifying the location of the third airfoil,
and "TZORD 3-2" might be the second card defining the mean camber
line for the third airfoil.  This identification is not used by
the program, but it is useful because all configuration data are
input in the same format, and it all looks alike.  Suggested
identifiers are provided.



                        Wing Data Cards


     If J1 = 0 or 2, no wing data is input.  Only one wing may be
defined for a configuration.  Input must include Wing Percent
Chord Location Card(s), Wing Airfoil Location Cards, and Wing
Airfoil Ordinate Cards.  Wing Mean Camber Line Cards are optional
depending on J1.


Wing Percent Chord Location Card(s): Format(10F7.0)  NWAFOR values
  are input, ten to a card.  (Identifier = XAF)

  XAF(I)        Locations in percent chord ((x/c)*100) at which the
                ordinates of all wing airfoils are to be specified.


Wing Airfoil Location Cards: Format(4F7.0)  NWAF cards are input,
  one for each airfoil, in order, from the most inboard airfoil to
  the most outboard.  (Identifier = WAFORG)

  Columns       Description

    1- 7        x coordinate of airfoil leading edge

    8-14        y coordinate of airfoil leading edge

   15-21        z coordinate of airfoil leading edge

   22-28        airfoil streamwise chord length


Wing Mean Camber Line Cards: Format(10F7.0)  Input only if J1 = 1.
  NWAFOR values are input for each airfoil, ten to a card.  Each
  airfoil is started on a new card.  NWAF sets of data are input,
  one for each airfoil.  (Identifier = TZORD)

  TZORD(I,J)    Delta z value, referenced to the z coordinate of
                the airfoil leading edge, at the Jth wing percent
                chord location for the Ith wing airfoil.


Wing Airfoil Ordinate Cards: Format(10F7.0)  NWAF sets of data are
  input, one for each airfoil. NWAFOR values are input for each
  airfoil, ten to a card.  Each airfoil is started on a new card.
  If NWAFOR < 0, the wing is not symmetric and two sets of data
  are input for each airfoil, the distance from the mean camber
  line to the upper surface followed (on a new card) by the
  distance from the lower surface to the mean camber line.  Both
  are expressed as percent chord as described below.  (Identifier
  = WAFORD)

  WAFORD(I,J)   Airfoil half-thickness ordinates of the wing,
                expressed as percent chord (100 * (t/c) / 2),
                at the Jth wing percent chord location for the
                Ith wing airfoil.



                      Fuselage Data Cards


     If J2 = 0 or 2, no fuselage data is input.  Otherwise, NFUS
sets of fuselage data are input.  Each set consists of Fuselage
Station Cards and, depending on the options specified on the
Geometry Input Control Card, Fuselage Camber Cards, Fuselage Area
Cards, and/or Fuselage cross section y coordinate and z coordinate
Cards.  Fuselage segments and stations within each segment must be
in order of increasing x.


Fuselage Station Card(s): Format(10F7.0)   NFORX(I) values are 
  input, ten to a card, for the Ith fuselage segment.  
  (Identifier = XFUS)

  XFUS(J,I)     x coordinate of the Jth station for the Ith
                fuselage segment


Fuselage Camber Card(s): Format(10F7.0)   Input only for circular,
  cambered fuselages (J2 = -1, J6 = 0).  NFORX(I) values are 
  input, ten to a card, for the Ith fuselage segment.  
  (Identifier = ZFUS)

  ZFUS(J,I)     z coordinate of the center of the Jth station of
                the Ith fuselage segment


Fuselage Area Card(s): Format(10F7.0)   Input only for circular
  fuselages (J2 = -1).  NFORX(I) values are input, ten to a card,
  for the Ith fuselage segment.  (Identifier = FUSARD)

  FUSARD(J,I)   Cross-sectional area of the Jth station of the Ith
                fuselage segment


