Self Righting Rig

Discussion in 'Sailboats' started by Wardi, Jun 9, 2004.

  1. Wardi
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    Wardi Senior Member

    It is intriguing to consider that for very tall rigs, it may be possible for the top to be inverted and provide sufficient negative heeling moment (positive righting moment) to balance the heeling moment from the rest of the rig lower down. Presumably if the rig is tall enough, or if a small sail or foil is set on the tip of a very tall mast, even above the sail, then we can have lots of righting moment with relatively little drag.

    This means we could in effect have a self righting rig! The big question is if it would be efficient??

    I have noticed that A-class cats set their rigs up so that the top section inverts in a strong breeze, sailboards are heading this way also.
    I have also noticed that in strong breezes, if I under rotate my wing mast and use heaps of fuff tension, this not only lets the top of the rig fall to leeward to depower, but also allows the top couple of battens to invert slightly, but with a very fair inverse curve due to the under rotated wing section. In the stronger gusts, the load comes off the rig, heeling is reduced and the boat really takes off!! Feels great and goes fast!

    Most sailors and classes recognise the benefit of flattening the top of the sail and twisting to depower. At the same time we have been aware that too much twist or backwinding will slow the boat, hence we have not taken this any further.

    I am not aware of anyone purposely trying to harness this self righting effect!

    If we follow this idea further, it should be possible to purposely design a rig to dynamically produce this effect as the breeze increases.

    Your thoughts appreciated!
     
  2. dionysis
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    dionysis Senior Member

    hmm...

    Hi Wardi,

    I read about the same idea in "The Symmetry of Saling " by Garrett. He seams to be confidant of the effect.

    The drag angles of opposing foils - one on top of the other: one lifting to leeward;one lifting to winward, directly oppose of each other: they will cancel each other out.

    But... if the top one is a lot smaller - so you do not pay the above penalty. It would have to be a LOT higher up - so as to create a big enough antiheel moment to cancel out the sail below.


    I have not done the maths for it so I could not guarantee the practical feasability for the idea, but you never know what the future may bring.

    cheers
     
  3. yipster
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    yipster designer

  4. MalSmith
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    MalSmith Ignorant boat designer

    Relf Righting Rigs

    The maths for this set up is fairly simple, as it is is just a matter of summing two opposing moments. In the past I have shetched up a few designs based on the principle (and if I could work out how to attach a file to this mesage, I would send a sketch). The system will work in principle, but the practicle difficulties are in maintaining the optimum angle of incidence of the top and bottom elements of the sail for cancellation of the heeling moment (particularly in waves). Efficiency increases with vertical separation of the opposing sail elements, so the more efficient rig layout will have more weight aloft, decreasing the static stability of the system. This makes incidence control all the more important and most of my efforts in the past have been directed towards developing self adjusting control systems. This may not be so inportant for dinghys relying on human control. I did not do a lot of development on vertical self righting rigs due to these design dificulties and have tended more towards using simpler canted rigs. See http://www.cybernautics.com.au/Vproa.html for examples.

    Mal.
     
  5. tspeer
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    tspeer Senior Member

    Ah, the self-balancing rig. Here's where the distinction between stability and trim becomes really important!

    Let's define the term "Center of Effort" to mean the height you get when you divide the heeling moment of the rig by the net lift on the rig. An equally valid definition of "Center of Effort" is the location of the moment reference center about which the net moment is zero. And let's define the "Aerodynamic Center" as the location of the moment reference center for which a change in the lift on the rig results in no change to the heeling moment. If you think of the lift on the whole rig as acting at one location, one might choose either of these centers as being the "location" of the lift.

    For the sake of simplicity, I'll consider a uniform wind and some simple aerodynamic theory - the lifting line approach. This is the simplest approximation to the flow that will let one calculate the span loading, center of effort and aerodynamic center, and the induced drag. A realistic wind gradient and a full lifting surface calculation will shift the details, but they won't alter the basic relationships and trends.

    In another thread, I posted this graph,
    [​IMG]
    showing the tradeoff between induced drag and the height of the center of effort, assuming that you designed the rig to have the very minimum induced drag possible for its span. The lines show how the drag and center of effort change for different gaps between the foot of the sail and the surface, and as the rig is made taller than some reference rig size.

