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Author Topic: Wing sweep as a pitch stabilizing factor  (Read 1891 times)

Online Mike Alimov

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Wing sweep as a pitch stabilizing factor
« on: September 21, 2021, 03:19:47 PM »
First, some definitions are in order.
 I will be referring to wing sweep as a sweep of its quarter chord (25% chord, including flaps) as viewed from the top; not the leading edge sweep as drawn on plans.
 Second, when I talk about stability, I will be talking about pitch stability (up/down as seen from the pilot's point of view).

Reference: in a 1980 article about his airplane, Anatoly Kolesnikov ('86 W.Ch) says that wings with low sweep contribute to better maneuverability, but does not explain why.

Data:  last weekend, I was trimming out two new-to-me airplanes.  In the end, both planes were trimmed out to give the same rate of turn (as or close as I could tell, flying them back to back on the same day).  Both planes have very similar wing area, airfoil, tail volume, weight, wing loading, powertrain and propeller, lines, lap times, etc.  Difference: one plane had wing that was swept forward (see definition above), and it ended up with CG at 23% of mean chord.  The one with the rear sweep ended up with CG at 25% of mean chord.

Based on this, it appears that rear wing sweep indeed makes them more stable in pitch compared to neutral or forward swept wings (thus requiring more rearward CG to turn just as well), but I can't explain why.  I can easily see how a swept back wing acts as a weathervane and helps with yaw stability, but why also pitch?

Offline Mark wood

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Re: Wing sweep as a pitch stabilizing factor
« Reply #1 on: October 07, 2021, 06:42:10 AM »
That's an interesting observation but a question arises out of the gate. How similar are the airplanes? Also when you say Mean Chord, how did you derive mean chord which is important to know. Average chord and mean aerodynamic chord are not the same.

In terms of sweep and maneuverability this has been a long topic in many circles. The most common good reason to sweep a wing is for aerodynamic drag where the wing is swept for high mach number operations in order to reduce the T/C ratio. Sweeping has positive and negative effects on an airplane. Sweeping the wing can help with yaw damping and provide some yaw / roll coupling. Depending on the the application these are positive effects.

Longitudinally sweeping the wings can, in fact, change the pitching moment of the wing for a given area and aspect ratio. Similar to the way increasing aspect ratio of a wing increases the lift slope sweeping the wing aft steepens the slope of the pitching moment and forward sweep decreases the slope. How this translates to operation is that an aft sweep would tend to increase the stability of a given planform while forward sweep would tend to decrease the stability. For the nit pickers, the moment coefficient is a negative value generally and increasing sweep results in a more negative Cm slope providing greater pitch damping.

It's not clear to me which configuration did what in your post. However for small sweep angles I wouldn't expect much variation in CG WRT the MAC, if any, for a given planform. The results posted tend to indicate measurement of the CG from the LE at a fixed location such as the fuselage. Sweep would move the MAC aft and a CG of 23% MAC would move aft with it and appear to be a shift in CG at the root making it appear to be 25%. This then would draw the conclusion sweep has improved the longitudinal stability. The most common way of relating the CG is in terms of its location WRT the LE of the MAC or LEMAC. Using this convention eliminate confusion of where the CG resides aerodynamically. I'm sure the transport jet guys will chime in on this one.

I'm not sure the results actually indicate increased stability as that test isn't in the description. Steady state cases such as level flight turns continuous looping don't necessarily indicate stability. Stability is more better defined by the return to condition after perturbation. Places where increased stability will show up are in the exit of the corners where some flight path "ringing" can occur. That little bobble that cycles a few times and damps out, that's where the stability of the system will show up the best. System including all connections including the meat servo feedback driver in the center which often is out of phase generating greater gyrations and masking any inherent positive stability of the air vehicle. However, the air vehicle is a significant portion of this element and any lack of stability is best highlighted there. In full size testing we use a series of rapid control inputs to drive this and watch for the damping after cessation of the inputs.

My experience with wing sweep is somewhat limited but I have some with both full size and model size testing. My input on models is that sweep brings with it a couple negatives which cause me to not consider design which incorporate any sweep. Number one is that a wing with sweep, when it stalls, unless it is flying with zero yaw, very unlikely, one wing will stall first driving the airplane in to a "snap". People call it tip stall. Number two is yaw - roll coupling. Any yaw rate will generate a rolling moment. I know, many of the very best models have some level of sweep to them and it could be that the sweep compensate for the angle of the lines to some degree. However every airplane I've flown with sweep exhibited some level of this negative and airplanes without sweep demonstrably much less. Again, I know, this is a subjective observation and not a definitive A-B-A test.
 
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Online Mike Alimov

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Re: Wing sweep as a pitch stabilizing factor
« Reply #2 on: October 11, 2021, 09:57:24 AM »
Mark, thank you for your input. Took me a while to digest all of that, but I think I got it and largely agree. 
Obviously, we are operating at deep subsonic (in fact, near-stall) speeds and vastly different Re numbers than any full-size aircraft.  Fruthermore, my comparison was not 100% scientific, because the two airplanes being compared are different designs, although they share many common numbers.  A pure test would have been to take a given airplane, and install wings at different sweep angles while maintaining CG location with regards to the mean chord and recording their response to abrupt control input.  I sent this request to my R&D department, but they said they are at least a year behind.  >:D

Offline Avaiojet

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Re: Wing sweep as a pitch stabilizing factor
« Reply #3 on: October 11, 2021, 12:13:53 PM »
Many of the EAA guys are steps ahead using sweep wings and finding no adverse flight characteristics with "some" of the designs which are currently flying. Many in fact.

