
XFOIL 6.9  User Primer                   THE last update   30 Nov 2001

Mark Drela, MIT Aero & Astro
Harold Youngren, Aerocraft, Inc.


General Description
===================
XFOIL is an interactive program for the design and analysis of subsonic
isolated airfoils. It consists of a collection of menu-driven routines
which perform various useful functions such as: 

  - Viscous (or inviscid) analysis of an existing airfoil, allowing
       * forced or free transition
	       * transitional separation bubble(s)
       * limited trailing edge separation
       * lift and drag predictions just beyond CLmax
       * Karman-Tsien compressibility correction

  - Airfoil design and redesign by interactive specification of
    a surface speed distribution via screen cursor or mouse. Two 
    such facilities are implemented.
       * Full-Inverse, based on a complex-mapping formulation
       * Mixed-Inverse, an extension of XFOIL's basic panel method
    Full-inverse allows multi-point design, while Mixed-inverse allows 
    relatively strict geometry control over parts of the airfoil.

  - Airfoil redesign by interactive specification of 
    new geometric parameters such as
       * new max thickness and/or camber
       * new LE radius
       * new TE thickness
       * new camber line via geometry specification
       * new camber line via loading change specification
       * flap deflection
       * explicit contour geometry (via screen cursor)

  - Blending of airfoils

  - Drag polar calculation with fixed or varying Reynolds and/or 
    Mach numbers.

  - Writing and reading of airfoil geometry and polar save files

  - Plotting of geometry, pressure distributions, and polars
     (Versaplot-derivative plot package used)

XFOIL is best suited for use on a good workstation.  A high-end PC 
is also effective, but must run Unix to support the X-Windows graphics.
The source code of XFOIL is Fortran 77.  The plot library also
uses a few C routines for the X-Windows interface.


History
-------
XFOIL 1.0 was written by Mark Drela in 1986.  The main goal 
was to combine the speed and accuracy of high-order panel methods
with the new fully-coupled viscous/inviscid interaction 
method used in the ISES code developed by Drela and Giles. 
A fully interactive interface was employed from the beginning
to make it much easier to use than the traditional batch-type 
CFD codes.  Several inverse modes and a geometry manipulator 
were also incorporated early in XFOIL's development, making 
it a fairly general airfoil development system.

Since version 1.0, XFOIL has undergone numerous revisions, 
upgrades, hacks, and enhancements.  These changes mainly originated 
from perceived shortcomings during actual design use, so XFOIL
is now strongly geared to practical airfoil development.
Harold Youngren provided the Xplot11 plot package which 
is a vast improvement over the grim Versaplot-type package 
used initially.  Enhancements and suggestions from Youngren 
and other people were also incorporated into XFOIL itself
along the way.

Over the past few years, bug reports and enhancement 
suggestions have slowed to practically nil, and so
after a final few enhancements from version 6.8, XFOIL 6.9 
is officially "frozen" and being made public.  Although 
any bugs will likely be fixed, no further development 
is planned at this point.  Method extensions are being 
planned, but these will be incorporated in a completely
new next-generation code.


Note to code developers and code enhancers...
XFOIL does not exactly have the cleanest implementation,
but it isn't too bad considering its vast modification 
history.  Feel free to muck with the code as you like,
provided everything is done under the GPL agreement.
Drela and Youngren will not be inclined to assist with 
any code modifications at this point, however, since we
each have a dozen other projects waiting.  So proceed
at your own risk.


Theory References
-----------------
The general XFOIL methodology is described in
  Drela, M., 
  XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils,
  Conference on Low Reynolds Number Airfoil Aerodynamics,
  University of Notre Dame, June 1989.

which also appears as a chapter in:
  Low Reynolds Number Aerodynamics.  T.J. Mueller (Editor).
  Lecture Notes in Engineering #54. Springer Verlag.  1989.
  ISBN 3-540-51884-3
  ISBN 0-387-51884-3

The boundary layer formulation used by XFOIL is described in:
  Drela, M. and Giles, M.B.
  Viscous-Inviscid Analysis of Transonic and Low Reynolds Number Airfoils
  AIAA Journal, 25(10), pp.1347-1355, October 1987.

The blunt trailing edge treatment is described in:
  Drela, M.,
  Integral Boundary Layer Formulation for Blunt Trailing Edges,
  Paper AIAA-89-2166, August 1989.

Other related literature:
  Drela, M.,
  Elements of Airfoil Design Methodology,
  Applied Computational Aerodynamics, (P. Henne, editor),
  AIAA Progress in Aeronautics and Astronautics, Volume 125, 1990.

  Drela, M.,
  Low-Reynolds Number Airfoil Design for the MIT Daedalus Prototype: A Case Study,
  Journal of Aircraft, 25(8), pp.724-732, August 1988.

  Drela, M.,
  Pros and Cons of Airfoil Optimization,
  Chapter in "Frontiers of Computational Fluid Dynamics, 1998",
  D.A. Caughey, M.M. Hafez, Eds.
  World Scientific, ISBN 981-02-3707-3


Inviscid Formulation
--------------------
The inviscid formulation of XFOIL is a simple linear-vorticity stream
function panel method.  A finite trailing edge base thickness is modeled
with a source panel.  The equations are closed with an explicit Kutta
condition.  A high-resolution inviscid calculation with the default 
160 panels requires seconds to execute on a RISC workstation.  Subsequent 
operating points for the same airfoil but different angles of attack 
are obtained nearly instantly.

A Karman-Tsien compressibility correction is incorporated, allowing
good compressible predictions all the way to sonic conditions.  The
theoretical foundation of the Karman-Tsien correction breaks down
in supersonic flow, and as a result accuracy rapidly degrades as the
transonic regime is entered.  Of course, shocked flows cannot be
predicted with any certainty.


Inverse Formulation
-------------------
There are two types of inverse methods incorporated in XFOIL:
Full-Inverse and Mixed-Inverse.  The Full-Inverse formulation
is essentially Lighthill's and van Ingen's complex mapping method,  
which is also used in the Eppler code and Selig's PROFOIL code.  
It calculates the entire airfoil geometry from the entire surface 
speed distribution.  The Mixed-Inverse formulation is simply 
the inviscid panel formulation (the discrete governing equations 
are identical) except that instead of the panel vortex strengths 
being the unknowns, the panel node coordinates are treated as 
unknowns wherever the surface speed is prescribed.  Only a part 
of the airfoil is altered at any one time, as will be described later.  
Allowing the panel geometry to be a variable results in a non-linear
problem, but this is solved in a straightforward manner with
a full-Newton method.


Viscous Formulation
-------------------
The boundary layers and wake are described with a two-equation lagged
dissipation integral BL formulation and an envelope e^n transition 
criterion, both taken from the transonic analysis/design ISES code.
The entire viscous solution (boundary layers and wake) is strongly 
interacted with the incompressible potential flow via the surface 
transpiration model (the alternative displacement body model is used 
in ISES).  This permits proper calculation of limited separation regions.
The drag is determined from the wake momentum thickness far downstream.
A special treatment is used for a blunt trailing edge which fairly
accurately accounts for base drag.  

The total velocity at each point on the airfoil surface and wake, with 
contributions from the freestream, the airfoil surface vorticity, and
the equivalent viscous source distribution, is obtained from the panel
solution with the Karman-Tsien correction added.  This is incorporated
into the viscous equations, yielding a nonlinear elliptic system
which is readily solved by a full-Newton method as in the ISES code.
Execution times are quite rapid, requiring about 10 seconds on a RISC
workstation for a high-resolution calculation with 160 panels.  For a 
sequence of closely spaced angles of attack (as in a polar), the 
calculation time per point can be substantially smaller.

If lift is specified, then the wake trajectory for a viscous calculation 
is taken from an inviscid solution at the specified lift.  If alpha is 
specified, then the wake trajectory is taken from an inviscid solution
at that alpha.  This is not strictly correct, since viscous effects will
in general decrease lift and change the trajectory.  This secondary
correction is not performed, since a new source influence matrix would
have to be calculated each time the wake trajectory is changed.  This
would result in unreasonably long calculation times.  The effect of this
approximation on the overall accuracy is small, and will be felt mainly
near or past stall, where accuracy tends to degrade anyway.  In attached
cases, the effect of the incorrect wake trajectory is imperceptible.


Data Structure
==============
XFOIL stores all its data in RAM during execution.  Saving of the data 
to files is NOT normally performed automatically, so the user must be
careful to save work results before exiting XFOIL.  The exception to
this is optional automatic saving to disk of polar data as it's being
computed in OPER (described later).

Stored airfoils and polars
--------------------------
XFOIL 6.9 stores multiple polars and associated airfoils and parameters
during one interactive session.  Each such data set is designated by its 
"stored polar" index:

polar 1:  x,y, CL(a), CD(a)...  Re, Ma, Ncrit...
polar 2:  x,y, CL(a), CD(a)...  Re, Ma, Ncrit...
 .
 .

