From: Al Bowers <bowers@orville.dfrc.nasa.gov>
Newsgroups: rec.aviation.military
Subject: Re: Flying Wing Aerodynamics
Date: 22 Apr 1999 15:13:32 -0700

bevnsag@netcom.com (Bev Clark/Steve Gallacci) writes:

> In article <HJoT2.185$mB5.146@news.rdc2.occa.home.com>,
> William D. Allen Sr. <ballensr@home.com> wrote:
> >Looking for sources regarding the aerodynamics of flying wing aircraft. In
> >particular are they severely limited in pitch authority for recovering from
> >steep dives? And are they effectively limited to subsonic speeds?

> I don't know of any formal data on such, but from what I understand,
> pitch and yaw contol are very dependent on wing sweep and airfoil.
> On things like the YB35/49, the modest sweep didn't help pitch or yaw any.
> Some of the Horton wings had both more sweep and better control. Their
> airfoil section and such might have been more helpful too.
> As for Mach, I don't really know, but the one thing a supersonic plane
> doesn't need is oodles of wing area, and the nature of most flyuing wing
> configs are in conflict with neat supersonic aerodynamics.

There are a couple of good books in the area, one being by Wohlfahrt
and Nickel (Dr Karl Nickel was one of the principals at Horten
Flugzeugebau), "Tailless Aircraft: In Theory and Practice" by the AIAA
in the USA and by Arnold in England.  There is also the book on model
flying wing theory by Bill and Bunny Kuhlman (aka B^2) called "On the
Wing..." published by them in Seattle WA USA.

It should be noted that while the theory of this class of flying wings
has been written about to some extensive detail, there are few (if
any) good books on the theory of flying wings as practiced by the
Horten brothers.  There are tremendously significant differences
bewteen flying wing aircraft as practiced by the Hortens and nearly
everyone else.  The Hortens were much more interested in flying wings
("Nurflugel" in German for "wing only") as _integrated_ aircraft, a
rather modern concept (system integration).  They were also very aware
of span loading as we think of the term today prior to 1940 (possible
as early as 1933).  You'll have difficulty finding a through
explanation of their complete theory (in any language), but I'll take
a stab at a quick summary:

Let us assume you begin with a given span.  It is well known that the
minimum induced drag for a given span and a given lift coefficient is
an elliptical span load.  Prandtl formulated that theory and one of
the his students, Max Munk, did the optimization for this problem back
in 1918.  However, this isn't necessarily the optimum solution (and in
fact this is where most aerodynamic theory books stop).  Using that
elliptical span load, you need integrate the span load to find the
wing root bending moment.  Given that elliptical span load's
associated wing root bending moment, what would happen if you
unconstrain span, holding the total lift and wing root bending moment
constant?

In fact, two people have done this, Ludwig Prandtl (Ref 1) and R T
Jones (Ref 2).  Both found the same result.  If you stretch the span,
you can achieve an 11% DECREASE in induced drag with a 22% INCREASE in
span (now remember, we held lift and wing root bending moment
constant) over an equivalent elliptical span load.  This is an
important finding, because if you introduce the structural constraint,
then the elliptical span load is not optimum.

This isn't the entire story, however.  It gets better.  Reimar Horten
developed an entore line of aircraft based on this theory (Ref 3).  If
the wing has an increased washin initially, this will increase the
upwash farther out towards the tip.  Then if the washout is displaced
to the tips, the resultant lift vector of the tip will be FORWARD of
the average angle of attack vector.  This implies that as you increase
the lift on one wing, the lift will pull that wing FORWARD.  Think
about what this implies for flying wings in the area of adverse yaw.
With a FORWARD component of an increased lift, the wing traveling UP
will move FORWARD also.  The span load of Prandtl and Jones negates
adverse yaw.

In fact, this was the basis of Dr Reimar Horten's PhD dissertation
which he completed while in prison in late 1945.  Horten had known
this for years and had been using in his sailplane designs, but he
didn't publish the work until 1945 (Ref 4).

It should be noted that the traditional "linear" twist distribution of
washout in swept wings will NOT produce the needed upwash at the wing
tips to overcome adverse yaw.  this twist distribution is the one that
most people use with a rectangular wing planform to achieve a near
elliptical span load.

The only conclusion I can draw is that Horten was a genius in the best
sense of the word.  Horten solved several very difficult and sticky
issues for flying wings with his span load work; he solved adverse
yaw, and wing root bending moment, while minimizing induced drag (for
the given structure).