Google "Synergy Aircraft," there should be plenty of reading plus photos plus information on this unusual aircraft, sweep wing design.

Years ago I developed an interest in this design, myself, being a washed up former commercial pilot, it wasn't difficult.  ;D

Sure, I contacted the man behind the design and with much in common, mostly the love of GA, (General Aviation,) John McGinnis sent me a great three view with the CG already placed. Sure, I had to promise a few things, never to make a commercial kit or sell plans of his design.

That's kind of funny because I know of no one interested in the concept or the design of this aircraft, except for John McGinnis' followers, employees and volunteers. Oh! and myself, LL~

Plenty of R/C guys have already copied the Synergy design and have great flying models.

John McGinnis built a large Electric powered model of his design which flies as smooth as silk. Google for the video.

I posted a few years back looking for help with the lead out location/bell crank location on this unusual sweep wing model. I finally decided to place the bell crank on the CG and place the lead outs in a favorable location.

This is not the kind of model many would be interested in, but I certainly enjoyed designing and framing this model. It's getting close to completion.

You can see the lead out location. I would have had a difficult time determining the actual CG if to wasn't for John McGinnis. What a guy!!  H^^

https://en.wikipedia.org/wiki/Synergy_Aircraft_Synergy

Charles
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Offline Howard Rush

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Re: Wing sweep as a pitch stabilizing factor
« Reply #4 on: October 13, 2021, 02:45:43 PM »
Sweeping the wing can help with yaw damping and provide some yaw / roll coupling. 

The old vacuum tube yaw dampers on early straight-wing jets were so unreliable that designers started sweeping wings so artificial yaw damping wouldn't be needed.  The reduced t/c was a bonus.
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Online frank williams

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Re: Wing sweep as a pitch stabilizing factor
« Reply #5 on: November 13, 2021, 08:27:05 PM »
Did someone say Sweep?  Try this.

Online Bob Hunt

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Re: Wing sweep as a pitch stabilizing factor
« Reply #6 on: November 14, 2021, 05:32:47 AM »
...or this.


Offline Dennis Toth

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Re: Wing sweep as a pitch stabilizing factor
« Reply #7 on: November 14, 2021, 08:55:44 AM »
Hey Bob, what about your swept forward experiment, did that do anything crazy in yaw or roll? As I remember it was a pretty good flying concept.

Mark,
I appreciate you detail but for the sake of many guys that have not taken any aero courses please at least once in each post spell out the complete name of the acronym being used.

I followed Mike's description, it was pretty straight forward and made sense between the two models. Seems a little sweep is not a bad thing but both models were able to be trimmed just fine.

Best,   DennisT

 

Offline Mark wood

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Re: Wing sweep as a pitch stabilizing factor
« Reply #8 on: November 14, 2021, 12:16:32 PM »
Hey Bob, what about your swept forward experiment, did that do anything crazy in yaw or roll? As I remember it was a pretty good flying concept.

Mark,
I appreciate you detail but for the sake of many guys that have not taken any aero courses please at least once in each post spell out the complete name of the acronym being used.

I followed Mike's description, it was pretty straight forward and made sense between the two models. Seems a little sweep is not a bad thing but both models were able to be trimmed just fine.

Best,   DennisT

My bad. I always the assumption that airplane people know what he various terms are. MAC Mean Aerodynamic chord (not the average chord most people use). LE leading edge. WRT With Respect To. LEMAC Leading Edge at Mean Aerodynamic Chord. T/C thickness ratio - airfoil thickness divided by chord.  Did I miss any? Life's rough for geeks who don't speak regular English.
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Offline Dennis Toth

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Re: Wing sweep as a pitch stabilizing factor
« Reply #9 on: November 14, 2021, 03:19:57 PM »
Mark,
Thanks, that helps us follow the thoughts in the post. I think you got them all.

Best,   DennisT

Offline Mark wood

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Re: Wing sweep as a pitch stabilizing factor
« Reply #10 on: November 15, 2021, 08:53:50 AM »
Frank, Bob. Not that you didn’t already know it, those planes are badasscooledness for sure.
Life is good AMA 1488
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Offline Howard Rush

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Re: Wing sweep as a pitch stabilizing factor
« Reply #11 on: November 15, 2021, 02:02:06 PM »
I'd fear rolling moment due to sideslip with that much sweep, but Don Hutchinson's F-86 flies great. 
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Offline Serge_Krauss

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Re: Wing sweep as a pitch stabilizing factor
« Reply #12 on: November 21, 2021, 07:28:19 PM »
As I suggested in the personal e-mails, find the actual aero center of each wing by computation from valid equations based on applying the MAC definition to the shapes of your wings. The lateral position for elliptical wings is wrong on the internet sites I've found (it is 4/(3 pi) - or .4244 - times the half span for any elliptical wing). But you're interested in the longitudinal position. If you have a well-defined wing, compute the position from the equation I provided, but if not, just make a rigid, uniform-density card board or foam cut-out in the accurate, scaled shape of your wing, and find its cg (center of gravity) or enter it in CAD to find the cg. Compute the MAC and then measure or calculate 1/4 of that computed MAC of the wing ahead of that balance point. That is the aero center from the basic definition. 1/4 of the MAC for the ellipse is [2/(3 pi)]Cr or .2122 times the root chord, independent of sweep.

