Can somebody pro/con a full vs. fin keel for a newbie (will learn to sail on said boat) and taking it thru the Caribbean? All I can seem to come up with so far is fin keel is better to the wind, and a full keel will protect your rudder.
Full or fin keel?
- Tags
- boat buying newbee advice
-
SailNet is a forum community dedicated to Sailing enthusiasts. Come join the discussion about sailing, modifications, classifieds, troubleshooting, repairs, reviews, maintenance, and more!
utchuckd
41 - 60 of 847 Posts
- Reaction score
- 7,948
In the case of your Morgan OI 33, if she does not appear to heel much it is as a result of whole bunch of reasons which have very little do with the type of keel that she has or the fact that she has a comparartively low-ballast to displacement ratio for a shoal draft boat.
In the case of the Morgan 33, these are very beamy boats, with small sail plans for their displacement. They also have a lot of freeboard so that the heel angle does not seem all that extreme since the rail remains high above the water at pretty large heel angles. In fairness though, designers like Charlie Morgan, Ted Hood, and Dieter Empachter were all able to model comparatively heavish displacement designs that are less drag than might otherwise be expected. Hood and Empachter, made up for the extra displacement with comparatively high ballast ratios and generous sail plans.....Morgan on the Out Island series, not so much.
In the case of the Morgan 33, these are very beamy boats, with small sail plans for their displacement. They also have a lot of freeboard so that the heel angle does not seem all that extreme since the rail remains high above the water at pretty large heel angles. In fairness though, designers like Charlie Morgan, Ted Hood, and Dieter Empachter were all able to model comparatively heavish displacement designs that are less drag than might otherwise be expected. Hood and Empachter, made up for the extra displacement with comparatively high ballast ratios and generous sail plans.....Morgan on the Out Island series, not so much.
Joined
·
6,696 Posts
- Reaction score
- 1,865
Thanks Jeff. I'm old, but I'm still learning more about sailing every day, thanks in a large part to the Sailnet.
Cheers,
Gary
Cheers,
Gary
Joined
·
16,464 Posts
- Reaction score
- 1,578
Not referring to centerboarders or swinging keels that are a particular case it is clear to me that the design of keels and the way they carry the ballast have suffered a technical big evolution on the last 40 years of the XX century, evolution made possible by new materials, new building techniques and computerized hydrodynamic analysis of hulls, keels and ruder and their behavior.
If it is true that a full keel has some advantages over a well designed fin keel it also true that the some of advantages that a fin keel brings makes its use more appropriated in almost all situations and the way the hull, keel and ruder design have evolved on the last 50 years are a proof of that.
Even in what concerns bluewater boats that is very evident. We can pick Halberg-Rassy, Najad, Malo or any other blue water cruising boat that is not made over a 30 or 40 year's old designs, but whose designs have been modified through the years to bring to the same initial program that lead to their design 50 years ago (blue water cruising), all the advantages and benefits that modern design and new materials and technologies permit.
Since Andrews have posted already a drawing of a Malo design from the 90's we can have a look at the Malo hull, Keel and ruder evolution through the last decades (the results with Halberg-Rassy or Najad would be similar):
From the 70's:
![Image]()
From the 80's:
![Image]()
From the 90's:
![Image]()
![Image]()
Already from this century:
![Image]()
Regards
Paulo
If it is true that a full keel has some advantages over a well designed fin keel it also true that the some of advantages that a fin keel brings makes its use more appropriated in almost all situations and the way the hull, keel and ruder design have evolved on the last 50 years are a proof of that.
Even in what concerns bluewater boats that is very evident. We can pick Halberg-Rassy, Najad, Malo or any other blue water cruising boat that is not made over a 30 or 40 year's old designs, but whose designs have been modified through the years to bring to the same initial program that lead to their design 50 years ago (blue water cruising), all the advantages and benefits that modern design and new materials and technologies permit.
Since Andrews have posted already a drawing of a Malo design from the 90's we can have a look at the Malo hull, Keel and ruder evolution through the last decades (the results with Halberg-Rassy or Najad would be similar):
From the 70's:
From the 80's:
From the 90's:
Already from this century:
Regards
Paulo
Jeff - idle curiosity - you didn't mention twin keels. I remember seeing these in the UK, where in areas with a large tidal range and shallow water you could see many smaller boats standing up high and dry, sitting happily on their twin keels, at low tide. I read somewhere that these were becoming more popular in the US also. Any opinions? Seems to me like potential for a lot of drag; perhaps stiffer; clearly more stable at on the hard!!