Not all of the data need to be present for each stored polar.
For example, x,y would be absent if the CL,CD polar was read in 
from an external file rather than computed online.

Earlier XFOIL versions in effect only allowed one stored airfoil 
and stored polar at a time.  The new multiple storage feature makes 
iterative redesign considerably more convenient, since the cases 
can contain multiple design versions which can be easily overlaid
on plots. 

Current and buffer airfoils
---------------------------
XFOIL 6.9 retains the concept of a "current airfoil"
and "buffer airfoil" used in previous versions.
These are the airfoils on which the various calculations
are performed, and they are distinct from the "polar" x,y coordinates 
described above.  The polar x,y are simply archived data, 
and do not directly participate in computations.  The polar
x,y must first be transferred into the current airfoil if 
they are to be used for computation.


Program Execution
=================

XFOIL is executed with

 % xfoil

When the program starts, the following top level menu and prompt appear: 

   QUIT   Exit program

  .OPER   Direct operating point(s)
  .MDES   Complex mapping design routine
  .QDES   Surface speed design routine
  .GDES   Geometry design routine

   SAVE f Write airfoil to labeled coordinate file
   PSAV f Write airfoil to plain coordinate file
   ISAV f Write airfoil to ISES coordinate file
   MSAV f Write airfoil to MSES coordinate file
   REVE   Reverse written-airfoil node ordering

   LOAD f Read buffer airfoil from coordinate file
   NACA i Set NACA 4,5-digit airfoil and buffer airfoil
   INTE   Set buffer airfoil by interpolating two airfoils
   NORM   Buffer airfoil normalization toggle

   BEND   Display structural properties of current airfoil

   PCOP   Set current-airfoil panel nodes directly from buffer airfoil points
   PANE   Set current-airfoil panel nodes ( 140 ) based on curvature
  .PPAR   Show/change paneling

  .PLOP   Plotting options

   WDEF f Write  current-settings file
   RDEF f Reread current-settings file
   NAME s Specify new airfoil name
   NINC   Increment name version number

   Z       Zoom    | (available in all menus)
   U       Unzoom  | 

 XFOIL   c>  


The commands preceded by a period place the user in another 
lower-level menu.  The other commands are executed immediately 
and the user is prompted for another top level command.  
The lowercase letters i,r,f,s following some commands indicate 
the type of argument(s) expected by the command:

  i  integer
  r  real
  f  filename
  s  character string

Commands will be shown here in uppercase, although they are not
case sensitive.

Typically, either the LOAD or the NACA command is issued first
to create an airfoil for analysis or redesign.  The NACA command
expects an integer argument designating the airfoil:

 XFOIL  c>  NACA 4415

As with all commands, omitting the argument will produce a prompt:

 XFOIL  c>  NACA

 Enter NACA 4 or 5-digit airfoil designation   i>  4415


The LOAD command reads and processes a formatted airfoil coordinate 
file defining an arbitrary airfoil.  It expects a filename argument:

 XFOIL  c>  LOAD e387.dat


The NACA or LOAD commands can be skipped if XFOIL is executed with 
a filename as an argument, as for example

 % xfoil e387.dat

which then executes the LOAD procedure before the first menu prompt 
is given.


Airfoil file formats
--------------------
LOAD recognizes four airfoil file formats:  Plain,  Labeled,  ISES,  MSES.
All data lines are significant with the exception of lines beginning
with "#", which are ignored.

Plain coordinate file
.....................

This contains only the X,Y coordinates, which run from the 
trailing edge, round the leading edge, back to the trailing edge 
in either direction:

X(1)  Y(1)
X(2)  Y(2)
 .     .
 .     .
X(N)  Y(N)



Labeled coordinate file
.......................

This is the same as the plain file, except that it also has an 
airfoil name string on the first line:

NACA 0012
X(1)  Y(1)
X(2)  Y(2)
 .     .

This is deemed the most convenient format to use.
The presence of the name string is automatically recognized if
it does not begin with a Fortran-readable pair of numbers.  Hence, 
"00 12 NACA Airfoil" cannot be used as a name, since the "00 12" 
will be interpreted as the first pair of coordinates.  "0012 NACA"
is OK, however.

Some Fortran implementations will also choke on airfoil names 
that begin with T or F.  These will be interpreted as logical
variables, defeating the name-detection logic.  Beginning the
name with _T or _F is a workable solution to this "feature".



ISES coordinate file
....................

This has four or five ISES grid domain parameters in addition to the name:

NACA 0012
-2.0 3.0 -2.5 3.0
X(1)  Y(1)
X(2)  Y(2)
 .     .

If the second line has four or more numbers, then these are interpreted
as the grid domain parameters.



MSES coordinate file
....................

This is the same as the ISES coordinate file, except that it can
contain multiple elements, each one separated by the line

999.0 999.0

The user is asked which of these elements is to be read in.  


Buffer airfoil normalization
----------------------------
XFOIL will normally perform all operations on an airfoil with the
same shape and location in cartesian space as the input airfoil.
However, if the normalization flag is set (toggled with the NORM 
command), the airfoil coordinates will be immediately normalized 
to unit chord and the leading edge will be placed at the origin.  
A message is printed to remind the user.

Buffer airfoil generation via interpolation
-------------------------------------------
The INTE command is new in XFOIL 6.9, and allows interpolating
or "blending" of airfoils in various proportions.  The polar shape 
of an interpolated airfoil will often be quite close to the 
interpolated polars of its two parent airfoils.  Extrapolation 
can also be done by specifying a blending fraction outside
the 0..1 range, although the resulting airfoil may be quite
weird if the extrapolation is excessive.

A good way to use INTE is to "augment" or "tone down" the
modifications to an airfoil performed in MDES or GDES.
For example, say airfoil B is obtained by modifying airfoil A:

 A -> MDES -> B

Suppose the modification changed A's polar in the right direction,
but not quite far enough.  The additional needed change can be
done by extrapolating past airfoil B in INTE:

Airfoil "0": A
Airfoil "1": B
Interpolating fraction 0..1 :  1.4
Output airfoil: C

Plotted along the "modification axis", the airfoils are:

A         B     C
0.0       1.0   1.4  ...

So airfoil C has 40% more of the change received by B in the redesign.  
Aifoil C's polar will also be changed about 40% more as intended.


Further buffer airfoil manipulation
-----------------------------------
The GDES facility allows very extensive manipulation of the buffer airfoil.
This will be described in much more detail in a later section.  If only
analysis is performed, the GDES facility would not normally be used.


Generation of current airfoil
-----------------------------
When the buffer airfoil coordinates are read from a file during startup,
or read in via the LOAD command, they are by default 
also copied directly into the ``current'', or working airfoil.  
Hence, no special action is needed to start analysis operations.  However, 
if the input airfoil has a poor point distribution (too many, too few, 
poorly spaced, etc), one can use PANE to create a better panel node 
distribution for the current airfoil on the splined buffer airfoil shape.  
The paneling routine increases the point density in areas of 
high curvature (i.e. the leading edge) and at the trailing edge 
to a degree specified by the user.  The user can also increase 
panel density over one additional interval on each airfoil side, 
perhaps near transition.  The current-airfoil paneling can be 
displayed and/or modified with PPAR. 

In some cases it is desirable to explicitly re-copy the buffer 
airfoil into the current airfoil via PCOP.  In previous XFOIL
versions this had to be done with the equivalent command sequence 
 LOAD
 GDES
 EXEC

With XFOIL 6.9, the GDES,EXEC commands after LOAD are now superfluous.

The NACA command automatically invokes the paneling routine to create 
a current airfoil with a suitable paneling.


Saving current airfoil coordinates
----------------------------------
A coordinate file in any one of these four formats can be written 
with the PSAV, SAVE, ISAV, or MSAV command, respectively.
When issuing the MSAV command, the user is also asked which element
in the file is to be overwritten.  XFOIL can thus be used to easily
"edit" individual elements in MSES multielement configurations.
Of course, normalization should not be performed on an element if 
it is to be written back to the same multielement file.
Only the current-airfoil coordinates can be saved to a file.
If the buffer or polar x,y coordinates need to be saved, they
must first be copied into the current airfoil.


Units
=====
Most XFOIL operations are performed on the airfoil's cartesian 
coordinates x,y , which do not necessarily have a unit chord c.
Since the chord is ambiguous for odd shapes, the XFOIL 
force coefficients CL, CD, CM are obtained by normalizing the 
forces and moment with only the freestream dynamic pressure
(the reference chord is assumed to be unity).  Likewise, the 
XFOIL Reynolds number RE is defined with the freestream velocity 
and viscosity, and an implied unit chord:

 CL = L / q           |     V = freestream speed
 CD = D / q           |     v = freestream kinematic viscosity
 CM = M / q           |     r = freestream density
 RE = V / v           |     q = 0.5 r V^2

The conventional definitions are

 Cl = L / q c
 Cd = D / q c
 Cm = M / q c^2
 Rc = V c / v

so that the conventional and XFOIL definitions differ only by 
the chord factor  c  or  c^2.

