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Mozzy Sails

Calculating Righting Moment (trapeze)

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What calculation do you need to do, to give the effective righting moment of a crew on trapeze. Kg/m or Newton-meters. 

What base information do you need for the calculation? The height of a persons centre of gravity, their mass, and the distance of their feet from the centre line?

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If the boat does not capsize, you have enough RM. ( sorry, I just could not resist ). I can imagine that the calculations are VERY involved. Maybe too many variables. Happy Sailing. 

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It's easy. In most cases it's just the distance of the centre of mass of the crew from the centreline of the boat, multiplied by their weight.

Assuming you can bounce on the gunwhale/rack while trapezing, your centre of mass is pretty close to your trapeze hook, so measure the distance from that to the ground when you're standing up straight, and add half of the boat's beam to get the distance.

It's a bit more complicated if you're sailing a cat (measure windward gunwhale/rack to centre of leeward hull), sail with a lot of heel (you're going to have to estimate where the centre of buoyancy of the boat is) or sail a foiler (horizontal distance from rack to a point directly above the centre of the foil at whatever angle of heel you're sailing), but for the vast majority of monohull trapeze dinghies, the centreline of the boat is close enough.

Edit: For a hiking crew, the distance from where your trapeze hook would be to the centreline of the boat will be pretty close, assuming you're hiking hard.

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39 minutes ago, Dave S said:

It's easy. In most cases it's just the distance of the centre of mass of the crew from the centreline of the boat, multiplied by their weight.

Assuming you can bounce on the gunwhale/rack while trapezing, your centre of mass is pretty close to your trapeze hook, so measure the distance from that to the ground when you're standing up straight, and add half of the boat's beam to get the distance.

It's a bit more complicated if you're sailing a cat (measure windward gunwhale/rack to centre of leeward hull), sail with a lot of heel (you're going to have to estimate where the centre of buoyancy of the boat is) or sail a foiler (horizontal distance from rack to a point directly above the centre of the foil at whatever angle of heel you're sailing), but for the vast majority of monohull trapeze dinghies, the centreline of the boat is close enough.

Edit: For a hiking crew, the distance from where your trapeze hook would be to the centreline of the boat will be pretty close, assuming you're hiking hard.

I’ve always thought that would be the case, so why do some trap crew lift their arms out over their head?

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16 minutes ago, Raz'r said:

I’ve always thought that would be the case, so why do some trap crew lift their arms out over their head?

to increase the height of their CoG?

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Thanks Dave

Our class has weight and leverage equalisation. The weight equalisation is easy to grasp, but the leverage compensation has a large matrix, with combined crew weigh on one axis, and combined crew leverage (measured off a plank on the other). From this you read off a rack setting. It seems to work well in practice, but I've always wanted to test for myself mathematically, how close the system is to theoretically matched. 

The only info I have for sailors is weight, and their righting moment (measured on a plank). Scales under a plank, feet at the pivot, to give KG/m. 

Can I divide their kg/m by their weight to give me their CoG in metres? 

I need to calculate the distance from centre line of the minimum rack setting, then the intervals of adjustment. This, combined with their individual CoG will give me the distance from the centilitre where their weight is on the lever arm. 

I then add the beam (plus rack setting,) to their CoG height and multiply by their weight to give me righting moment for each crew member, on their given rack setting in kg/m?

If the system is working they should all end up with pretty close kg/m values after rack equalisation... fingers crossed. 

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Just now, Raz'r said:

I’ve always thought that would be the case, so why do some trap crew lift their arms out over their head?

That will move your centre of mass a bit; the increase in righting moment will be approximately the weight of your arm multiplied by the distance it moves (roughly twice the distance from your shoulder to your elbow).

Let's put some numbers in this to make it a bit more real. Take the example of two 6' tall 85Kg sailors in an Int14 (180cm wide).

