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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.