Ref 1: Prandtl, L.: "Uber Tragflugel des kleinsten unduzierten
Widerstandes"; Zeuts. Flugtechnik und Motorluftschiffahrt, Vol 24, pp
305-306, Nov 1933.

Ref 2: Jones R T: "The Spanwise Distribution of Lift for Minimum
Induced Drag of Wings having a Given Lift and a Given Bending Moment";
NACA TN 2249, Dec 1950.

Ref 3: Horten, Reimar, and Selinger, Peter: "Nurflugel: Die Geischicte
der Horten-Flugzeuge 1933-1960"; Weishaupt Verlag, Graz, 1983.

Ref 4: Myhra, David; "The Horten Borthers: and their all wing
aircraft"; Schiffer, Atglen PA, 1998.


Al Bowers

From: Al Bowers <bowers@orville.dfrc.nasa.gov>
Newsgroups: rec.aviation.military
Subject: Re: Flying Wing Aerodynamics
Date: 26 Apr 1999 12:48:26 -0700

agmessier@aol.com (Agmessier) writes:

Thanks to Andy, Dan Ford, and Walt for their kind words...

> Al, I found you post very interesting and informative.  I'm usually
> too bent on aerodynamic theory and flight mechanics to consider
> structural constraints to increase the efficiency of a wing.  It
> makes a lot of sense, though.  A couple of questions(by the way, I
> intend to read more about Horten after reading your post, but I
> don't want to wait for answers.):

I think the Hortens had a very fresh look at the problem.  On of the
things that took me _YEARS_ of digging to resolve was how Reimar
Horten, the protoge, could throw out the elliptical span load created
by his own mentor, Ludwig Prandtl?  It made no sense to me.  In fact,
it was work that Prandtl did in exploring the span load that led to
the work of the Hortens.  But it was the Hortens that found the
adverse yaw benefits and did the flight mechanics work to expand the
theory of these span loads.

>> If you stretch the span, >you can achieve an 11% DECREASE in >
>> induced drag with a 22% INCREASE in span

> 1. How badly does this affect parasite drag? 22% longer span would
> have to increase your parasite drag substantially.  If this is
> significant, wouldn't this only benefit low speed performance?  This
> would lower your optimum cruising speed for a given aircraft(all
> other things being equal), but would it ultimately improve the range
> of such a design?

This is a problem.  One of the things the Hortens did NOT have access
to during WWII was a wind tunnel.  So all their work had to be solved
through flight experiments.  And the only way to effectively make
changes in flight experiments was to make them _small_.  This allowed
the changes to be easily made and the results could be tested rather
quickly.  There are corollaries to this, but the opposite approach was
taken by Jack Northrop with his flying wings.  I think that had
Northrop stuck to smaller aircraft for longer he might have solved
more of the problems in his airplanes (though this may not have been
true).  But it IS a fact that changes to large aircraft are difficult
to effect.

There is an optimum at which the span load works.  In some simple
analysis I've done on a couple of Horten designs (with generous help
from David Lednicer and Reinhold Stadler; both to whom I am deeply
indebted) shows that the benefits are not across the entire envelope.
As a lower lift coefficient is trimmed to, the span load is less and
less effective than at higher lift coefficients.  Unfortunately, this
goes hand in hand with lower and lower directional stability.  So it
is the worst of both worlds at low lift coefficients because the
directional stability is decreased and the adverse yaw arises again.

Now my analysis was done for a simple elevon configuration (if you are
familiar with Horten wings, my analysis was for the Horten H Xc
configuration).  A full trailing edge multiple elevon configuration
_might_ be able to solve the trimmed lift coefficient problem and
maintain the Horten span load.  I don't know, I haven't done that
analysis.  I suspect that was part of the complexity of the control
system used on the Horten H IX and Horten H XI sailplanes.  But
aeroelastics start to affect the validity of the results as David
Lednicer found.

> >If
> >the wing has an increased washin initially, this will increase the
> >upwash farther out towards the tip.  Then if the washout is displaced
> >to the tips, the resultant lift vector of the tip will be FORWARD of
> >the average angle of attack vector.  This implies that as you increase
> >the lift on one wing, the lift will pull that wing FORWARD.  Think
> >about what this implies for flying wings in the area of adverse yaw.
> >With a FORWARD component of an increased lift, the wing traveling UP
> >will move FORWARD also.  The span load of Prandtl and Jones negates
> >adverse yaw.