Height of trapeze hook 108cm (I'm 6' tall, just measured myself), so total lever arm is 108+180/2 = 198cm. On Earth, multiply mass in Kg by 9.8 to get weight in N

Righting moment of 2 crew = 2 x 85 x 9.8 x 1.98 ~= 3,299 Nm

Weight of an arm according to Google is ~5% of total body weight. I've just measured the distance between my shoulder and elbow to be ~30cm. So if one crew moves an arm from their side to above their head, increase in righting moment is:

0.05 x 85 x 9.8 x 0.3 x 2 ~= 25Nm

That's a 0.7% increase in righting moment, so we're into marginal gains territory. Every little helps, but you might be better off doing something useful with that arm, like steering or trimming something. Lowering yourself on the trapeze may help more; if you're trapezing 20 degrees above horizontal, your centre of mass will move something like 7cm closer to the boat; in the above example that will reduce your righting moment by ~117Nm. Raise yourself another 10 degrees and you lose another 124Nm, so you've lost 7% of your righting moment (or 10 arms' worth).

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3 minutes ago, Mozzy Sails said:

Our class has weight and leverage equalisation. The only info I have for sailors is weight, and their righting moment (measured on a plank). Scales under a plank, to give KG/m. 

Can I divide their kg/m by their weight to give me their CoG in metres? 

I need to calculate the distance from centre line of the minimum rack setting, then the intervals of adjustment. 

I then add the beam (plus rack setting,) to their CoG height and multiply by their weight to give me righting moment for each crew member, on their given rack setting in kg/m?

If the system is working they should all end up with pretty close kg/m values after rack equalisation... fingers crossed. 

How's the measuring plank set up? If it's done with their feet above the pivot and the scale is 1m from the pivot and measuring kg, you're effectively getting their righting moment if they trapezed off the daggerboard. If that's the case, divide righting moment by their weight to get CoG height, exactly as you say.

Thereafter, the arithmetic works just as you say.

Keeping the units in Kgm keeps things simple; no need to convert to Nm as I've done.

Note that it's Kgm, not Kg/m. You can increase the leverage by increasing either the Kg (weight) or the m (lever arm). Contrast with speed in m/s where you can increase the speed either by increasing the m (distance) or DEcreasing the s (time).

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It's actually a 2m plank, then multiply the scale reading by two to give their righting moment in kg.m.

Cool, I've done the calcs on fleet for CoG and they seem to be between 92cm and 106cm and correlate well with what I know about peoples height from walking around the dinghy park. I think these might be slightly more accurate than hook height, as hooks tend to be a little higher than CoG. Plus, as it's measured is should take in to account variation in body composition.

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Yep, that makes sense. Hook height is probably "good enough" if you're using the righting moment to estimate something like rig loads, but taking actual measurements will definitely give you better numbers, which is essential if you're using them to determine rack positions.

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The actual acting center of buoyancy is some inches or as much as a foot or more to leeward of the centerline in a trapeze dinghy. Nobody sails upright except windsurfers and hydrofoilers (and they aren't upright either but the other way...).

Boats with wide decks but narrow waterlines (505) have less of this effect. Boats with wider waterlines (FD) have more. 49er is flatter than a 505 but not sailed as heeled so effect is probably fairly small there.
 

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I think the majority do sail upright, or even heeled to windward.

Either way, for a righting moment correction you need to assume people are sailing their boats well, so that you're correcting for their theoretical optimum.

Any extra leverage people get from centre of buoyancy moving to leeward is offset by
a) a tall rig off to leeward that gives negative leverage
b) having to trapeze lower than the gunwale to get 'flat'. 
c) the rack also moving to leeward as the boat heels
d) weather helm
e) tip losses?

Anyway, here is a snapshot of the fleet equalised (blue) and the alternative scenario where everyone sails off a middle rack setting and zero lead (red).

You can see the equalised group together, where ~5 kg.m is about the difference between each rack setting, and 3 kg is the weight of each lead. So there's a bit of luck there where you fall relative to the cut offs for the settings.