For example, a NACA 4412 airfoil is operated in the OPER menu at
 
 RE   = 500000
 ALFA = 3

first with chord=1.0, and then with chord=0.5 (changed with SCAL 
command in the GDES menu, say).  The results produced by XFOIL are:

 c = 1.0 :    CL = 0.80    CD = 0.0082    (RE = 500000, Rc = 500000)
 c = 0.5 :    CL = 0.40    CD = 0.0053    (RE = 500000, Rc = 250000)

Since CL is not normalized with the chord, it is nearly proportional
to the airfoil size.  It is not exactly proportional, since the true
chord Reynolds number Rc is different, and there is always a weak 
Reynolds number effect on lift.  In contrast,  the CD for the smaller 
airfoil is significantly greater than 1/2 times the larger-airfoil CD, 
since chord Reynolds number has a significant impact on profile drag.  
Repeating the c = 0.5 case at RE = 1000000, produces the expected 
result that CL and CD are exactly 1/2 times their c = 1.0 values.

 c = 0.5 :    CL = 0.40    CD = 0.0041    (RE = 1000000, Rc = 500000)


Although XFOIL performs its operations with no regard to the size 
of the airfoil, some quantities are nevertheless defined in terms 
of the chord length.  Examples are the camber line shape and BL trip 
locations, which are specified in terms of the relative x/c,y/c along 
and normal to the airfoil chord line.  This is done only for the user's 
convenience.  In the input and output labeling, "x,y" always refer 
to the cartesian coordinates, while "x/c,y/c" refer to the chord-
based coordinates which are shifted, rotated, and scaled so that 
the airfoil's leading  edge is at (x/c,y/c) = (0,0), and 
the airfoil's trailing edge is at (x/c,y/c) = (1,0).  The two 
systems cooincide only if the airfoil is normalized.


Analysis
========
Most of the commands in the top level XFOIL menu merely put the user 
into some lower command level with its own menu and prompt.  Issuing
The OPER command, for instance, will produce the prompt 

 .OPERi  c>

Typing a " ? " will result in the OPER analysis menu being displayed:


   <cr>     Return to Top Level
   !        Redo last ALFA,CLI,CL,ASEQ,CSEQ,VELS

   Visc r   Toggle Inviscid/Viscous mode
  .VPAR     Change BL parameter(s)
   Re   r   Change Reynolds number
   Mach r   Change Mach number
   Type i   Change type of Mach,Re variation with CL
   ITER     Change viscous-solution iteration limit
   INIT     Toggle BL initialization flag

   Alfa r   Prescribe alpha
   CLI  r   Prescribe inviscid CL
   Cl   r   Prescribe CL
   ASeq rrr Prescribe a sequence of alphas
   CSeq rrr Prescribe a sequence of CLs

   SEQP     Toggle polar/Cp(x) sequence plot display
   CINC     Toggle  minimum Cp  inclusion in polar
   HINC     Toggle hinge moment inclusion in polar
   Pacc i   Toggle auto point accumulation to active polar
   PGET f   Read new polar from save file
   PWRT i   Write polar to save file
   PSUM     Show summary of stored polars
   PLIS i   List stored polar(s)
   PDEL i   Delete stored polar
   PSOR i   Sort stored polar
   PPlo ii. Plot stored polar(s)
   APlo ii. Plot stored airfoil(s) for each polar
   ASET i   Copy stored airfoil into current airfoil
   PREM ir. Remove point(s) from stored polar
   PNAM i   Change airfoil name of stored polar
   PPAX     Change polar plot axis limits

   RGET f   Read new reference polar from file
   RDEL i   Delete stored reference polar

   GRID     Toggle Cp vs x grid overlay
   CREF     Toggle reference Cp data overlay
   FREF     Toggle reference CL,CD.. data display

   CPx      Plot Cp vs x
   CPV      Plot airfoil with pressure vectors (gee wiz)
  .VPlo     BL variable plots
  .ANNO     Annotate current plot
   HARD     Hardcopy current plot
   SIZE r   Change plot-object size
   CPMI r   Change minimum Cp axis annotation

   BL   i   Plot boundary layer velocity profiles
   BLC      Plot boundary layer velocity profiles at cursor
   BLWT r   Change velocity profile scale weight

   FMOM     Calculate flap hinge moment and forces
   FNEW rr  Set new flap hinge point
   VELS rr  Calculate velocity components at a point
   DUMP f   Output Ue,Dstar,Theta,Cf vs s,x,y to file
   CPWR f   Output x vs Cp to file
   CPMN     Report minimum surface Cp
   NAME s   Specify new airfoil name
   NINC     Increment name version number

The commands are not case sensitive.  Some commands expect multiple 
arguments, but if the arguments are not typed, prompts will be issued.

The most commonly-used commands have alternative short forms, 
indicated by the uppercase part of the command in the menu list.
For example, the menu shows...

   Alfa r   Prescribe alpha
   CLI  r   Prescribe inviscid CL
   Cl   r   Prescribe CL
   ASeq rrr Prescribe a sequence of alphas
   CSeq rrr Prescribe a sequence of CLs

The "A" command is the short alternative form of "ALFA", and "C" 
is the short alternative of "CL".  Likewise, "AS" and "CS"
are the short forms of "ASEQ" and "CSEQ".  The CLI command 
has no short form (as indicated by all capitals in the menu), 
and must be fully typed.


Hopefully, most of the commands are self-explanatory.  For inviscid 
cases, the CLI and CL commands are identical.  For viscous cases, 
CLI is equivalent to specifying alpha, this being determined a priori 
from the specified lift coefficient via an inviscid solution.  CL will 
return a viscous solution with the specified true viscous lift 
coefficient at an alpha which is determined as part of the solution 
(prescribing a CL above CLmax will cause serious problems, however!).
The user is always prompted for any required input.  When in doubt, 
typing a " ? " will always produce a menu. 

After an ALFA, CL, or CLI command is executed, the Cp vs x distribution
is displayed, and can be displayed again at any time with CPX.
If the viscous mode is active, the true viscous Cp is shown as a solid
line, and the inviscid Cp at that same alpha is shown as a dashed line.
Each dash covers one panel, so the local dashed line density is also 
a useful visual indicator of panel resolution quality.  If the inviscid
mode is active, only the inviscid Cp is shown as a solid line.

The difference between the true viscous Cp distribution (solid line)
and the inviscid Cp distribution (dashed line) is due to the
modification of the effective airfoil shape by the boundary layers.
This effective airfoil shape is shown superimposed on the actual
current airfoil shape under the Cp vs x plot.  The gap between 
these effective and actual shapes is equal to the local displacement 
thickness delta*, which can also be plotted in the VPAR menu.  
This is only about 1/3 to 1/2 as large as the overall boundary 
layer thickness, which can be visualized via the BL or BLC commands
which diplay velocity profiles through the boundary layer.
BL displays a number of profiles equally spaced around the
airfoil's perimeter, while BLC displays profiles at cursor-selected 
locations.  The zooming commands Z, U, may be necessary to better 
see these small profiles in most cases.

If the Cp reference data overlay option is enabled with CREF, 
initiating a Cp vs x plot will first result in the user being
prompted for a formatted data file with the following format:

x(1)  Cp(1)
x(2)  Cp(2)
 .      .
 .      .

The Cp vs x plot is then displayed as usual but with the data overlaid.
If FREF has been issued previously, then numerical reference values
for CL, CD, etc. will be requested and added to the plot next to the
computed values.

Boundary-layer quantities are plotted from the VPLO menu:

   H      Plot kinematic shape parameter
   DT     Plot top    side Dstar and Theta
   DB     Plot bottom side Dstar and Theta
   UE     Plot edge velocity
   CF     Plot skin friction coefficient
   CD     Plot dissipation coefficient
   N      Plot amplification ratio
   CT     Plot max shear coefficient
   RT     Plot Re_theta
   RTL    Plot log(Re_theta)

   X  rrr Change x-axis limits
   Y  rrr Change y-axis limits on current plot

   Blow   Cursor blowup of current plot
   Rese   Reset to default x,y-axis limits
   SIZE r Change absolute plot-object size
  .ANNO   Annotate plot
   HARD   Hardcopy current plot

   GRID   Toggle grid plotting
   SYMB   Toggle node-symbol plotting
   LABE   Toggle label plotting
   CLIP   Toggle line-plot clipping


This menu is largely self-explanatory.  The skin friction
coefficient plotted with the CF command is defined as

                             2
      Cf = tau / 0.5 rho Qinf

This differs from the standard boundary layer theory definition 
which uses the local Ue rather than Qinf for the normalization.
Using the constant freestream reference makes Cf(x) have the
same shape as the physical shear stress tau(x).

