Cruisers Forum
 


Join CruisersForum Today

Reply
 
Thread Tools Rate Thread Display Modes
Old 31-10-2012, 23:38   #31
Registered User

Join Date: Jan 2010
Location: Narragansett Bay
Boat: Able 50
Posts: 3,060
Re: Paradoxical Lee Helm Puzzle

Failing that, just balance the rig from the start.
__________________

__________________
savoir is offline   Reply With Quote
Old 31-10-2012, 23:54   #32
Registered User

Join Date: Feb 2012
Posts: 2,441
Re: Paradoxical Lee Helm Puzzle

In the hope of putting this red herring to bed, here's a typical photo of the same syndrome. Photos create the misleading illusion that this is a steady-state condition, as if they showed a constant heel, rather than the momentary peak of a recurring roll.

It's a bit like the photos of ski-racers 'sitting back' which had recreational skiers skiing around looking ridiculous, with their hips permanently aft of their heels.
What they failed to realise was that the maneouvre caught on photos was a momentary acceleration of the skis to get them away from under the racer, whose upper body would take a short cut and catch up as the skis turned and came back under the skier. (Late 60s, through much of the 70s)



This is a sight you'd see in almost any IOR race in the early eighties.

The left photo below shows another (these are SORC) - Boat is definitely sailing dead down wind:

It was to combat this that a fellow-countryman invented the blooper, shown in the third photo. The point was not to increase sail area (in fact sometimes the main had to be reefed to keep it full)
What it set out to do was to scoop a constant flow of wind from far to leeward and flow it across the spinnaker, reinforcing one vortex from the mainsl leech and cancelling the one from the luff.

Maybe this is what savoir meant with his cryptic comment to 'balance the rig'?

Doesn't help solve our paradox, though......
Attached Thumbnails
Click image for larger version

Name:	Jubilation rolls to windward (SORC).jpg
Views:	213
Size:	91.8 KB
ID:	49085   Click image for larger version

Name:	Intuition (SORC) w blooper.jpg
Views:	867
Size:	93.8 KB
ID:	49087  

__________________

__________________
Andrew Troup is offline   Reply With Quote
Old 01-11-2012, 00:18   #33
Registered User

Join Date: Oct 2012
Posts: 19
Quote:
Originally Posted by savoir

The boat doesn't have enough power meaning the keel can't do its thing leaving the bow at the mercy of the waves so it is pushed down.
I think you might be right. If the OP was sailing with a strongly de-powered sail as he seems to indicate, he might have just stalled the boat.
__________________
flo617 is offline   Reply With Quote
Old 01-11-2012, 01:07   #34
Moderator Emeritus
 
Ex-Calif's Avatar

Cruisers Forum Supporter

Join Date: May 2007
Location: Singapore
Boat: Maxi 77 - Relax Lah!
Posts: 11,514
Images: 4
This is sorta getting silly.

I think I will go back to sailing IRL where things are pretty clear rather than all this armchair stuff.

I dont even think we are trrying to solve anyone's trim issues,

BTW - it will be interesting to watch and see if anyone wants to interoret the pink spinnaker situation - LOl.
__________________
Relax Lah! is For Sale <--- Click
Click--> Custom CF Google Search or CF Rules
You're gonna need a bigger boat... - Martin Brody
Ex-Calif is offline   Reply With Quote
Old 01-11-2012, 03:18   #35
Registered User

Join Date: Jan 2010
Location: Narragansett Bay
Boat: Able 50
Posts: 3,060
Re: Paradoxical Lee Helm Puzzle

Cryptic ? Nothing cryptic about it - just keep the same sail area to leeward of the mast as you have to windward and the rig will be balanced. IOR hulls with skinny transoms will need further tuning.

What's cryptic is this thread. It is all a far cry from a guy close reaching with lee helm. I'm outta here.

__________________
savoir is offline   Reply With Quote
Old 01-11-2012, 17:23   #36
Registered User

Join Date: Feb 2012
Posts: 2,441
Re: Paradoxical Lee Helm Puzzle

I feel the need to provide a diagramatic framework here, partly to be able to discuss the theories others have floated, and partly to hang my own theory on.

Firstly I want to address the textbook explanation of helm balance. In simplest form, it shows a boat side on, as in View 4 below.

