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    Posted: 03 Jan 22 at 5:33pm
page 181 of Frank Bethwaites "High Performance Sailing"


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KazRob View Drop Down
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Post Options Post Options   Quote KazRob Quote  Post ReplyReply Direct Link To This Post Posted: 03 Jan 22 at 6:12pm
Any basic mechanics book will explain it all. If there is a fundamental problem with these principles I'm sure they would have been noticed by now. As Tink said - all that matters is the overall moment and balance of forces. If you do a free body diagram and include the angles of the wires etc you'll see it makes sense.


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Post Options Post Options   Quote Sam.Spoons Quote  Post ReplyReply Direct Link To This Post Posted: 03 Jan 22 at 6:19pm
Originally posted by A2Z

Interesting isn’t it?  Lots of people have told you that you are wrong about moving the trapeze attachment outboard increasing righting moment but no one has really explained why.  

I can't think of a simpler way to explain it...

Originally posted by Sam.Spoons

Tall people have more righting moment not because the trap hook is further from the boat but because their CoG is further from the boat. Moving the hook doesn't change that.

How high up the mast the wire attaches (almost always at the hounds IME) is also irrelevant WRT righting moment but the lower it is the more load on your legs to stay standing horizontally off the side of the boat

You have to have the trap hook at or slightly (but only slightly)* above your CoG to be able to move around the boat, if it's too far above and you feet slip off the gunnel your legs will fall in the water, if to low your head/body will fall into the water.

* In practice slightly above your CoG has proven to be most efficient.
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Post Options Post Options   Quote Guests Quote  Post ReplyReply Direct Link To This Post Posted: 03 Jan 22 at 6:40pm
Sorry, but there hasn’t been an explanation as to why the trapeze wire coming out at a more horizontal angle if attached higher up the body doesn’t increase the righting moment. The only explanation given is that righting moment = body weight x distance from centre of buoyancy, which is correct but doesn’t explain why the trapeze angle method is wrong. After all, if you were trying to pull a tree over you would find it easier if pulling more horizontally and less down (from the same attachment point) so why isn’t the same true for dinghy stability?  
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Post Options Post Options   Quote Sam.Spoons Quote  Post ReplyReply Direct Link To This Post Posted: 03 Jan 22 at 6:45pm
Because to pull more horizontally/less down you would have to stand further from the tree (for the same attachment point on the tree). If you stood further from the boat (either on stilts or WHY) you would have a higher downward force not because of the angle of the trap wire but because you were further from the boat. But it's not a valid analogy because to pull the tree down you would be pulling sideways and the sideways component of your effort would be what pulls the tree over not the vertical component.

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Post Options Post Options   Quote Guests Quote  Post ReplyReply Direct Link To This Post Posted: 03 Jan 22 at 6:47pm
No, the trapeze line (or tree rope) is more horizontal if the line is attached at the chest rather than the knees.  The man is no taller and has no more inherent leverage. 
I know the answer to this, but no one has yet explained it despite deriding GRF for asking the question.  


Edited by A2Z - 03 Jan 22 at 6:54pm
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Post Options Post Options   Quote Grumpycat Quote  Post ReplyReply Direct Link To This Post Posted: 03 Jan 22 at 6:48pm
Originally posted by tink

Originally posted by iGRF

I've worked it out but you'll have to wait.

Mrs iGRF is not happy, I've tried to explain to her but she won't 



Please tell me Mrs iGRF is a professor of pure physics 

No she is a a saint in human form  Wink
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Post Options Post Options   Quote Sam.Spoons Quote  Post ReplyReply Direct Link To This Post Posted: 03 Jan 22 at 6:53pm
Originally posted by iGRF

Had to revert back to schoolboy maths and moments, now this is not a statement, it's still a question.

So lets say racks, and our helm is 90 kgs and the racks are 2.5 metres out from the pivot point which we'll call the mast base. So Distance from pivot times mass to get moment is 2.5 x 90kg equals 225Nm yes?

Yes

So now with a trapeze do we not have to accept that the pivot distance changes from the foot of the mast to the end of the rack, to the foot of the mast to the point at which the weight is acting on the mast which is the new lever at say 4 mtrs to the hounds? So our 90 kilo mass now supported flat wiring from the mast must be 4 x 90 kgs and 360 Nm?

No, the crew's CoG is still only 2.5m from the mast foot

This doesn't asnwer my question but it does give some maths to start with.

Or, do we totally discount the mast lever suggestion because it's neutralised by the sail sideforce and the calculation remains directly from the pivot point to the point at which the harness is attached or the height of the sailor?

Yes, it's purely the hight of the sailor (or more correctly how far, horizontally, from the mast foot his CoG is

If it's the harness hook attachment point then my suggestion holds water, if it's the height of the sailor then it doesn't.

See above 

Those holding the racks trapeze makes no difference answer will hold with the view that wether racks or trap the c.o.g of the sailor distance prevails, i.e. 250 so 225 Nm righting moment either way.

Yes

I maintain that there is an element of mast leverage and probable weight reduction as a result, but it's an interesting thing to continue to work on and I hate maths, but there has to be a formula there somewhere to support what I'm sure I've read somewhere along the path.

