The advantage of a dinghy trapeze: a bit of maths (or is it physics?)

Greenheart

Greenheart

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A simple question that's been bothering me since about 1985...

...how substantially does it increase a dinghy's righting moment, to shift the weight of oneself (parked on the gunwale), outboard until one is trapezing? Is there a formula for calculating the advantage?

I suppose it relates to the boat's beam, and one's tallness, more than stoutness. I can only make changes to the latter. :(

Isn't there a fairly simple guide, eg, 100 kilos sitting on the sidedeck equals 75 kilos 'standing' horizontally on the gunwale?

Most interested to read any observations/calculations. :)
 
As a simple mechanics problem in SI units, you can simply multiply mass in kg by distance from the pivot in metres to get the moment.

Obviously the real world is a bit more complex, partly because you have the dynamic forces as the whole thing moves about, because your weight doesn't all act at a single point, and also because you don't have a fixed pivot to measure from but some combination of buoyancy, centre of gravity, etc. But to a first approximation, it's just distance times weight. Getting twice as fat will have the same effect as moving twice as far outboard.

Pete
 
prv said:
As a simple mechanics problem in SI units, you can simply multiply mass in kg by distance from the pivot in metres to get the moment.

Obviously the real world is a bit more complex, partly because you have the dynamic forces as the whole thing moves about, because your weight doesn't all act at a single point, and also because you don't have a fixed pivot to measure from but some combination of buoyancy, centre of gravity, etc. But to a first approximation, it's just distance times weight. Getting twice as fat will have the same effect as moving twice as far outboard.

Pete
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Not quite. The total all up weight of the boat + crew will be more. And it will require more force to push it through the water.

Just getting more righting moment by going out on the trapeze for the same weight gives you an advantage as you can carry more sail, hence have more force to push you through/over the water for the same all up weight.

So lay of the choccies, and get a trapeze......
 
Speaking from personal experience, trapezing is less effective if your bracing foot slips and you swing in a graceful arc round the bow and into the briny. This inevitably results in a capsize: partly because the weight is transferred from a helpful to a harmful position, but mostly because the helmsman is laughing his silly head off and becomes incapable of exercising any effective control over the vessel.
 
michaelchapman said:
...lay off the choccies, and get a trapeze......
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I never doubted that was the best strategy. Just wondering how my recent loss of two stone (14kg) will have diminished my power to right an average dinghy...and how much more effective 70 KG will be on the wire, than it would have been, leaning off the side-deck. :rolleyes:
 
benjenbav said:
Speaking from personal experience, trapezing is less effective if your bracing foot slips and you swing in a graceful arc round the bow and into the briny. This inevitably results in a capsize: partly because the weight is transferred from a helpful to a harmful position, but mostly because the helmsman is laughing his silly head off and becomes incapable of exercising any effective control over the vessel.
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+1!
 
I am no mathematician, but does the fact that a proportion of your weight on the trapeze is acting high up on the mast rather than just on the side-deck not have some bearing on the question?
 
Leighb said:
I am no mathematician, but does the fact that a proportion of your weight on the trapeze is acting high up on the mast rather than just on the side-deck not have some bearing on the question?
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No. A sliding plank of negligible weight would work the same.
 
I'll try my basic logic and be prepared to be put in the corner of shame for schoolboy errors...

A simple moment is derived from a force (or vector to be precise) F * distance x... it is this 'x' component you are changing by hanging out on the trapeze. For simplicity's sake, if you take your crown jewels as being the centre of mass in your body, then the moment arm when sitting on the gunwhale is your mass (F) * 'x'... ('x' being the distance of said crown jewels from the centreline of the boat to keep things simple). Out on the trapeze you would have F * ('x' + the additional distance your crown jewels are from their original position)... the link above shows you how to calculate a moment when things are not perpendicular.
 
If the dinghy had a beam of say 1.5m and sitting out you could get your centre of gravity 0.3m outside the gunwhale (by using toestraps) then the distance from the centreline of the boat to your centre of gravity would be 1.5/2 + 0.3 = 1.05m.

If you are 1.8m tall with your feet on the gunwale using a trapeze with your body horizontal and your centre of gravity half way up your height, then the distance from the centre of the boat to your centre of gravity is 1.5/2 + 1.8/2 = 1.65m. So you have increased your contribution to the righting moment by about 60%.

