How does washout reduce spiral instability or promote roll stability?

[steveseibel]

Can someone give me an accurate answer to the above question, as well as to why washin tends to promote spiral instability? If these assertions are in fact true? To keep things from being too easy, let's assume that we are trimmed to fly fast enough that no part of the wing is in danger of stalling.

Please don't hesitate to pull out all the stops and consider all relevant variables, I have a semi-solid background in basic stability and control issues...or just give the basic idea...

Directions to other on-line or off-line resources that bear on this question would be welcome as well...

This is in relation to some webpages I'm building, see for example http://www.aeroexperiments.org/SUATspiralstabflex.shtml

PS did I ever show you my variable-geometry Zagi, see for example http://www.aeroexperiments.org/SUATZagiexps.shtml

PPS sorry for posting in multiple forum sections but I just discovered this one, and it seems the most appropriate place...

Thanx much...

[RCAV8R13]

I was very interested to see if the explination of how dihedral works was correct. It is, but you have to look for it. The root of how dihedral works is on another page.
8.9. Long-Tail Slip
"Now let’s see what happens while the airplane is in an established turn. In particular, let’s consider an airplane with a fairly long fuselage, flying in a fairly tight turn. As shown in figure 8.9, there is no way that the airflow can be lined up with the front part of the fuselage and the back part of the fuselage at the same time. The fuselage is straight, and the path through the air is curved. You can’t have a straight line be tangent to a circle at two different points. You have to choose.


Figure 8.9: Airplane in a Tight Turn --- Rudder Neutral

If left to its own devices, the airplane will choose to have the vertical fin and rudder lined up with the airflow. The fin/rudder combination is, after all, an airfoil. Airfoils are good at producing tremendous forces if the wind hits them at an angle of attack. Besides, the tail is way back there where it has a lot of leverage.

Because of the air hitting the sides of the fuselage, and other effects, the fin/rudder might not completely determine the slip angle, but it will be the main determining factor. For sure, the airflow at the front of the fuselage --- and over the wing --- will have a significant slip component.

This will occur whenever the airplane is in a turn (unless you explicitly deflect the rudder to compensate). I call this the long-tail slip effect. This slip sounds like a bad thing, but in fact it can be put to good use; without it there would be no roll-wise stability, for reasons discussed in section 9.3. Remember: an inadvertent turn will be a slipping turn."

This "long tail slip" effect is widley overlooked, it's nice to see someone is on the ball.
RCA
P.S. To answer your question, I don't see how wash-in or wash-out would have any effect on spiral stability. Unless.. one wing had wash-in and the other had wash-out!

[steveseibel]

First I want to remind readers that my main question is still about washout, and any thoughts on that are most welcome. But as far as the "long-tailed slip" effect goes, a problem I have with emphasizing the interaction between the curving airflow and the "long tail", rather than emphasizing the fact the outside wingtip tends to experience more airspeed and also more drag which leads to yaw and slip, is that the former way of looking at things tends to suggest that if we increase the size of the vertical tail, we'll increase the amount of slip that the wing feels and this will give the dihedral more chance to act and this will decrease the aircraft's spiral instability or enhance roll stability. In actual practice the opposite is usually true, see for example these links

http://history.nasa.gov/SP-367/f148.htm

and

http://www.rcuniverse.com/forum/m_1535695/anchors_1545177/mpage_1/key_/anchor/tm.htm#1545177

and

http://www.b2streamlines.com/EffectiveDihedral.pdf

Maybe someone can offer some resolution to this apparent paradox, or maybe we just need to be careful not to put to much emphasis on the long-tailed slip effect as a root cause of roll stability.

I do think that the "See how it flies" website that RCAC8R13 referred to (see http://www.av8n.com/how/ ) is pretty darned cool.

I was very interested to see if the explination of how dihedral works was correct. It is, but you have to look for it. The root of how dihedral works is on another page.
8.9. Long-Tail Slip
"Now let’s see what happens while the airplane is in an established turn. In particular, let’s consider an airplane with a fairly long fuselage, flying in a fairly tight turn. As shown in figure 8.9, there is no way that the airflow can be lined up with the front part of the fuselage and the back part of the fuselage at the same time. The fuselage is straight, and the path through the air is curved. You can’t have a straight line be tangent to a circle at two different points. You have to choose.


