News:


  • October 03, 2024, 08:21:56 PM

Login with username, password and session length

Author Topic: Twin Tails  (Read 6180 times)

Online Ken Culbertson

  • 24 supporter
  • Trade Count: (0)
  • Admiral
  • *
  • Posts: 6473
Twin Tails
« on: October 30, 2021, 04:28:12 PM »
I have had several, perhaps as many as 5 twin tail PA planes over the years including my latest.  I see very little difference in the way they fly the pattern once trimmed but I do think that they have less problem with stability and seem to fly a bit better overhead.  Could it be that the rudders are outside of the propwash and are therefore more effective?  I have searched the forum and cannot find any general discussions that include twins.

Ken
AMA 15382
If it is not broke you are not trying hard enough.
USAF 1968-1974 TAC

Offline Tim Wescott

  • 2016 supporter
  • Trade Count: (0)
  • Admiral
  • *
  • Posts: 12840
Re: Twin Tails
« Reply #1 on: October 30, 2021, 05:25:40 PM »
I doubt the rudders are that far outside the propwash -- maybe the total effective area of the rudders tends to be larger, or the air is cleaner outside of the fuselage's general area?

I'm not even sure that being outside of the propwash would make that much difference -- I suspect that by the time you get that far back, the propwash is bent enough by yaw that the rudder would be working just fine.
AMA 64232

The problem with electric is that once you get the smoke generator and sound system installed, the plane is too heavy.

Offline Mark wood

  • 24 supporter
  • Trade Count: (0)
  • Captain
  • *
  • Posts: 899
  • I'm here purely for the fun of it.
Re: Twin Tails
« Reply #2 on: October 30, 2021, 07:43:30 PM »
That's an interesting question and responses. At speed propwash is more like beats than a directional airstream. We tend to want to treat it as a steady stream which it isn't, it's more like turbulence the airplane flies through.  I used a yaw string, a piece of yarn just above eye level on the canopy to indicate yaw, on my full size Laser which, at speed worked just fine. During high power, slow airspeed high angle of attack operation the string would yaw from the propwash. Of course it would also indicate weirdness when backing up in a tail slide.  I have been flying tuft tests on my SV-11 with a camera mounted on the tail looking forward and it shows the same thing. Gust response from going around the circle with a wind is more prevalent in yaw response although I have to say the tension in the lines damp out a majority of expected yaw oscillations, far more than I would anticipate. It actually surprised me how much of a side component the wind creates as the airplane goes around the circle and didn't produce much of a result yaw motion.

It's very difficult to characterize the capability of two versus one based upon a subjective observation of a one off configuration. The way to make a true evaluation is to fly a convertible airplane back to back twin verticals and single verticals with identical total areas. Mathematically the two cases should be nearly identical.

When we turn the focus on the pitch response and stability there is a very clear case for differences. Wing fences work very well and would expect there to be a noticeable difference in handling with and without. I went through a period of experimentation using winglets and fences in my free flight models and determined they do work. They don't quite work well enough to over come the weight penalty however, nor the handling and damage risks which ultimately was the reason I abandoned them. A model with fences that is properly trimmed is unflyable if one of the fences has any significant damage. Damage could come from landings which aren't always good with a FF model. There is plenty of research data which also supports this. I think the primary reason we don't see them on aircraft today is for the same reasons I had for leaving them behind. The weight and structural complexity doesn't make them a good cost benefit when a simpler lighter design can work 80% as good, spelled winglet. 

I'll likely be posting some of my tuft test videos on my youtube channel in an unpublished fashion which means I'll have to share a link for you to see. I currently have the camera test video up and it is public. 
Life is good AMA 1488
Why do we fly? We are practicing, you might say, what it means to be alive...  -Richard Bach
“Physics is like sex: sure, it may give some practical results, but that’s not why we do it.” – Richard P. Feynman

Offline Tim Wescott

  • 2016 supporter
  • Trade Count: (0)
  • Admiral
  • *
  • Posts: 12840
Re: Twin Tails
« Reply #3 on: October 30, 2021, 10:59:58 PM »
... I have to say the tension in the lines damp out a majority of expected yaw oscillations ...

I'm not sure you're coming to the correct conclusion there, or perhaps you're not using "damped" in the dynamic systems sense.

