Critical Mach number, Coefficient of Drag at transonic speed

I began to wonder why exactly most transport aircraft cruise between
Mach=0.8 and Mach=0.9 or so. Of course in the back of my mind I knew
that drag coefficient increased dramatically at some point, what would
be a flat drag curve at low velocity (Mach <= 0.3) would start to rise
slowly then at some point called the "drag divergence Mach number" the
drag coefficient would dramatically rise - going from a slow linear
growth to a suddenly exponential growth. For shapes that look pretty
close to the nosecone of an aircraft, this Machdd number is right around
Mach=0.85, and drag for example could climb from a Cd of 0.25 to one of
0.45 between Mach 0.85 and Mach 1.0.

After Mach 1.0 (usually around Mach 1.2 ?) different shapes have a
dramatic effect on Drag as it relates to Mach number. A sphere continues
to increase and levels off eventually. Sharpened cones Cd's drop, and
sooner or later seem to reach about the same drag coefficient as the
subsonic value.

I have a textbook from a years ago college physics course ("Classical
Dynamics of Particles & Systems") that has a single sample graph, and
there are certain web resources for different shapes, but this all seems
to be emperical data.

Does anyone know how to mathematically or computationally model drag?
Does anyone have any good references for this kind of thing? How do
flight simulators do it? Is there a reasonably simple mathematical model
to cover it?

Thanks guys!

"Vareck Bostrom" <bostrov@mac.com> wrote in message
news:bostrov-2C2AF5.20565801122003@news.easynews.com...
....How do

Well I've learned a lot recently about how FS does it since I started making
my first model. In the sim, they only account for the flight
surfaces-wings, vertical stabilizer, horizontal stabilizer, flaps, rudder,
etc., the sim doesn't even know what shape or exact size the fuselage is.
Basically, the larger a flight surface is, the more drag it causes. The
more lift a surface provides, the more drag it causes. That's what the sim
looks at. There are also options for the designer of the model to add or
reduce this drag, but in theory the sim should calculate drag accurately
without any other info.

In article <roYyb.63498$gQ6.37004@newssvr25.news.prodigy.com> ,
"Gary L." <someone@123.net> wrote:


I don't think this is true once the aircraft (or any object) is
transsonic - different wing shapes and nose cone shapes seem to have
very dramatic changes in the onset of the Mach critical number.

"Vareck Bostrom" <bostrov@mac.com> wrote in message
news:bostrov-C99021.01175302122003@news.easynews.com...
drag?
model
making
rudder,
is.
sim
or

Actually, you're both right! :-)

Transonic drag rise is a whole subject unto itself and goes way beyond
simple increases in drag coefficients. It involves the onset of shock, which
is again a whole subject unto itself.
It's extremely hard to discuss the transonic region without dealing with a
specific shape. There are a few constants, but not nearly enough to reduce
the issue to any reasonable generalizations.
I should think that reproducing true transonic transition on a desktop is a
real stretch for the pocketbook, and really unnecessary. You have to realize
I think, that in dealing with a desktop simulator, there is a point where
you can get way too bogged down in creating what is going on in the
background with complicated physics, where the result of all that physics
can be duplicated short cutting around it to present the operator with an
answer that satisfies the needs of the simulator.
I realize of course that this flies in the face of those who want all this
realism programmed in. What I'm saying here is that the ultimate realism,
even if possible to produce, might exceed the design demographics for the
simulator's market.
In other words, to express it with Occam's Razor......."it might be
possible, but they ain't gonna do it......cause you ain't gonna want to pay
for it!!!!! :-)))
Dudley Henriques
International Fighter Pilots Fellowship
Commercial Pilot/ CFI Retired
For personal email, please replace
the z's with e's.
dhenriquesATzarthlinkDOTnzt

Hi Vareck;


"Vareck Bostrom" <bostrov@mac.com> wrote in message
news:bostrov-2C2AF5.20565801122003@news.easynews.com...

If this is of any help, there is a measurement system called a Reynolds
Number which is used to measure airflow efficency around an object. It's a
relationship of interial force divided by viscuous force. Would it point
you in the desired direction?

Cheers,
John

How does X-Plane handle it? Anyone know?