I say do this, because you may find that regardless of whatever you choose as sweep, these computed a.c.'s for your wings might actually explain your experimental results. If you have ribs aligned at some given percent chord, my 3rd equation will work. Otherwise, find the c.g. of the wing by CAD or the rigid model experiment. This is the same position computed by the usual MAC formulas. Then choose your c.g. positions an equal % of the MAC ahead of the quarter-MAC points of your wings and compare. I'd be interested in whether your chosen (experimentally determined) aircraft cg's differ uniformly from the computed ones, realizing of course that things like yaw damping, flap moments, tail volumes, etc., may ultimately have caused your different choices.

Note that the c.g. of the wing in the CAD or balancing is not the same as the chosen c.g. for the flying model.

I do realize that putting things like these into words is awkward.

Offline Air Ministry .

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Re: Wing sweep as a pitch stabilizing factor
« Reply #13 on: November 21, 2021, 09:36:20 PM »
The converse is a straight wing , where gusts etc rock the tips & you get yaw .

But sweeping it sounds a bit of a oversimplification when youd be better off elliptical .  VD~

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Offline phil c

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Re: Wing sweep as a pitch stabilizing factor
« Reply #14 on: December 01, 2021, 01:28:29 PM »
...or this.

Yikes! An Electrified Combat Design for PA!
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Online frank williams

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Re: Wing sweep as a pitch stabilizing factor
« Reply #15 on: December 09, 2021, 10:13:28 PM »
To answer the question "is wing sweep a stabilizing factor" ...... yes.

The terms stability and stabilizing take a beating sometimes in "stunt physics".  We really are wanting to talk about "dynamic stability" and sometimes can't get past "static stability".  Dynamic stability is concerned with the oscillations after a disturbance.  As Mark said above, the standard test of "pitch dynamic stability" is to put a quick step input into the elevator and watch the oscillations of the plane.  The quicker the oscillation damps out, the better the stability.  In our case, the test input is the quick elevator input in a corner.  The plane that flies out of the corner flat and true with no oscillation is prized and said to have good stability, dynamic stabillity.  Stability in the "static stability" sense merely means that a moment is produced to oppose the disturbance.

The airplane design parameter that is most associated with pitch dynamic stability is the horizontal tail.  The tail area should be thought of as a "dash pot" or "shock absorber".  As it is rotated through the fluid, it creates a reaction force that is opposite to the direction of rotation and proportional to the velocity of the rotation.  It tries to damp the upset rotation.  This term (stability derivative) is called Cmq, coefficient of pitching moment due to rotation q.  There is another term that describes the resulting moment due to the changes in angle of attach at the tail.

Other parts of the airplane also contribute to the pitch damping like the fuselage and the wing. If the wing is a simple straight wing with no sweep, the chord of the wing as it rotates about the cg produces a fluid damping action.  A high aspect ratio wing with narrow chord has less damping than a low aspect ratio wing with more area fore and aft of the cg.  It is easy to see that a swept wing will have much more 'stuff' fore and aft of the cg as it rotates, and will contribute a greater moment to the pitch damping.

Data from a Bell X-1 style plane (at low Mach ~0,16) with a straight wing and a wing swept 35 degrees ,shows that the damping terms (Cmq and Cma-dot) for the two planes are about twice as large for the swept wing configuration.  If we assume the tail and tail length are about the same (I'm not sure for this data) then there is definitely a higher damping from the swept wing.

The old "Sweet Sweep" combat ship always had excellent stability for such a small tail area.  A very unique plane.  A well known stunt flyer who had never flow one, built one, and was amazed at its stability.  "It flies like a stunt ship", he said.

To answer the question "is wing sweep a stabilizing factor" ...... yes, definitely.

Offline Serge_Krauss

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Re: Wing sweep as a pitch stabilizing factor
« Reply #16 on: December 10, 2021, 11:41:40 AM »
Of course Frank's answer is correct and intuitively so as well. The main question, though, is why the static margins are different. The MAC and related derivations take into account all moments in the horizontal plane, meaning that the MAC's 1/4-chord point will itself determine a.c.'s and thus c.g.'s biased as in Frank's discussion. Assuming that Mike, as an engineer, used MAC (really calculated as a purely geometrical concept) as opposed to "mean" chords, the c.g. positions relative to the 1/4-MAC point should theoretically have been the same. At least, it seems to me that the "de-stabilizing" forward tips vs. the "stabilizing" rearward ones should be accounted for.

I have thought that the discrepancy has resulted from the empirical approximation inherent in the 1/4-chord idea for an a.c., combined with the first approximation in the mathematical derivation that lift is equal throughout the area (i.e. the derivation is simply that of finding the c.g. of a surface). An actual average chord would lead to a different "answer." In private correspondence, I learned that plan forms varied too, and approximations here might have led to a discrepancy. I apologize for not making that clear in my earlier post.