I've purposely shown a boat whose mast is so far aft and keel so far forward that lee helm would seem (according to conventional theory) to be impossible.
A naval architect would say the boat I've sketched had negative "lead". I've done this to provide a rigorous test of my explanation of paradoxical lee helm. The theory I've come up with seems to me strong and persuasive enough that it might even apply for a radically weather-helm-happy design like the monster depicted here.

I plan to use the same hull and rig in all future diagrams on this topic, for consistency.

If I create a different diagram in order to do more justice to someone else's theory, I'll make the hull a different colour to save confusion.

A very simplistic view would be that positive lead implies lee helm. In practice, all yachts have positive lead, because almost every other attribute of a boat in the real world creates weather helm. More on that later.

- - - - -

View 3 shows a more realistic way of measuring helm balance on a close reach, but is still highly simplistic, even misleading, because there are so many other factors not captured.

Note that the actual lever arm is very close to the simplified 'side view' version which "lead" is based on, on this point of sail and with the boat upright.

In View 5, the force component of mainsail drive available for forward thrust happens to look the same as the simplistic lever arm, but this is mere chance.

The vector of force just happens to be the right length to create this illusion: the "lead" is a distance, whereas the forward thrust component is a force, measured to the tip of the vector rather than the yellow pivot axis, so there's no relationship.

- - - - -

The yellow pivot axis passes through the CLR, the notional centre of lateral resistance for the keel, rudder and immersed hull surfaces.
If this was a model, and you dragged it sideways through the water hanging onto the yellow lollipop stick, you'd know it was in the right place if the hull didn't pivot to line up with (or against) the direction you dragged it.

The simplistic text-book explanation of helm balance works pretty well in light winds, or for very stiff yachts (or yachts with movable ballast) which sail upright.

I first suspected it didn't tell the whole story when I tried to apply the reasoning to get underway on a windsurfer. In anything above a light breeze, my classic newbie technique of inclining the rig forwards to stop the board rounding up was a miserable failure. It had to be so exaggerated (given there's no rudder) that I would always end up sinking the bow and/or getting pulled off.
Attached Thumbnails
Click image for larger version

Name:	TDILH - 1.1.PNG
Views:	121
Size:	33.5 KB
ID:	49126  
__________________
Andrew Troup is offline   Reply With Quote
Old 01-11-2012, 18:47   #37
Senior Cruiser

Cruisers Forum Supporter

Join Date: Dec 2006
Location: Seattle
Boat: Cal 40
Posts: 2,401
Images: 7
Re: Paradoxical Lee Helm Puzzle

If I understand correctly, so far with your examples you are showing that no matter what the arrows show weather helm?

The windsurfer is easy to explain. Most people when learning sheet in slowly and not all the way, so only the back half of the sail is not luffing. Since the wind is only pushing on the sail near the clew far aft of the CLR you round up hard. Back in the early days with 9 foot booms and pin head sails you had to fall back nearly into the water then sheet in as quickly as possible all the way until the sail wasn't luffing anywhere to get started without rounding up. Modern sails with shorter booms, fat head sails, and more stable shapes have reduced this problem quite a bit. You can actually take a bite, as you find you can't hold the sail, quickly luff, fall back a little, sheet in, repeat until you're far enough out your weight can balance the power of the sail with the sail full.

Back to lee helm, as long as some of the sail is not luffing the aft part of the sail is filled putting all the lift force way aft, causing weather helm. If it luffs completely the drag of the sail is essentially at the mast, which on many boats is in front of the CLR, causing lee helm. Add to this that if drive is reduced enough and many modern boats have more windage forward than aft then windage could become dominant.

John


Quote:
Originally Posted by Andrew Troup View Post
I feel the need to provide a diagramatic framework here, partly to be able to discuss the theories others have floated, and partly to hang my own theory on.

Firstly I want to address the textbook explanation of helm balance. In simplest form, it shows a boat side on, as in View 4 below.

I've purposely shown a boat whose mast is so far aft and keel so far forward that lee helm would seem (according to conventional theory) to be impossible.
A naval architect would say the boat I've sketched had negative "lead". I've done this to provide a rigorous test of my explanation of paradoxical lee helm. The theory I've come up with seems to me strong and persuasive enough that it might even apply for a radically weather-helm-happy design like the monster depicted here.

I plan to use the same hull and rig in all future diagrams on this topic, for consistency.