Fuselage Coordinate Card(s): Format(10F7.0)  Input only for
  arbitrary cross section fuselages (J2 = 1).  NRADX(I) values are
  input, ten to a card, for the y coordinate followed by NRADX(I)
  values for the z coordinate for the points defining a
  half-section of the Jth station of the Ith fuselage segment.
  The z coordinates are started on a new card.  The points are
  ordered from bottom to top.  (Identifiers = Y and Z)

  Y(K,J,I)      y coordinate of the Kth point defining the Jth
                station of the Ith fuselage segment

  Z(K,J,I)      z coordinate of the Kth point defining the Jth
                station of the Ith fuselage segment



                    Pod (Nacelle) Data Cards 


     If J3 = 0 or 2, no pod data is input.  Otherwise, NP sets of
cards are input, one for each pod defined.  Each set consists of a
Pod Location Card and Pod Station and Radius Cards.  Pods are
located symmetrically, i.e., unless the y coordinate is 0., a
mirror image at -y is asssumed.  If y = 0., a single pod on the
configuration centerline is defined.


Pod (Nacelle) Location Card: Format(3F7.0)  One card is input
  in each set defining the pod location.  (Identifier = PODORG)

  Columns       Description

    1- 7        x coordinate of the origin of the Ith pod

    8-14        y coordinate of the origin of the Ith pod

   15-21        z coordinate of the origin of the Ith pod


Pod (Nacelle) Station Card(s): Format(10F7.0)   NPODOR values are 
  input, ten to a card, for the pod currently being defined.
  (Identifier = XPOD)

  XPOD(I,J)     X location of the Jth station for the Ith pod
                referenced to the pod origin, i. e., the first
                value must be zero, and the last value is the
                length of the pod.


Pod (Nacelle) Radius Card(s): Format(10F7.0)   NPODOR values are 
  input, ten to a card, for the pod currently being defined.
  (Identifier = PODR)

  PODR(I,J)     Pod radius at the Jth station of the Ith pod



                  Fin (Vertical Tail) Data Cards 


     If J4 = 0 or 2, no fin data is input.  Otherwise, NF sets of
cards are input, one for each fin defined.  Each set consists of a
Fin Planform Card, a Fin Percent Chord Location Card, and Fin
Airfoil Ordinate Card(s).  Fins are located symmetrically, i.e.,
unless the y coordinates are 0., a mirror image at -y is asssumed.
If y = 0., a single vertical tail on the configuration centerline
is defined.


Fin (Vertical Tail) Planform Card: Format(3F7.0)  One card is
  input in each set defining the fin location and planform.
  (Identifier = FINORG)

  Columns       Description

    1- 7        x coordinate of the lower airfoil leading edge

    8-14        y coordinate of the lower airfoil leading edge

   15-21        z coordinate of the lower airfoil leading edge

   22-28        Chord length of the lower airfoil

   29-35        x coordinate of the upper airfoil leading edge

   36-42        y coordinate of the upper airfoil leading edge

   43-49        z coordinate of the upper airfoil leading edge

   50-56        Chord length of the upper airfoil


Fin (Vertical Tail) Percent Chord Location Card: Format(10F7.0)
  NFINOR values are input.  (Identifier = XFIN)

  XFIN(I,J)     Locations in percent chord ((x/c)*100) at which
                the airfoil ordinates of the Ith fin are to be
                specified.


Fin (Vertical Tail) Airfoil Ordinate Card(s): Format(10F7.0)
  NFINOR values are input.  If NF < 0, the fin airfoil is not
  symmetric with respect to the inclined plane defined on the Fin
  Planform Card and two sets of ordinates are input, the distance
  from the inclined plane to the outboard surface followed by the
  distance from the inboard surface to the inclined plane.  Both
  are expressed as percent chord as described below.
  (Identifier = FINORD)

  FINORD(I,J)   Airfoil half-thickness ordinates of the Ith fin,
                expressed as percent chord (100 * (t/c) / 2).