Offline Mark wood

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Re: Wing sweep as a pitch stabilizing factor
« Reply #17 on: December 10, 2021, 01:04:18 PM »
To answer the question "is wing sweep a stabilizing factor" ...... yes.

The terms stability and stabilizing take a beating sometimes in "stunt physics".  We really are wanting to talk about "dynamic stability" and sometimes can't get past "static stability".  Dynamic stability is concerned with the oscillations after a disturbance.  As Mark said above, the standard test of "pitch dynamic stability" is to put a quick step input into the elevator and watch the oscillations of the plane.  The quicker the oscillation damps out, the better the stability.  In our case, the test input is the quick elevator input in a corner.  The plane that flies out of the corner flat and true with no oscillation is prized and said to have good stability, dynamic stabillity.  Stability in the "static stability" sense merely means that a moment is produced to oppose the disturbance.

The airplane design parameter that is most associated with pitch dynamic stability is the horizontal tail.  The tail area should be thought of as a "dash pot" or "shock absorber".  As it is rotated through the fluid, it creates a reaction force that is opposite to the direction of rotation and proportional to the velocity of the rotation.  It tries to damp the upset rotation.  This term (stability derivative) is called Cmq, coefficient of pitching moment due to rotation q.  There is another term that describes the resulting moment due to the changes in angle of attach at the tail.

Other parts of the airplane also contribute to the pitch damping like the fuselage and the wing. If the wing is a simple straight wing with no sweep, the chord of the wing as it rotates about the cg produces a fluid damping action.  A high aspect ratio wing with narrow chord has less damping than a low aspect ratio wing with more area fore and aft of the cg.  It is easy to see that a swept wing will have much more 'stuff' fore and aft of the cg as it rotates, and will contribute a greater moment to the pitch damping.

Data from a Bell X-1 style plane (at low Mach ~0,16) with a straight wing and a wing swept 35 degrees ,shows that the damping terms (Cmq and Cma-dot) for the two planes are about twice as large for the swept wing configuration.  If we assume the tail and tail length are about the same (I'm not sure for this data) then there is definitely a higher damping from the swept wing.

The old "Sweet Sweep" combat ship always had excellent stability for such a small tail area.  A very unique plane.  A well known stunt flyer who had never flow one, built one, and was amazed at its stability.  "It flies like a stunt ship", he said.

To answer the question "is wing sweep a stabilizing factor" ...... yes, definitely.

Nicely stated Frank

However there is a error, which would be interesting to discuss, in your description which is adequate for the level here on SH. The tail plane doesn't specifically work as a dash pot as you describe. A dash pot is a velocity dependent energy dissipater which the angle dependent force (moment) developed by the tail plane doesn't do. In a simple spring oscillator we know that F=-kX and in the case of an airplane the moment is M= -length x (dCl x apha) x area x q where dCl is the slope of Cl. Since length is part of both sides of the airplane moment version and the other terms could be considered constant they can all be reduced to k or F=-k x alpha. This is an over simplification but it highlights that the tailplane isn't the dynamic damping element only the static displacement force which, in this case, we use the tailplane on a boom to balance the moment generated by the wing.

The sum of those two moments combined are the total aircraft moment and when that moment is zero we say the airplane is in trim. All of the surface respond in the same basic manor to the incoming air an can be combined in to total moment coefficient, "Cmq" and this can tell us allot about the airplane. Any displacement in angle from trim will result in a change in the moment as function of Cmq. The faster the moment increases resisting displacement the more statically stable to aircraft will be. This is is what we term the slope ( I know you know this Frank, tis not for you). The static stability derivative is the slope of the restoring moment dCm/dAplha. 90% of what an airplane does that we need to be knowledgeable on can be understood by the foregoing static analysis.

In order to under the dynamic stability is much more difficult. In that we must start with the energy state of the system. To calculate the basis oscillatory period we begin with the sum of the total energy of the frictionless system. Without friction the system will continue to oscillate indefinitely. The question is where does the friction come from. Or the resistance. In the case of a rotating system, like airplanes pivoting about the CG, some of that comes from the inertia of the mass, the second product moment of the mass distribution. And some comes from friction in the form of drag. The drag term is the only term which takes energy away from the equation. All of the elements in dynamic stability include the flight path of the aircraft due to the energy exchanges that take place.

What this means is that a perturbation will cause a response. Such as entering a gust or an elevator pitch input.  In the former the airplane might enter a phugoid oscillation in pitch but there will never be a change in angle of attack as the altitude and airspeed change.  The initial energy is increased by the gust and the airplane will oscillate in pitch, airspeed and altitude until the damping factor (drag/mass) slows it to the original condition. The latter a resulting phugoid oscillation may occur in which case there is an oscillation in AOA as well as altitude and airspeed. Again damping until the airplane is once again in it initial condition. Both cases the period has dependency upon the static stability margin ie the k term.

Within the system we would write the differential equation:

F(t) = md2x/dt2 + c dx/dt +kx Where c is the damping function of the dashpot. The lift from the stabilizing element fits in the kx term and drag fits in the c dx/dt term and is also a function of alpha which makes the solution even more complicated.