Then there are six boats above the equalisation. These are sailing off rack 1, so there RM is diminished, but weight identical as they're not carrying lead (versus the notional rack 5, zero lead non equalised scenario). 

There are four boats off the bottom of the scale, who get max racks at 10, and 5 leads (15 kg). 

So where do you want to be? That depends on the sail power really. The equalisation pulls people to 151-154 kg and 297-302 kg.m. If the optimum size is in this range then you want to hit the equalisation. The variance within that cluster is very small compared to any other class I've sailed. You're talking whether the crew has drunk fluids or shit that day.

There are two boats that are off the weight equalisation light, but still putting out comparable righting movement. I think they're in a very nice spot, but the results don't back it up. So just shows there is more to it than just weight v righting moment!

Much further off the scale light and it becomes ever harder to still find the RM. I think you can get away with being on the lower side of the equalised RM (~296 kg.m) if you're also a couple of kilos lighter than the fleet. But below 290 kg.m there becomes a time that despite having less weight for the boat to carry, you start to struggle to get planning upwind. 
image.png.e2a196af9361a603460f8f28a0b4580a.png 

 

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That's quite an effective equalisation within the range. One factor you can't equalise is the impact on boat handling - a lighter crew will have further to run in tacks and gybes, and will generally have to move around more in gusts and lulls, but I should imagine the impact will be pretty small, and you can't equalise everything.

@fastyacht - I can only speak for the boats I've sailed (14s and 18s), but if you didn't have them pretty damned flat upwind and on 2-sail reaches the rudder didn't work. We did sail the 14 with a bit of heel on tight/marginal 3-sail reaches in some conditions, but I suspect sailing around with the kite up, jib flogging and main inside-out is a bit of a niche 14 thing; I don't think I've seen many other classes doing that on purpose...

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2 hours ago, Dave S said:

That's quite an effective equalisation within the range. One factor you can't equalise is the impact on boat handling - a lighter crew will have further to run in tacks and gybes, and will generally have to move around more in gusts and lulls, but I should imagine the impact will be pretty small, and you can't equalise everything.

@fastyacht - I can only speak for the boats I've sailed (14s and 18s), but if you didn't have them pretty damned flat upwind and on 2-sail reaches the rudder didn't work. We did sail the 14 with a bit of heel on tight/marginal 3-sail reaches in some conditions, but I suspect sailing around with the kite up, jib flogging and main inside-out is a bit of a niche 14 thing; I don't think I've seen many other classes doing that on purpose...

I've had my 505 main "inside out" plenty of times on a reach. Haha.

When I say "nobody sails upright" I mean the difference between onboard perception "we were dead flat" and photographic or outside evidence "5 degrees heel." This is a nearly universal thing. The shift of the buoyancy creates power and you instinctively sail the boat to its power curve. Too much heel you lose control and or slow down. But the sweet spot you find through the feedback loop.

Without a doubt the 18 and some other skiffs are special beasts and uproght is a thing there,\. Here is an example.

 

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There's a few subtle difference in boat handling and feel. It's hard to say which wins out. From personal experience I'd struggle to pick a favourite, but one thing is that it's best to turn up to the event well practised of your given setting, otherwise the boat can feel a bit alien.  

Wider racks you certainly have to move further in manoeuvres. On the flip side it means you have more intermediate locations to place yourself in light winds. You can substitute a 3 kg lead for a set of intermediary bars... rack ten it's quite a step out!

The racks also angle up, so you get a bit more free board as the racks go wider. But as the boat comes to windward in a lull that free board soon evaporates.

Being out far from the boat you really get swung around with over exuberant tiller movements. 

If you've over stood and are reaching on your ear the wider racks catch the water more.

The wider racks gives you a wider lane on the start. 

The trapeze also feels different, with narrow racks the mast is more forward of you, making trapping straight a bit harder , it feels like unless you bend your back leg you will swing forward, and puts more stress on the front leg.  Whereas the wider racks it's easier to hold a good balance.

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