- Reaction score
- 7,948
I think that there are a lot of very practical reasons why Bilge Keels (twin Keels) make sense, but none of them have much to do with sailing ability. Which is not to say, that it is not possible to design a very workable bilge keel design, which will offer reasonable performance, shallower draft and so on, but twin keels generally require taking a hit on performance as compared to the same hull and rig with a deeper draft fin keel. The reality is that by necessity, bilge keels with a shallower draft will have end up with some trade off of greater displacement (since more ballast is required to achieve the same vertical center of gravity), less stability, and/or more drag (more wetted surface and frontal area).
In theory you can try to optimize the configuration of the bilge keels to produce the best performance possible, but you can also do the same thing with a deeper fin keel, so it becomes something an arms race with the deeper fin wining in term of performance at any level of optimization.
Similarly, a deeper fin keel of equal stability and weight to a particular bilge keel design would also tend to have a better motion comfort since its deeper draft would generate a higher roll moment of inertia and better dampening.
But in a broad general sense, cruising boats are rarely optimized for out and out performance. Instead they are optimized for the practical requirements of their purpose, which means greater carrying capacity, simplicity, and robustness than would appropriate for a goal of simply going as fast as a boat possibly can. In that vein, bilge keels might be seen as simply another worthwhile compromise in performance for cruising practicality.
I don't know where you read that bilge keels are becoming more popular in the U.S. but I personally don't believe that bilge keel boats are becoming more popular around here. If anything I would suggest that they are a very hard sell here on the U.S. Atlantic Coast and so would probably take a bigger depreciation hit at resale time. That said, they may be a cult boat that holds their value since so few models are available on the market.
My own personal concern with bilge keels and the reason that I personally would not buy one for myself, is is similar to my concern with wing keels. In my experience when you accidentally run either aground, it is far harder to get free. An argument might be be made that a shallower draft boat is less likely to run aground as frequently, and that arguement may have merit for some people, but it does not work acceptably well for my own personal preferences.
Jeff
In theory you can try to optimize the configuration of the bilge keels to produce the best performance possible, but you can also do the same thing with a deeper fin keel, so it becomes something an arms race with the deeper fin wining in term of performance at any level of optimization.
Similarly, a deeper fin keel of equal stability and weight to a particular bilge keel design would also tend to have a better motion comfort since its deeper draft would generate a higher roll moment of inertia and better dampening.
But in a broad general sense, cruising boats are rarely optimized for out and out performance. Instead they are optimized for the practical requirements of their purpose, which means greater carrying capacity, simplicity, and robustness than would appropriate for a goal of simply going as fast as a boat possibly can. In that vein, bilge keels might be seen as simply another worthwhile compromise in performance for cruising practicality.
I don't know where you read that bilge keels are becoming more popular in the U.S. but I personally don't believe that bilge keel boats are becoming more popular around here. If anything I would suggest that they are a very hard sell here on the U.S. Atlantic Coast and so would probably take a bigger depreciation hit at resale time. That said, they may be a cult boat that holds their value since so few models are available on the market.
My own personal concern with bilge keels and the reason that I personally would not buy one for myself, is is similar to my concern with wing keels. In my experience when you accidentally run either aground, it is far harder to get free. An argument might be be made that a shallower draft boat is less likely to run aground as frequently, and that arguement may have merit for some people, but it does not work acceptably well for my own personal preferences.
Jeff
Joined
·
16,464 Posts
- Reaction score
- 1,578
There are some cruising boats that in their low draft version have the ruder at almost the same draft as the keel. That looks dangerous to me and on those cases a skeg rudder seems to make semse to me.A cruising requirement for me is a skeg hung rudder, whatever you do, do that, my 2 cents.