Figure 8.9: Airplane in a Tight Turn --- Rudder Neutral

If left to its own devices, the airplane will choose to have the vertical fin and rudder lined up with the airflow. The fin/rudder combination is, after all, an airfoil. Airfoils are good at producing tremendous forces if the wind hits them at an angle of attack. Besides, the tail is way back there where it has a lot of leverage.

Because of the air hitting the sides of the fuselage, and other effects, the fin/rudder might not completely determine the slip angle, but it will be the main determining factor. For sure, the airflow at the front of the fuselage --- and over the wing --- will have a significant slip component.

This will occur whenever the airplane is in a turn (unless you explicitly deflect the rudder to compensate). I call this the long-tail slip effect. This slip sounds like a bad thing, but in fact it can be put to good use; without it there would be no roll-wise stability, for reasons discussed in section 9.3. Remember: an inadvertent turn will be a slipping turn."

This "long tail slip" effect is widley overlooked, it's nice to see someone is on the ball.
RCA

[Ollie]

http://www.glide.dyndns.org/on-the-wing4/index.html

On the Wing 4 contents:

161 Twist distributions for Swept Wings. Part 1
An introduction to twist distributions.
162 Twist distributions for Swept Wings. Part 2
Stalling patterns for twisted wings.
163 Twist distributions for Swept Wings. Part 3
Reducing adverse yaw.
164 Twist distributions for Swept Wings. Part 4
Lift distribution.
165 Twist distributions for Swept Wings. Part 5
Alternative twist distributions.

[vintage1]

Intersting info.

I woudl have said that in yaw, the same rules govern as do the rules for pitch stability with respect to wing area, tail area and tail moment arm. That is if the effective center of lateral pressure is behind the CG and moves further back as slip angle increases, stability is assured. To the point at which a large tail will produce a reluctance to 'turn in' at all..

Certainly the Zagi 'death spiral' is known to be inducable with a rearward CG.. which amounts to reducing tail area/moment aft of the CG.

With dihedral, the situation may be far more complex though. Add swept wings in and its a whole new ball game as well.

I haven't gotten my brain around all the factors, bit in the case of the OP, a simple test to move the CG a bit more forward would be at least the starting point to investigate the problem.

Anyone who thinks kit models ae designed and tested and modified by anyone with the sort of expertize found in thise fora, is in for a shock. Particularly with a foamie - modifying moulds is horrendously expensive.

[steveseibel]

Ollie, thanks much for this invaluable link. I haven't yet quite found the answer to my original question in here, but maybe a more careful reading/thinking about the ideas in these articles will shed some more light on it; there is a lot of great information in those articles. Steve

[QUOTE=Ollie]http://www.glide.dyndns.org/on-the-wing4/index.html

On the Wing 4 contents:
QUOTE]

[peterangus]

Steve

I note that you acknowledge the overriding importance of practical tests.

Here is an account of such a test, carried out fifteen years ago.
--------------------------------------------------------------------------
The Liberator model [photo] initially refused to fly straight.

Trimmed for straight, it would gradually go into a very tight turn, either way.

Altitude could be maintained with lots of up elevator.

Full opposite rudder would very slowly cancel the turn, but unless I was very careful, it would immediately flip into the opposite tight turn.

The root and tip wing sections were as A.

Adding a droop leading-edge, as B, completely cured the bad behaviour.
--------------------------------------------------------------------------
Many subsequent models [see my web] have employed sections as C, with no problems. Plain tip section, but root leading-edge tweaked upwards.
--------------------------------------------------------------------------
This is my presumption with regard to the initial condition of the Liberator:

There was some flow breakaway near the tips. This was producing a yaw instability [ie. as the yaw increased, the breakaway on the trailing tip became worse, and on the leading tip it improved]
--------------------------------------------------------------------------

[Ollie]

http://www.b2streamlines.com/OTW.html
KUBIAK PARAMETERS This single PDF document has all four installments of a series on the interrelationships between the center of gravity, pitching moment, sweep angle, and design coefficient of lift. The Panknin methodology is used extensively to provide relevant examples. Originally published in RCSD during 1994 and 1995 to answer some questions asked by Bill Kubiak.

http://www.b2streamlines.com/Culver.html
http://www.nurflugel.com/Nurflugel/Horten_Nurflugels/theory/theory.html
http://www.mh-aerotools.de/airfoils/global_index.htm
Index and download:
flying wings:
basic design of flying wings
airfoils for flying wings and tailless airplanes
airfoil design for tailless airplanes:
part 1, part 2, part 3, part 4, part 5, part 6, part 7, part 8

After reading, then you can ask a better question.

