From: jdawson@magnus.acs.ohio-state.edu (Jonathan A Dawson)
Subject: More on Computational Simulations and Kiting!!! (What fun..)
Organization: The Ohio State University
Date: Mon, 14 Sep 1992 21:38:22 GMT

O.K, now that I have a little more time to post something coherent, I'll
try to address the issue of computers/engineering/kiting in a more clear
manner.

I saw a few posts discussing the use of computers for sails and I saw a
television program on that a year or so ago, so my memory of the specifics
in it are not too good.  My impression of the use of computers for sails
is that sails CAN be modeled on a computer, but this is because after the
sails are rigged and filled with wind, that they become essentially a 
rigid body (mentioned in my previous post).  Now, the analogous computation
for kites would have a kite that only takes ONE specific wind produced shape.
The result is that you are modeling either a: a single line kite with little
to no oscillation, or b: a dual line kite that is not being stunted (is
that a word ;-) around (i.e. this option is pretty boring).  An algorithm
for computing flow parameters on a kite would need to go something like this:

Choose a geometry of a kite (i.e. pick a kite)
Choose an initial incoming wind condition
Now, compute all parameters for this wind (while the kite is still)
   (now, if you want to get items of interest like minimum turn
    radius and other types of parameters that are normally gauged
    while the kite is moving you need to add...)
Change the angle of the incoming wind slightly (say a few degrees)
Compute the all parameters for this wind angle 
See if this lift/drag/pressure combination will produce the 
   kite shape assumed at the beginning.  If not...
Change the shape of the kite (billow/stretch/bend) to conform to
   the flow parameters previously calculated.
Recompute the flow parameters with this new shape and see if the 
   pressure will produce the assumed shape.  If not...
And repeat until the assumed shape produced from the calculated
   pressure distribution is close (about 5% maybe) to your original
   shape assumption.
   (This is one of the nasty parts of this computation.  It may take
    one iteration, but more likely will take many iterations to 
    acheive a "good" shape assumption.  This shows that the Navier-Stokes
    equations governing fluids are coupled with the Newtonian mechanics
    that govern the structure of the kite) 
Now, continue to move the wind a few degrees and repeat the entire last part 
   until you have turned the kite through the entire chosen angle.

(In the above, the parameters that I mentioned are the u, v, and w velocity
components that correspond to the x, y, and z directions, and the pressure
field within the boundary layer surrounding the kite).

Most of the computer programs currently available (that I know of at least)
only solve the problems of the first 3 lines of the proceedure above.  I
have heard of a program that couples Navier-Stokes with a shape solver, but
I don't remember where my reference is.  Regardless, it does take a long 
time to solve the initial problem on its own, and to ask a computer to
solve a moving kite would be insane.  It could maybe be done, but the 
amount of time required (and therefore $$$$) would be prohibitive.

Then there is the problem of what type of code you want to use and what
type of accuracy you want.  The BIGGEST problem in fluid dynamics (if they
ever solve this one, I can just go home and retire) is the problem of
turbulence.  It is not currently solved.  Turbulent flow does all sorts
of weird stuff that current theory is just NOW being able to BEGIN to 
explain.  A lot of this stuff has been observed for decades, but no viable
(or I suppose sufficient) description of the mechanism for these things
was available until much more recently.  Just in the 50's turbulent flow
was thought to be random in nature.  Now, there it is common knowledge that
there are many defined coherent blobs of fluid (called structures) in
turbulent flow (see for example, Robinson, Annual Review of Fluid Mech. ,1990)
(or 1991, I don't have it with me currently).  So, we currently don't even
know all that's going ON in turbulent flow and that is the problem with
solving turbulent flow problems.

For example, how much computational work is done on automobiles.  Not a lot
when it comes to the fluid dynamics part.  I am aware of some, but it's not
a common occurance to do simulations on them just because they are so
big and have so many curves and bends.  Simulations usually work best
on flat or semi-curved surfaces, but this is rapidly changing and improving.
Currently, there is quite a bit of numerical work on delta wing configurations
(but a lot of this is supersonic (greater than the speed of sound) work) and
not usable to kiting applications.

Also, a kite does not move slow.  Wasn't a flexi clocked at 120 mph? (or
about that).  When you figure out the Reynolds number per unit length of
this flow, it's not small (I'm not going to do it just cause I'm lazy ;-)
and then to consider that a kite has bends, kinks, spreader (which produce
wakes) and seams (which would act as turbulent trips) and also, that a
kite doesn't even fly at a decent angle of attack (What I mean by this
is that on a plane when it's cruising, the angle of attack is small, but
a kite can fly at a very high angle of attack.  This will produce separation
over a lot if not all of the kite back, which again introduces another
problem to solve.) the problem just get more and more complicated.

Well, I've rambled on long enough about this, and if anybody has any
questions, gimme a yell, but I don't guarantee I'll be able to get back
to you real soon.

Well, hope this starts some discussion,
Jonathan Dawson
jdawson@magnus.acs.ohio-state.edu