No, different forces, the CoG of the 90kg crew is roughly at his navel, say 1m from his feet. Now lets assume he can use toe straps just outboard of the gunnel and flat hike with his feet touching the gunnel, his CoG will be 1m out from the gunnel regardless of how wide the racks are (as long as they are wide enough for him to hike off). Now remove the racks and put him on a trap wire so he can stand horizontally off the gunnel with his CoG in exactly the same place relative to the boat and he will generate exactly the same righting moment and will be able to balance exactly the same amount of power from the rig. I'm almost tempted to make a mock up to prove it but have other stuff I have to do first.


Edited by Sam.Spoons - 03 Jan 22 at 6:58pm
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Post Options Post Options   Quote Mozzy Quote  Post ReplyReply Direct Link To This Post Posted: 03 Jan 22 at 6:58pm
Wacko

changing the heights of the hook or termination on the mast obviously won't effect the moments. But it does change the forces which is of some importance to both the mast (and it's shape and structure) and the human body. 

Hook height... the further you place the hook up the body the more weight is on the feet. If you move the hook very low, you fall out backwards (or have to start tucking you feet under the gunwale). Generally I prefer a lower hook as it gives a bit more freedom to move the upper body around. 

If the hook height is very high it gets in the way, but also means more strain holding you bum up with the glutes. The same could be said for a low hook height and holding you shoulders up with your abbs (but you have shoulder straps and back support for that). 

Hook height on the mast is usually just set to the hounds as from a structural point of view its the best supported point of the mast and usually is still about full section before the mast tapers. So there is less you have to do to the mast to modify it to carry one or more sailors. 

What is also noticeable on the 800 with the equalisation it that as the racks go out the wires pull you inwards more. So you generally have more load on your feet. The negative is it's noticeably harder pointing your toes. But on the positive side when the boat comes on top you can have more heel before you start to swing away from the hull. 

Most 800 set their rigs up the same (or attempt to). Initially this makes a lots of sense as there isn't much variance in righting moment or all up weight so the theoretical fastest set up for all would be the same. But that lien of thinking doesn't account for how the varying body sizes load the rig and from which angle.  First of all the heavier sailors will put more compression in to the rig (duhh they're heavier) which means their windward shroud starts to flap around sooner. Lighter sailors will produce less compression, but also their wires pull more sideways. 

This creates a bit of a catch 22, where 800 sailors who are very light might be able to run less tension as they are unlikely to get the windward shroud flapping, and they will get little extra compression due to body weight on the wires which can leave the rig over straight and have them feeling over powered, despite the equalisation system giving them the same RM.  Whereas the bigger sailors might end up with flappy shrouds, which means they are getting more mast compression and more mast bend making their rig feel less powerful. Those problems are eventuated the further outside the weight range. The answer would be adjustable spreaders to get the correct mast curve with varying tension, but the spreaders are fixed. 

Interesting stuff, I think. But I don't want to derail the enthralling discussion about whether hook height changes the righting moment. 


Edited by Mozzy - 03 Jan 22 at 7:09pm
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Post Options Post Options   Quote KazRob Quote  Post ReplyReply Direct Link To This Post Posted: 03 Jan 22 at 7:05pm
Perhaps another way to look at it is a hybrid between a sliding seat and a trapeze. Imagine a model yacht with a plank pivoted at the gunwhale, and held up by a wire connected somewhere up the mast (or for that matter a structure on the boat). Moveable ballast (i.e. the sailor) is simply a weight which can be fitted to the plank at a single point equivalent to the full size sailors CoG. The total righting moment provided by this is only a function of the weight and where it is along the plank and not where the supporting wire is attached. The closer to the pivot point the wire attaches, the higher the vertical reaction load at that point. The further out the wire, the less the vertical reaction load has to be to remain in balance.

i.e. 2m long weightless plank fitted 100mm out from boat CL with a 1kg weight at it's midpoint. For static equilibrium we need the sum of the moments around the boat CL to be zero. Assume the wind load balances the heeling load perfectly and the boat heels around it's CL to simplify things. 
Moment from weight around hull CL =1000+100 * 1kg * 9.81N/kg = 10791Nmm
To balance this we need a vertical reaction to this 
  1. Wire at +100mm from pivot requires Sum of moments must equal zero so vertical load = 10791Nmm/(100mm+100mm) = 53N = 5.5kg
  2. Wire at +1000mm from pivot (ie at CoG) requires Sum of moments must equal zero so vertical load = 10791Nmm/(100mm+1000mm) = 9.81N = 1kg
  3. Wire at +2000mm from pivot requires Sum of moments must equal zero so vertical load = 10791Nmm/(100mm+2000mm) = 5.14N = 0.52kg
If the sideways force from teh sail acting around the hull buoyancy is not in balance the boat will heel one way or the other. 

The actual load in the supporting wire will depend on the angle it attaches to the plank. As wire can only take tension loads, the tension will vary inversely with the cosine of the angle between vertical and the wire. Wire vertically above connection point (0deg, cos =1, load = vertical reaction force); wire at 45deg to vertical (cos = 0.707, load = 1.41x vertical reaction force); wire at 60deg to vertical (cos = 0.5, vertical load = 2x vertical reaction load).

On teh question of why does the windward shroud go slack when trapezeing, the answer is in two parts. The load on the trapeze wire takes some load of the shroud and may be enought o take all the load off it. There is also a substantial downward load that may increase bend in the mast through column buckling, reducing it's length and taking tension off the shroud


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