> 2. Is adverse yaw a problem with flying wings?  I had always
> understood that adverse yaw was an attribute of forward swept wings,
> which is why they're so unstable.  I know that wing sweep and tail
> fins both contribute to roll-yaw coupling in a favorable direction,
> right?  Do you mean that N sub p (Yaw due to roll rate), N sub
> beta(yaw due to slideslip or roll angle(indirectly)), or N sub
> p-dot(yaw due to roll acceleration or rolling moment) is adverse?
> Your discussion leads me to believe it is N sub p-dot(not N sub
> beta, which is traditionally studied as the definitive derivative
> for roll-yaw coupling).  Why is this adverse?  I'm thinking it may
> be the products or moments of inertia of your typical long span,
> high aspect flying wing, but I'm not sure.  Please explain.

Yes, adverse yaw is a problem in flying wings without verticals (the
"classic" Horten design).  It needs to be noted that proverse yaw (the
opposite of adverse yaw) is also not desirable.  In fact a pilot can
tolerate more adverse yaw than proverse yaw (this is documented in Mil
Std 1797a for handling qualities).

Adverse yaw is usually explained as an artifact of induced drag.  The
wing the pilot commands to rise increases the lift.  This increases
the adverse yaw, which drags the up-moving wing aft, opposite to the
desired yaw direction.  This isn't dependent on wing sweep (if I
misunderstood this part of your question, and I suspect I did, please
let me know).

So far the work I have done has been on the initialization of the
roll, so the proverse and adverse moments are (in my notation) Cnda
(or coefficient of yaw due to delta aileron; which is differential
elevon; in your notation it would be N sub da?).  Once beta is
introduced, then Cnb (N sub beta) and Clb (L sub beta) drive the
dynamics.  And once a roll is estabilshed, there are additiional Cnp,
Clp, Cnr and Clr terms that come into play.  As for the acceleration
terms, Clpdot, Cnpdot, Clrdot, and Cnrdot, it get REALLY confusing
because you really should break those out into betadot and pdot and
rdot terms (please, lets ignore this, it is hard enough trying to
explain this in English without waving my arms and hands in the air!).

All the moments I've dealt with are for static moments.  To introduce
moments of inertia for the actual accelerations (steady state
rotations don't need inertias) in transient motion.  I'm trying to
solve the simple static problems first.  there are others who have
worked some of the dynamic transient stuff (Gregg MacPherson of New
Zealand, and Robert Osbourne of England, are two).

Al Bowers

From: Al Bowers <bowers@orville.dfrc.nasa.gov>
Newsgroups: rec.aviation.military
Subject: Re: Flying Wing Aerodynamics
Date: 26 Apr 1999 13:02:26 -0700

waltbj@oneimage.com writes:

> Al Bowers <bowers@orville.dfrc.nasa.gov> wrote:
> >>bevnsag@netcom.com (Bev Clark/Steve Gallacci) writes:

> There was a recent articel oncerning flying the Horten glider in an
> aviation mag - since I scanned it in store I unfortunately do not
> recall the title nor the name of the mag itself. But I gathered the
> machine wasn't very stable in pitch - as one can imagine.

Actually, pitch stability of the Horten wings was always very strong.
Their span load creates a very strong pitch trim moment, which can
only be countered with a rather far forward CG.  However, in years of
work, the Hortens never were able to achieve a sustained spin or
tumble in their designs.  The two most serious losses were in
departures from their traditional work.  A short synopisis:

H IVb: used a laminar flow wing at the wrong Reynolds numbers.  the
resulting separation resulted in a spin which was unrecoverable.  The
pilot was fatally injured.

H IX V2: this was the Horten twin jet fighter prototype.  the engine
out characteristics with insufficient procedural background (in the
early development of jets, this was pretty endemic).  Loss of
directional stability resulted in ground impact during an aborted
single engine landing.  Fatal to the pilot.

many other Hortens were lost due to ground handling or landing
accidents (overshot and flew through trees, lost in hail storms, PIO
into the ground) but most were due to errors on the part of the pilot
or pilot technique (particularly the PIO problem wich was aeroelastic
coupled with novices); not due to poor design (which you may have
gathered, I am biased towards the Horten aircraft!).