But if a boat has the keel considerably deeper than the rudder, the chances of hitting with the rudder instead of the keel are not considerable and a more efficient spade rudder is the way to go :
Loose pounds, get better feel, reduce maintenance, improve lift, reduce drag and re-learn
the joy of driving your boat.
http://www.fastcomposites.ca/publications/WhitePapers/BetterSpadeRudder.pdf
Regards
Paulo
Joined
·
17,138 Posts
- Reaction score
- 2,213
If it were financially possible I'd have that later model Malo (or Hallberg Rassey) in a flash and given the overall build quality of the beasts I have no doubt that the Malo spade would be stronger than many skeg hung rudders.Already from this century:
![Image]()
Regards
Paulo
While I would never consider a deep fin/torpedo with leading edge exposed arrangement, improvements in underwater design allow us to have faster cruising boats that do not sacrifice their load carrying capacity. It may not seem much but that extra knot or two makes one hell of a difference on even a coastal passage and without doubt enhances the simple pleasure of the sailing.
Joined
·
248 Posts
- Reaction score
- 42
Caveats: As people have already mentioned, the full/fin keel discussion is complicated by the fact that displacement and hull shape are often related to the designers fin choice. Also, the type of person who decides to go offshore cruising in a fin keel boat is probably a different person than the type of person who decides to go offshore cruising in a full keel boat.
We are on a fin keel, skeg hung rudder, reverse sloped transom sloop.
A few observations from cruising down the N American coast to Mexico:
- Cruisers motor a lot.
- Cruisers in fin keel boats motor less often.
- Although one hopes one's major passages are mostly downwind, we have done a fair amount of beating coastally, particularly if we are sailing on and off our anchor.
- There are a lot of offshore cruisers in fin keel boats.
We are on a fin keel, skeg hung rudder, reverse sloped transom sloop.
A few observations from cruising down the N American coast to Mexico:
- Cruisers motor a lot.
- Cruisers in fin keel boats motor less often.
- Although one hopes one's major passages are mostly downwind, we have done a fair amount of beating coastally, particularly if we are sailing on and off our anchor.
- There are a lot of offshore cruisers in fin keel boats.
Joined
·
6,696 Posts
- Reaction score
- 1,865
Fuzzy,
I'm by no means an expert at sailboat designs, but looking at the above photo the first thing that comes to mind is both the prop and rudder could easily be susceptible to damage from something as small as a piece of driftwood, especially if the engine was running hard against the current. In my mind I can readily picture a partly submerged snag washing down the hull, being drawn into the prop, and jamming into the rudder hard enough from the engine's torque to blow the rudder and rip out the boat's bottom. I don't see this as a remote possibility with a full-keel boat and skeg mounted rudder. To me, it just seems like common sense, but maybe there's something I'm missing. And, of course, things like this don't happen when the weather's calm and conditions are ideal. For some unexplained reason, all of these incidences seem to occur during nasty storms and dangerous conditions.
Here's a photo of a friend's 32.5 Morgan which clearly shows it would be difficult to take out the rudder or prop even when hard aground.
Gary
Joined
·
3,112 Posts
- Reaction score
- 670
If you take advantage of the twin keel being more upright, thus each only having to be half the size of a single keel ,they have no more wetted surface than a long fin keel, and have far less wetted surface than a full length keel.
I hope to experiment with tip shapes, to eliminate the tip vortexes of twin keels. Shouldn't be too hard to accomplish.
I hope to experiment with tip shapes, to eliminate the tip vortexes of twin keels. Shouldn't be too hard to accomplish.
Joined
·
324 Posts
- Reaction score
- 28
Between Jeff_H and my fellow barn-door-rudder brethren, I don't have much to add. As a relatively new skipper, I can't tell you how much tight marina's scare me. Jeff is bang on with his technical points above... but the original poster is a self-proclaimed newbie which perhaps gives me a more recent perspective since I've recently gone through the same question and discovery.
In my quest for a boat, I sailed on as many as I could. Three examples,
1) I sailed a Shark 24 numerous times ( http://www.shark24.org/membership/images/plan3.jpg ) which was passable but I didn't like the boat. Tacking was easy enough but required a little time to get through the wind.
2) I then had the opportunity to skipper a J24. This thing quickly and accurately pivoted around a central point. It tacked so quickly that I would often over shoot my intended angles. Quick, easy and I needed very little input to get it through the wind in a second.
3) I settled on my lovely little Contessa 26... a modified full keel with a keel hung rudder. Oh boy. If I though the shark was slow through the corners, the full-keel takes a loooong time. I won't be dicing it up in a match racing duel any time with my baby.