    The angle of attack is uniform all along the span and the sails are not twisted. So the span loads look like this
    [​IMG]
    no matter what the angle of attack is. For these rigs the center of effort and the aerodynamic centers are the same. If the angle of attack goes to zero, the lift on all parts of the rig goes to zero.

    You can reduce the height of the center of effort by tapering the planform and adding twist so the span loads look like this:
    [​IMG]
    To get the most out of every bit of sailcloth, you'd want the local angle of attack and the lift coefficient to be the same at all spanwise stations, and you can do this if the planform has the same shape as the lift distribution and the sail has a linear twist from foot to head like this:
    [​IMG]

    Compared with the previous designs, these reduced moment designs have a lower center of effort, but more induced drag for a given span:
    [​IMG]

    If you follow this design trend further, you can drive the center of effort right down to zero, with a considerable increase in drag, but you can make up the drag by making the rig taller. After all, there's no heeling moment, so there's no stability-related limit to how tall the rig can be! Right?

    Here's the first step along that path - these are the optimum spanwise lift distributions where the chord is tapered to zero at the head. To lower the center of effort any more, you have to start appying a negative load at the head.
    [​IMG]
    Not surprisingly, these designs need even more twist to keep everything evenly loaded:
    [​IMG]

    The center of effort for these planforms, sized to just the reference span, is shown as the isolated dash-dot line in the second carpet plot above. If you follow the trend in the drag vs center of effort (say, the upper right or lower right corners), you can see the trend is going to take you way out there on the drag axis by the time you get to zero center of effort. But you're going to make it up in span, right?

    Now consider the first set of reduced moment designs that looked like sailboard rigs. If you made them out of sheet metal so the design twist was frozen, and then reduced the angle of attack until the net lift was zero, you'd find that the foot was still producing positive lift while the twisted-off head was producing negative lift. This is called the "basic lift distribution", and for these designs it looks like this:
    [​IMG]

    As the angle of attack increases from the zero lift angle of attack, there's an incremental addition to the lift. This is called the "additional lift distribution". One consequence of having a more tapered planform than the minimum drag planform is that the change in lift with angle of attack is greater at the head than at the foot. You can see this in the difference between the design load distribution and the basic lift distribution - both experience the same change in angle of attack, starting from the design condition in which all parts are loaded to the same lift coefficient, but the head goes all the way to a negative lift coefficient while the foot doesn't even get reduced to zero.

    This change in the local section lift coefficient with a change in angle of attack or total lift is shown in this figure:
    [​IMG]
    At the foot, the local lift coefficients only increase at 80% of the rate you'd expect based on the change in lift of the rig as a whole. At the head, each section is getting loaded 50% faster than what you'd expect based on the rig as a whole.

    So when you consider where the additional lift is being applied, it's being applied disproportionately to the head compared to the foot. The aerodynamic center is the effective location of this additional lift, and it's above the center of effort. Here's how the aerodynamic center compares to the center of effort for the whole design space:
    [​IMG]

    The significance of the aerodynamic center is this is where a gust will seem to operate. You can ballast to counter the moment represented by the center of effort - that's the steady-state trim. But the change in moment due to a change in lift on the rig has to counter the moment represented by the aerodynamic center - that's stability, the ability to return to the original balance point after the disturbance is gone.

    If you compare the design approaches on the basis of aerodynamic center vs drag, there's no free lunch:
    [​IMG]
    If you lower the aerodynamic center you pay the same drag penalty, whether you do it by making the rig shorter or if you do it by tapering and twisting off the head of the sail.

    What this means for the self-balancing rig is, yes, you can create a rig with negative lift at the top that cancels the moment due to the rest of the rig. The taller you make the rig, the better this will work because it gives the balance surface more leverage and it reduces what would otherwise be a crippling drag penaly.

    But when the gust hits, the rig won't behave like a self-balanced rig. It's going to have an aerodynamic center way up there. It's going to get knocked down in an instant unless it's mounted on a very stable platform or there's some really fast acting ballast. Hit a lull, and the balance surface is going to fling the rig to windward. So the self-balancing rig doesn't eliminate the need for stability in the hull (and crew).