> The problem as I see it is reconciling the need for low speed lift
> to get airborne with the shift in aerodynamic center with change of
> angle of attack due to the necessity for low speed lift. A
> symmetrical wing doesn't have that shift but then it doesn't have
> much low speed lift either. In addition because of the short moment
> arm in pitch the CG must be kept within very close limits. Tough
> problem in operation!

This is another design departure between Horten/Lippisch and the
approach by Northrop.  Northrop felt that symmentic airfoils would
allow him to achieve the performance he desired.  As a result, in many
photos, you'll note the outboard elevons deflected slighty up in the
Northrop wings.  In the case of the Hortens and Lippisch, both used
cambered reflexed airfoils (mostly Goettinen developed airfoils) to
achieve positive lift coefficients at zero pitching moment.

> Biggest problem for airline use would be getting into a gate
> somewhere without folding the wings.

There was a good article in "Flight International" (Apr 98 Vol 54 No
4) about flying wing airliners.  I'm afraid that is all I can say
about that.  The article is worth looking up and reading.

> Another problem one doesn't think of is ground effect which would
> commence about semi-span altitude.  This coupled with loss of pitch
> control effectivity at low speed could cause real probems trying to
> control touchdown attitudes.

Porposing is a problem because of the close coupling too.  there have
been lots of "wrong" answers to the ground handling and power approach
work done on flying wings.  Eventually, someone will figure them out.

Best regards,

Al Bowers

From: Al Bowers <bowers@orville.dfrc.nasa.gov>
Newsgroups: rec.aviation.military
Subject: Re: Flying Wing Aerodynamics
Date: 28 Apr 1999 11:16:15 -0700

maury@remove_this.istar.ca.invalid (Maury Markowitz) writes:

> In <19990427191151.06061.00000293@ng-cs1.aol.com> Agmessier wrote:

>> Thanks for clarifying.  I was thinking of 'adverse yaw' in terms of
>> free body roll-yaw coupling (in which sweep IS a factor), not as a
>> control response.  Thanks for clarifying, it all makes sense now.

>   Whoa, I missed this one and it's one I always wanted to know.  What is the
> cause of roll-yaw coupling?  And if it's sweep related, why was the X-3 one
> of the classic examples for it?

Classical "roll-yaw" inertia coupling (of which the X-3, X-1A, F-100
(early), and F-101 had problems) is caused by angle of attack, and the
distribution of mass.

For a really GOOD treatise on this, read:

Day, Richard E.: "Coupling Dynamics in Aircraft: A Historical
Perspective", NASA SP-532.


Coupling dynamics can produce either adverse or beneficial stability
and controllability, depending on the characteristics of the
aircraft. This report presents archival anecdotes and analyses of
coupling problems experienced by the X-series, Century series, and
Space Shuttle aircraft.  The three catastrophic sequential coupling
modes of the X-2 airplane and the two simultaneous unstable modes of
the X-15 and Space Shuttle aircraft are discussed. In addition, the
most complex of the coupling interactions, inertia roll coupling, is
discussed for the X-2, X-3, F-100A, and YF-102 aircraft. The mechanics
of gyroscopics, centrifugal effect, and resonance in coupling dynamics
are described. The coupling modes discussed are interacting multiple
degrees of freedom of inertial and aerodynamic forces and moments. The
aircraft are assumed to be rigid bodies. Structural couplings are not
addressed. Various solutions for coupling instabilities are discussed.

Available on-line at:

http://www.dfrc.nasa.gov/DTRS/

And search for "Day".

Al Bowers

From: Al Bowers <bowers@orville.dfrc.nasa.gov>
Newsgroups: rec.aviation.military
Subject: Re: Flying Wing Aerodynamics
Date: 28 Apr 1999 11:17:58 -0700

d93mlu@efd.lth.se (Michael Lundahl) writes:

> This is to everyone in the thread (and others).
> The Nurfugel-site contains much information about flying-wing aircraft.
> Among others it has alot of information about the Horten Nurfugels
> and I must say I was very impressed with those birds, especially
> Horthen IX (Ho 229).
> http://www.nurflugel.com/

Dr David Myhra is about to release a new book (actually a three volume
set) on the Horten H IX/Ho-229.  I was able to see a pre-print of it,
and it should prove to be the definitive work on the subject.  From
Schiffer Military Publishing, perhaps late this summer or this fall...

Al Bowers