From a newbie perspective, the type of keel & rudder combination drastically affects the handling of the vessel. In a car metaphor, a fin keel is going to be more like a twitchy sports car that will respond to lesser steering inputs (to varying degrees of course) and will require greater attention to your course. A full keel will feel more like a limo... you plan your corners ahead of time and will be more forgiving to newbie-skipper steering input. We often lapse in our ability to sail in a steady course for long periods of time.
As a newbie, a full keel seems easier to steer for long distance without the aid of autohelm, but is harder to dock, reverse and handle in tight quarters.
Another point that wasn't mentioned above is the turning radius. From my limited experience, I've found that the narrower the fin keel, the tighter the turning radius. The Farr 30 (Mumm 30) on which I sometimes race spins on a dime as does the J24. The Shark less so but still quite tight. My longer keeled Contessa likes a wide arc. I suspect this is primarily due to keel shape but I'll leave that as a homework exercise for Jeff_H to explain. ;-)
In my quest for a boat, I sailed on as many as I could. Three examples,
1) I sailed a Shark 24 numerous times ( http://www.shark24.org/membership/images/plan3.jpg ) which was passable but I didn't like the boat. Tacking was easy enough but required a little time to get through the wind.
2) I then had the opportunity to skipper a J24. This thing quickly and accurately pivoted around a central point. It tacked so quickly that I would often over shoot my intended angles. Quick, easy and I needed very little input to get it through the wind in a second.
3) I settled on my lovely little Contessa 26... a modified full keel with a keel hung rudder. Oh boy. If I though the shark was slow through the corners, the full-keel takes a loooong time. I won't be dicing it up in a match racing duel any time with my baby.
From a newbie perspective, the type of keel & rudder combination drastically affects the handling of the vessel. In a car metaphor, a fin keel is going to be more like a twitchy sports car that will respond to lesser steering inputs (to varying degrees of course) and will require greater attention to your course. A full keel will feel more like a limo... you plan your corners ahead of time and will be more forgiving to newbie-skipper steering input. We often lapse in our ability to sail in a steady course for long periods of time.
As a newbie, a full keel seems easier to steer for long distance without the aid of autohelm, but is harder to dock, reverse and handle in tight quarters.
Another point that wasn't mentioned above is the turning radius. From my limited experience, I've found that the narrower the fin keel, the tighter the turning radius. The Farr 30 (Mumm 30) on which I sometimes race spins on a dime as does the J24. The Shark less so but still quite tight. My longer keeled Contessa likes a wide arc. I suspect this is primarily due to keel shape but I'll leave that as a homework exercise for Jeff_H to explain. ;-)
Joined
·
4,525 Posts
- Reaction score
- 1,928
I think you make a choice and with the choice comes a particular set of advantages and disadvantages. I also think that it is quite simplistic to say that full keels are this and fin keels are that. A lot depends on the quality of design of the particular boat, i.e there are some full keels that are very well-designed and some that are not. Same for fin keels, centerboarders, and bilge keelers. If I was a full keel person I could find full keel boats that were terrible to sail and fin keelers that I would love to sail.
I have a skeg-mounted rudder now but have had fins as well. On an earlier boat (S&S designed 29') I was amazed to see how little strength the skeg had when the rudder was removed. The strength of the unit was coming from the rudder shaft, not the skeg. The reason why the rudder was off, was that it had been broken when the boat came down onto the tip of the rudder (it went downward a bit from the skeg) on a sandbar at a harbor I should not have been trying to enter with waves as they were. The force tore the rudder blade away from the shaft which jammed the rudder againt the fairing that came down from the hull. If it has been a spade rudder, I suspect that the damage might have been similar although perhaps less tearing and more bending of the shaft.
Final point - the keel does not exist in isolation from the rest of the design. You can't buy an XYZ 34 with a long keel and the same boat with a modern fin - so what we are getting when we make a choice is the whole package of design choices and compromises.
I have a skeg-mounted rudder now but have had fins as well. On an earlier boat (S&S designed 29') I was amazed to see how little strength the skeg had when the rudder was removed. The strength of the unit was coming from the rudder shaft, not the skeg. The reason why the rudder was off, was that it had been broken when the boat came down onto the tip of the rudder (it went downward a bit from the skeg) on a sandbar at a harbor I should not have been trying to enter with waves as they were. The force tore the rudder blade away from the shaft which jammed the rudder againt the fairing that came down from the hull. If it has been a spade rudder, I suspect that the damage might have been similar although perhaps less tearing and more bending of the shaft.
