# GZ characteristic curve on a model vessel - Help!

Discussion in 'Stability' started by mallia.s, Mar 11, 2010.

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### mallia.sJunior Member

HI all,

I am working on a project and am required to extract the GZ curve of a model replica of an existing fishing boat

The real boat weighs 2600kg, displaces 2.54m^3 water, length 6.7m (salt water - 1025kg/m3)

The replica is 1:14 scale - measuring 0.479m. (fresh water - 1000kg/m3)

How should I calculate the displacement of the replica? [If you had to divide the mass by 14, it results in 185kg! ... not very realistic I suppose!] Do I need to divide something qubed (^3)?

steve

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### Perm StressSenior Member

Weight scale as (scale)^3, area, as (scale)^2

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### Perm StressSenior Member

This mean , weight of model have to be 14^3=2774 times less as prototype. 2600/2774=~0.95kg

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### mallia.sJunior Member

Please correct me if I am wrong.

weight must be ^3 since as density = mass/volume, and since volume must be also scaled by 14^3, this is directly proportional to mass [ mass (dir. prop) vol.const ] in which case, the constant is the varying density from salt to fresh water.

And

the reason volume has to be ^3 in the first place, since for a simple 3d shape such as an oblong, as the 3 individual dimensions (L, B, H) must be scaled individually.

Hence, for a complex shape - hull form, the volume is scaled in qubed proportion.

Thanks

steve

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### Perm StressSenior Member

Yes, volume scales as Scale^3, while density remain the same.
And yes, because 3D object has 3 dimensions, and each of them is scaled M times, volume (and consequently, weight) will be scaled M^3 times.

It easy to prove mathematically, with 3D Integrals, if there is sufficient familiarity with this sort of mathematics.
Or physically, using same 3D shapes of different scale from the same material: modeling clay, wood, lead (easy to cast), or even buckets of similar shape, but different size, filled with water.

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### mallia.sJunior Member

Indeed it has to be proved by integration

regards

steve

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### jehardimanSenior Member

As a point, you understand that the GZ curve you get from the model will not be the same as the real vessel, but also well be off due to scale effects, it will have ~1/14 the scaled stability of the real vessel (i.e. ~ 1/14^2)?

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### Perm StressSenior Member

Because GZ is a linear parameter, (measured in m), it will scale the same as 1/14. Then the only issue left is the accuracy of measurements, as all the errors and inaccuracies will multiply by 14 when recalculated to full size.

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### jehardimanSenior Member

Ok, BM tracks scale, but I seem to recall a scale factor issue as to why scale models are not used for stability.Maybe I need to dig out Bhattacharyya as it might be a dynamic factor as opposed to the static ones.

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### Perm StressSenior Member

One of the issues I know is the surface tension effects. For ~1m model it has a measurable (in the order of 0.5% if I recall correctly) influence. One more thing could be of importance -accuracy of actual CG location in the model.

However, main issue I think is it actually much simpler and cheaper to use calculations.

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### jehardimanSenior Member

No, you need the models to get the added mass matrix for dynamic stabilities in the seakeeping problem. Testing at NSWCCD is done in the Maneuvering And Sea Keeping (MASK) tank there. I'll need to dig out my notes for what does, and does not, simply scale. I know the periods observed in the models are all off the scale factors as are wind loads, which is why I got confused with GZ. Give me a day or two to look it up, I think there is a table somewhere that shows how they scale.

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### Perm StressSenior Member

An original post was about GZ curve, i.e. a static stability diagram. For this one, only overall weight and position of CG is important, no matter by what distribution of mass.

Of course, for dynamics, like rolling, sea-keeping, maneuvering, all the mass distribution characteristics became important and need to be modeled correctly.

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### mallia.sJunior Member

Hi,

actually what I think is of utmost importance, is that the vessel heels about the centre of floatation. Ballast weight will be added as necessary to ensure that the vessel achieves the scaled draught, thus to mimic the same displacement, in a scaled manner.

thanks

steve

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### Perm StressSenior Member

It also important to mimic location of CG accurately. If longitudinal location of CG will be off, slight difference in trim will alter water-plane properties, and consequently, stability characteristics. This inaccuracy is generally not that much for small trim (in the order of 1-2 %), but still something to be avoided.

What is more important, is vertical position of CG. If VCG is off, all the righting levers will be also off.
It depend on how much loading conditions you need to explore. If there are only 2-3 load cases, it is more time-efficient to mimic displacement, LCG and VCG accurately for each of them and make series of inclinings for every load case. If there are tens of load cases, it is more efficient to make some series of inclining tests, extract hull form stability parameters from them, and do the rest of work by normal stability calculation routine.

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### mallia.sJunior Member

I would only require 1 load case, that of the vessel and equipment on board. I presume that finding the right position for the vertical centre of gravity is going to be the most time consuming pain in the *** procedure!

Any ideas to how this can be done effectively for the model?

thanks

steve

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