The dissipation coefficient CD' (this is NOT the drag coefficient!!!)
is plotted with the CD command.  CD'(x) is proportional to the local
energy dissipation rate due to viscous shear and turbulent mixing.
Hence, it indicates where on the airfoil drag is being created.
It is in fact a much better indicator of drag production than Cf(x),
since Cf does not account for pressure drag.  CD', on the other
hand, accounts for everything.  Its relationship to the total 
profile drag coefficient is simply

      /
 CD = | 2 CD' ds
      /

with the integration performed over both boundary layers and also 
the wake.  It will be seen that if the flow is separated at the 
trailing edge, much of the drag contribution (energy dissipation) 
of CD' occurs in the wake.


As mentioned earlier, all forces are normalized with freestream
dynamic pressure only.  CL, CD, CM are the usual chord-based
definitions only if the airfoil has a unit chord -- in general, 
they will scale with the airfoil's chord.  Also, CM is defined 
about the cartesian point (xref,yref) = (0.25,0.0), which is not
necessarily the airfoil's 1/4 chord point.


                -- Force calculation --

The lift and moment coefficients CL, CM, are calculated by direct
surface pressure integration:

            /     _                   /
 CL = L/q = | Cp dx        CM = M/q = | -Cp [(x-xref) dx + (y-yref) dy]
            /                         /

          _
  where   x = x cos(a) + y sin(a)     ; a = angle of attack
          _ 
          y = y cos(a) - x sin(a)


The integrals performed in the counterclockwise direction
around the airfoil contour.  The pressure coefficient Cp is 
calculated using the Karman-Tsien compressibility correction.

The drag coefficient CD is obtained by applying the Squire-Young
formula at the last point in the wake --- NOT at the trailing edge.

                                          (H+5)/2
    CD = D/q = 2 Theta_i  =  2 Theta (u/V)

 where     Theta = momentum thickness |  
               u = edge velocity      |  at end of wake
               H = shape parameter    |

               V = freestream velocity
         Theta_i = momentum thickness at "downstream infinity"


The Squire-Young formula in effect extrapolates the momentum 
thickness to downstream infinity.  It assumes that the wake behaves 
in a asymptotic manner downstream of the point of application.  
This assumption is strongly violated in the near-wake behind an 
airfoil with trailing edge separation,  but is always reasonable 
some distance behind the airfoil.  Hence, the usual application 
of Squire-Young at the trailing edge is questionable with separation 
present, but its application at the last wake point (typically 
1 chord downstream) is always reasonable.  Also, application at 
the last wake point also results in the formula having a smaller 
effect in any case, since there  u ~ V,  and hence  Theta_i ~ Theta.

In most 2-D airfoil experiments, drag is measured indirectly by 
measuring  2 Theta/c  in the wake, often within one chord of the
airfoil's trailing edge.  For consistency, this should be compared 
to the  Theta  value predicted by XFOIL at the same wake location, 
rather than the "true"  Cd = 2 Theta_i/c  value which is effectively 
at downstream infinity.  In general,  Theta_i  will be smaller 
than  Theta.  In most airfoil drag measurement experiments, this 
difference may amount to the drag measurement being several
percent too large, unless some correction is performed.

In addition to calculating the total viscous CD from the wake
momentum thickness, XFOIL also determines the friction and pressure
drag components CDf,CDp of this total CD.  These are calculated by

          /     _
  CDf  =  | Cf dx              CDp  =  CD - CDf
          /

Here, Cf is the skin friction coefficient defined with the 
freestream dynamic pressure, not the BL edge dynamic pressure
commonly used in BL theory.  Note that CDp is deduced from 
CD and CDf instead of being calculated via surface pressure
integration.  This conventional definition

         /     _
 CDp  =  | Cp dy    
         /

is NOT used, since it is typically swamped by numerical noise.


                -- Transition criterion --

Transition in an XFOIL solution is triggered by one of two ways:

  free  transition:  e^n criterion is met
 forced transition:  a trip or the trailing edge is encountered

The e^n method is always active, and free transition can occur
upstream of the trip.  The e^n method has the user-specified 
parameter "Ncrit", which is the log of the amplification factor
of the most-amplified frequency which triggers transition.
A suitable value of this parameter depends on the ambient
disturbance level in which the airfoil operates, and mimics
the effect of such disturbances on transition.  Below are typical 
values of Ncrit for various situations.

     situation             Ncrit
  -----------------        -----
  sailplane                12-14
  motorglider              11-13
  clean wind tunnel        10-12
  average wind tunnel        9     <=  standard "e^9 method"
  dirty wind tunnel         4-8

Note: The e^n method in XFOIL is actually the simplified envelope 
version, which is the same as the full e^n method only for flows 
with constant H(x). If H is not constant, the two methods differ
somewhat, but this difference is typically within the uncertainty
in choosing Ncrit.

The e^n method is only appropriate for predicting transition in 
situations where the growth of 2-D Tollmien-Schlichting waves via
linear instability is the dominant transition-initiating mechanism.  
Fortunately, this happens to be the case in a vast majority of airfoil 
applications.  Other possible mechanisms are:

* Crossflow instabilities. These occur on swept wings with significant  
  favorable chordwise pressure gradients.

* Attachment-line transition.  This requires large sweep, large LE
  radius, and a large Reynolds number.  Occurs primarily on big jets.

* Bypass transition.  This occurs in cases with sufficient wall
  roughness and/or large freestream turbulence or vibration levels.
  The linear-instability phase predicted by the e^n method is
  "bypassed", giving relatively early transition.  Usually occurs
  in favorable pressure gradients, while the linear-instability
  mechanism usually dominates in adverse pressure gradients.

If any of these alternative transition mechanisms are present, the
trips must be set to mimick their effect.  The bypass transition
mechanism can be mimicked to some extent by the e^n method by 
setting Ncrit to a small value --- Ncrit=1 or less.  This will 
cause transition just after linear instability begins.  For
very large freestream turbulence or roughness in favorable
pressure gradients, bypass transition can occur before the 
linear instability threshold, and in this case trips will have 
to be set as well.


Numerical accuracy
------------------

-- Panel density requirements --
If strong separation bubbles are present in a viscous solution, then 
it is very important to have good panel resolution in the region of the 
bubble(s).  The large gradients at a bubble tend to cause significant 
numerical errors even if a large number of panels is used. If a separation
bubble appears to be poorly resolved, it is a good idea to re-panel the 
airfoil with more points, and/or with points bunched around the bubble 
region.  The paneling is controlled from the PPAR menu. A good rule of 
thumb is that the shape parameter Hk just after transition in the bubble 
should not decrease by more than 1.0 per point.  Likewise, the surface 
velocity Ue/Vinf should not change by more than 0.05 per point past
transition, otherwise there may be significant numerical errors in the 
drag.  The point values can be observed by issuing SYMB from the VPLO menu.
Moderate chord Reynolds numbers (1-3 million, say) usually require the 
finest paneling, since the bubbles are still important, but very small. 
On many airfoils, especially those with small leading edge radii,
the development of the small bubble which forms just behind the 
leading edge can have a significant effect on CLmax.  For such cases,
the default paneling density at the bubble may not be adequate.
In all cases, inadequate bubble resolution results in a "ragged" 
or "scalloped" CL vs CD drag polar curve, so fortunately this is 
easy to spot.

-- Differencing order of accuracy --
The BL equations are normally discretized with two-point central
differencing (i.e. the Trapezoidal Scheme), which is second-order
accurate, but only marginally stable.  In particular, it has problems
with the relatively stiff shape parameter and lag equations at
transition, where at high Reynolds number the shape parameter must
change very rapidly.  Oscillations and overshoots in the shape parameter
will occur with the Trapezoidal Scheme if the grid cannot resolve this
rapid change.  To avoid this nasty behavior, upwinding must be introduced,
resulting in the Backward Euler Scheme, which is very stable, but has
only first-order accuracy.  Previous versions of XFOIL allowed a specific
constant amount of upwinding to be user-specified.  Currently,
XFOIL automatically introduces upwinding into the equations only
in regions of rapid change (typically transition).  This ensures
that the overall scheme is stable and as accurate as possible.

Since only a minimal amount of upwinding is introduced in the 
interest of numerical accuracy, small oscillations in the shape 
parameter H will sometimes appear near the stagnation point if
relatively coarse paneling is used there.  These oscillations
are primarily a cosmetic defect, and do not significantly affect
the downstream development of the boundary layer.  Eliminating them 
by increasing upwiding would in fact produce much greater errors 
in the overall viscous solution.