Final point - the keel does not exist in isolation from the rest of the design. You can't buy an XYZ 34 with a long keel and the same boat with a modern fin - so what we are getting when we make a choice is the whole package of design choices and compromises.
On the bluewater boards, they make it sound like if you aren't in a traditional full keeled boat 40' or better, you are suicidal to sail in anything larger than a 1 acre pond.
The number of fin keeled boats in transoceanic races somewhat belies that. The large number of small fin keelers in the Carribean also kinda belies that.
So I would say any respectable built sail boat thats not too big for your crew to handle, and that YOU can dock comfortably, will take you anywhere you are likely to go as long as you respect it's, and your limitations.
After all how many of us have rounded the capes in winter, or done a Northwest passage, or rounded Antartica?
I prefer sailing in tropical lattitudes outside of hurricane season. That makes it unlikely that I will see anything over a F8 in open water. Even more likely I will be running for the lee of the nearest landmass as soon as a storm is forming in the area, long before the waves build to dangerous levels.
Would a "bulletproof" ship be nice, well yes; but I probably wouldn't sail it as much as I would a light cheap production boat that is easy to dock.
The number of fin keeled boats in transoceanic races somewhat belies that. The large number of small fin keelers in the Carribean also kinda belies that.
So I would say any respectable built sail boat thats not too big for your crew to handle, and that YOU can dock comfortably, will take you anywhere you are likely to go as long as you respect it's, and your limitations.
After all how many of us have rounded the capes in winter, or done a Northwest passage, or rounded Antartica?
I prefer sailing in tropical lattitudes outside of hurricane season. That makes it unlikely that I will see anything over a F8 in open water. Even more likely I will be running for the lee of the nearest landmass as soon as a storm is forming in the area, long before the waves build to dangerous levels.
Would a "bulletproof" ship be nice, well yes; but I probably wouldn't sail it as much as I would a light cheap production boat that is easy to dock.
Joined
·
4,525 Posts
- Reaction score
- 1,928
Capt Bill, some responses
1. I think the bluewater board folks need to get out more. From what we see there are more fin-keeled (think Bob Perry, fairly conservative fins) boats that full-keeled boats (lets say attached rudder types).
2. Don't try to take too many conclusions based on trans-oceanic race boats. Their crews are different and so are their priorities 1) make it and 2) win - comfort or ease of handling are way down the list, if on it at all.
3. For extended cruising ease of docking is not much of a priority since you so rarely do it. We docked in Panama, Tahiti, and Australia on a trip from Florida to Australia.
4. You can get more than F8 in the tropics during the recommended time of the year. We got F10 SE of Tahiti.
5. We are circumnavigating Antarctica (and the North Pole too), but will never be closer than around 1800 nm (in South Africa), and it will be in summer, but I still have considerable trepidation about that part of the trip.
Some responses - based on our experiences
1. I think the bluewater board folks need to get out more. From what we see there are more fin-keeled (think Bob Perry, fairly conservative fins) boats that full-keeled boats (lets say attached rudder types).
2. Don't try to take too many conclusions based on trans-oceanic race boats. Their crews are different and so are their priorities 1) make it and 2) win - comfort or ease of handling are way down the list, if on it at all.
3. For extended cruising ease of docking is not much of a priority since you so rarely do it. We docked in Panama, Tahiti, and Australia on a trip from Florida to Australia.
4. You can get more than F8 in the tropics during the recommended time of the year. We got F10 SE of Tahiti.
5. We are circumnavigating Antarctica (and the North Pole too), but will never be closer than around 1800 nm (in South Africa), and it will be in summer, but I still have considerable trepidation about that part of the trip.
Joined
·
3,112 Posts
- Reaction score
- 670
My first boat had a long keel with rudder attached. She tacked on a dime , whether you wanted her to , or not.
My second boat, with a much longer keel, was not much better, and tacked much quicker than my current boat, with short twin keels. The difference was hull balance; hull shape.
Keel length had little effect on directional stability.
Some race boats, slow to tack, have been said to have 'Excess directional stability." That is due to hull shape, not keel length.