If I create a different diagram in order to do more justice to someone else's theory, I'll make the hull a different colour to save confusion.

A very simplistic view would be that positive lead implies lee helm. In practice, all yachts have positive lead, because almost every other attribute of a boat in the real world creates weather helm. More on that later.

- - - - -

View 3 shows a more realistic way of measuring helm balance on a close reach, but is still highly simplistic, even misleading, because there are so many other factors not captured.

Note that the actual lever arm is very close to the simplified 'side view' version which "lead" is based on, on this point of sail and with the boat upright.

In View 5, the force component of mainsail drive available for forward thrust happens to look the same as the simplistic lever arm, but this is mere chance.

The vector of force just happens to be the right length to create this illusion: the "lead" is a distance, whereas the forward thrust component is a force, measured to the tip of the vector rather than the yellow pivot axis, so there's no relationship.

- - - - -

The yellow pivot axis passes through the CLR, the notional centre of lateral resistance for the keel, rudder and immersed hull surfaces.
If this was a model, and you dragged it sideways through the water hanging onto the yellow lollipop stick, you'd know it was in the right place if the hull didn't pivot to line up with (or against) the direction you dragged it.

The simplistic text-book explanation of helm balance works pretty well in light winds, or for very stiff yachts (or yachts with movable ballast) which sail upright.

I first suspected it didn't tell the whole story when I tried to apply the reasoning to get underway on a windsurfer. In anything above a light breeze, my classic newbie technique of inclining the rig forwards to stop the board rounding up was a miserable failure. It had to be so exaggerated (given there's no rudder) that I would always end up sinking the bow and/or getting pulled off.
__________________
cal40john is offline   Reply With Quote
Old 01-11-2012, 19:12   #38
Registered User

Join Date: Oct 2010
Location: michigan
Boat: CORBIN 39
Posts: 301
Re: Paradoxical Lee Helm Puzzle

Quote:
Originally Posted by ozskipper View Post
It appears you were heading towards a Chinese Gybe "perhaps". Was the boat healing to windward as she lost control? My guess is that rolling motion allowed your mast to lean out to windward, moving your COE outside of the hull itself.

Notice that on the image below, the mast has moved to windward of the hull.
If you were to draw a vertical line down to the centre of the boat, you will see that there is more sail to windward. (on the starboard side in this case). The COE will be momentarily well outboard of the hull and lee helm would be increased

http://surfabike.files.wordpress.com...t-20-59-06.png
This boat is just doing death rolls,racing sailors do this a lot. no fun but it is racing
__________________
sailr69 is offline   Reply With Quote
Old 01-11-2012, 19:30   #39
Registered User

Join Date: Feb 2012
Posts: 2,441
Re: Paradoxical Lee Helm Puzzle

I became further inclined to be skeptical about the textbook explanation when I first encountered really heavy winds on a sailboat. Provided the breeze was constant, the helm often balanced best with only a storm jib, even sailing as close to the wind as conditions allowed. On a simple diagram, this looks impossible.

I'd already found that the way to balance the chronic weather helm on a windsurfer which hasn't got up to speed was to incline the rig to windward (rather than towards the bow) before sheeting in.
(For those who haven't windsurfed, you have to be roughly on a beam reach to get underway, so this means inclining sideways to the hull.)

In stronger winds, as Cal40 says, it takes more commitment.

You had to (especially with the early sail shapes) fall backwards, and catch yourself by sheeting in. This lets you put your body weight to immediate use, in counterbalancing the force trying to pull you to leeward.
But in both cases, you are creating a lever arm by moving the rig to the side which far exceeds anything you can achieve by moving it forwards.
 
So putting these observations together, it was quickly obvious that the lever arm was radically different in the context of major amounts of heel angle than the textbook diagram suggested.
So much so that under extreme conditions it was even possible to round up so viciously in a gust that it amounted to a broach, while sailing to windward with just a storm jib. According to the textbook, the opposite should happen.
 
Hence my perplexity when I later encountered the opposite syndrome, described in my OP. A sudden surplus of lee helm under extreme conditions, exactly the opposite of what we'd just been struggling with a moment before, conflicted drastically with all our experience up until then.

Under all previous circumstances, weather helm was only ever increased by increasing windstrength and heel. This new experience seemed to invalidate the more sophisticated theories we'd built up.

