# Roll Period calculation of a 1:4 scale model

Discussion in 'Stability' started by Howlandwoodworks, Dec 28, 2020.

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### HowlandwoodworksMember

Hello again,
Can I use the roll period of a 1:4 scale model for the Approximated GM Calculation?
GM=(0.44*WL Beam)/(Roll Period in Seconds)

Or a Calculated GM by Inclining Experiment?
GM=(Wt. Moved*Distance Moved* Pendulum Length)/(Disp*Pendulum Movement)

If so how would I account for the size difference?
I am working toward the transverse metacenter, GM, G, Z, B, B1 @10, B2@20, B3@30, & their GZ, etc...
My quarry is the Dellenbaugh Angle. Like I don't already know everyone on board will be climbing up the leeward side on every change of tack with a full set of sails with anything over 12 knots.

John

Last edited: Dec 28, 2020
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Is the correct/preferred way.

Like everything else related from model to ship experiments/calculations. Using the scale, or geosim size.

In this case, roll period (model) = roll period (ship) x scale^(1/2)

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### HowlandwoodworksMember

Thanks,
For this special purpose,

I have thought that the model would be a great tool but I am not inclined to build or look to buy a Mechanical Integrator at this time. If there is a simpler way to acquire the Transverse Metacenter-M through a Inclining Experiment I would be interested in that.
I think just squaring off the 10, 20 and 30 degree angle at the Heeled Center of Buoyancy of B, B1, B2, and B3 would be sufficient and cross checking that with the Approximated GM Calculation. I am only looking to acquire the M or Transverse metacenter at this time for GM.
I do appreciate the reference to the geosim size, it is a large piece of knowledge that I have been looking for.
Thanks again, I am indebted to you,
John

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### jehardimanSenior Member

Be very careful here. geosim scaling works on only complete geosims which includes force distribution. The problem when trying to scale a sailing vessel is that the ability to carry sail and the sail area do not scale the same. Generally speaking the model has only (scale factor) the apparent stiffness as the parent. This is because the righting moment is reduced by (scale factor)^3 while the sail area is only reduced by (scale factor)^2.

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John
Not 100% clear here..are you saying you are happy to proceed with doing an inclining expt on the model,
or
are you saying is there a simpler method?

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### HowlandwoodworksMember

I believe there two simpler method.
I was going to do them both and compare one to the other. (as I tried described in the third post .)
The Mechanical Integrator is a wonderful tool but way more than I will need for my one little boat.
I was going to check with some friends at the university here to see if they have one laying around but the prospect would be slim.

Maybe someone know of some simpler Mechanical Integrator for an Inclining Experiment to Calculated GM? But the prospect would be slim as I see them.

There seems to be more than one way to get to M or GM, so I will keep on looking and start with Approximated GM Calculation.

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John

It seems you're getting confused.
A Planimeter or mechanical integrator as you call it, only established a series of hydrostatics for the hull, at the given waterline. That is all.
You need the hydrostatics for the GM calculation via the inclining expt.

The mechanical integrator is a "tool" only, it is not the inclining experiment. It just provides a series of data which you use once you have inclined the vessel. Since the inclining expt is to establish the KG of the vessel - you cannot do that with just the mech integrator!. Once you have the KG from the Inc Expt, you can then establish the GM.

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### HowlandwoodworksMember

Here is this YouTube on an IncliningExperiment. It seems reasonable.

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### HowlandwoodworksMember

You be right about being confused.
I started working on the Dellenbauger angle last week.
Oh and as I think about it part of the Mechanical Integrator is Planimeter. Always want a good Planimeter.
I think I will give it a break and work on my Water Lines and Tables of Offsets at 10, 20, and 30 degrees angles for Simpsons rules for a while.

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### DCockeySenior Member

The standard use of an incline experiment is to determine KG. The experiment yields the righting moment per degree of heel. If the displacement is known GM can be calculated. If KM is known from hydrostatic calculations or otherwise then KG = KM - KG

If the the "lines" or a surface model of the vessel are available with sufficient accuracy and resolution then displacement and KM can be calculated using the lines. This is the usual situation with larger vessels. KM is thn determined using the results of an incline experiment.

For small boats or a model the weight (displacement) can be measured directly, and KG can be determined by an incline experiment in air, a tilt table or other similar methods.

If displacement and KG is known then an incline experiment can be used to determine KM. GM is established from the experiment and KM = KG + GM.

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### DCockeySenior Member

Used planimeters are available on eBay for under \$100. I assume planimeters are no longer used in most naval architecture and engineering offices, having been replaced by calculations on a computer or similar.

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### HowlandwoodworksMember

Would this be the formula for a 1:4 scale model of an Approximated GM Calculation? The width and seconds are random number.
GM=(0.44*WL Beam)/(Roll Period in Seconds) x (scale^(1/2))
0.66=(0.44*6/2)*(0.25^0.5)

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### GunawanNew Member

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### GunawanNew Member

Hi, Excuse me, I am Naval Architecture student, and I have not much knowledge about that, so may you teach me about Naval Architec? Thanks

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