There is no such thing as "Excess directional stability" on an offshore cruising boat; the more the better.
You see fewer and fewer boats cruising offshore with full length keels. Even out there, they are increasingly rare.
My second boat, with a much longer keel, was not much better, and tacked much quicker than my current boat, with short twin keels. The difference was hull balance; hull shape.
Keel length had little effect on directional stability.
Some race boats, slow to tack, have been said to have 'Excess directional stability." That is due to hull shape, not keel length.
There is no such thing as "Excess directional stability" on an offshore cruising boat; the more the better.
You see fewer and fewer boats cruising offshore with full length keels. Even out there, they are increasingly rare.
Joined
·
324 Posts
- Reaction score
- 28
Hi newbee,
You should post this question as a new thread, rather than in a this unrelated thread. You'll likely get more exposure and more advice that way. Perhaps the mods can help separate the last few posts into a new thread for you?
Cheers,
J.
Joined
·
247 Posts
- Reaction score
- 5
The Hobby Horse action while even at a mooring is one disadvantage on some full keel boats. I was a Bay Host a reasonably protected bay (Leinster Bay, St John USVI), a year or so back, when a Ferry Boat passing a quarter mile away caused one boat to hobby so bad it cause some injury to two occupants who were not expecting it. The major problem is the boat continued to hobby horse well after all other boats were totally stable again... actually for probably 2 full minutes.
I responded to a cry for help and was some 70 yards away and by the time I deployed my dink and arrived some 3 min later I was just able to board the boat which was still having Hobby Horse movements. The two had minor bruises and one a cut to the head from hitting something when thrown down in the cabin. Nether wanted / would allow medical assistance to be called but did show bruises for several days.
Most other boats in the harbour were fin keel boats and Cats but at least one other appeared to be a 3/4 keel but was further up in the bay and did not suffer any significant disturbance.
I've seen many full keel boats similarly effected by swells of a short duration that seem to trip the hobby horse effect. often causing the bow sprints to go under water and most of the Rudders to be exposed while adjacent fin keel and cats had only a minor effect. It would have been Very difficult/ dangerous to effect any forward deck work during these events.
All boats have good and some not so good responses to specific weather/ sea conditions, you can only go with what you feel is best for your type and location of cruising and be prepared for what comes.
I responded to a cry for help and was some 70 yards away and by the time I deployed my dink and arrived some 3 min later I was just able to board the boat which was still having Hobby Horse movements. The two had minor bruises and one a cut to the head from hitting something when thrown down in the cabin. Nether wanted / would allow medical assistance to be called but did show bruises for several days.
Most other boats in the harbour were fin keel boats and Cats but at least one other appeared to be a 3/4 keel but was further up in the bay and did not suffer any significant disturbance.
I've seen many full keel boats similarly effected by swells of a short duration that seem to trip the hobby horse effect. often causing the bow sprints to go under water and most of the Rudders to be exposed while adjacent fin keel and cats had only a minor effect. It would have been Very difficult/ dangerous to effect any forward deck work during these events.
All boats have good and some not so good responses to specific weather/ sea conditions, you can only go with what you feel is best for your type and location of cruising and be prepared for what comes.
Probably the single most important reason why full keel boats are considered blue water has been discussed for over a hundred years, but interestingly enough not yet pointed out on this thread thus far.
Below is a picture taken from the book "Yacht Architecture" written in 1897. Notice that they were quite familiar with fin keels and bulb ballast as they describe in this book. Contrary to popular belief, a very old design.
What they knew back one hundred years ago was that hull form can create a significant amount of righting moment. And these two hulls create radically different hull righting moments. The flat bottom bulb keel creates considerably more hull righting moment than the full keel design because it has a flatter bottom.
So the full keel design is given more ballast. The ratio of ballast righting moment to hull righting moment is much higher in the full keel boat. This causes the full keel boat to be considerably more friendly in rough water. The reason is that the full keel tends to remain upright on waves, yet the flat bottom boat tends to heel with the wave angle.
And as we all know a full keel boat is more comfortable in rough seas. That is well documented in hundreds of years of Yacht design. So if you really want to put a number on "Blue Water", you should look at the ratio of mass righting moment to hull righting moment. The full keel by its very design forces a high ratio.
Bryce
Attachments
41 - 60 of 847 Posts
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
-
?