Yes, line tension does a whole lot to make the yaw average out to whatever it's demanding.  But I have at least one plane in my stable, self-designed, that came with a too-small vertical stab the first time around.  It had a rather exciting, only slightly damped oscillation in yaw, that would get excited any time I did a square maneuver.  It was bad enough that you could feel the thing going slack on the lines then bumping back into them later in the circle.  The average yaw was definitely around the center value that was being enforced by the pendulum effect of the lines and leadouts.  But the instantaneous yaw was definitely wiggle-waggling all over the sky.

I reviewed the plans, compared to other planes, said "oops" and just about doubled the vertical area -- and poof, the oscillation went away.

I think what you're calling "damping" is the line tension enforcing yaw by pendulum effect.  If you whack the tail off of that SV-11, I think you'll discover what a control engineer means when they say "under damped".
AMA 64232

The problem with electric is that once you get the smoke generator and sound system installed, the plane is too heavy.

Offline Mark wood

  • 24 supporter
  • Trade Count: (0)
  • Captain
  • *
  • Posts: 899
  • I'm here purely for the fun of it.
Re: Twin Tails
« Reply #4 on: October 31, 2021, 06:14:02 AM »
Damping. Resistance of an oscillatory system to oscillate as the result of energy dissipating friction or resistance. In the case of line tension the term Mz = b/2 x Tsin(theta) where Mz = the moment around the vertical axis,  b = wingspan, T = line tension and theta = the yaw angle with respect the the steady state neutral position. We could get completely wound up in the math but suffice it to say, I have a pretty good handle on what a harmonic oscillator is and aerodynamics. The line tension is a very significant damping element in the tethered airplane system. Case in point, the airplane travels in a circle as a result of the line tension. What I did not say is that the vertical stab plays no part, my statement is the tension has a larger influence on the stability of the system. Case in point, tailless combat plane. Combat planes don't do weird sit while flying squares. At least the Winders I built as a young man didn't and they do a fairly good rendition of the pattern in 14.5 seconds.

The squares and poor behavior is a very interesting topic and from my observation there are several aspects including some "hinging" kinds of things. I have watched what the only thing I can say is if the airplane weren't tethered it would do a snap roll but yet it doesn't and there are some resulting interesting "pulsations" in the lines. This is part of why I have tufted the airplane and am making video flights. Actually this is one of two reasons the other being how much flap deflection is causing separation and consequently drag.

I think I posted a video of a tufted wing test I did of the 4/4 scale Laser doing a snap roll. The way spins and snap rolls occur is that one wing stalls before the other creating a divergent condition where the forces generated cause the stalled wing to decelerate increasing the angle of attack and the less stalled wing to accelerate decreasing it's angle of attack. The result is the the wing decelerating wings lift decreases further while the drag increases causing and acceleration in yaw and roll rates. This condition is what is termed autorotation.  Note, at no point is rudder required to drive the condition in fact I demonstrate this to my student pilots with the rudder nearly centered. The only thing necessary is a slight bit of yaw be present at the point when stall occurs.

During my initial flight testing the SV-11 had a similar "oddity" during the squares similar to Tim's partly because of the ham handed meat servo. I was working on adjusting tip weight and fix some hinging. During this I observed that not so hard pulls would fly cleanly while less than not so hard pulls would create some hinging and really hard pulls would create the "whifferdill" extremely violent motion. After a couple of repeats, my conclusion, given the build up tests, was that some of the hinging and definitely the violent case was the result of the wing stalling. My control set up had more elevator deflection that flap and reducing the elevator deflection, reducing AOA per control input, made strides to removing the arrant behavior. Moving the CG forward made a difference as well.

That increasing the size of the vertical would "fix" this condition isn't surprising, especially if the area balance of the airplane is biased forward of the CG causing the airplane to "skid" in it's flight path. Watch the tail cam video where I am flying in windy conditions of about 8 mph. In this video it can be seen that there is a definite wind element but the airplane has minimal yaw response.  Without enough vertical surface the airplane would yaw adversely to gusts. In terms of maneuvering this is also important, especially with the asymmetric design of the airplanes being used. The flap areas being different will generate a large yaw moment which will in turn result in yawing of the aircraft. As stated above, stalling with yaw can result in autorotation. 