Viscous solution acceleration
-----------------------------
The execution of a viscous case requires the solution of a large
linear system every Newton iteration.  The coefficient matrix of
this system is 1/3 full, although most of its entries are very small.
Substantial savings in CPU time (factor of 4 or more) result when
these small entries are neglected.  SUBROUTINE BLSOLV which solves the
large Newton system ignores any off-diagonal element whose magnitude
is smaller than the variable VACCEL, which is initialized in SUBROUTINE
INIT, and which can be changed at runtime from the VPAR menu with the
VACC command.  

A nonzero VACCEL parameter should in principle degrade the convergence rate 
of the viscous solution and thus result in more Newton iterations, although 
the effect is usually too small to notice.  For very low Reynolds number 
cases (less than 100000), it MAY adversely affect the convergence rate 
or stability, and one should try reducing VACCEL or even setting it 
to zero if all other efforts at convergence are unsuccessful.  
The value of VACCEL has absolutely no effect on the final converged 
viscous solution (if attained).


Polar calculations and plotting
-------------------------------
The polar calculation facility driven from the OPER menu deserves
a detailed description.  It has been considerably upgraded from
previous XFOIL versions.

The simplest way to create a polar is to issue the PACC command
which sets the auto polar accumulation toggle and asks for the 
optional save and dump filenames.  If either filename is
given, each computed operating point will be stored internally
and also written to the specified file.  If no filename is given,
the automatic writing is not performed.

The polar's operating points can be computed individually with ALFA,
or more conveniently en masse with ASEQ.  One can also use CL or CSEQ,
although these will not work close to CLmax.

The polar can be plotted anytime with PPLO.  If previous polars have been 
computed or read in with PGET, they can be plotted as well.  If a polar
is deemed incomplete, additional points can be computed as needed.

If automatic writing of a polar was not chosen (no filename was given
for PACC), the polar can be written later all at once with the PWRT
command.  The only drawback to this approach is that if the program
crashes during a polar calculation sweep for whatever reason, the 
computed polar and all other stored information will be lost.

If existing filenames are given to PACC, the subsequent computed
points will be appended to these files, but only if the airfoil name 
and flow parameters in the file match the current parameters.
This is to prevent clobbering of the polar file with "wrong" 
additional points.  Messages are always produced informing 
the user of what's going on.

Off-line polar plotting
----------------------
Polar save file(s) can also be plotted off-line with the separate 
program PPLOT.  This is entirely menu driven, and is simply executed:

 % pplot

The file  pplot.def  contains plotting parameters, and is read 
automatically if available.  If it's not available, then internal
defaults are used.

Like the RGET,FREF commands in OPER, PPLOT permits reference data 
to be overlaid.  A reference polar data file has the following form:

CD(1)  CL(1)
CD(2)  CL(2)
 .      .
 .      .
999.0  999.0
alpha(1)  CL(1)
alpha(2)  CL(2)
  .       .
  .       .
999.0   999.0
alpha(1)  Cm(1)
alpha(2)  Cm(2)
  .       .
  .       .
999.0   999.0
Xtr/c(1)  CL(1)
Xtr/c(2)  CL(2)
  .        .
  .        .
999.0   999.0

The number of points in each set (CD-CL, alpha-CL, etc.) is arbitrary,
and can be zero. 

The contents of a polar dump file can be selectively plotted with
the separate menu-driven program PXPLOT.  It is executed with:

 % pxplot <dump filename>
 
This allows surface plots of Cp vs x, H vs x, etc. for any or
all of the saved operating points.  Of course, these plots can
be generated in XFOIL for any individual operating point, so PXPLOT 
and the dump file itself are somewhat redundant in this respect.



Re, Mach dependence
-------------------
A few comments are in order on the TYPE command, which allows the 
user to set the dependence of the Mach and Reynolds numbers on CL.  
Any CL-CD polar can be of the following three types:

 Type   parameters held constant       varying      fixed
 ----   ------------------------       -------   -----------
   1    M          , Re            ..   lift     chord, vel.
   2    M sqrt(CL) , Re sqrt(CL)   ..   vel.     chord, lift
   3    M          , Re CL         ..   chord    lift , vel.

* Type 1 corresponds to a given wing at a fixed velocity going over
an angle of attack range, as in a wind tunnel test alpha sweep or 
a sudden aircraft pullup.  This is also the common form for an 
airfoil polar.

* Type 2 corresponds to an aircraft in level flight at a given altitude 
undergoing trim speed changes.  This is the most useful airfoil polar 
form for determining a drag polar for an aircraft at 1-g.  For this case, 
The "Mach number" input with the MACH command is actually interpreted 
as the product  M sqrt(CL), and the "Reynolds number" input with the 
VISC or RE commands is actually interpreted as  RE sqrt(CL).  For a wing 
in level flight, these products can be computed from the following exact 
relations, with  Re  based on the mean chord:

                         1/2                                1/2
              |  2  W/S |                     1  | 2 rho W |
 M sqrt(CL) = | --- --- |       RE sqrt(CL) = -- | ------- |
              | 1.4  p  |                     mu |    AR   |

 W  = weight         p   = ambient pressure
 S  = wing area      mu  = dynamic viscosity
 AR = aspect ratio   rho = ambient air density

* Type 3 corresponds to a wing of "rubber chord" with a given lift 
at a given speed.  This is best used for selecting an optimum CL 
for an airfoil while taking Reynolds number changes into account.  
The product  RE CL  can be computed from the following:

           2 W
  RE CL = ------       b = span = sqrt(S*AR)
          mu V b


Caution must be used with Types 2 and 3 so as to not allow the CL 
to go negative.  In addition, with non-zero Mach and Type 2, 
the CL must not fall below that value which makes Mach exceed 
unity.  Warning messages are printed when these problems occur.


Output
======
All output goes directly to the terminal screen.  H. Youngren's plot 
package Xplot11 (libPlt.a) used by XFOIL drives monochrome and color 
X-Windows graphics, and generates B&W or color PostScript files for 
hardcopy.  The default setup assumes color X-Windows graphics 
(if available), and B&W PostScript.  These defaults are controlled 
by the IDEV and IDEVRP flags in SUBROUTINE INIT (in xfoil.f).

The Xplot11 library should work on all Unix systems.  The Makefile
in the ./plotlib/ directory requires some modifications for some 
machines.

The default X-graphics window is in Landscape mode, with a black
(reverse-video) background.  Normal-video can be selected by setting 
the Unix shell variable

 % setenv XPLOT11_BACKGROUND white

before Xfoil is started.  The nicer reverse-video is restored with:

 % unsetenv XPLOT11_BACKGROUND

See the plotlib/Doc file for more info on the plot library.


Xplot11 provides a built-in Zoom/Unzoom capability which can
be applied to whatever is on the screen.  Zooming/Unzooming
can be perfomed with the "Z" and "U" commands from nearly all
the menus --- these commands are not listed to reduce clutter.

Some of the menus also have their own Blowup/Reset commands.  
The distinction is that XFOIL's plots don't try to adjust 
themselves to Zoom parameters, so a highly-"Zoomed" plot may 
show nothing at all.  In contrast, Blowup/Reset instructs 
XFOIL to change its own plot scales, so a highly-"Blown-up"
plot will at least show the axes.


Plot Hardcopy
=============
For hardcopy, the current screen plot can be echoed to a PostScript file
plot.ps  with the HARD command.  The size of the plot objects on the 
screen and on hardcopy can be changed with the SIZE command from most
menus.  The number requested is the width of the plot in inches.  


*** NOTE ***
If the plot.ps file is to be previewed with some X-Windows PostScript
viewer, or imported into word-processing systems, XFOIL must be exited 
with QUIT in order for the plot.ps file to be properly terminated.  
For just printing, this may or may not be necessary.


*** NOTE ***
For the geometry plot in GDES, and the Qspec(s) plots in QDES and MDES 
(described below), the hardcopy plot size will also be affected if 
the graphics window is resized with the cursor at the window manager 
level.  This is because the plot is always scaled so that it fills 
up as much of the window as possible.  If the window size is left 
at its start-up size, the hardcopy plot widths will come out with the 
specified size in inches.  If any window dimension is increased from
its default value, then a subsequent hardcopy plot will probably not
fit on a standard 8.5" x 11.0" sheet.


Full-Inverse Design Routine (MDES)
==================================
XFOIL's Full-Inverse complex-mapping facility (MDES) takes as input 
a speed distribution "Qspec" specified over the entire airfoil surface, 
modifies it somewhat to satisfy the Lighthill constraints, and generates 
a new overall geometry.  First a bit of the underlying theory...