On Tue, 02 Dec 2003 15:34:19 GMT, "Dudley Henriques"
<dhenriques@nowhere.net> wrote:




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"John Fraser" <jfraser@ns.sympatico.ca> wrote in message
news:my2zb.3172$IF6.140108@ursa-nb00s0.nbnet.nb.ca...
Reynolds
a

Reynolds is quite handy in determining how far back on the airfoil you can
get the drag divergence mach number (Mdd) without boundary layer separation
which is a critical design factor in getting the airplane through the
transonic region with minimum turbulence problems on the airframe, and has a
direct relationship to thrust requirements in the transonic range and the
avoidance of high wave drag early on in that transition.
I'll tell you one thing here fellas. By the time you guys get finished
designing this desktop simulator you're talking about, I'm going to have to
dig into my wife's mad money to afford the damn thing.
:-))))
Dudley Henriques
International Fighter Pilots Fellowship
Commercial Pilot/ CFI Retired
For personal email, please replace
the z's with e's.
dhenriquesATzarthlinkDOTnzt

Sorry. Not up on X plane at all.
DH
"George Lewis" <glewistn@nospam.earthlink.net> wrote in message
news:3ugpsv0h55udvcut2a6las02h6aplr4t5k@4ax.com...
The
the
add
accurately
which
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reduce
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realize
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News==----
Newsgroups
=---

In article <%h2zb.1264$Qd6.307@newsread1.news.atl.earthlink.n et>,
"Dudley Henriques" <dhenriques@nowhere.net> wrote:


I'm not actually intending on writing a desktop simulator, I'm more
curious about the possibility that someone else write one. I did order a
Computational Fluid Dynamics textbook this afternoon though, it could
turn into an interesting hobby...

I don't think a full fluid-flow simulation is possible in real time on
the desktop - yet. But desktop computational power is increasing
rapidly, the next couple iterations of flight simulator may well have
multiple 10 GHz processors to run on. At that level of power,
simulations of that accuracy are computationally possible, at least.
That level of computational power is on the order of 1990's vector
supercomputers such as the Cray Y-MP C90, on which real CFD was run for
real aircraft that we're flying around now in :-)

I have this personal belief that once the aircraft is simulated as an
interactive, changing object within an environment that more of the
'feel' may be captured, and in particular more extreme situations might
be captured.

You're right in that the simulator shouldn't become bogged down from a
theoretical perspective. It's easy to imagine this type of simulation
moving from airflow around the wing and airframe to airflow around the
propeller or turbofan and compressor staging, to the requirements on the
outside of FS2016 reading "Aerospace Engineeing degree from accredited
4-year university".

That's going too far, perhaps, but I think FS2004 doesn't go far enough.
In low speed flight, the physics is fairly simple and I think FS2004
does a good job with that, once you move to higher speed flight (above
Mach = 0.3, but still below the transonic range) it seems that things
become more complicated and at the transonic range to get any kind of
realism (from what I can tell so far) you need to be running some level
of realtime CFD or at least have a much more detailed lookup table done
from precomputed CFD or test/wind tunnel data.

Another aspect is this would make flight simulator more fun from an
expiremental perspective: how would the kingair 350 perform with small
turbofans instead of the turboprops? I had heard a rumor or something
saying that a prototype kingair 350 was considered with turbofans at one
point. We'll never see that kind of aircraft and entering table lookup
data would all just be guesses, but a simulator that could run a more
detailed airflow and engine simulation would at least have some basis in
reality and might capture the feel of it. I would hope at least.

The other thing that flight simulator 2004 doesn't really capture is the
'randomness' of flight as a basis in reality. We all know that if we
have icing turned on, and forgot to turn on pitot heat, when flying
through a cloud at approximately the right temperature we may suddenly
lose our airspeed indicator. You instantly know what the problem is. The
more interesting problems, I think, are what real pilots have to deal
with that are the result of a complex system (the aircraft and engines)
operating in a complex environment - I already mentioned the air florida
flight 90 situation - icing or other blockage on the engine turbine
inlet pressure sensor causing an incorrect differential reading and
thereby an incorrect EPR reading. The pilots of that flight didn't
instantly know what the problem was, the comments in the transcript were
on the order of "that's not right" or "that's curious" -

it's that aspect of flight I would hope to capture in a simulator. Would
it have helped if air florida 90 had run up the engines for 20 seconds
prior to takeoff to "de-ice" the interior of the engines? The engine
simulator should answer that, heat flows should all be computed in
realtime, surface icing across the entire aircraft, all insterments, etc
should be simulated.

Anyway, I think that'd be pretty cool.

"Vareck Bostrom" <bostrov@mac.com> wrote in message
news:bostrov-AD74BB.14372302122003@news.easynews.com...
started
fuselage
The
the
add
accurately
which
a
reduce
is a
realize
where
physics
an
this
realism,
the
pay

I agree. The possibilities are endless for doing these things. In the end,
it might very well be the potential sales market demographic rather than
available hardware and software technology that dictates how deeply they go
with simulation to the general public.
I also agree that watching this develop in the next several years will be
most interesting. Actually, I can tell you that from a purely personal
viewpoint, I've thoroughly enjoyed what they have already accomplished,
especially MS. It was a real pleasure taking part, even in the very small
way I did, with their development team on COF. They are a very highly
skilled and motivated bunch of people. I have no doubt at all that when this
stuff is developed for the average Joe, it will be MS in it up to their
armpits!
DH