What is your purpose?

[Ollie]

There is more.

From Dr. Drela's message to me:

"I find the Cm curve is more typically S-shaped,
with a positive slope at small and large Cl's,
and a larger negative slope at intermediate Cl's.

{Edited graph}

The nonzero slopes of the curve cause the stability margin to vary
considerably with Cl, or equivalently, the aerodynamic center
to shift with Cl.

The shift in the AC, as a fraction of chord, is

delta( x_AC / chord ) = (-dCm/dAlpha) / (dCl/dAlpha)

At small and large Cl's the shift is forward (destabilizing),
while at intermediate Cl's the shift is rearward (stabilizing).

The positive and negative slopes of the curve increase as Re decreases,
as Ollie mentioned. On small gliders the more troublesome forward
AC shifts are 10% of the chord or more. On large gliders, shifts
of less than 5% are more typical.

These predicted shifts closely match the differences I observe between
the AC position as computed by theory, and the AC position observed
by incrementally moving the CG backwards on the glider until
instability is reached. "Theory" here refers to the vortex-lattice
method, with correction to account for the nonlinear Cm curve.
So it is possible to pick a stability margin and very closely nail
the correct CG location and decalage before the first flight, but
this requires doing the vortex lattice and Xfoil polar calculations.


The AC shifting has practical implications to the more casual RC glider pilot.
A glider which is stable in cruise (stable intermediate-Cl region),
can become unstable and tuck into a dive if the speed is increased
until the positive-slope left part of the Cm curve is entered
Having the CG below the wing, like on a poly glider, also contributes
to the tuck-in behavior, as does a flexible wing and/or tailboom.
In any case, one needs sufficient stability margin to overpower
the combined destabilizing effects of the nonlinear Cm curve,
poly/dihedral, and elasticity. The "dive test" is useful in that
it represents the worst-case situation where all these destabilizing
effects gang up, and hence it reveals the farthest-forward
AC position that the glider will ever see.


The existence of the "stable" middle part of the curve can be
demonstrated with a small flat plank of balsa with ballast on
the leading edge. This plank can be made to glide slowly at moderate Cl
even though it has no reflex camber (not possible with a flat Cm curve).

Free-flight HLG's and some paper airplanes make use of this phenomenon.
A FFHLG has nearly zero decalage to allow a high non-looping launch.
If there was no stabilizing Cm curve, such a glider would not be able
to glide slowly after launch.


>What is the cause?

The culprit is the variation of the boundary layer thickness
and the movement of the separation bubble with Cl.
The boundary layer and bubble changes the effective camber shape
of the airfoil, which then causes the Cm to change. The effective
shape of the airfoil is plotted in Xfoil under the Cp vs x/c plot.

As you increase the Reynolds number the boundary layer and the
bubble get thinner, so the modifications to the camber line
get smaller. Hence the Cm variations get smaller as well.

- Mark


Center of pressure location is
x_cp = 0.25 - cm/cl

Aerodynamic center location is
x_ac = 0.25 - (dcm/dalpha)/(dcl/dalpha)"

It means that you must consider enough static margin to allow for the aerodynamic center to shift with Cl.

[steveseibel]

Thanks again Ollie for the very interesting information. I may not have a good enough grasp of some of these areas to ask the question in the best way possible. I think I may not have a good enough understanding of how a given change in a lift curve, due to an increase or decrease in washout, is likely to affect an aircraft's spiral stability characteristics. My questions do have more to do with roll stability than pitch stability though.

The basic situation I'm trying to explain is this. I've done some experiments with hang gliders. I'm convinced that tightening the "variable geometry" (VG) system significantly reduces the anhedral in the outboard parts of the wings, which are the parts that will create the most roll torque in the presence of a sideways (slipping) airflow, as they are furthest from the CG. Therefore tightening the VG system can be thought of as creating an decrease in anhedral. It's not necessary to explain here exactly how the "VG" system works or why most people think it increases anhedral (the opposite of what I found) when it is "'tightened", i.e. when it is "on".

The VG system also decreases wingtip washout when it is tightened or "on".