Here's Tail Cam 1. The camera is mounted on the tail. There is another camera, Fuse Cam. It did not die but it did spend the evening in the field. It didn't fly nearly as far as I thought it did and I had to review the footage frame by frame to figure out it's initial trajectory which was pretty much straight down when it released and landed in the grass. I subsequently made a much better mount out of ABS as the Command tape wouldn't hold to the balsa.

Here's the video, I have more:



Added for your amusement, the departure of the fuse cam:


 
« Last Edit: October 31, 2021, 06:48:28 AM by Mark wood »
Life is good AMA 1488
Why do we fly? We are practicing, you might say, what it means to be alive...  -Richard Bach
“Physics is like sex: sure, it may give some practical results, but that’s not why we do it.” – Richard P. Feynman

Online Ken Culbertson

  • 24 supporter
  • Trade Count: (0)
  • Admiral
  • *
  • Posts: 6473
Re: Twin Tails
« Reply #5 on: October 31, 2021, 07:55:26 AM »
..everything..
I am fascinated with the tufted video.  Especially the one where you lost the camera.  Question, how tight do you think your corners were?  The average "expert" corners I see (and have traced) , excluding the very top fliers are around 14' and about 10' for the top F2B fliers.   Where the separation occurs is important to me in determining the flap/elevator ratio that will tighten my corners without having to resort to extra trim.  This in turn will help in getting the 1:1 or even 1.5:1 ratio that produces nice rounds into my next logarithmic horn.

Once I translate your observations into English I think what you are leading to is what I have observed with the twin tails.  Not much difference in performance but some added stability.  I did notice on the tail cam video that there did seem to be more turbulence around the fuselage but not enough to blanket the wind. 

Next step - permanent camera mounts built into the design! LL~

Ken
AMA 15382
If it is not broke you are not trying hard enough.
USAF 1968-1974 TAC

Offline Mark wood

  • 24 supporter
  • Trade Count: (0)
  • Captain
  • *
  • Posts: 899
  • I'm here purely for the fun of it.
Re: Twin Tails
« Reply #6 on: October 31, 2021, 08:40:19 AM »
I am fascinated with the tufted video.  Especially the one where you lost the camera.  Question, how tight do you think your corners were?  The average "expert" corners I see (and have traced) , excluding the very top fliers are around 14' and about 10' for the top F2B fliers.   Where the separation occurs is important to me in determining the flap/elevator ratio that will tighten my corners without having to resort to extra trim.  This in turn will help in getting the 1:1 or even 1.5:1 ratio that produces nice rounds into my next logarithmic horn.

Once I translate your observations into English I think what you are leading to is what I have observed with the twin tails.  Not much difference in performance but some added stability.  I did notice on the tail cam video that there did seem to be more turbulence around the fuselage but not enough to blanket the wind. 

Next step - permanent camera mounts built into the design! LL~

Ken

I'll follow up soon. The corners were consistent with advanced / expert level turns. Tight not super tight. I have more videos pushing the turn to very tight and I need to push the CG back to get back to where the "whifferdill" occurs.

The effort centers around the Log crank mechanism I am working on and understanding the flap angle.
Life is good AMA 1488
Why do we fly? We are practicing, you might say, what it means to be alive...  -Richard Bach
“Physics is like sex: sure, it may give some practical results, but that’s not why we do it.” – Richard P. Feynman

Offline Mark wood

  • 24 supporter
  • Trade Count: (0)
  • Captain
  • *
  • Posts: 899
  • I'm here purely for the fun of it.
Re: Twin Tails
« Reply #7 on: October 31, 2021, 12:51:08 PM »

Next step - permanent camera mounts built into the design! LL~

Ken

That isn't actually outside the realm of reasonable, especially if you consider the ability analyze flight behavior. There are some limitations to that though as some of the motion is not super easy to see. I did a flight with the camera simply Command stripped to the side of the fuselage which works really good, too good in fact, to the level of pealing the moneycote. That and needing a better view of the wing is why I did the stand which the balsa version didn't work out so well. That video is actually kind of a cool selfie. In it you can see that my model has a little bit of roll during maneuvers which has annoyed me a lot as it is hard to sort out watching from the inside. With the low fuse cam you can see the slight roll by observing the wing tip and me. During inside maneuvers the tip is up and you can hardly see me while outsides the tip is down and I am very visible indicating the roll. Over the top of the wingover the wing tracks. This means that the balance of weight and aileron effect of the flaps are not equal.

