Clarity wanted: heavy vs light

2 identical 50ft catamarans in shape and form (theoretical of course)

One weighs 10000 kg
One weighs 20000 kg

Both have sufficient sail area up to do 10knts in 20knts true

Sudden sustained gust to 40knts/60knts/80knts.

Which one gets in to trouble first?

I assume it is the lighter one but it isn't immediately obvious to me.

The lighter cat has half the RM but is probably carrying less than half the sail area (and has less whetted surface area).
From 20 to 40knts the wind power increases 8 fold for both cats. The lighter cat will accelerate quicker to respond and while in some circumstances that might be a blessing, in others it is likely a curse. It is also more likely to react quicker to lift the hull.

Am I totally off base? Am I missing anything (apart from a NA education and the actual knowledge to truly understand this )?

Thanks!

 

Without the two sail plans being specified, how could you make a calculation ?

 

Would you need more than twice the propulsive power and sail area for twice the displacement?

 

GJ,

There are too many undefined variables to say which boat gets "in to trouble" first.
However, given that they'll only do half the wind speed, I'd say neither!

 

BlueBell is correct here, way too many unknowns. You have to do all the hydrostatic and hydro/aerodynamic stability calculations because a 10K cat on 50 ft Loa is an entirely different shape than a 20K cat on 50 ft Loa ( assuming good general practice). Also, as pointed out, the sail area and hull parameters to get "10knts in 20knts true" depends totally on heading. Upwind or downwind, STW, SOG and VMG are radically different things.

 

The usual rule of thumb is that the forces scale by the square of the speed, giving a factor of 4 (not 8).

 

Isn't the real problem the resultant seas from 80 knot winds?

And then isn't is also relevant that you want the faster hull to keep you from 80 knot winds?

And, in an 80 knot wind, you are either running engines or nothing, so the heavier boat requires more engines and more fuel in all cases; perhaps save downwind, but I doubt even that.

The question reminds me of the classic event of trying to outrun hurricanes in a sailboat. And it is not advised because the winds can die. (Heavier vessel is assumed slower). And then when the shtf, neither vessel can safely sail, bit the lighter one may have made port.

If both vessels are equivalently seaworthy in 80 knot stew, I choose the faster vessel under sail and power because I don't want an 80 knot experience.

This is the non-sailor's perspective.

Do be kind!

 

Wow, thanks for all the replies!

To start with the sail plan from Mr Efficiency:
You are right in that the sailplan specifics are probably needed to calculate the CoE for each (and the fact that a smaller sail area would result in a lower CoE is something that I'd temporarily forgotten).

Propulsive power for twice the weight:
My rough guess would come from the SA/D formula which would mean disp in cubic feet to 2/3 power (which would result in about 1.6 times the sail area). This is probably flawed and someone will probably be along shortly to correct me.

Not getting in to trouble when doing half wind speed:
Quite possible. But I wanted to pick a realistic boat speed for a very heavy 50ft cat carrying a fair amount of sail and a very light cat deliberately slowing itself down. This is obviously just a thought experiment to improve on my knowledge and hopefully discuss the pros and cons of going light vs going heavy. (One aspect admittedly).

Too many undefined variables:
Pick a design you have or know really well and fill them in. As I said, imagine all other things are identical. Boom above water height, windage, hull profile (admittedly to be accurate for genuine polars you'd need things like submersion under load but I am not sure how relevant it would be for this calculation). Then compare. I would hope those with the correct formulas for these things might be able to cancel things out when comparing or make notes on assumptions. Just take a cat of 10K kgs weight and big rig and work out sail area for 10 kts in 20 kts true (45deg, 90deg, & 135deg) and then do the same when adding an unrealistic 10K payload. Ignore submersion and windage changes if you like. Also assume the same Centre of Mass and Centre of Buoyancy.

jehardiman:
I agree you'd design them differently (and I am not belittling the analysis and thought process that would go into it) but do you think they would react so differently that you can't make some assumptions in the interest of investigation? Are you saying you can't work out the rough stability curve of a catamaran without a full hydrostatic analysis? (This may be true but I would be surprised).

Power only 4 not 8 times:
Thank you Doug, I mistakenly thought it would be based on the volume of air hitting the sail and thought 'volume' = 'cube'. Happy to be corrected.