    Now take another look at the twist required for the reduced moment designs. The X axis (twist) has been normalized by the lift coefficient. The required twist is proportional to the lift on the sail. As sailors have discovered with fat-headed mains, this works out very nicely for a flexible sail. When the sail is loaded more heavily, it stretches and feeds more twist in automatically. This lowers the effective aerodynamic center. So for a flexible sail, the effective aerodynamic center and the center of effort don't have to be very far apart.

    But that's not true of the self-balanced rig. The balance surface is going to see a positive increase in lift for a positive increase in angle of attack. In order to restore the equilibrium, it has to be deflected through an even greater angular change in the negative direction. This points to the need for some kind of active control system to achieve what a normal sail can do naturally.

    That's the story on self-balancing rigs as I see it. I think it's going to be pretty hard to make a self-balancing rig be competitive with a normal rig in terms of aerodynamics, stability required of the hull, or complexity. Zero lift at the head is the practical limit, in my opinion.
     
  6. dionysis
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    dionysis Senior Member

    nothing is free...

    I'll need a couple of minutes to absorb your reply Tom. ;) Though as much - you cannot get anything for nothing.
     
  7. des

    des Guest

    I might be misinterpreting the graphs but it looks to me like you can get something for nothing. By reducing the gap at the bottom of the sail you not only get a reduction in the induced drag but also a lower center of effort. The reduction in drag is something I had known but the lower center of effort is something I had not considered.
     
  8. gonzo
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    gonzo Senior Member

    However, the windspeed at low altitude approaches zero, so there is no real benefit.
     
  9. Wardi
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    Wardi Senior Member

    Tom, many thanks for your contribution.
    You have raise an interesting limitation, which I agree is a major limitation ie:
    If you use a normal rig arrangement then I agree entirely with this conclusion.

    One question that comes to mind is if we can construct a rig which effectively has the top section operating separately to the bottom but with the two linked in relation to the wind. This way if you pull the sail on, the top will move out to provide compensating heeling moment, ease the sheet and the top returns in line with the sail in proportion, in order to maintain neutral righting moment at all times. Not a simple thing to do I grant you, but not impossible either! This would overcome the problem you have forseen with a standard rig arrangement.

    The question I have is, if this were feasible mechanically, would there be a net benefit to do this?. Would it be best to do it within the one sail or have a separate small sail or foil way up the top?.
     
  10. dionysis
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    dionysis Senior Member

    seperate sails

    I think seperate is better, and some kind of computer feedback control too.

    The wind speeds up the higher you go too: so the high sail could be proportionately smaller. This helps.
     
  11. gonzo
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    gonzo Senior Member

    That is the topsail schooner system. It works well even in its primitive form.
     
  12. tspeer
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    tspeer Senior Member

    I doubt any schooners sheeted their their topsails so far forward that the sails were inverted and driving backwards.
     
  13. Doug Lord

    Doug Lord Guest

    "normal" + kite?

    Maybe a practical upwind solution could involve a kite? Especially if the kite was high enough to take advantage of a different wind direction....hmmmmm
    Calling Dave Culp........
     
  14. MalSmith
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    MalSmith Ignorant boat designer

    Below is an old hand sketh of mine showing a possibe configutaion for a zero heeling moment rig based on the principle being discussed. The hull configuration is a three point trimaran. Each hull rotates independantly, but in synchronisation (somehow) with the other two. A tail sail element maintains alignment with the wind and the righting sail element is mounted well above the main sail element. Enjoy!

    [​IMG]

    Mal.
     

  15. daveculp
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    daveculp Junior Member

    eliminating heeling moments

    We've been using non-heeling free flying kites to sail to windward for 3 decades. It's not rocket science and works very, very well. For nearly 30 years I have wondered why sailors work so hard at counteracting heeling moments when eliminating them altogether is so fundamentally simple.

    See http://www.dcss.org for some examples of upwind kites. See http://www.kiteship for simple inexpensive spinnaker replacement kites (good for square reaching to dead running)

    Dave Culp
     
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