On the SV-11 the inboard flap is slightly larger than the outboard flap which will drive a roll and is likely the cause of trouble with getting the balance correct. In subsequent flights I did what Igor does and added a tab to the TE of the outboard flap equal to area difference. That fixed the rolling or mostly fixed anyway.




Have have more. Two cameras ten ish flights. Lots of processing time. Worse, I kept crummy notes.
Life is good AMA 1488
Why do we fly? We are practicing, you might say, what it means to be alive...  -Richard Bach
“Physics is like sex: sure, it may give some practical results, but that’s not why we do it.” – Richard P. Feynman

Offline Dennis Toth

  • 2020 supporter
  • Trade Count: (0)
  • Admiral
  • *
  • Posts: 4304
Re: Twin Tails
« Reply #8 on: November 13, 2021, 05:49:32 AM »
Does the twin tail design give an equivalently larger tail area? It would seem that if the rudders were balanced top and bottom they would act like tip plates and give the effect of a larger area. This would be like Fancherizing the tail and could allow more rearward CG. Some of the Classic era ships that had them like the Olympic I don't think tried the more rearward CG as it wasn't in Vogue at the time. Today we might push that a bit and with current power these ships could really do well.

Best,   DennisT 

Online Ken Culbertson

  • 24 supporter
  • Trade Count: (0)
  • Admiral
  • *
  • Posts: 6473
Re: Twin Tails
« Reply #9 on: November 13, 2021, 03:36:10 PM »
Does the twin tail design give an equivalently larger tail area? It would seem that if the rudders were balanced top and bottom they would act like tip plates and give the effect of a larger area. This would be like Fancherizing the tail and could allow more rearward CG. Some of the Classic era ships that had them like the Olympic I don't think tried the more rearward CG as it wasn't in Vogue at the time. Today we might push that a bit and with current power these ships could really do well.

Best,   DennisT
I think I agree with your assessment.  I am fishing for the why these planes seem better.  I have had 6 of them that I can count and all flew better overhead than any of my single rudder planes.  My rudders are larger than the Olympic, Ballerina, Trident which were not much more than a glorified tip plates.  I still fall back on one rule of thumb though, if it is better you would see it more in the top 10.  There has to be a reason hardly anybody uses them. But then there is the OS35s which was the best stunt engine of it's day that never won the Nats.

Ken

Ken
AMA 15382
If it is not broke you are not trying hard enough.
USAF 1968-1974 TAC

Offline Trostle

  • 22 supporter
  • Trade Count: (0)
  • Admiral
  • *
  • Posts: 3358
Re: Twin Tails
« Reply #10 on: November 14, 2021, 10:10:20 AM »
But then there is the OS35s which was the best stunt engine of it's day that never won the Nats.

Ken

Hi Ken,

This is really off the topic, but I still want to comment about the OS .35s.

It did not get much, if any publicity, but the Walker Cup was won in 1970 with a model powered by an OS .35s.  It was stock and used the matching OS Jet Stream muffler.  (Plans were published in Dec 68 Model Airplane News.  Also, used a Top Flight 10-6 Power Prop.  Airframe still exists, though the silk covering is a bit tattered.)

Even more off topic, but as a side note, the first time a muffler was used for a Walker Cup win was by Bob Gialdini with his Stingray in 1965, though I am not aware of any published pictures that shows this.

Even more off topic:  The photo shows the state of disrepair of the Walker Cup in 1970.  This was before Al Rabe took possession of the Cup in 1973, as in won, and had it refurbished to its original condition by the firm who originally made it.  Later, the West Coast Cabal with coordination with PAMPA added the elongated base to hold the name plates for many more years of National Stunt Champions.

Keith
« Last Edit: November 19, 2021, 01:03:45 PM by Trostle »

Offline Trostle

  • 22 supporter
  • Trade Count: (0)
  • Admiral
  • *
  • Posts: 3358
Re: Twin Tails
« Reply #11 on: November 20, 2021, 09:53:56 AM »
Bump

Offline phil c

  • 21 supporter
  • Trade Count: (0)
  • Admiral
  • *
  • Posts: 2480
Re: Twin Tails
« Reply #12 on: November 20, 2021, 03:00:22 PM »

...although I have to say the tension in the lines damp out a majority of expected yaw oscillations, far more than I would anticipate.