               Canard (Horizontal Tail) Data Cards 


     If J5 = 0 or 2, no canard data is input.  Otherwise, NCAN
sets of cards are input, one for each canard or horizontal tail
defined.  Each set consists of a Canard Planform Card, a Canard
Percent Chord Location Card, and Canard Airfoil Ordinate Card(s).


Canard (Horizontal Tail) Planform Card: Format(3F7.0)  One card is
  input in each set defining the canard location and planform.
  (Identifier = CANORG)

  Columns       Description

    1- 7        x coordinate of the inboard airfoil leading edge

    8-14        y coordinate of the inboard airfoil leading edge

   15-21        z coordinate of the inboard airfoil leading edge

   22-28        Chord length of the inboard airfoil

   29-35        x coordinate of the outboard airfoil leading edge

   36-42        y coordinate of the outboard airfoil leading edge

   43-49        z coordinate of the outboard airfoil leading edge

   50-56        Chord length of the outboard airfoil


Canard (Horizontal Tail) Percent Chord Location Card:
  Format(10F7.0)  NCANOR values are input.  (Identifier = XCAN)

  XCAN(I,J)     Locations in percent chord ((x/c)*100) at which
                the airfoil ordinates of the Ith canard are to be
                specified.


Canard (Horizontal Tail) Airfoil Ordinate Card(s): Format(10F7.0)
  NCANOR values are input.  If NCAN < 0, the outboard canard
  airfoil is different from the inboard airfoil, and two sets of
  ordinates are input, inboard airfoil data followed (starting on
  a new card) by outboard airfoil data.  If NCANOR < 0, the canard
  airfoil is not symmetric with respect to the inclined plane
  defined on the Canard Planform Card and two sets of ordinates
  are input, the distance from the inclined plane to the upper
  surface followed by the distance from the lower surface to the
  inclined plane.  If both NCAN < 0 and NCANOR < 0, four sets of
  ordinates are required in the following order: inboard upper
  surface, outboard upper surface, inboard lower surface, and
  outboard lower surface.  Each set is started on a new card.
  (Identifier = CANORD)

  CANORD(I,J)   Airfoil half-thickness ordinates of the Ith canard,
                expressed as percent chord (100 * (t/c) / 2).



                     Case Definition Input Data


Case Control Card: Format(A4,11I4)  Integer input must be right
  justified in the indicated 4-column field.  As many Case Control
  Cards as desired may be input.  If NREST > 0, the Case Control
  Card is followed by a Restraint Card, but only one Restraint
  Card may be input per configuration.

 Variable   Columns    Description

  NCASE       1- 4     Case number or other 4 character descriptor

  MACH        5- 8     Mach number * 1000

  NX          9-12     Number of intervals on x axis

  NTHETA     13-16     Number of thetas

  NREST      17-20     Number of restraint points for drag
                       minimization (maximum = 10)

  NCON       21-24     Configuration control
                       = 1, A new configuration follows this case.
                            (Title Card, Geometry Input Control Card,
                            etc.) This option is normally used when
                            only minor geometry changes are desired.
                       = 0, Otherwise (another case or nothing)

  ICYC       25-28     Number of Optimization cycles ( < 10)

  KKODE      29-32     Slope check control
                       = 0, Turn on slope checking
                       = 1, No slope checking

  JRST       33-36     Equivalent body data control
                       = 0, Compute equivalent body areas, drags etc.
                       = 1, Perform minimum calculations required for
                            wave drag (saves ~25% execution time)

  IALPH      37-40     Angle of attack x 100

  IUP1       41-44     Unit number for plot tape 1 which contains Mach
                       sliced area data for theta = -90 degrees
                       = 0, Plot tape not written
                       = Integer > 6, plot data on file PLOT1

  IUP2       45-48     Unit number for plot tape 2 which contains
                       equivalent body area data
                       = 0, Plot tape not written
                       = Integer > 6, plot data on file PLOT2


Restraint Card: Format(10F7.0)  Input only if NREST > 0

  XREST(I)      X locations of fuselage restraint points.  The
                fuselage cross-sectional area is held constant at
                these locations during optimization.