The geometry and the surface velocities can both be computed from 
a set of complex mapping coefficients "Cn" in the form

 x + iy  =  z(w;Cn)
 u - iv  =  f(w;Cn,alpha)

where w= 0..2*pi is the independent parameter going around the airfoil.
The z and f functions are rather complicated but this is not important
here.  The key to the full-inverse method is that the mapping coefficients 
Cn can be computed from a known contour angle theta(w) = arctan(dy/dz)
OR from a surface speed q(w) = |u-iv|.  The other quantity the follows.
In summary, the operations and their commands are...

 a) Direct  problem:  theta  ->  Cn  ->  u-iv, q          (QSET)
 b) Inverse problem:  Qspec  ->  Cn  ->  x+iy, theta      (EXEC)


Creation of seed surface speed distribution
-------------------------------------------
MDES performs QSET and sets Qspec = q automatically upon entry 
if Qspec does not exist.  This Qspec is then the starting point
for subsequent design operations.

This default initialization in effect makes MDES a redesign method 
in which the surface speed distribution of an existing airfoil is 
used as a starting point to generate a new speed distribution.  
A ``pure'' design code which requests the entire surface speed 
distribution every time is often less natural to use, since airfoil 
design is invariably an iterative process involving repeated 
analyze/fix cycles.  The MDES menu is shown below.

   <cr>   Return to Top Level
   !      Redo previous command

   INIT   Re-initialize mapping
   QSET   Reset Qspec <== Q
   AQ r.. Show/select alpha(s) for Qspec
   CQ r.. Show/select  CL(s)   for Qspec

   Symm   Toggle symmetry flag
   TGAP r Set new TE gap
   TANG r Set new TE angle

   Modi   Modify Qspec
   MARK   Mark off target segment for smoothing
   SMOO   Smooth Qspec inside target segment
   FILT   Apply Hanning filter to entire Qspec
   SLOP   Toggle modified-Qspec slope matching flag

   eXec   Execute  full-inverse calculation

   Plot   Replot Qspec (line) and Q (symbols)
   VISC   Qvis overlay toggle
   REFL   Reflected Qspec overlay toggle
   SPEC   Plot mapping coefficient spectrum

   Blow   Blowup plot region
   Rese   Reset plot scale and origin
   Wind   Plot window adjust via cursor and keys

   SIZE r Change absolute plot-object size
  .ANNO   Annotate plot
   HARD   Hardcopy current plot

   PERT   Perturb one Cn and generate geometry


As described above, the initial Qspec distribution is taken from 
"Q", the speed distribution corresponding to the current 
geometry at the last angle of attack employed in OPER.  Qspec 
can be set back to this Q with QSET anytime.


Modification of surface speed distributions
-------------------------------------------

-- Cursor input of modifications --
Qspec can be modified to whatever is desired with the MODI command 
by specifying points with the screen cursor which are then splined.  
The points can be entered in any order.  The last point can be 
erased by clicking on the "Erase" button or simply typing "e"
in the graphics window.  The input sequence is terminated by
clicking on the "Done" button or by typing "d" in the graphics window.
The "Abort" button or typing "a" aborts the MODI command and
returns to the MDES menu.  The BLOW command can be used to enlarge 
regions of interest at any time by specifying opposite corners 
of the blowup region.  

-- Modification endpoint blending --
Normally, the modified piece of Qspec(s) is blended into the current 
Qspec(s) with matching values and slopes at the piece endpoints.  
The slope matching can be turned on/off with the SLOP toggle command.  
If slope matching is turned off, the modified piece will match only 
the existing value, but a slope discontinuity will be allowed.

-- Smoothing --
Qspec can be smoothed with the SMOO command, which normally operates 
on the entire distribution, but can be confined to a target segment 
whose endpoints are selected with the MARK command.  The smoothing 
acts to alleviate second derivatives in Qspec(s), so that with many
consecutive SMOO commands Qspec(s) will approach a straight line
over the target segment.  If the slope-matching flag is set, the 
endpoint slopes are preserved.  

The FILT command is an alternative smoothing procedure which acts on 
the Fourier coefficients of Qspec directly, and is global in its effect.
It is useful for "cleaning up" the entire Qspec(s) distribution if
noise is present from some geometric glitch on the airfoil surface.
Also, unintended noise might be introduced into Qspec from a poor
modification via the cursor.  

FILT acts by multiplying the Fourier coefficients by a Hanning window 
filter function raised to the power of a filter parameter "F".  This 
tapers off the high frequencies of Qspec to varying degrees.  A value 
of F = 0.0 gives no filtering, F = 1.0 gives the standard Hanning filter,
F = 2.0 applies the Hanning filter twice, etc. The standard Hanning 
filter appears to be a bit too drastic, so a filter parameter of 
F = 0.2 is currently used.  Hence, issuing FILT five times corresponds 
to the standard Hanning filter.  The SPEC command displays the mapping 
coefficient spectrum at any time.

-- Symmetry forcing --
The symmetry-forcing option (SYMM toggle) is useful when a symmetric 
airfoil is being designed.  If active, this option zeroes out all
antisymmetric (camber) Qspec changes, and doubles all symmetric 
(thickness) changes.  This unfortunately has the annoying side 
effect of also doubling the numerical roundoff noise in Qspec 
every time a MODI operation is performed.  This noise sooner or later
becomes visible as high-frequency wiggles which double with each 
MODI command.  Issuing FILT occasionally keeps this parasitic 
noise growth under control.

-- Adjustment for Lighthill constraints --
The MODI, BLOW, MARK, SMOO, SLOP, FILT commands can be issued repeatedly 
in any order until Qspec is modified to have the desired distribution.
In general, the surface speed distributions actually plotted will not 
exactly match what was input with the cursor, since corrections are 
automatically added to maintain the specified trailing edge gap and 
to enforce consistency with the freestream speed.  These are known
as the Lighthill constraints on the surface speed.

The trailing edge gap is initialized from the initial airfoil and can 
be changed with TGAP.  To reduce the "corrupting" effect of the 
constraint-driven corrections, a good rule of thumb is that the 
Qspec distribution should be modified so as to preserve the total CL.  
The CL is simply twice the area under the Qspec(s) curve (=  2 x circulation),
so that this area should be preserved.

-- Multipoint surface speed display --
A very useful feature of the MDES facility is the ability to display 
and modify a number of Qspec distributions corresponding to different 
alpha or inviscid CL values.  These values are displayed and/or selected 
via the AQ or CQ commands.  When any one Qspec distribution is modified, 
the result of modification is also displayed on all the other distributions.
This allows rapid design at multiple operating points.  When the Qspec 
curves correspond to specified CL values, the alpha for each curve will be 
adjusted after each Qspec modification so as to preserve that curve's CL.  
The resulting Qspec will therefore not match the input cursor points 
exactly because of this alpha correction.  

Generation of new geometry
--------------------------
The EXEC command generates a new buffer airfoil corresponding 
to the current Qspec distribution.  If subsequent operations on 
this airfoil are to be performed (SAVE, OPER, etc.), it is 
necessary to first generate a current airfoil from this buffer 
airfoil using PANE at the top level menu.  This seemingly 
complicated sequence is necessary because the airfoil points 
generated by EXEC are uniformly spaced in the circle plane, 
which gives a rather poor point (panel node) spacing distribution 
on the physical airfoil.  This sequence also prevents the current
airfoil from being overwritten immediately when EXEC is issued.  
Once the new current airfoil is generated with PANE, it can 
then be analyzed in OPER, modified in GDES, or whatever.

The PERT command allows manual input of the complex mapping
coefficients Cn which determine the geometry.  These coefficients
are normally determined from Qspec(s) (this is the essence of
the inverse method).  The PERT command is provided simply
as a means of allowing generation of geometric perturbation
modes, possibly for external optimization or whatever.

The manually-changed Cn values result in changes in geometry
as well as the current Qspec(s) distributions.  The QSET command
will restore everything to its unperturbed state.

The Full-Inverse facility is very fast, after an initialization 
calculation of several seconds (on a RISC workstation), it requires 
only a fraction of a second to generate the new buffer airfoil.  


Mixed-Inverse Design Routine (QDES)
===================================
XFOIL's Mixed-Inverse facility (QDES) is useful in certain redesign 
problems where parts of the airfoil cannot be altered under any 
circumstances.  The Mixed-Inverse menu is shown below.

   <cr>   Return to Top Level

   QSET   Reset Qspec <== Q

   Modi   Modify Qspec
   MARK   Mark off target segment
   SMOO   Smooth Qspec inside target segment
   SLOP   Toggle modified-Qspec slope matching flag

   eXec i Execute mixed-inverse calculation
   REST   Restore geometry from buffer airfoil
   CPXX   CPxx endpoint constraint toggle

   Plot   Plot Qspec (line) and Q (symbols)
   VISC   Qvis overlay toggle
   REFL   Reflected Qspec overlay toggle

   Blow   Blowup plot region
   Rese   Reset plot scale and origin
   Wind   Plot window adjust via cursor and keys

   SIZE r Change absolute plot-object size
  .ANNO   Annotate plot
   HARD   Hardcopy current plot


The QDES menu above is intentionally geared for the redesign of a segment
of an existing airfoil (with its surface speed distribution calculated 
previously in OPER) rather than the generation of a totally new airfoil. 