During a constant-banked turn at a given bank angle and airspeed or angle-of-attack the pilot also must maintain a stronger rolling-out control input to prevent the bank angle from increasing when the VG sytem is "tight" or "on" than when it is "loose" or "off". (Or at higher airspeeds where the glider is less spirally unstable, during a constant-banked turn at a given bank angle and airspeed or angle-of-attack the pilot must maintain a weaker rolling-in control input to prevent the bank angle from decreasing when the VG sytem is "tight" or "on" than when it is "loose" or "off".) I hope I'm being somewhat clear here, the exact control input required of the pilot to hold the bank angle constant depends on both the airspeed and the bank angle, as well as the VG setting, but in all cases, for a given airspeed or a-o-a the glider "wants" to settle into a steeper bank angle when the VG is "tight" or "on" than when the VG is "loose" or "off".

It therefore appears to me that when the VG is tightened, the decrease in wingtip washout is somehow creating a net increase in the glider's spiral instability (i.e. requiring the pilot to make a stronger rolling-out command to prevent the bank angle from increasing), even though the anhedral is also being decreased.

So, I'm trying to understand why this would happen.

For whatever it's worth, the wing is swept and a tuft near the trailing edge about 1/3 of the way out along the span, on the top surface, typically starts to reverse in a low-airspeed turn regardless of the VG setting, but I think the conventional wisdom would suggest that the flow further out toward the tip is not stalling. That may or may not be actually true. The tips have a great deal of washout even with the VG tight.

I guess I'm hoping for a fairly global answer that is not highly dependent on the details of the airflow around this particular wing at this particular airspeed, as these same dynamics are basically common to all modern flex-wing hang gliders. Also I'm fairly sure that the same basic dynamics (a stronger rolling-out control input required when the VG is tight than when it is loose) continue to exisit even during turns at fairly high airspeeds (when no part of the wing should be stalling), though I'm putting this on my list of things to double-check sometime.

So again I'm wondering if there are parallels in the world of rigid (non-flexible) flying-wing aircraft, i.e. if there are cases where increasing the washout has been found to decrease the spiral instability, over a wide airspeed range.


In the link below I've written up the underlying question in a bit more detail with some musings as to answers, I'm not sure yet which of the possible approaches is the closest to being on the right track. From the link below you can also navigate to some more observations relating to the yaw-roll coupling characteristics of the wing in question (there is a stronger "negative" coupling between yaw or slip, and roll, when the VG is loose or "off" than when it is tight or "on", which matches my observations re anhedral.)

http://www.aeroexperiments.org/SUATspiralstabflex.shtml

Steve

There is more.

[BMatthews]

....So again I'm wondering if there are parallels in the world of rigid (non-flexible) flying-wing aircraft, i.e. if there are cases where increasing the washout has been found to decrease the spiral instability, over a wide airspeed range.....

WOW! And folks have accused ME of being long typed... :D

I have no idea why washout works but I know it sure helps. It's a fairly common trick in low wing scale rubber models like fighter models to add considerable washout in lieu of rediculous dihedral angles. It seems to work from the models I've seen evenly over the entire, though admitedly small, speed range of such models.

[steveseibel]

That sounds pretty similar to the effects I saw--I guess I don't have to know why either! I'm just hoping to find an answer that's a bit more generalized than "avoiding tip stalling" or "avoiding airflow detachment" and haven't yet managed to pick something more general out of the papers etc that have been offered, though it's undoubtedly in there somewhere!


I have no idea why washout works but I know it sure helps. It's a fairly common trick in low wing scale rubber models like fighter models to add considerable washout in lieu of rediculous dihedral angles. It seems to work from the models I've seen evenly over the entire, though admitedly small, speed range of such models.

[rofujiyama]

http://www.pbase.com/herb1rm/birds_in_flight&page=all

Hi steve,
I was looking for photos like these along time. Hope they fuel your curiousity ;)
Roland

[steveseibel]

Amazing! Thanks for posting those!

http://www.pbase.com/herb1rm/birds_in_flight&page=all

Hi steve,
I was looking for photos like these along time. Hope they fuel your curiousity ;)
Roland

[Ollie]

The key to your question about washout requires specific design numbers.
Aspect Ratio?
Sweepback?
Twist?
Taper?

There is a program that gives the lift distribution. The lift distribution changes with AOA and washout. That's lift distribution changes for the key to the answers about control with some changes in "variable geometry" (VG).