These included things like the asymmetrical underwater shape.
The heeled shape presents the lee bow to the oncoming water at an angle of attack.
See the third diagram below, showing only the underwater part of the blue boat, heeled at 40 degrees.

It's a bit like a wedge of cheese being dragged through the water, pointy end first but slewed in such a way that the water hits one long face (representing the lee bow) at an angle while sliding smoothly aligned along the other long face. The leebow of the wedge of cheese tries to pivot "upwind".

The more you heel, the faster you sail, and the wider the stern sections in comparison with the bow, the more weather helm this creates.

But the consideration which trumps everything else is the 3D lever arm.

This is very influential when the sails are at full hoist. Even in the very deeply reefed condition shown in the blueboat diagrams, View 10, when compared with View 3 from the previous post, shows that the lever arm is increased by 1780/1170 or half as much again, simply by heeling to 40 degrees. With only one reef in, it could easily double, which would double the contribution of sail force to weather helm, without considering the hull asymmetry.

In extreme conditions, I believe that these two factors trump almost all others.
- - - - - -
Someone raised the question of windage on the bow. I think that's a valid concern.

As the sail area decreases, other areas about the boat start to compete for pre-eminence in the total force stakes.

Certainly the angle of attack on the bow topsides, when close reaching, is more severe than the glancing angle on the stern quarter, although in partial compensation, the latter present significantly more area for a modern hull form as shown. (See View 13).

In recognition of this angle of attack difference, I've shown a wind force twice as great on the bow (shown by the longer arrow) as on the stern. With the help of some fag-packet calculations, I think this guess errs strongly on the side of favouring the "windage on the bow creating lee helm" theory.

However, in View 10, the lever arm of the bow windage ON THIS POINT OF SAIL is only half that of the stern, so it seems likely there could be an approximate balance.

The slewing force is simply arrived at by multiplying the force times the lever arm.
The two 'factors of two' cancel out.

I overstated the influence of angle of attack per the para before last, partly to compensate for the fact that the blue boat's keel is forward of the real position on the yacht in question (per the lines drawing below), which somewhat exaggerates the difference between A and B in this view.

Someone else raised the possibility of the seas knocking the bow downwind, creating the illusion of lee helm.
However, as I mentioned in the OP, the waters were sheltered so the fetch was very limited, and for the duration of the killer gust in question, the minimal crests were blown flat.

Nevertheless I think it's a valid consideration, because the wind-driven spume was virtually level with the rail, and it seems to me that the added mass of transported liquid water in the air mass means the forces on the hull (mentioned above) could increase more than would be expected for an increase of wind (by my estimate) of only 10%.

I'm open to the idea that this was a contributing factor, but it doesn't seem to me to explain the sudden transition from massive weather helm to almost irresistable lee helm. There was already a lot of airborne spume when we still had strong weather helm.

- - - - - -

I've left something off all the diagrams so far. Anyone see something missing?

To me, it's the elephant in this particular room.

And, I think, crucial to the explanation for the sudden transition.
Attached Thumbnails
Click image for larger version

Name:	TDILH - 2.PNG
Views:	117
Size:	65.9 KB
ID:	49130   Click image for larger version

Name:	DW#3 processed - reduced.jpg
Views:	105
Size:	59.0 KB
ID:	49132  

Click image for larger version

Name:	TDILH - 2 u-water shape.PNG
Views:	118
Size:	35.3 KB
ID:	49133  
__________________
Andrew Troup is offline   Reply With Quote
Old 01-11-2012, 19:37   #40
Registered User
 
cfarrar's Avatar

Join Date: Apr 2008
Location: Brooklin, Maine U.S.A
Boat: Allures 44
Posts: 734
Images: 2
Re: Paradoxical Lee Helm Puzzle

There's usually a shift in helm as a boat begins to plane. It often shifts from a slight weather helm to a more neutral (and dynamic) feel. Even before it planes, a keel boat can rise above its waterline with enough speed. So perhaps your boat was going fast enough that it lifted slightly, decreasing the lateral resistance of the hull, especially in the bow, which caused the center of resistance to shift aft.