I'll likely be posting some of my tuft test videos on my youtube channel in an unpublished fashion which means I'll have to share a link for you to see. I currently have the camera test video up and it is public. 
[/quote]

I fly mostly combat Mark.  Combat planes virtually never yaw from any gusts or any maneuvers.

The fuselage with the rudder and elevators must be acting as a very short span wing.  The airflow has to respond somehow when the the AOA changes abruptly with the propwash effectively sends a burst down the fuselage.

The video was interesting.  When the elevator or flap  went below the wing it had no effect on the strings. When the flap rose above the wing the strings lifted up off the wing, but not helter-skelter.  To me this would indicate the both surfaces are always generating lift and drag.  It's just that when the  controls make one surface or the other predominantly produce lift.

The control movement didn't seem to make the plane yaw.  I built several large, Laser like designs- fairly steep taper, almost midwing,  700+ squares, about a 68in. span, 49 ounces with a Rabe Rudder.  It did all the round maneuvers quite nicely. I never did get the squares to look good.  ex.  The first turn in the square loop would roll some, the second corner rolled even more.  If I could catch it right and get it headed straight down in the third turn it would make the 4th turn OK.   Because he outside was even worse  because it was trying to yaw in.  By the time it hit the 4th turn it had slowed too much from the yaws.

All the shenanigans would slow it down too much making it even harder.  Good luck with your plane.

Phil C                                                   
phil Cartier

Offline Mark wood

  • 24 supporter
  • Trade Count: (0)
  • Captain
  • *
  • Posts: 899
  • I'm here purely for the fun of it.
Re: Twin Tails
« Reply #13 on: November 20, 2021, 04:41:21 PM »


I fly mostly combat Mark.  Combat planes virtually never yaw from any gusts or any maneuvers.

The fuselage with the rudder and elevators must be acting as a very short span wing.  The airflow has to respond somehow when the the AOA changes abruptly with the propwash effectively sends a burst down the fuselage.

The video was interesting.  When the elevator or flap  went below the wing it had no effect on the strings. When the flap rose above the wing the strings lifted up off the wing, but not helter-skelter.  To me this would indicate the both surfaces are always generating lift and drag.  It's just that when the  controls make one surface or the other predominantly produce lift.

The control movement didn't seem to make the plane yaw.  I built several large, Laser like designs- fairly steep taper, almost midwing,  700+ squares, about a 68in. span, 49 ounces with a Rabe Rudder.  It did all the round maneuvers quite nicely. I never did get the squares to look good.  ex.  The first turn in the square loop would roll some, the second corner rolled even more.  If I could catch it right and get it headed straight down in the third turn it would make the 4th turn OK.   Because he outside was even worse  because it was trying to yaw in.  By the time it hit the 4th turn it had slowed too much from the yaws.

All the shenanigans would slow it down too much making it even harder.  Good luck with your plane.

Phil C                                                   

Hi Phil

Lots built in to all of that. Yes, combat airplanes should not respond to sidewind gusts as a result of not  having any vertical side area. The tufts in my video are a bit too heavy and stiff for the job they are doing. Mounted on the top positive G maneuvers helps keep them in the boundary flow and you can see the results. The negative G maneuvers cause them to move away from the wing surface and loose the boundary layer. I'm searching for an alternate yarn to use but haven't succeeded as of yet.

It's really hard to say what your airplane behavior was the result of. However when the taper ratio gets to be in the 1.5-2 zone there is a large difference in Reynolds number which can impact the stall characteristics. This is the basis of the "tip stall" theories which have some basis. Some of my experience fixing models that do that is to change the airfoil to something a little smoother and make the tip a little thicker at the tip. So, a root airfoil of 18% would blend to 20% at the tip. By doing that correctly the stall AOA of the new airfoil is greater than the root airfoil and the tip stall doesn't happen.

It is common to build in asymmetry in the CL models. I have found that I have fewer trimming issues with very minimal asymmetry. With my SV I could not fix some minor hinging until I calculated the flap area between the inside and outside flaps and add a tab to the outside flap to equalize the areas. Problem solved.