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Offline Mark wood

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Re: Wing sweep as a pitch stabilizing factor
« Reply #18 on: December 10, 2021, 01:28:15 PM »
Of course Frank's answer is correct and intuitively so as well. The main question, though, is why the static margins are different. The MAC and related derivations take into account all moments in the horizontal plane, meaning that the MAC's 1/4-chord point will itself determine a.c.'s and thus c.g.'s biased as in Frank's discussion. Assuming that Mike, as an engineer, used MAC (really calculated as a purely geometrical concept) as opposed to "mean" chords, the c.g. positions relative to the 1/4-MAC point should theoretically have been the same. At least, it seems to me that the "de-stabilizing" forward tips vs. the "stabilizing" rearward ones should be accounted for.

I have thought that the discrepancy has resulted from the empirical approximation inherent in the 1/4-chord idea for an a.c., combined with the first approximation in the mathematical derivation that lift is equal throughout the area (i.e. the derivation is simply that of finding the c.g. of a surface). An actual average chord would lead to a different "answer." In private correspondence, I learned that plan forms varied too, and approximations here might have led to a discrepancy. I apologize for not making that clear in my earlier post.

MAC and average chord are almost universally incorrectly interchanged. Depending upon the author publishing information in the model press these can and do cause a ton of confusion.

Average chord is a geometric average of the chords. MAC is the ratio of the sum of the area moments about the quarter chord to the sum of area. Similar to calculating center of gravity of mass which is the sum of the mass moments about a datum divided by the sum of the mass. MAC is the integral from the root to the tip of Y(X)C(x) dx divided by the integral of C(x)dx where Y(x) is the distance to the quarter chord and C(x) is the chord as a function of x. The MAC can be found graphically much easier.

Simply stated as you point out, for given CG sweeping the wing moves the MAC rearward which in turn increases the static margin. It doesn't take differential equations and callus to understand that. Being the uber geek that I am, I loose sight of that.

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Offline Howard Rush

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Re: Wing sweep as a pitch stabilizing factor
« Reply #19 on: December 10, 2021, 01:56:23 PM »
To answer the question "is wing sweep a stabilizing factor" ...... yes.

The terms stability and stabilizing take a beating sometimes in "stunt physics".  We really are wanting to talk about "dynamic stability" and sometimes can't get past "static stability".  Dynamic stability is concerned with the oscillations after a disturbance.  As Mark said above, the standard test of "pitch dynamic stability" is to put a quick step input into the elevator and watch the oscillations of the plane.  The quicker the oscillation damps out, the better the stability.  In our case, the test input is the quick elevator input in a corner.  The plane that flies out of the corner flat and true with no oscillation is prized and said to have good stability, dynamic stabillity.  Stability in the "static stability" sense merely means that a moment is produced to oppose the disturbance.

The airplane design parameter that is most associated with pitch dynamic stability is the horizontal tail.  The tail area should be thought of as a "dash pot" or "shock absorber".  As it is rotated through the fluid, it creates a reaction force that is opposite to the direction of rotation and proportional to the velocity of the rotation.  It tries to damp the upset rotation.  This term (stability derivative) is called Cmq, coefficient of pitching moment due to rotation q.  There is another term that describes the resulting moment due to the changes in angle of attach at the tail.

Other parts of the airplane also contribute to the pitch damping like the fuselage and the wing. If the wing is a simple straight wing with no sweep, the chord of the wing as it rotates about the cg produces a fluid damping action.  A high aspect ratio wing with narrow chord has less damping than a low aspect ratio wing with more area fore and aft of the cg.  It is easy to see that a swept wing will have much more 'stuff' fore and aft of the cg as it rotates, and will contribute a greater moment to the pitch damping.

Data from a Bell X-1 style plane (at low Mach ~0,16) with a straight wing and a wing swept 35 degrees ,shows that the damping terms (Cmq and Cma-dot) for the two planes are about twice as large for the swept wing configuration.  If we assume the tail and tail length are about the same (I'm not sure for this data) then there is definitely a higher damping from the swept wing.

The old "Sweet Sweep" combat ship always had excellent stability for such a small tail area.  A very unique plane.  A well known stunt flyer who had never flow one, built one, and was amazed at its stability.  "It flies like a stunt ship", he said.

To answer the question "is wing sweep a stabilizing factor" ...... yes, definitely.

Linearized pitch dynamics in most airplanes is a 4th-order system.   This comprises two second-order modes: a "short-period" mode that Frank is talking about and a "phugoid" mode that Mark is talking about. Yes, Cmq, pitch moment due to pitch rate, contributes to short-period mode pitch damping.  See https://courses.cit.cornell.edu/mae5070/Caughey_2011_04.pdf , for example.

I'm not sure how these modes shake out in CL stunt and combat planes, but I've always liked Cmq, and from the looks of at least one plane Frank brought to the Nats, he likes it, too.  I had either forgotten or never knew about sweep causing pitch damping.  Thanks for bringing that up, Frank, and answering the original question. 

I wonder how much pitch damping you get from sweep relative to tail length.  If I wanted more of it, I'd lean toward making the tail longer, sweep entailing Evil.  Brett sees Evil in tail length, too, so I guess I should study the issue more and maybe try some stuff.   
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Re: Wing sweep as a pitch stabilizing factor
« Reply #20 on: December 10, 2021, 02:04:21 PM »
Mark, I don't have but a minute to reply now, but I will say that I am not wrong about the tail being the critical component in aircraft longitudinal dynamic stability.