Lots of high performance dinghies these days have racks or wings for the crew to trapeze from so that their feet are further from the centreline to maximise the righting moment.
 
prv said:
... because your weight doesn't all act at a single point, ...
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Except that when on a trapeze your weight will act at the point of attachment of the wire, assuming that your feet only press horizontally on the gunwale.

Normally your weight would act through your centre of gravity, which is where you would dangle if suspended. This may be where it is most comfortable to put the trapeze harness - I've never worn one!

Mike.
 
mjcoon said:
Except that when on a trapeze your weight will act at the point of attachment of the wire, assuming that your feet only press horizontally on the gunwale.

Normally your weight would act through your centre of gravity, which is where you would dangle if suspended. This may be where it is most comfortable to put the trapeze harness - I've never worn one!

Mike.
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More confortable slightly above your centre of gravity. Then you will tend to pivot feet downwards rather than feet upwards. This way is more natural - also generally you will not be quite horizontal - but a little above. In this way you have some force pushing onto your feet so you don't just float around the forestay.......
 
If you want to know all about righting moment, sail carrying power and the like settle down with a copy of "High Perfomance Sailing" by Frank Bethwaite.

We never did the sums, but we always reckoned that 3 big lads on our 18 was a lot more righting moment than a pesky keel dangling under a yacht somewhere! Nice and flat too (talented driver obviously...;))

5147757553_208c5e8da5.jpg


This boat was one of the later Murray 18 "one designs"...the old GP 18s were so wide that they had "tacking" wings...the leeward wing was raised when the crew weight was on the windward wing. And Frank Bethwaite's son, Julian, (designer of the 49er) also experimented with going super wide, and going to two crew rather than three...plan being losing 90kg out the boat and substituting it for righting moment was bound to be faster! I can tell you that even with 3 of you an 18 is a busy place to be!
 
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Iain C said:
If you want to know all about righting moment, sail carrying power and the like settle down with a copy of "High Perfomance Sailing" by Frank Bethwaite.

We never did the sums, but we always reckoned that 3 big lads on our 18 was a lot more righting moment than a pesky keel dangling under a yacht somewhere! Nice and flat too (talented driver obviously...;))
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In the keel of my yacht I have a lump of lead of 13 tons 2.4m under the surface of the water.

Those may be big lads, but they are nowhere near 13 tons and nowhere near 2.4m!!!!
 
The biggest difference is if the dinghy in question was designed and had the sails cut for trapeze use. The extra weight of a bloke on a trapeze greatly effects the mast bending characteristics and resulting sail shape.
 
Michaelchapman...it goes a bit deeper than that ('scuse the pun!). When your yacht is flat, your keel is giving zero righting moment. RM will increase with heel...this is basically why canting keel boats were invented...all the weight becomes RM rather than simply dead weight underneath you. 3 chunky lads a long way off the centreline of a very flat boat is a lot of RM...whilst your keel is pretty extreme at 13 tons I'd be interested how the RM of an average sized AWB with only 25 degrees of heel heading upwind compares to us!

Fishermantwo...I disagree. Take an old school trapeze boat like a Fireball. The only mast support is the jib luff wire, the shrouds working in conjunction with he spreaders, and something at mast gate level (chocks or strut). There is very little difference in mast shape when the crew hits the wire...Cunningham and kicker will affect the bend far more. Also factored in would initial rig settings for the wind conditions, in terms of rake, pre-bend, tension, and spreader length and sweep...all of which are not really changed on the water and are tiny, incremental tweaks, and may not be possible on some classes (49ers have fixed spreaders for example)

For example, there is very little difference in cut between a Fireball (trapeze) main and a Phantom (hiker)...in fact they are almost interchangeable. If a dinghy sail is getting pulled out of shape when the crew hits the wire, on all classes I am familiar with there is something badly wrong with the setup...most likely insufficient rig tension.
 
johnalison said:
No. A sliding plank of negligible weight would work the same.
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I don't think that is entirely correct - the weight on the mast changes the shape of the mast and therefore sail too.

I always found it best to get someone on the wire ASAP - even if the other sat well inboard
 
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