That this happens during the square corner and not a smoother corner points to an airfoil modification being necessary. Yawing during the maneuver as would result from a rudder deflection would make the problem even worse as the yaw angle changes the relative AOA across the wing.
Life is good AMA 1488
Why do we fly? We are practicing, you might say, what it means to be alive...  -Richard Bach
“Physics is like sex: sure, it may give some practical results, but that’s not why we do it.” – Richard P. Feynman

Offline Howard Rush

  • 22 supporter
  • Trade Count: (0)
  • Admiral
  • *
  • Posts: 7852
Re: Twin Tails
« Reply #14 on: November 21, 2021, 03:23:02 AM »
Even more off topic: 

Please identify the personnel in that photograph.
The Jive Combat Team
Making combat and stunt great again

Online Ken Culbertson

  • 24 supporter
  • Trade Count: (0)
  • Admiral
  • *
  • Posts: 6473
Re: Twin Tails
« Reply #15 on: November 21, 2021, 06:57:21 AM »

...Even more off topic:...
Keith
Keith:  In my original posting I did say that "I have searched the forum and cannot find any general discussions that include twins."  In the picture, are they twins?

Ken
AMA 15382
If it is not broke you are not trying hard enough.
USAF 1968-1974 TAC

Offline Trostle

  • 22 supporter
  • Trade Count: (0)
  • Admiral
  • *
  • Posts: 3358
Re: Twin Tails
« Reply #16 on: November 21, 2021, 09:52:53 AM »
Please identify the personnel in that photograph.

Keith:  In my original posting I did say that "I have searched the forum and cannot find any general discussions that include twins."  In the picture, are they twins?

Ken

Howard, Ken,

Thanks for asking.  When that picture was taken in 1970 the two people there were about 2 and 4.  Charles and Diane have grown up.  When your youngest turns 50 (several years ago), it makes you wonder what has happened and where has the time gone?  They are both doing very well with families of there own, living here in the Denver area.  (That is why grandma said that we are moving from Tucson where we both thought would be our retirement home.)   Charles does have twins, now almost 8 years old.

Keith

Online Ken Culbertson

  • 24 supporter
  • Trade Count: (0)
  • Admiral
  • *
  • Posts: 6473
Re: Twin Tails
« Reply #17 on: November 21, 2021, 04:01:45 PM »
Guess if the thread is going to go way off subject I might as well put this here.

Has anybody ever tried a rack & pinion "bellcrank"? 

Ken
AMA 15382
If it is not broke you are not trying hard enough.
USAF 1968-1974 TAC

Offline Dennis Toth

  • 2020 supporter
  • Trade Count: (0)
  • Admiral
  • *
  • Posts: 4304
Re: Twin Tails
« Reply #18 on: November 21, 2021, 05:41:42 PM »
Ken,
I guess you could combine Ted Fancher's circular bellcrank with a 3D printed gear and rack and it could work. It is just a lot of work but depending on the diameter you make the gear could give nice slow controls and more or less constant control pressure.

Best,   DennisT

Online Ken Culbertson

  • 24 supporter
  • Trade Count: (0)
  • Admiral
  • *
  • Posts: 6473
Re: Twin Tails
« Reply #19 on: November 21, 2021, 06:50:47 PM »
Ken,
I guess you could combine Ted Fancher's circular bellcrank with a 3D printed gear and rack and it could work. It is just a lot of work but depending on the diameter you make the gear could give nice slow controls and more or less constant control pressure.

Best,   DennisT
It is interesting.  I have done a circular BC and it worked well but was a lot of trouble.  This would be worse but it does have the smell of better control.  It's building season  LL~
AMA 15382
If it is not broke you are not trying hard enough.
USAF 1968-1974 TAC

Offline Scientifiction .

  • Trade Count: (0)
  • Admiral
  • ******
  • Posts: 5090
Re: Twin Tails
« Reply #20 on: November 21, 2021, 09:33:06 PM »
Someone said in a mag. years back , the area works like normal , but the side wind / cross wind bother them less , as ' side view ' theres less to blow on .

Course , ona twi , theyed both bein the propwash , where a central one isnt , so twin wouldnt on a single , till the tails up and flying . Or suchlike .

[center][b][size=20pt] [url=http://ritchsbrew.com/rb.html][img]https://stunthanger.com/smf/ritch-s-brew/ritch-s-brew-the-winners-choice/?action=dlattach;attach=351357;image][/img][/url][/center]
Advertise Here
Tags: