Cruisers Forum
 


Reply
  This discussion is proudly sponsored by:
Please support our sponsors and let them know you heard about their products on Cruisers Forums. Advertise Here
 
Thread Tools Search this Thread Rate Thread Display Modes
Old 23-01-2013, 21:44   #181
Moderator
 
Seaworthy Lass's Avatar

Cruisers Forum Supporter

Join Date: Oct 2008
Boat: Bestevaer 49
Posts: 16,151
Re: Inaccurate RYA Teaching : CTS - Quest For a New Method

Quote:
Originally Posted by jackdale View Post
In these examples I have used your data from post 34

In the first one I used the mean current 1.8 knots (5.5 /3)
The distance measured from A to D is 3.5 miles which equates to a SMG of 3.5 knots.

In the second I used the cumulative current 5.5 knots
The distance measure from A to D is 10.75 miles which equates to a speed of 10.75/3=3.5 knots
Yes, I agree with all that. Your computed SMG using the RYA method is 3.5 knots in this case. I get the same result using the RYA method for this example.

The only problem if you look at your ground track following the RYA CTS, you skirt the destination point (I have reproduced the diagram for the RYA method below) and you would at some stage have to change your compass heading to get to B, slowing you down. So you would actually never achieve this SMG of 3.5 knots computed using the RYA method.

Quote:
Originally Posted by jackdale View Post
In both cases the CTS is 62T
It is actually 62.7 degrees (rounded off equals 63 degrees), but I won't quibble about that. It is actually incorrect by 5 degrees. The correct CTS is 58 degrees. If you use my method you will arrive at the right answer!

Quote:
Originally Posted by jackdale View Post
I did not use a calculator to measure do the math. I can still do long division. I also did not need a cosine.
I do not need to use any trigonometry at for my method either. Where have I done that? All my results including SMG can be computed using long division as well.

Quote:
Originally Posted by jackdale View Post
The key to the RYA method is that it provides an SMG is just as important as a CTS.
So does my method (as I explained earlier in post #160).
And it in fact does so more simply as when I have my CTS, I don't need to then draw any extrapolated lines as you do to work out the SMG.

My SMG is the course length divided by the time taken.
The time taken is the length KB divided by boat speed
.

In this example:
The time taken = 10 / 4 = 2.5 hours
The SMG = 8.5 / 2.5 = 3.4 knots.
This is the actual SMG and unlike your computations, it WILL be achieved if all the data is correct.
Attached Thumbnails
Click image for larger version

Name:	image.jpg
Views:	115
Size:	113.7 KB
ID:	53403  
__________________
SWL (enthusiastic amateur)
"To me the simple act of tying a knot is an adventure in unlimited space." Clifford Ashley
"The cure for anything is salt water: sweat, tears or the sea." Isak Dinesen

Unveiling Bullseye strops for low friction rings
Seaworthy Lass is offline   Reply With Quote
Old 23-01-2013, 21:47   #182
Moderator
 
Dockhead's Avatar

Cruisers Forum Supporter

Join Date: Mar 2009
Location: Denmark (Winter), Helsinki (Summer); Cruising the Baltic Sea this year!
Boat: Cutter-Rigged Moody 54
Posts: 33,764
Re: Inaccurate RYA Teaching : CTS - Quest For a New Method

Quote:
Originally Posted by Andrew Troup View Post
Dockhead, I'm surprised, stunned actually, at your cavalier dismissal.

I didn't realise you would have zero appetite for metaphor, or parable.

I wasn't describing a trip.

I feel almost embarassed on your behalf, that I have to spell this out, but now I've started I supposed I have to continue.

I was setting out a close and careful analogy for the SwL method of planning a trip.

It was fanciful in the hope that it might keep the reader's interest, and perhaps for a few twisted individuals, even be memorable.

The unrealistic omissions you complain about (eg not knowing whence or whereto) are the parts I omitted for the sole and specific purpose of demonstrating that SeaWorthy's method does not (as you incorrectly believe) make any call on the rhumb line.

Maybe someone else will see what is (to my surprise) completely opaque to you.

Even better, maybe you will summon up the goodwill to repay the compliment I paid you by thinking you would get my drift, and the effort, by having another crack at it, in the light of what I've now told you?
Ekh, all right Andrei (Andrew) Strelok, I'll look through it again, but not until this evening. I'm on a train and heading into meetings and don't have a lot of time for this fun at the moment.
Dockhead is offline   Reply With Quote
Old 23-01-2013, 21:53   #183
Moderator
 
Seaworthy Lass's Avatar

Cruisers Forum Supporter

Join Date: Oct 2008
Boat: Bestevaer 49
Posts: 16,151
Re: Inaccurate RYA Teaching : CTS - Quest For a New Method

Quote:
Originally Posted by Wotname View Post
Here is a link to act as primer in case (like me) you might need it .
http://www.stefanv.com/aviation/flight_computers.html

SWL, you might like to have a quick look at this also as in my mind, the wind triangle is essentially the same as a current triangle.
Thanks Wotname, will do later.
__________________
SWL (enthusiastic amateur)
"To me the simple act of tying a knot is an adventure in unlimited space." Clifford Ashley
"The cure for anything is salt water: sweat, tears or the sea." Isak Dinesen

Unveiling Bullseye strops for low friction rings
Seaworthy Lass is offline   Reply With Quote
Old 23-01-2013, 21:56   #184
Moderator
 
Dockhead's Avatar

Cruisers Forum Supporter

Join Date: Mar 2009
Location: Denmark (Winter), Helsinki (Summer); Cruising the Baltic Sea this year!
Boat: Cutter-Rigged Moody 54
Posts: 33,764
Re: Doctrine of the Imperative Triangle

Quote:
Originally Posted by Seaworthy Lass View Post
No need to draw the pencil line at all in my method. I measure the distance between A and B, but after that I do not refer to that line AT ALL.

There is no triangle in my method if the tides are not all perpendicular to the course line.
My dear, of course there's a triangle there, there's always a triangle -- you can't get away from vector triangles in navigation

One leg is the sum of all the tide vectors (pay no attention that you build up that leg through a crooked path)

One leg is the bearing and distance to where you want to go

The last leg is the water track

Every one of these things is needed in order to know how to get to where you want to go -- you must have the length of all of these legs to get the angle of the water track and thus your CTS. When you build up the leg which is the sum of the tide vectors, you also get one angle of the overall vector triangle. So now you have everything you need -- length of two legs and one angle -- to solve the whole triangle, and thus know how to get where you want to go . Solving the triangle is the fundamental mathematical operation you do to get your CTS (and you easily get time also, thus VMG and all the other parameters). Whether you do it with pencil and paper, calculator, slide rule, computer, or protractor, doesn't make any difference -- you are still solving a triangle.

Just because you don't draw the triangle doesn't mean it's not there.


I'm still struggling to understand why you think the 'rhumb line' has anything to do with the problems of the RYA method. Makes me thing that either you or I don't understand something about the method. I thought it's pretty obvious that the RYA method's failure is simply that they stop before they finish all the calculations? Just because the course line is handy to construct a valid vector triangle of the wrong size , doesn't make it guilty, does it?
Dockhead is offline   Reply With Quote
Old 23-01-2013, 22:00   #185
Moderator
 
Seaworthy Lass's Avatar

Cruisers Forum Supporter

Join Date: Oct 2008
Boat: Bestevaer 49
Posts: 16,151
Re: Inaccurate RYA Teaching : CTS - Quest For a New Method

Quote:
Originally Posted by DeepFrz View Post
If a sailor gets used to drifting off the rhumb line on a constant CTS, unless he plots his track points (as has SWL) he will not know how far off a hazard he may be. She will also not be sure of her position should she have to start a DR plot in the case of sudden fog.
If you are ever using a CTS it is ESSENTIAL to plot your ground track. These are the dotted red lines on most of my examples.

If the RYA is not teaching this when they teach CTS , then they definitely should. How else do you know what hazards you will encounter?

If I hit fog it is oh so easy! I just continue on my same heading until the predicted time taken gets close . What could be simpler?

You on the other hand will need to keep changing your course hourly to stay on the course line! Much harder IMHO .
__________________
SWL (enthusiastic amateur)
"To me the simple act of tying a knot is an adventure in unlimited space." Clifford Ashley
"The cure for anything is salt water: sweat, tears or the sea." Isak Dinesen

Unveiling Bullseye strops for low friction rings
Seaworthy Lass is offline   Reply With Quote
Old 23-01-2013, 22:07   #186
Moderator
 
Dockhead's Avatar

Cruisers Forum Supporter

Join Date: Mar 2009
Location: Denmark (Winter), Helsinki (Summer); Cruising the Baltic Sea this year!
Boat: Cutter-Rigged Moody 54
Posts: 33,764
Re: Inaccurate RYA Teaching : CTS - Quest For a New Method

Quote:
Originally Posted by Seaworthy Lass View Post
If you are ever using a CTS it is ESSENTIAL to plot your ground track. These are the dotted red lines on most of my examples.

If the RYA is not teaching this when they teach CTS , then they definitely should. How else do you know what hazards you will encounter?

If I hit fog it is oh so easy! I just continue on my same heading until the predicted time taken gets close . What could be simpler?

You on the other hand will need to keep changing your course hourly to stay on the course line! Much harder IMHO .
The degree of awareness required depends on where you are and what hazards there are, and what tools you have. In the middle of the English Channel out of sight of land, it's the SHIPS lined up 3 miles apart, barrelling down the Channel at 18 knots with 19-year old Ukrainian OOW's who don't answer VHF calls and hell-bent on running you down which is the problem , not rocks. A glance at the chart plotter from time to time is enough, in that case, for avoiding the hard bits .

In other places, YMMV.
Dockhead is offline   Reply With Quote
Old 23-01-2013, 22:10   #187
Moderator
 
Seaworthy Lass's Avatar

Cruisers Forum Supporter

Join Date: Oct 2008
Boat: Bestevaer 49
Posts: 16,151
Re: Doctrine of the Imperative Triangle

Quote:
Originally Posted by Dockhead View Post
My dear, of course there's a triangle there, there's always a triangle -- you can't get away from vector triangles in navigation

One leg is the sum of all the tide vectors (pay no attention that you build up that leg through a crooked path)
One leg is the bearing and distance to where you want to go
The last leg is the water track
Yes, you could draw all sorts of triangles if you wanted to for navigation. what I meant to say was that you not actually use ANY TRIANGLES AT ALL in my method until it comes to drawing in the ground track.
This is what makes my method unique and quite different in this repect to the RYA method


Quote:
Originally Posted by Dockhead View Post
Every one of these things is needed in order to know how to get to where you want to go -- you must have the length of all of these legs to get the angle of the water track and thus your CTS. When you build up the leg which is the sum of the tide vectors, you also get one angle of the overall vector triangle. So now you have everything you need -- length of two legs and one angle -- to solve the whole triangle, and thus know how to get where you want to go . Solving the triangle is the fundamental mathematical operation you do to get your CTS (and you easily get time also, thus VMG and all the other parameters). Whether you do it with pencil and paper, calculator, slide rule, computer, or protractor, doesn't make any difference -- you are still solving a triangle.
Nope, sorry, not a hint of a triangle considered anywhere in my method .
I do not look at or consider any triangles until I need to plot my ground track.
Nice huh?

Quote:
Originally Posted by Dockhead View Post
I'm still struggling to understand why you think the 'rhumb line' has anything to do with the problems of the RYA method. Makes me thing that either you or I don't understand something about the method. I thought it's pretty obvious that the RYA method's failure is simply that they stop before they finish all the calculations? Just because the course line is handy to construct a valid vector triangle of the wrong size , doesn't make it guilty, does it?
Wait for my next example and it will become clearer .
The course line will not only be pronounced guilty, but hopefully sentenced to death!
__________________
SWL (enthusiastic amateur)
"To me the simple act of tying a knot is an adventure in unlimited space." Clifford Ashley
"The cure for anything is salt water: sweat, tears or the sea." Isak Dinesen

Unveiling Bullseye strops for low friction rings
Seaworthy Lass is offline   Reply With Quote
Old 23-01-2013, 22:28   #188
Moderator
 
Seaworthy Lass's Avatar

Cruisers Forum Supporter

Join Date: Oct 2008
Boat: Bestevaer 49
Posts: 16,151
Re: Inaccurate RYA Teaching : CTS - Quest For a New Method

Quote:
Originally Posted by Andrew Troup View Post
NOTE FROM HER IMAGINARY ROYAL HIGHNESS: "We are not amused. Our loyal subjects will note that the Exchequer was considerably depleted pursuant to the requisition for the Current Machine. Our pockets are deep, but there are limits."

Here endeth the gospel about "the Immaculate Conception by SeaWorthy, founding member and first President of the Republican Boating Association". Not a bad sheila, and not at all stuck-up.


Rhumb line? Schmum line !
Thanks for all your wonderful support Andrew xxxxxx.
Lovely to have you in my corner. I have been staying out of your discussion with Dockhead, but I agree with all you have said although you haven't directed any posts to me .

And I was hoping for a knighthood for services rendered to yachting. My endeavours will be so appreciated, it will probably be 'Dame Seaworthy' soon LOL .
__________________
SWL (enthusiastic amateur)
"To me the simple act of tying a knot is an adventure in unlimited space." Clifford Ashley
"The cure for anything is salt water: sweat, tears or the sea." Isak Dinesen

Unveiling Bullseye strops for low friction rings
Seaworthy Lass is offline   Reply With Quote
Old 23-01-2013, 22:46   #189
Registered User
 
DeepFrz's Avatar

Cruisers Forum Supporter

Join Date: Mar 2006
Location: Winnipeg
Boat: None at this time
Posts: 8,462
Re: Inaccurate RYA Teaching : CTS - Quest For a New Method

But not until you admit you are using triangles. As I said before, just because you don't draw the line doesn't mean you aren't using triangulation. For instance you measure the distance from A to B (which you have to) hence you are using triangulation.

And I am off to bed...
DeepFrz is offline   Reply With Quote
Old 23-01-2013, 22:59   #190
Moderator
 
Seaworthy Lass's Avatar

Cruisers Forum Supporter

Join Date: Oct 2008
Boat: Bestevaer 49
Posts: 16,151
Re: Inaccurate RYA Teaching : CTS - Quest For a New Method

Quote:
Originally Posted by bewitched View Post
I've been following this thread with interest. These are my comments and observations. I hope they are objective and not too critical.
Hi Bewitched
Welcome to the thread .
It is great to be finally be getting feedback from people after all the silence on the other thread where all of this started (I think only Conachair and Wotname chimed in after a while with some support for my calculations, although not for my method - very luckily as although that original method produced a better result than the RYA method, it was still flawed. The method in this thread has been altered to remove all reference to the course line - a critical thing to do I think.

Quote:
Originally Posted by bewitched View Post
The RYA method attempts to give a single course to steer that would in x hours put you on the course line and close to your destination or waypoint (B). It aims to get you moving over the chart as close to your intended course line as is possible if restricted to only steering a single course for some reason.
I agree, but that is one of the problems, they want you arriving "on the course line".

Think about this - if you end up perpendicular to your destination for the final part of the current, and the direction of the current is taking you straight to B, imagine trying to find a point on the course line to steer to (particularly if the ONLY point you can select is actually miles from B) when you are actually being pushed to B at that stage?

Why would you want to be heading in a stupid direction at that stage to head to some point on the course line miles from where you want to go instead of going straight to B?

Quote:
Originally Posted by bewitched View Post
Therefore, the course line is not simply a construct from which to draw tidal and CTS vectors as has been suggested in this thread, it is fundamentally the course that you intend to take, over the ground, that keeps you away from danger.
Sorry, your ground track is NOT the course line if you are steering the CTS and the current varies along the way. Maybe this is where the source if confusion is for some people? Look at my diagrams - in most of them I have dotted a thick red line to indicate the ground track, both for the RYA method and for mine. It is DEFINITELY not along the course line for either the RYA or the SWL methods .

Quote:
Originally Posted by bewitched View Post
The SWL method, as far as I can make out, and please correct me if I'm wrong, attempts to provide a single CTS that takes you directly to the destination (B) and therefore it is accounting for that little bit of distance at the end that the RYA method ignores. So naturally the CTS will be slightly different for each method because they are aiming at different end points.
Yes, but it may not be a "little bit" out. The current at the end of the journey may be critical (not just in it's strength, but particularly in it's direction), as I am about to show when I finish answering the overnight posts.

Quote:
Originally Posted by bewitched View Post
They are both planning methods which must be verified where possible by observation during the passage. However, as a planning method, the SWL approach does have the serious flaw that there is no intended course plotted onto the chart. So how do you know if things are going to plan or not?
LOL, how do you know in the RYA method until you actaully arrive at D, a point removed from A on the course line? It is pretty arbitrary to pick the line between A and B as the point you MUST arrive at if your ground track has been nowhere near the course line during the journey.
__________________
SWL (enthusiastic amateur)
"To me the simple act of tying a knot is an adventure in unlimited space." Clifford Ashley
"The cure for anything is salt water: sweat, tears or the sea." Isak Dinesen

Unveiling Bullseye strops for low friction rings
Seaworthy Lass is offline   Reply With Quote
Old 23-01-2013, 23:00   #191
Registered User
 
bewitched's Avatar

Join Date: Sep 2009
Location: SE Asia
Boat: Swan 56
Posts: 891
Images: 3
Re: Inaccurate RYA Teaching : CTS - Quest For a New Method

Quote:
Originally Posted by Dockhead View Post
ALL constant heading passages over moving water take you off the rhumb line, including the RYA method.

It is most definitely not part of the RYA method, any more than it is part of Seaworthy's, to try to keep you on "the course that you intend to take, over the ground, that keeps you away from danger." None of the constant heading approaches even considers the ground track. In a typical Channel crossing, you will deviate 12 miles or more from the rhumb line, whether you are navigating by RYA method, Seaworthy's, or mine. To "keep away from danger" you have to figure out separately where you think you're going to be over ground at any given time -- it's a different problem (and of course, an important one).
It seems I have a significantly different understanding from you on the function of the RYA method. Firstly, the RYA call it the course line, not the rhumb line for a very good reason. It is the course, over the ground, that it is intended that the boat will travel. Sure it is a straight line between 2 points in the examples which have been put forward, but that is only because the RYA method is very simplistic and ignores many variables. If the course line was plotted by a routing software, the course line would be far from straight and could never be confused with a rhumb line.

It is definitely the intention to follow this course line during the the passage, whether straight or not, as closely as possible. That is why it is put on the chart and our progress checked against it. I'm afraid if I came up on watch and my helmsman had taken us 12 miles off the course line he would not be in my favour, regardless of any protest he may have for wanting to maintain a single CTS.

So the question is; how do we ensure we sail along our course line? Well, if we have basic boat instruments and navigation electronics on board, which is pretty much the norm these days, it is simply a case of altering our heading until our course over the ground equals our course line on the chart.

Even if we are assuming a straight course line, rather than a routing software generated one, the heading will need to be constantly altered to maintain the desired COG. This is because wind, wave, tide etc are not constant.

So why does the RYA propose a method that employs a single course to steer over a route which clearly has constantly changing conditions? Well firstly it is assuming that you are not getting position information from any source, otherwise it would be easy just to follow the course line wouldn't it?

I believe, the intention of the RYA tidal method is to provide a simple means to keep you close to your course line during a passage undertaken without the ability to determine position. The single course to steer, rather than several courses to steer is simply a mechanism to reduce potential error caused by the varying tide rates. It is one small step in the effort to navigate by dead reckoning.
bewitched is offline   Reply With Quote
Old 23-01-2013, 23:02   #192
Moderator
 
Seaworthy Lass's Avatar

Cruisers Forum Supporter

Join Date: Oct 2008
Boat: Bestevaer 49
Posts: 16,151
Re: Inaccurate RYA Teaching : CTS - Quest For a New Method

Quote:
Originally Posted by DeepFrz View Post
But not until you admit you are using triangles. As I said before, just because you don't draw the line doesn't mean you aren't using triangulation. For instance you measure the distance from A to B (which you have to) hence you are using triangulation.

And I am off to bed...
DeepFrz, why does measuring the distance between two points mean I am triangulating anything?
I repeat, I am NOT using triangles for anything other than determining the ground track once I have finished all my calculations.

Sleep tight . And Lodesman too.
You will have a very interesting example to check out when you wake up .
__________________
SWL (enthusiastic amateur)
"To me the simple act of tying a knot is an adventure in unlimited space." Clifford Ashley
"The cure for anything is salt water: sweat, tears or the sea." Isak Dinesen

Unveiling Bullseye strops for low friction rings
Seaworthy Lass is offline   Reply With Quote
Old 23-01-2013, 23:11   #193
Moderator
 
Seaworthy Lass's Avatar

Cruisers Forum Supporter

Join Date: Oct 2008
Boat: Bestevaer 49
Posts: 16,151
Re: Inaccurate RYA Teaching : CTS - Quest For a New Method

Quote:
Originally Posted by Dockhead View Post
The degree of awareness required depends on where you are and what hazards there are, and what tools you have. In the middle of the English Channel out of sight of land, it's the SHIPS lined up 3 miles apart, barrelling down the Channel at 18 knots with 19-year old Ukrainian OOW's who don't answer VHF calls and hell-bent on running you down which is the problem , not rocks. A glance at the chart plotter from time to time is enough, in that case, for avoiding the hard bits .

In other places, YMMV.
As you get close to your destination, how do you know were you will be and from what side you are approaching unless you have done a plot of your ground track beforehand? You also want to check there is nothing close to the departure point either, as your initial heading could take you just about anywhere!

If your departure and arrival points and a wide area between them are all in totally open water then you don't need to plot your ground track beforehand, but this would have to be a very unusual situation (in fact I can't think when this would ever crop up).

PS Do you speak Ukrainian? Maybe that is another requirement for crossing the channel LOL. Should I perhaps alert the RYA to that fact as well?
__________________
SWL (enthusiastic amateur)
"To me the simple act of tying a knot is an adventure in unlimited space." Clifford Ashley
"The cure for anything is salt water: sweat, tears or the sea." Isak Dinesen

Unveiling Bullseye strops for low friction rings
Seaworthy Lass is offline   Reply With Quote
Old 23-01-2013, 23:24   #194
Moderator
 
Seaworthy Lass's Avatar

Cruisers Forum Supporter

Join Date: Oct 2008
Boat: Bestevaer 49
Posts: 16,151
Re: Inaccurate RYA Teaching : CTS - Quest For a New Method

Quote:
Originally Posted by Dockhead View Post
A bit like the fairytale of Andrei Strelok, whom the tsar orders to "Go hence, I know not where, bring back something, I know not what ("Poidi tyuda, ne znayu kuda, prenesi chto, to ne znayu" ).
In the case of computing CTS, it is actually a case of "go forth on a heading that depends on the current displacement in the final pert of the journey, when the current displacement depends on your CTS".

This is the problem that the RYA found too hard to handle (it would be solvable using calculus) and so they decided to use the course line to deal with it. Even the original faulty method I came up with on the other navigation thread did better than they do though!

The new SWL method demonstrates a very elegant solution I think.
__________________
SWL (enthusiastic amateur)
"To me the simple act of tying a knot is an adventure in unlimited space." Clifford Ashley
"The cure for anything is salt water: sweat, tears or the sea." Isak Dinesen

Unveiling Bullseye strops for low friction rings
Seaworthy Lass is offline   Reply With Quote
Old 23-01-2013, 23:28   #195
Registered User
 
bewitched's Avatar

Join Date: Sep 2009
Location: SE Asia
Boat: Swan 56
Posts: 891
Images: 3
Re: Inaccurate RYA Teaching : CTS - Quest For a New Method

Quote:
Originally Posted by Seaworthy Lass View Post
Sorry, your ground track is NOT the course line if you are steering the CTS and the current varies along the way. Maybe this is where the source if confusion is for some people? Look at my diagrams - in most of them I have dotted a thick red line to indicate the ground track, both for the RYA method and for mine. It is DEFINITELY not along the course line for either the RYA or the SWL methods .
Hi - I'm still very open to your method - just trying to be objective.

I realise that the track will differ from the course line. Without regular positional information (GPS) it will be virtually impossible to follow the course line exactly. What I believe that both the RYA and your methods aim to achieve is to get the boat back on to the course line at some point in the future. The RYA in x hours and your method when you arrive at the destination.

I really have no strong opinion on which is preferable, I think both have merits.

As I said, my only real comment is that your method doesn't actually show a course line.
bewitched is offline   Reply With Quote
Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
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


Advertise Here


All times are GMT -7. The time now is 08:58.


Google+
Powered by vBulletin® Version 3.8.8 Beta 1
Copyright ©2000 - 2024, vBulletin Solutions, Inc.
Social Knowledge Networks
Powered by vBulletin® Version 3.8.8 Beta 1
Copyright ©2000 - 2024, vBulletin Solutions, Inc.

ShowCase vBulletin Plugins by Drive Thru Online, Inc.