Play around this:
http://aero.stanford.edu/WingCalc.html

[steveseibel]

Thanks, that's helpful. Now, where is the version that shows both wings, and allows me to enter bank angle, and considers the difference in airspeed between the left and right tips during curving flight? (Just kidding--I guess!) I have to run now, will be logging onto to the net less frequently in the near future but still will continue to explore these issues... Steve

The key to your question about washout requires specific design numbers.
Aspect Ratio
Sweepback?
Twist?
Taper?
Washout?

There is a program that gives the lift distribution. The lift distribution changes with AOA and washout. That's lift distribution changes for the key to the answers about control with some changes in "variable geometry" (VG).

Play around this:
http://aero.stanford.edu/WingCalc.html

[BMatthews]

There's something else to consider here. Swept flying wings have been trying for years to succeed with no fins. The Horten bros. where successful with their form of washout twist distribution but others with similar top view planforms were not. The secret would seem to be that the washout distribution plays a part in the spiral stability of the design. I mention this as a swept flying wing with no fins is obviously a borderline scenario and provides yet another view of the issue that is unclouded by fuselage interference and the like.

The lift coefficient (seen as flying speed) would also seem to be part of the issue as well. I've seen reports that some Zagi wings are OK while at speed but can get very yaw unstable when approaching the stall.

[rofujiyama]

http://nurflugel.com/Nurflugel/nurflugel.html
Hi another cool site for full size flying wing study , my friend showed me this, he really is into horten style stuff.
Roland

[steveseibel]

Thanks for the thoughts, they are highly relevant as my questions ultimately are aimed at understanding hang glider flight dynamics and hang gliders usually have no fins. Steve

There's something else to consider here. Swept flying wings have been trying for years to succeed with no fins. The Horten bros. where successful with their form of washout twist distribution but others with similar top view planforms were not. The secret would seem to be that the washout distribution plays a part in the spiral stability of the design. I mention this as a swept flying wing with no fins is obviously a borderline scenario and provides yet another view of the issue that is unclouded by fuselage interference and the like.

The lift coefficient (seen as flying speed) would also seem to be part of the issue as well. I've seen reports that some Zagi wings are OK while at speed but can get very yaw unstable when approaching the stall.

[kf2qd]

Washout help stability because a slight downward twist in the leading edge of the wing towards the tips delays the stall toward the wing tip. this means that when the wings starts to stall it stalls near the fuselage first which doesn't cause much roll to the plane, and the tips are still flying which means that you still have some control over roll. Without washout the whole wing stalls and if one wing stalls before the other the plane falls off toward the stalled wing.

Angle of attack affects stall and the washout give the tip a lower angle of attack. Most large aircraft will 2 degrees of washout either by a twist in the wing, or a change in airfoil from the root to the tip. I think it's the B29 that has 5 different airfioils from the root to the tip.Each airfoil has a slightly different effective anggle of attack.

[BMatthews]

Kf2qd, you've described how the washout operates for pitch stability in flying wings or during a stall but that isn't the issue in this thread. It's about the YAW stability in the pre stalled condition. In otherwords during normal flight.

[steveseibel]

Kf2qd, you've described how the washout operates for pitch stability in flying wings or during a stall but that isn't the issue in this thread. It's about the YAW stability in the pre stalled condition. In otherwords during normal flight.

Actually, this was the original question:


Discussion - How does washout reduce spiral instability or promote roll stability?

Can someone give me an accurate answer to the above question, as well as to why washin tends to promote spiral instability? If these assertions are in fact true? To keep things from being too easy, let's assume that we are trimmed to fly fast enough that no part of the wing is in danger of stalling.

Here are some thoughts:

*When I talk about "spiral instability" I'm basically thinking of the amount of rolling-out control input that the pilot must maintain in order to keep the bank angle constant during a turn.

* An aircraft's "effective span" is very important to its spiral instability characteristics. As we've already noted, the longer an aircraft's wingspan and the slower it flies, the more the pilot typically needs to maintain a rolling-out control input to hold the bank angle constant. This is because the faster-moving outside wingtip tends to develop more lift than the slower-moving inside wingtip.

* Washout decreases the lift developed by the tip areas of the wing. In other words, the tip areas become less important in terms of the total lift distribution of the wing. In other words, the "effective span" of the wing is decreased.