Fallguy:
You are probably right about the real danger of sustained 80kts but this is more about sudden freak 40 to 80 knot bursts that have been know to trouble catamarans. I was trying to work out if all you ever wanted to do was sail at 10kts in 20kts+ wind, whether you'd be safer in a lighter cat or heavier cat. I didn't want to mention that as it is more likely to send the topic into another area (cats don't flip, have your hand on the sheets, upsideup, go bigger, go mono blah blah).

Thanks again everyone. I'd love it if someone actually posted a formula that you might use to calculate the stability. Feel free to make any reasonable assumptions. CoE 70% height for lighter cat, start at 4m for boom height, that kind of thing. If it is too much work then feel free to just give me your gut feeling!

 

Okay, with all that said then I'm going to say, generally speaking, the lighter one "gets in to trouble first".
But, for the record, I don't think it a reasonable, or even productive, question.

It's a hypothetical question, right.
So, my decision is based on identical boats but one is twice the weight.
If they are identical, then one is much heavier built than the other.
Presumably it is then much stronger...

The harder I try to answer your query, the more I don't like it.
It also depends on what "gets in to trouble" means.
Breaking? Dismasting? Flipping?

 

I was thinking flipping more than breaking.

It was supposed to be more about righting moment and stability than things breaking. That isn't to say the rest aren't important but then you would need to get into build strengths and loads and all that other good stuff.

There's a lot of speculation on other forums about some capsizes of cruiser/performance based cats that encountered freak winds. That is what started my train of thought and I was hoping the people here would be more knowledgable but didn't want to use boat or incident specifics for the conversation as that often causes situation specific thread drift so I tried to eliminate what I could from the question.

I was curious if a heavy boat, doing similar speed in the same conditions, might have had the same problems.

Thanks for your honesty.

 

Kind of like a catamaran that is once build out of light composite and then build with aluminium or steel? Hull form and sail adjusted but otherwise the same model.

I've looked at a paper once where they did that for cost analysis, seemed like a big effort.

I think somewhere along their training marine architects undergo conditioning to hate hypothetical questions Or maybe it just happens naturally once you go down the rabbit hole of constantly going around your design choices and adjusting them to fit an SOR.

PS: This one Does it pay to play with the construction material of a sailing yacht - Balasz@hiswasymposium-2006

 

It should not be too hard to work this out, just calculate the resistance curves for both boats, and if the extra sail area required on the heavy boat, to get similar performance, is out of proportion to the weight ratio of the two boats, it will mean the lighter boat will be more resistant to being "blown over".

 

Correct, but not very relevant. And for apparent wind, not true wind. Notice that propulsive power is force times boatspeed, not force times apparent windspeed, end therefore propulsive power does not scale the same as wind power.

Correct. But force is not the same thing as wind power and they do not scale the same.

 

If both are cruising types with bridgedeck with full headroom, the lighter can tolerate much higher gust before lifting a hull than the heavier one.

In upwind mode, the lighter cat has relatively more windage and less hull drag, and a gust will cause a greater increase in windage, thus it will not accelerate much more than the heavier one. The less under rigged it initially sails, the more likely it becomes that it can even accelerate less than the heavier cat. Apparent windspeeds therefore remain in the same magnitude for both boats, but the lighter one has lower CofE and less sail area, product of those is a smaller fraction of the heavier one that for the righting moment.

Downwind the windage is almost insignificant or help the lighter one accelerate even more, allowing it to reduce apparent compared to the heavier one by going faster. thus it's again the heavier one that lifts a hull first. But perhaps more importantly, the heavier one with the same free board will dip it's nose under first and is far more likely to pitchpole. The lighter one has a much higher longitudinal GM than the heavier one and also tolerates more bow down trim angle without dipping.

On a beam reach it's possible that the lighter one looses it's advantage, and gets overpowered sooner, because it will have more apparent by going much faster.

In real world of course the freeboards can be different, higher for the heavier cat, but you asked to compare the cats with similar dimensions and similar windage.

 

fastsailing:
You sir, are a hero. Precisely the response I was after. And loads in there I wouldn't have guessed but makes total sense.