Longitudinal airplane dynamics is described as a torsional spring mass system.  The eom are developed with a spring stiffness and damping moments proportional to rotational velocity.  Pitch rate is the key driver in producing a force on the tail and a resulting moment that opposes the given airplane pitch rotation.  Same thing as a linear spring mass system, just in a circle.

Frank

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Re: Wing sweep as a pitch stabilizing factor
« Reply #21 on: December 10, 2021, 03:28:33 PM »
Mark, I don't have but a minute to reply now, but I will say that I am not wrong about the tail being the critical component in aircraft longitudinal dynamic stability.

Longitudinal airplane dynamics is described as a torsional spring mass system.  The eom are developed with a spring stiffness and damping moments proportional to rotational velocity.  Pitch rate is the key driver in producing a force on the tail and a resulting moment that opposes the given airplane pitch rotation.  Same thing as a linear spring mass system, just in a circle.

Frank

You shouldn't be receiving the message that you are wrong per se. However moment generated by the tailplane is static in nature and not dynamic. It does not act as a dash pot rather a spring. It has no velocity dependence. The static stability does play a roll in dynamic stability as I suggested.
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Re: Wing sweep as a pitch stabilizing factor
« Reply #22 on: December 10, 2021, 05:35:52 PM »
You shouldn't be receiving the message that you are wrong per se. However moment generated by the tailplane is static in nature and not dynamic. It does not act as a dash pot rather a spring. It has no velocity dependence. The static stability does play a roll in dynamic stability as I suggested.

The static moment generated by the tailplane, moment due to angle of attack, is static.  That's all you'll see mentioned in these parts except by folks like Frank and Igor.  However, there are pitch moments due to pitch rate and angle of attack rate that are dynamic.  Behole eqn. 5.69 in the reference I posted above.  Zeta has Mq in it.  Compare a Teosawki to a combat plane.  Damping from the tail is obvious. 
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Re: Wing sweep as a pitch stabilizing factor
« Reply #23 on: December 10, 2021, 06:30:55 PM »
Mark ... I'm  not sure where to begin .... also I mean no offense .....

The sum of those two moments combined are the total aircraft moment and when that moment is zero we say the airplane is in trim. All of the surface respond in the same basic manor to the incoming air an can be combined in to total moment coefficient, "Cmq" and this can tell us allot about the airplane. Any displacement in angle from trim will result in a change in the moment as function of Cmq. The faster the moment increases resisting displacement the more statically stable to aircraft will be. This is is what we term the slope ( I know you know this Frank, tis not for you). The static stability derivative is the slope of the restoring moment dCm/dAplha. 90% of what an airplane does that we need to be knowledgeable on can be understood by the foregoing static analysis.






I'm not sure why you use the term Cmq for the total moment on the airplane.  The subscript notations for angular rotations about the roll, pitch, and yaw axes are usually p,q,and r.  Cmq describes the moment about the pitch axis due to pitch rotational velocity.  This term, Cmq along with Cm/alpha dot, are the dominant damping factors in dynamic stability.  What you have described is static stability.

Static stability ..... if there is a disturbance from trim, is there a force or moment to right the disturbance.

Dynamic stability ...... if there is a disturbance from trim, is the resulting oscillation one that increases over time (unstable), one that stays the same (neutrally stable), or one that damps out over time.

As Howard points out, pitch dynamics is described by a set of 4th order de's.  They are broken down into two sets of 2nd order de's.  One solution results in a long period oscillation (the phugoid) and the other solution is a short period oscillation.  The phugoid is often poorly damped in airplanes and sometimes even left unstable.  The short period oscillation is of great importance to the pilot.

In order to under the dynamic stability is much more difficult. In that we must start with the energy state of the system. To calculate the basis oscillatory period we begin with the sum of the total energy of the frictionless system. Without friction the system will continue to oscillate indefinitely. The question is where does the friction come from. Or the resistance. In the case of a rotating system, like airplanes pivoting about the CG, some of that comes from the inertia of the mass, the second product moment of the mass distribution. And some comes from friction in the form of drag. The drag term is the only term which takes energy away from the equation. All of the elements in dynamic stability include the flight path of the aircraft due to the energy exchanges that take place.
A description that I'm not sure what to do with this paragraph .... "energy exchanges"?  phugoid solution .. ok   "mass, inertial" ok  "friction ..the drag is the only term which takes energy away from the equation" ........ Not quite right

I think that you are slightly mixing static and dynamic stability
 

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Re: Wing sweep as a pitch stabilizing factor
« Reply #24 on: December 10, 2021, 08:48:38 PM »
Well, I certainly have demonstrated a shortage of understanding as compared to yours and I concede to your expertise. Apologies for upsetting you.
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Re: Wing sweep as a pitch stabilizing factor
« Reply #25 on: December 10, 2021, 10:40:42 PM »
Average chord is a geometric average of the chords. MAC is the ratio of the sum of the area moments about the quarter chord to the sum of area. Similar to calculating center of gravity of mass which is the sum of the mass moments about a datum divided by the sum of the mass. MAC is the integral from the root to the tip of Y(X)C(x) dx divided by the integral of C(x)dx where Y(x) is the distance to the quarter chord and C(x) is the chord as a function of x. The MAC can be found graphically much easier.