Of course, I wouldn't expect this while sailing on a pure beam reach. On a broad reach, more likely. So my answer is probably worthless, here.
__________________
cfarrar is offline   Reply With Quote
Old 01-11-2012, 19:57   #41
Registered User
 
cfarrar's Avatar

Join Date: Apr 2008
Location: Brooklin, Maine U.S.A
Boat: Allures 44
Posts: 734
Images: 2
Re: Paradoxical Lee Helm Puzzle

Wait, you were heeled over 40 degrees? And you're in a centerboard boat?

OK, how about this:

1) the big gust creates enormous parasitic drag on the mast, stays, boom, and luffing sail. This cancels the forward component of the sail's drive, removing the "lever arm" that creates weather helm. With the wind ever so slightly forward of the beam this could easily create a "lever arm" that induces lee helm.

2) You say that you heeled to 40 degrees. As you do, the foils stall, shifting the center of resistance aft, creating lee helm.
__________________
cfarrar is offline   Reply With Quote
Old 01-11-2012, 20:30   #42
Registered User

Join Date: Feb 2012
Posts: 2,441
Re: Paradoxical Lee Helm Puzzle

cfarrar

Nice post !

(regarding 40 deg heel): in my defence: I did say in the OP that the boat was tender, the rig was tall, and it was blowing hard enough to remove the crests off the waves.... and that we had to feather a triple reefed main even before the killer gust which induced the paradoxical lee helm....

Incidentally, we'd spent a reasonable proportion of the previous hours beam reaching at a similar or greater heel angle: in order to save the rig, rather than feathering the sail, we'd keep it hard sheeted and just let the boat lie down in the gusts - or more accurately white squalls - without once encountering lee helm. The helm would certainly go soggy as we hunkered down, sheltered by the topsides as the wind roared overhead, missing us entirely and just kissing the sail, which was also largely in the windshadow of the beamy hull. Quite a formative experience for young'uns.


Your post broadly agrees with my conclusion (especially point 1, but point 2 in some measure)

Dave, in the first reply of all, also realised the mast drag could be a factor, but his reply referred solely to the "simple textbook" yardstick: how far forward is the mast from the CLR.

Once heeled, I personally think that becomes a minor factor in determining the lever arm of the sacrificial drag from the topmast, and it an attempt to substantiate that, my hypothetical blue boat has the mast ridiculously far aft - in fact, aft of the notional CLR.

I hope to show by diagrams that the bare pole of the topmast acts at a REALLY large lever angle, and the drag is directly downwind (and the nett force very nearly so; the bare section will create a very small amount of lift)

The lever arm is so long (due to the topmast being so much further out from the pivot axis than any other part of the boat) that this can happen WITHOUT necessarily cancelling out the forward component of the sail's drive.

We were in fact still making way during the episode, implying that there was nett forward drive available.
I don't think the foils stalled out completely, but they were certainly compromised, with so much sideforce and so much heel.
__________________
Andrew Troup is offline   Reply With Quote
Old 01-11-2012, 21:27   #43
Registered User

Join Date: Feb 2012
Posts: 2,441
Re: Paradoxical Lee Helm Puzzle

OK: Here's the kicker: refer diagram below (by now there's just about smoke pouring out my poor little laptop's CPU fan outlet). I've added in the elephant in the room (or at least, I think so ) - the arrow representing sacricificial drag on the topmast. (And the topmast standing rigging)

The lever arm from the topmast drag, acting downwind, is over three times the lever arm from the triple reefed main.

So the main would have to develop over three times the lift as the topmast and top rig was incurring drag, simply to balance the lee helm arising from the latter.

This is simply not likely to happen once the wind reaches a critical speed, requiring the main to be feathered (dumping lift).

Remember that this is with a hypothetical boat which, according to the usual theories adhered to by most sailors, should NEVER demonstrate lee helm, at least not bareheaded.

An interesting thing about topmast drag is that the lever arm gets rapidly smaller as a boat bears away from a close reach, while remaining steeply heeled. By the time the apparent wind is abeam, the lever arm has disappeared. Below a beam reach, it's inducing weather helm.

So while at the time it feels pretty scary, runaway lee helm is not going to 'follow you down', which would be truly dangerous and spin the boat completely out of control.

- - - - - -
Other points:

As 'savoir' acutely observed before opting out of the discussion, a boat which lifts the rudder out of the water moves the CLR suddenly forwards, causing a roundup into the wind, which, with no rudder, it is impossible to resist.