Creation of seed surface speed distribution
-------------------------------------------
When QDES is entered, the specified speed distribution Qspec is 
initialized to the current speed distribution Q last set in OPER.
If a direct solution for the current airfoil hasn't been calculated yet, 
QDES goes ahead and calculates it, using the last-set angle of attack.
If this isn't the desired angle, it can be set in OPER using ALFA.
QSET can then be used to set Qspec from the current Q distribution.
The QSET command can be used anytime later to "reset" Qspec if the
modification has been botched.

Modification of surface speed distribution
------------------------------------------
Qspec can be repeatedly modified with the screen cursor and the MODI
command, exactly as in MDES.  It is also necessary to mark off the 
target segment where the geometry is to be modified with the 
MARK command.  

Generation of new airfoil geometry
----------------------------------
EXEC modifies the airfoil over the target segment to match Qspec 
there as closely as possible.  The remainder of the airfoil 
geometry is left unaltered.  EXEC requests the number of Newton
iterations to be performed in the inverse calculation.  Although as
many as six iterations may be required for convergence to machine zero,
it is _not_ necessary to fully converge a Mixed-Inverse case.  Two 
iterations are usually sufficient to get very close to the new
geometry.  In any case, the new surface speed distribution Q 
which actually results from the inverse calculation will typically 
differ somewhat from the specified distribution Qspec by function 
modes which are added to Qspec.  At least two modes are added, 
with their magnitudes determined by geometric closure requirements 
at the inverse segment endpoints.  As with the MDES complex-mapping
routine, the necessary modifications to Qspec will be smallest if
Qspec is modified so that CL (the area under the Qspec(s) curve) is 
roughly preserved.

Issuing PLOT after the EXEC command finishes will compare the specified 
(Qspec) and resulting (Q) speed distributions.  If extra smoothness 
in the surface speed is required, the CPXX command just before EXEC 
will enable the addition of two additional modes which allow the 
second derivative in the pressure at the endpoints to be unchanged 
from the starting airfoil.  The disadvantage of this option is that 
the resulting surface speed Q will now deviate more from the 
specified speed Qspec.  It is allowable to repeatedly modify Qspec, 
set or reset the CPXX option, and issue the EXEC command in any order.

The Mixed-Inverse modification is performed on the current airfoil 
directly, in contrast to Full-Inverse which generates the buffer 
airfoil as its output.  In fact, it is important _not_ to issue the 
PANE or PCOP commands at top level after doing work in the QDES menu, 
as the new current airfoil will be overwritten with the old buffer 
airfoil.


Geometry Design Routine
=======================
Executing the GDES command from the top level menu will put the user
into the GDES routine.  It has a rather extensive menu:

   <cr>     Return to Top Level
   !        Redo previous command

   GSET     Set buffer  airfoil <== current airfoil
   eXec     Set current airfoil <== buffer  airfoil
   SYMM     Toggle y-symmetry flag

   ADEG r   Rotate about origin (degrees)
   ARAD r   Rotate about origin (radians)
   Tran rr  Translate
   Scal r   Scale about origin
   LINS rr. Linearly-varying y scale
   DERO     Derotate (set chord line level)

   TGAP rr  Change trailing edge gap
   LERA rr  Change leading edge radius

   TCPL     Toggle thickness and camber plotting
   TFAC rr  Scale existing thickness and camber
   TSET rr  Set new thickness and camber
   HIGH rr  Move camber and thickness highpoints
  .CAMB     Modify camber shape directly or via loading

   BEND     Display structural properties of buffer airfoil

   Flap rrr Deflect trailing edge flap

   Modi     Modify contour via cursor
   SLOP     Toggle modified-contour slope matching flag

   CORN     Double point with cursor (set sharp corner)
   ADDP     Add    point with cursor
   DELP     Delete point with cursor
   MOVP     Move   point with cursor

   UNIT     Normalize buffer airfoil to unit chord
   Dist     Determine distance between 2 cursor points
   CLIS     List curvatures
   CPLO     Plot curvatures
   CANG     List panel corner angles
   CADD ri. Add points at corners exceeding angle threshold

   Plot     Replot buffer airfoil
   INPL     Replot buffer airfoil without scaling (in inches)
   Blow     Blowup plot region
   Rese     Reset plot scale and origin
   Wind     Plot window adjust via cursor and keys

   TSIZ     Change tick-mark size
   TICK r   Toggle node tick-mark plotting
   GRID     Toggle grid plotting
   GPAR     Toggle geometric parameter plotting
   Over f   Overlay disk file airfoil

   SIZE r   Change absolute plot-object size
  .ANNO     Annotate plot
   HARD     Hardcopy current plot

   NAME s   Specify new airfoil name
   NINC     Increment name version number


Creating seed buffer airfoil
----------------------------
The first command typically executed is GSET, which sets the temporary
buffer airfoil from the current airfoil.  Sometimes it might be desired 
to operate directly on the coordinates of an already existing buffer
airfoil.  It typically contains coordinates read in from a disk file 
by LOAD at Top Level, or coordinates generated by EXEC from the MDES 
menu, depending on what was done last.  In either of these cases, GSET 
is skipped.  

Point addition (typ. to Eppler and Selig airfoils)
--------------------------------------------------
If the buffer airfoil has an excessively coarse point spacing,
additional points can be added with the CADD command.  Using the
PANE command at top level also does this, but CADD allows the point
addition to be restricted to locations with excessive corner angles
(displayed with CANG), and also to locations which fall within a specified
x-range.  Different spline parameters can also be used to determine 
the inserted spline points.  For example, the command

 .GDES  c>  CADD 10.0  2  -0.1 0.2

will add spline points adjacent to each existing point whose panel
angle exceeds +/-10 degrees, and only if the added point will fall
within the interval -0.1 < x < 0.2.  The "2" indicates that an 
arclength spline parameter is to be used.  The PANE command will
always use the arclength spline.

Some archived airfoils, notably the Eppler airfoils and some of the 
Selig airfoils have an excessively coarse point spacing around 
the leading edge.  The spacing has apparently been tailored for
a uniform-parameter spline, and often produces a badly shaped 
leading edge with the arclength-parameter spline used in Xfoil.
The following command will insert additional points giving 
a much smoother shape for subsequent analysis.

 .GDES  c>  CADD 10.0  1  -0.1 1.1

The 10.0 degree angle tolerance can be varied as needed (1/2 of the max 
angle is the default).  The "1" argument (also a default) specifies 
a uniform-parameter spline for the interpolation since this works best 
for Eppler airfoils), and the default x range indicates that the 
entire airfoil is to be treated.  The CADD command can be repeated
to keep reducing the max panel angle, but this may or may not 
improve the smoothness of the resulting splined airfoil.


Modifying buffer airfoil
------------------------
Once the buffer airfoil is suitably initialized, most of the GDES 
commands can then be used to modify it.  The resulting new shape 
will usually be replotted immediately in a highlighted color.
The plot can be refreshed anytime with the PLOT command.

Sometimes a sequence of commands is necessary to achieve the desired 
effect.  For instance, suppose an airfoil with the current thickness 
envelope is to be given an entirely new camber line. Issuing TSET and 
hitting a <cr> (keep same thickness) and a new camber 
of 0 will result in the current thickness envelope unchanged and the 
current camber eliminated, so that a symmetrical airfoil remains. 
The new camber line can then be added in the CAMB sub-menu:

   <cr>    Return to GDES
   TFAC rr Scale existing thickness and camber
   TSET rr Set new thickness and camber
   HIGH rr Move camber and thickness highpoints
   WRTC    Write airfoil camber x/c,y/c to file

   RDAC    Read   added camber  x/c,y/c from file
   SETC    Set    added camber  x/c,y/c from camberline
   INPC    Input  added camber  x/c,y/c from keyboard
   MODC    Modify added camber  x/c,y/c with cursor
   INPP    Input  added loading x/c,DCp from keyboard
   MODP    Modify added loading x/c,DCp with cursor
   SLOP    Toggle modified-camber,dCp slope matching flag
   SCAL r  Scale the added camber
   CLR     Clear the added camber
   ADD     Add added camber to the existing camberline

   DCPL    Toggle DCp plot
   CPLI rr Change DCp axis plot limits

   Blow    Blowup plot region
   Rese    Reset plot scale and origin

   SIZE r   Change absolute plot-object size
  .ANNO     Annotate plot
   HARD     Hardcopy current plot

..CAMB   c>


INPC takes the new camber line as a sequence of x/c,y/c coordinate
pairs which are splined.  INPP takes a sequence of  x/c,delta(Cp)
pairs instead.  This delta(Cp) (i.e. loading) distribution, defined as 

delta(Cp) = (Cp)lower - (Cp)upper

is then used in Glauert's thin-airfoil relations to define the
x/c,y/c camber line.