Simply stated as you point out, for given CG sweeping the wing moves the MAC rearward which in turn increases the static margin. It doesn't take differential equations and callus to understand that. Being the uber geek that I am, I loose sight of that.

Just for my own curiosity, I'd like to compare my more elementary analysis to what you feel is important here (and learn anything I might have missed along the way).

I did start with the basic definitions and used my freshman calculus to derive MAC's, their placements, and a.c.'s for certain chord distributions and their variants, including varying sweeps and alignments. I discovered that most internet determinations of span-wise locations of elliptical-wing MAC's are incorrect. Early on I tried finding the MAC graphically, but errors in where oblique lines cross could be great. It's easiest to use on-line calculators for straight tapered wings, but for elliptical distributions Mac's and their positions are just the same fractions of half-spans and root chords. The MAC location that we calculate is just the geometrical c.g. of a planar plan-view shape. So, it seems to me that we start with that inaccurate, idealized assumption to get an MAC length, balance it at that fictitious a.c., and choose the 24%-25% point of it as our "true" a.c. Is that how you see it?

Regardless of how accurate this is, it gives a uniform starting point for corrections, but obviously the tail too makes a difference in the flyer's preferences of c.g. position, and just the wing's action on the tail can vary that, all else being "equal."
« Last Edit: December 13, 2021, 08:22:25 PM by Serge_Krauss »

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Re: Wing sweep as a pitch stabilizing factor
« Reply #26 on: December 11, 2021, 08:55:49 AM »
Well, I certainly have demonstrated a shortage of understanding as compared to yours and I concede to your expertise. Apologies for upsetting you.

Mark .... I'm not upset at all, trust me ..... its so difficult to communicate on the internet without sometimes sounding more intense than intended.  I applaud your work with folding prop precession , inflight tuft visualizations with flow direction measurements, and aerodynamic "attachments" to the stunt ship to enhance its flight.  Keep it up.  You will have nay-sayers that cry that its been tried before, don't listen, follow your scientific and pilot based intuitions, and above all .... publish.

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Re: Wing sweep as a pitch stabilizing factor
« Reply #27 on: December 11, 2021, 01:22:21 PM »
Mark .... I'm not upset at all, trust me ..... its so difficult to communicate on the internet without sometimes sounding more intense than intended.  I applaud your work with folding prop precession , inflight tuft visualizations with flow direction measurements, and aerodynamic "attachments" to the stunt ship to enhance its flight.  Keep it up.  You will have nay-sayers that cry that its been tried before, don't listen, follow your scientific and pilot based intuitions, and above all .... publish.
Frank:  Probably just my deteriorating eyesight but the swept wing canard picture appears to have a tractor prop on it.

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Re: Wing sweep as a pitch stabilizing factor
« Reply #28 on: December 11, 2021, 05:39:36 PM »
Good eyesight ..... Its an ST60 with a left handed crank!

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Re: Wing sweep as a pitch stabilizing factor
« Reply #29 on: December 11, 2021, 06:51:24 PM »
Good eyesight ..... Its an ST60 with a left handed crank!
Then the prop is on backwards! LL~
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Re: Wing sweep as a pitch stabilizing factor
« Reply #30 on: December 12, 2021, 07:24:18 PM »
Ken …. I remember now the history of this picture.  The plane had been hanging in the garage in a slightly damaged condition, when I quickly put masking tape on the canard and dropped an arbitrary ST60 into the mounts just so I could take a picture of it.  As flown the plane had a reverse ST60, fitted with a regular tractor prop,…. Put on  backwards.  That gave me a pusher. 

This airplane design, which I’ve been meaning to start a thread about, is based on the desire to have high rotation rate with maximum damping.  The swept wing, like we said above, had the benefit of higher damping than a straight wing and I could mount the power in the crotch of the trailing edge and have weight concentrated near the cg.  Lower pitch moment of inertial.  Lower pitch inertial potentially yields faster rotation rate, and better damping.

The canard configuration also is something that modelers keep trying to make work in a stunt ship.  In theory the canard could be a two pronged benefit for stunt design.  The canard essentially doubles the Cmq or damping due to pitch rate.  It also reduces Cm.alpha.  A low Cm.alpha promotes a quicker response to control inputs.  Quick response and robust damping as the controls are fixed.

The history of the test flights (2) of this plane is worthy of discussion on this thread, and is germane to the topics of swept wings, stability, and locating a/c aerodynamic center (neutral point).

As I said, the plane had two flights total.  As you can see, mounted on the canard surface is a SuperTigre muffler.  This was for the first flighs.  It was stuffed with lead.   Like, a bunch of lead.  I had no idea where the c.g. of the airplane should be.  I tried calculating where the NP was, but like Serge is finding out, I didn’t really trust the numbers I was getting.  So … I added a bunch of nose weight to be safe for the first flight.