So it's not in any way an explanation of what happened here, but here's another reason it doesn't apply in the particular case under discussion (although that would not be obvious from the OP)

The boat was very willing to lift her rudder out, even after we lengthened the blade to the profile shown in the lines drawing (rather deeper and narrower than designed, and considerably more effective)

HOWEVER: this was apparent only when sailing off the wind in waves. On this occasion, in rather flat water, it was not a problem.
 
- - - - - -
 
So, one last question, as well as inviting anyone who's gone to the trouble of following this argument carefully, to expose weaknesses in this theory, either in the physics or the logic:

For anyone who concedes that this mechanism of topmast drag might be the main cause of the sudden lee helm:

What do you reckon would be a useful spur of the moment reaction ?
(boathandling and/or trim) ?
Attached Thumbnails
Click image for larger version

Name:	TDILH - 3.PNG
Views:	108
Size:	42.4 KB
ID:	49135  
__________________
Andrew Troup is offline   Reply With Quote
Old 05-11-2012, 13:47   #44
Registered User
 
cwyckham's Avatar

Join Date: Apr 2011
Location: Vancouver, BC
Boat: Niagara 35
Posts: 1,870
Re: Paradoxical Lee Helm Puzzle

Very interesting write-up. I can't argue with your vectors, they make sense and you've proven it in the real world.

What to do to respond? As you say, the moment diminishes quickly with increasing apparent wind angle, so the problem will sort itself out, just with the boat going in a different direction! Hopefully you're not too close to a lee shore at that point.

In a gust, I can't see what you could do except take the hit (assuming that rudder input is overpowered). In a sustained wind increase, you'll have to ease jib and accept a new point of sail, I suppose. Sheeting in the main will help somewhat, but not if you're already over at 40 degrees of heel.
__________________
cwyckham is offline   Reply With Quote
Old 05-11-2012, 16:49   #45
Registered User

Join Date: Feb 2012
Posts: 2,441
Re: Paradoxical Lee Helm Puzzle

cfarrar

You make an interesting point about the lee shore. Prior to this formative experience, I would always stay close to the leeward side, when sailing through narrow harbour moles in tender boats in extreme conditions, being mindful of the possibilty of rounding up uncontrollably into something unforgiving.

Now, heavily reefed in such a boat, I steer a slightly more middle course, knowing that there's also a chance of the opposite. Particularly if there's any chance of a strong gust also being a header. However, as you picked up from my lengthy dissertation, it only takes you down as far as a beam reach, so it's not something which needs to be overdone.

Nor is the remedial action - perhaps the worst case would be racing or sailing in close quarters, with a boat to leeward which was rounding up in a gust, and you (perhaps with a taller rig) found yourself unable to luff out of their way.

Races, even here, are usually abandoned when it gusts harder than 50 knots or so, and sailing in close quarters in such conditions is only something one would do in an emergency, so it's not a likely scenario.

I think the range of possible responses is interesting to explore, though, because it seems to me the person calling the shots needs to run in the opposite direction to what experience and intuition both suggest.

This is a unique situation, I think, because it's the only circumstance I know in which excessive heel is the cause of lee helm.

Normally we know it to be inextricably bound up with weather helm. I think your answer reflects this: If I faced this situation again I would immediately feather the main and try to stand the boat up a bit (not enough to shred the sail, but in the hope of holding a close reach)

It's a strange notion, to ease the main in response to lee helm, but it inescapably seems to me to be the logical thing to do.

I suppose that there's a countervailing impulse to ease the main in response to the boat sailing further off the wind: I reckon that's the impulse to go with.

(Can't ease jib in the OP scenario, because the boat is sailing bareheaded - which is what makes lee helm so paradoxical)
__________________

__________________
Andrew Troup is offline   Reply With Quote
Reply

Tags
helm

Thread Tools
Display Modes Rate This Thread
Rate This Thread:

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are Off
Refbacks are Off




Copyright 2002- Social Knowledge, LLC All Rights Reserved.

All times are GMT -7. The time now is 06:34.


Google+
Powered by vBulletin® Version 3.8.8 Beta 1
Copyright ©2000 - 2017, vBulletin Solutions, Inc.
Social Knowledge Networks
Powered by vBulletin® Version 3.8.8 Beta 1
Copyright ©2000 - 2017, vBulletin Solutions, Inc.

ShowCase vBulletin Plugins by Drive Thru Online, Inc.