With INPC and INPP, a slope discontinuity in y(x) or Cp(x) can 
be specified with two identical consecutive x/c values, which 
prevents splining across this point.  INPP can thus easily 
generate a camber line with a piecewise-linear delta(Cp) loading 
distribution, as for example an  a=0.8 NACA 6-digit airfoil:
 x/c delta(Cp)
 0.0   0.5
 0.8   0.5
 0.8   0.5
 1.0   0.0

This results in a constant   delta(Cp) = 0.5  for  0.0 < x/c < 0.8 , 
then decreasing linearly to  delta(Cp) = 0.0  for  0.8 < x/c < 1.0 

Once a suitable added camber is input, it is added to the 
existing buffer airfoil camber via the ADD command.


The various GDES commands for modifying camber-line, thickness, leading
edge radius, etc. should suffice for most geometry modification tasks.  
If truly frustrated, the user can "draw" the new contour with the MODI 
command, which accepts cursor inputs in the same manner as the MDES 
and QDES procedures.  Slope matching at the modified-piece endpoints 
can likewise be enabled/disabled with the SLOP toggle command.  The 
only important difference is that here the points must be entered 
in consecutive order along the new contour, although one can "erase"
a previously-entered point by clicking on "Erase" or type "e" in the
graphics window.

A point can be doubled with the CORN command.  A doubled point is 
useful wherever a sharp corner is required, such as at a flap break.
Normally, the spline routine enforces slope continuity at all points,
effectively preventing sharp corners.  A doubled point, marked by 
a small diamond symbol on the plot, causes separate splines to be 
generated on each side of the corner, thus allowing the slope 
break.  The doubled point is eliminated by clicking on it after 
issuing the DELP command.  Using DELP on a normal single point will 
delete that point entirely.  

The TGAP command sets the thickness (or gap) of the blunt trailing edge.
The gap "ds" is defined as the distance between the upper and lower
coordinate endpoints:  ds^2 = dx^2 + dy^2.  If the gap is already nonzero,
then the new TE base vector (dx,dy) will have the same orientation as 
the old one, i.e.

  dy|       dy|
  --|    =  --|
  dx|       dx|
     new       old

If the gap is zero to begin with, then the new base vector will be
perpendicular to the trailing edge bisector.  If the base orientation
comes out in an unexpected way, it probably means that the gap was
not *exactly* zero.  The fix is to first set the gap to zero, and
then set it again to the desired value.

After a new gap size is input, a "blending distance/c" will also be
requested.  This controls how rapidly the new TE blends into the
original airfoil, and is essentially the length scale for the blending 
function, which is exponential in x/c.  The limiting values are:

distance/c = 0:  Only the upper- and lower-surface TE points are changed
           = 1:  A linear "wedge" is added or subtracted from the airfoil


Saving buffer airfoil into current airfoil
------------------------------------------
Once the desired buffer airfoil is created, a new current airfoil is set
directly from the buffer airfoil with the EXEC command (equivalent to
PCOP at top level).  Alternatively, the new current airfoil can be 
re-paneled from the buffer airfoil with the PANE command at top level.  
The new current airfoil can then be analyzed in OPER.  If the buffer 
airfoil has any doubled corner points, the doubled points will be 
eliminated, but a current-airfoil node will fall exactly on each 
buffer-airfoil corner.



Start-up Defaults
=================
XFOIL has hardwired parameters (in subr. INIT) controlling the
paneling, plotting, and viscous execution.  Most of these can 
be changed at runtime in the various menus.  To avoid the need 
to change the parameters everytime XFOIL is executed, they
can be saved to the default file  xfoil.def  with the WDEF
command at TOP LEVEL.  This file has the format:

   140       1.0000   0.1500   0.2000 | Npan    PPanel  TErat  REFrat
    1.0000   1.0000   1.0000   1.0000 | XrefS1  XrefS2  XrefP1 XrefP2
   10.0000   0.5500   0.0150   0.8500 | Size    plotAR  CHsize ScrnFr
   11.0000   8.5000   0.0000   0.0000 | Xpage   Ypage   Xmargn Ymargn
  F        T                          | Lcolor  Lcursor
    1.0000  -2.0000  -0.5000          | CPmax   CPmin   CPdel
    0.0900   0.7000                   | XoffAir ScalAir BLUwt
    0.0000   1.5000   0.5000          | CLmin   CLmax   CLdel
    0.0000   0.0200   0.0100          | CDmin   CDmax   CDdel
   -4.0000  10.0000   2.0000          | ALmin   ALmax   ALdel
    0.0000   0.3000   0.1000          | CMmin   CMmax   CMdel
   1         0.0000   0.0100          | MAtype  Mach    Vaccel
   1         0.0000   9.0000          | REtype  Re/10^6 Ncrit
    1.0000   1.0000                   | XtripT  XtripB

Line  1: Paneling parameters from the PPAR menu  
Line  2: Paneling refinement locations                 
Line  3: Specifies the absolute plot size, the plot aspect ratio,
          and scales the character, number, and symbol heights   
Line  4: Defines page size and page margins, in inches
Line  5: Flags for color PostScript output, cursor screen input
Line  6: Defines the Cp axis annotations               
Line  7: x-offset and scale for airfoil on Cp vs x plot, BL u profile scale
Line  8: CL axis annotations on polar plot
Line  9: CD axis annotations on polar plot
Line 10: alpha axis annotations on polar plot
Line 11: CM axis annotations on polar plot
Line 12: Mach-CL dependence type, Mach number, solution acceleration parameter
Line 13: Re-CL dependence type, Reynolds number, transition parameter 
Line 14: Forced transition x/c locations on top,bottom sides

This file will be read at any time with the RDEF command, thus
avoiding the manual entry of all the information.


Caveats
=======
The XFOIL code is not foolproof, and requires some level of aerodynamic
expertise and common sense on the part of the user.  Although the
inviscid analysis (OPERi), geometry design (GDES), and Full-Inverse
(MDES) routines are nearly invulnerable to failure, the Mixed-Inverse
(QDES) design routines and especially the viscous analysis (OPERv) 
routines will fail if a "reasonable" problem is not specified.  
Typical failure scenarios are:

 - Viscous Analysis  (OPERv)
     * Massive separation from excessive airfoil thickness,
         flap deflection, or angle of attack
     * Inherently unsteady flow (von Karman vortex street, etc.)
     * Poor resolution of leading edge pressure spike
     * Poor resolution of small viscous features
         (e.g. separation bubbles)
     * Reynolds number too low

 - Mixed-Inverse Surface Speed Design  (QDES)
     * Re-entrant airfoil shape (negative thickness)

A possible consequence of these occurences is an arithmetic fault 
causing program failure.  This is unlikely, but it does happen
occasionally. It is therefore a good idea to save any previous work 
before an ambitious calculation is attempted.


The following situations may give problems strictly due to numerical 
roundoff:

 - Excessively small panel(s) somewhere on the airfoil

 - Airfoil located too far from origin

 - Airfoil too thin

These situations will rarely result in an arithmatic failure, 
but will typically result in a "ragged" Cp distribution.
Examine the paneling in the GDES menu, making the GSET command 
if neceesary to set the current paneling.  Eliminate excessively
small panels my deleting one or more panel nodes with the
DELP command.


When performing viscous analysis calculations, it is always a good idea
to sequence runs so that alpha does not change too drastically from one
case to another.  The Newton solution method always uses the last
available solution as a starting guess for a new solution, and works
best if the change from the old to the new solutions is reasonably
small.  For this reason, it is best to perform difficult calculations
(such as past CLmax) by gradually increasing alpha.  The ASEQ command in
OPER is convenient for this.  If the user insists on a large change from
one point to another, it is best to force a re-initialization of the
boundary layers with the INIT command from the VPAR menu in OPER before
the radical calculation is performed.  INIT should always be executed
whenever the viscous solution blows up but the program doesn't crash.

The viscous analysis will execute no more Newton iterations than
set by the current iteration limit each time an ALFA, CL, etc. command 
is issued.  If convergence is not achieved within this limit, ALFA or CL 
can be issued as often as needed (most easily with "!"), with another 
set of Newton iterations being performed each time.  This iteration 
limit can be changed from its default value of 10 with the ITER command 
in OPER.

One should always be wary of trusting solutions which show regions
of supersonic flow.  Such flows can be reliably predicted only with 
a truly nonlinear field method (such as the MSES code).  As a rule
of thumb, if the maximum Mach number doesn't exceed 1.05 anywhere,
shock losses will be very small, the Cp distributions will be 
reasonably accurate, and the drag predicted by XFOIL is likely
to be accurate.