It flew ….. not too bad for a first flight …. It had a blinding corner and wasn’t really twitchy in level flight,  It came out of the blinding corners flat and stable, and It did glide relatively well to a landing.
Second flight ….. lets take out some nose weight ….. how much?  I dono … maybe half of what’s in there? …… OK.  Takeoff … good enough.  Maneuvers in flight still outstanding.  Blinding, after having removed nose weight.  Motors getting ready to quit ….. gain a little height so I can see the glide tendencies.

The motor quits …… the plane cones to a dead stop instantly, 24 feet up in the air.  It immediately, I mean immediately, flips over inverted and spirals gently down to the ground like a leaf.  If it was unstable why did it fly?  When the motor quit it became severely unstable.  What happened?

The conclusion is that with the motor running, increased velocity over the tailplane due to the prop wash, was enough to provide stability.  As soon as the motor stopped, the velocity on the tail fell, the “effectiveness” of the tail was reduced and the plane was no longer stable.  The application of this to “normal” designs is that the tail area close to the propwash is more effective than that out at the tips of the stab/elevator.  Low aspect ratio tails may be good (as we’ve found to be true).

I will close by saying what Brett always recommends .... you can measure and calculate all you want, but it really comes down to flight test and how it feels and performs.

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Re: Wing sweep as a pitch stabilizing factor
« Reply #31 on: December 13, 2021, 01:38:46 PM »
Mark .... I'm not upset at all, trust me ..... its so difficult to communicate on the internet without sometimes sounding more intense than intended.  I applaud your work with folding prop precession , inflight tuft visualizations with flow direction measurements, and aerodynamic "attachments" to the stunt ship to enhance its flight.  Keep it up.  You will have nay-sayers that cry that its been tried before, don't listen, follow your scientific and pilot based intuitions, and above all .... publish.

Well, I'm obviously not the bestest at the dynamic stability arena. When I look at the spring oscilator model and aero dynamic version, I really haven't done much of the math. I did look deeper into the Cornell text book and have, I think, figured out where the energy dissipation term is being treated in terms of the tail plane and what you were conveying. The simple L= K alpha q isn't a dashpot, however the derivation of the various moments create a velocity term for the tail plane area which is. I need some time to better understand that part. I will at some point and may create a Matlab model but I'm really trying to get to a point of actually finishing a design. For a model a first order TVC calculation is enough to create the first version. Well, I'm doing the big flap with 25% hinge line  treatment so there is going to be some trim calculations too. I had to shut off SH for a while so I could focus on that design effort.

I need to do some follow up discussion on the propeller project. The model I was flying it one had an incident which totaled the airplane and propeller including the hub. I have another prop and hub which will work on the Smoothie I recently. I have plans to fly an A-B test with a Fuse cam and perhaps the visual stand thingy in order to see the precession during flight. The previous testing was subjective and the video can show the result visibly.

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Re: Wing sweep as a pitch stabilizing factor
« Reply #32 on: December 13, 2021, 01:57:32 PM »
Just for my own curiosity, I'd like to compare my more elementary analysis to what you feel is important here (and learn anything I might have missed along the way).

I did start with the basic definitions and used my freshman calculus to derive MAC's, their placements, and a.c.'s for several chord distributions and their variants, including certain sweeps and alignments. I discovered that most internet determinations of span-wise locations of elliptical-wing MAC's are incorrect. Early on I tried finding the MAC graphically, but errors in where oblique lines cross could be great. It's easiest to use on-line calculators for straight tapered wings, but for elliptical distributions it's just fractions of half-span and root chords. The MAC that we calculate is just the geometrical c.g. of a planar plan-view shape. So, it seems to me that we start with that inaccurate, idealized assumption to get an MAC length, balance it at that fictitious a.c., and choose the 24%-25% point of it as our "true" a.c. Is that how you see it?

Regardless of how accurate this is, it gives a uniform starting point for corrections, but obviously the tail too makes a difference in the flyer's preferences of c.g. position, and just the wing's action on the tail can vary that, all else being "equal."

Well, I honestly use my CAD to do that as it is easier than solving the math. The reality is that flight testing will provide the correct answer. I think we do a best we can understand method and create rules of thumb that work well enough. The problem we run in to is the geek children, like me, can't just do that. Elliptical wings are pretty and can be problematic to both build and make fly right. I'm a fan of them but have moved away because the elliptical lift distribution can be achieved other ways without the Reynolds variations which cause the  troubles. One thing I do is to not sweep the wing. I do this for two reasons, first being is that wings tend to behave better with no sweep at stall and second it is easier for me to know where the 25% aft CG "limit" is. Sweep can also create a rolling moment couple with yaw which contributes to the stalling misbehaviors. If it were me making an elliptical wing, as long as the CG is in front of that point it will more than likely fly well enough to not kill it on first flight and then can be trimmed from there. I do all of the geek stuff because it entertains my intellectual side.
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Re: Wing sweep as a pitch stabilizing factor
« Reply #33 on: December 27, 2021, 07:29:43 AM »
While coming through the NASA document server I came across an interesting report on stability and control of Swept wings. It's very long and can't be posted here so here's a link in case you be interested:

https://ntrs.nasa.gov/api/citations/19930085677/downloads/19930085677.pdf

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“Physics is like sex: sure, it may give some practical results, but that’s not why we do it.” – Richard P. Feynman


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