* More precisely, I'm suggesting that when the wingtips have less incidence and angle-of-attack (more washout), the difference in airspeed between the left and right wingtips creates a weaker difference in lift, and therefore a weaker rolling-in torque, than when the wingtips have more incidence and angle-of-attack (less washout).

Or for an alternative/ supplementary line of argument: (only valid for DESCENDING turns)

* Note that the extreme case of a descending turn is a rolling vertical dive with the direction of roll being the same as the original direction of the turn. Note that the extreme case of an ascending turn is a rolling vertical dive with the direction of roll being opposite from the original direction of the turn.

* The rolling motion inherent in a constant-banked descending turn increases the angle-of-attack of the inside wingtip and decreases the angle-of-attack of the outside wingtip. Assuming that the wing section in question is not operating near the stall angle-of-attack, in general a given increase or decrease in angle-of-attack creates a slightly larger increase or decrease in lift when a wing section is operating at a low angle-of-attack (where the slope of the lift curve is steeper) than when a wing section is operating at high angle-of-attack (where the slope of the lift curve is shallower). (This dynamic is largely responsible for an aircraft's pitch stability, see for example this link http://www.indoorduration.com/INAVPitchStability.htm for an elementary treatment of this idea.) Therefore it seems that decreasing the incidence of the wingtips (i.e. increasing the washout) might actually increase the amount of rolling-out torque created by the difference in angle-of-attack between the wingtips that arises from the rolling motion inherent in a descending turn. To the extent that this effect is significant, increasing the washout will tend to reduce the aircraft's spiral instability.

Comments?

(PS, I know, with a more refined understanding of the true shape of the lift curve etc I could ask the questions more intelligently but this will have to do for the moment...)

[Ollie]

http://www.djaerotech.com/dj_askjd/dj_questions/dihedral.html
http://www.djaerotech.com/dj_askjd/dj_questions/stability.html
http://www.djaerotech.com/dj_askjd/dj_questions/flywingfly.html
http://www.djaerotech.com/dj_askjd/dj_questions/forwardswept.html
http://www.djaerotech.com/dj_askjd/dj_questions/fwingdihedral.html
http://www.djaerotech.com/dj_askjd/dj_questions/flywing.html
http://www.djaerotech.com/dj_askjd/dj_questions/sweepwash.html
http://www.djaerotech.com/dj_askjd/dj_questions/flywingtheory.html

[steveseibel]

Lots of good stuff in the last post, I'm familiar with most of the basic ideas here but I'd like to see a more detailed explanation of why dihedral can increase performance (decrease sink rate) during a low-airspeed small-radius thermal turn. Also in relation to my own particular questions I need to give some more thought to the details in this one in particular:

http://www.djaerotech.com/dj_askjd/dj_questions/sweepwash.html

[Ollie]

If you want to decrease sink rate, then remove some wing loading, cut induced drag and cut profile drag. However, that means a larger chord and much larger span, etc. Then improve the wing torque stiffness, etc. One perfomance aspect effects every other part of a design!!!! A flying wing design are many conflicts in formation.

[biber]

Dihedral is actually one possible way to reduce the cw_i.
Winglets e.g. can be considered as an extreme kind of dihedral
and they can very well reduce the cw_i.

biber

[steveseibel]

If you want to decrease sink rate, then remove some wing loading, cut induced drag and cut profile drag. However, that means a larger chord and much larger span, etc. Then improve the wing torque stiffness, etc. One perfomance aspect effects every other part of a design!!!! A flying wing design are many conflicts in formation.

Here are the D and J links (including 2 you posted below) suggesting that dihedral can reduce the sink rate in some situations. Again I'd like to know more about why. However, we should note that many of the smaller raptors (e.g. Sharp-shinned hawk, American Kestrel and all the other falcons, Broad-winged hawk) typically do NOT use dihedral while thermalling and many much larger raptors (eg Golden Eagle) do use much dihedral while soaring, which goes against some of D and J's observations. In particular D and J are flat wrong to state that the Prairie Falcon uses lots of dihedral while soaring, but I think we can forgive them ;) Steve

http://www.djaerotech.com/dj_askjd/dj_questions/wizarddihedral.html
http://www.djaerotech.com/dj_askjd/dj_questions/dihedral.html
http://www.djaerotech.com/dj_askjd/dj_questions/stability.html