# Metacentric height



## jim garnett

I know this calculation is done during commissioning;however is there any requirement for it to be done at regular intervals.A cruise passenger recently told me they were held up in Sydney on one of the Princess line ships before the cruise started for some tests,which from her description seem to be a re-calibration of the meta-centric height.They were given a refund and offered a substantial discount for a future trip of their choosing.As an ex chief engineer who only knew enough about meta-centric height to scrape through the Naval architecture part of the chief's ticket.Can any one enlighten me?
Jim Garnett


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## Pat Thompson

Greetings,

The initial position of the metacentre is calculated using the inclining experiment, this would be part of the build. It is carried out through the ship's life if significant changes to the distributed permanent weight.

The position of the centre of gravity of the ship should be calculated for every departure condition and the corresponding arrival condition to ensure the ship maintains adequate stability for the intended voyage.

GM, the measure of statical stability is the differrence between "G" the height of the centre of gravity above the keel, or KG.

"M" the position of the metacentre above the keel "KM" as deduced from the last and declared in the Stability Book for the ship inclining experiment.

The difference between KG and KM is the GM the measure of stability. The larger the GM the stiffer the ship, the smaller the GM the more tender the ship as GM defines the size of the righting lever if the ship is inclined by an external force.

Some ships have a set of tanks specifically for the rapid transfer of liquid transversly within the ship which effectively carries out an inclining experiment for the current condition which allows the results from the stability computer to be verified. My only experience of a ship so fitted was RFA Reliant (3), formerly MV Astronomer (Harrisons) but she was in dockyard (Camell Lairds) hands for the conversion for the entire period so I was unable to use the facility


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## John Cassels

Thought GZ was the measure of statical stability !.

Also , to complete the inclining test ,the position of M must be known and this
found from the position of C of B.


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## CodyW

Isn't GZ the righting lever?


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## John Cassels

CodyW said:


> Isn't GZ the righting lever?


Yup , also known as the righting lever.


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## Pilot mac

really stretching thr grey matter here, its been a long time! If a vessel becomes bilged like for example the Costa, and the deck edge becomes immersed then 'M' shifts (BM = I/V). The shift of M plus additional weights and free surface moments thus created may well make a previously stable ship unstable.
Again stretching the grey matter, I thought passenger ships had to be fitted with a system of cross flooding to at least allow them to sink bodily and allow the lifeboats to be launched as well as preventing deck edge immersion. I may well be wrong its 30 years since Master FG !

Dave


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## makko

I remember when I was still in school going along with my Dad (Marine Lecturer at B'head Tech.) and a group of Eng. Cadets on a visit to Cammell Lairds. An interesting part was going onto a vessel in the wet basin which was undergoing GM-GZ calculation. They had welded some tracks across the deck upon which was mounted a small, flat railway type wagon. Onto this were mounted concrete blocks and the wagon rolled from side to side in order to measure the inclination at varying draughts. The whole concept fascinated me, that is why I haven't forgotten it! I remember my Dad saying,"It's been doon the same way since the Middle Ages". When at sea, I used to go up to the bridge and "Keep my hand in" shadowing the OOW's GZ calc.
Pure Nostalgia!
Rgds.
Dave


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## jim garnett

thanks for all the above.I understand how important it is in loading of cargo vessels but i'm still mystified as to why it would be suddenly found necessary to re-calibrate it on a cruise ship at a time when it interrupted it's scheduled sailing.
I still have my old Hogg's " Naval architecture and ship construction"published in 1942 reprinted in 1950 two years before I bought it and the explanation of metacentric height has not changed a bit since then apparently.


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## makko

Well Jim, see my Dad's comment! I suppose it would be like general cargo and its "density" - Other than that, I don't know!
Rgds.
Dave


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## uisdean mor

Jim 
Pure guess work BUT other than the vessel actually having some repair/modification and hence a need to recalibrate - then it may have been necessary due to sailing conditions. 

For instance - was it to be a short crossing was the vessel "pressed" or light ship, were there a full compliment of passengers/crew ( cargo after all) . Particularly re cruising was the water on board in several or just a few tanks and how much. 

Really a bit of stab in the dark. The vessel may have had an on board computer which took all these variables into account and the officers were alerted to a possible issue and a decision then made that the test had to be carried out.


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## CAPTAIN JEREMY

jim garnett said:


> I know this calculation is done during commissioning;however is there any requirement for it to be done at regular intervals.A cruise passenger recently told me they were held up in Sydney on one of the Princess line ships before the cruise started for some tests,which from her description seem to be a re-calibration of the meta-centric height.They were given a refund and offered a substantial discount for a future trip of their choosing.As an ex chief engineer who only knew enough about meta-centric height to scrape through the Naval architecture part of the chief's ticket.Can any one enlighten me?
> Jim Garnett


For passenger ships, they have to have a lightweight survey every 5 years.

If there is found to be a deviation of 2% from the original lightweight, or a deviation of 1% in the longitudinal centre of gravity, another inclining experiment must be carried out.


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## Michal-S

For some container vessels, according to company manuals, pre-departure GM check has to be performed every time, utilising anti-heeling system. Gangway has to be hoisted and ropes slackened at the time of such brief heeling experiment. On some vessels the procedure is fully automatic-transfer of ballast water and calculations are done after just pressing the button on computer keyboard.


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## John Cassels

How can one do a roll period test using ballast ?.


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## NoR

For those of us who wish to undertake a refresher in 'stability' here is an American online study site.


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## Pilot mac

Michal/JC, never come across this system but I guess it pumps a definate mass of water to a specific tank and the resultant heel measured, this should enable you to calculate your KG (or I think it should). In theory a great idea to give you the comfort and ease of finding your stability prior to sailing, never very satisfactory in my time on container ships having to rely on shore weights! I cant remember how many times I've let go and thought I dont like the feel of this, time to put some ballast in.

Dave


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## Michal-S

Hello again, exactly-the amount of water to be transferred is pre-determined, lateral distance between tanks' centres of gravity (the lever) is known, actual displacement is input fom draught sensors (or manually), same for water density. Thence coming the formula tangent of heeling angle equals to (mass multiplied by lever) and divided by (displacement multiplied by GM). Converting it:
GM equals to (mass multiplied by lever) divided by (tangent of heeling angle multiplied by displacement). True, of course, for relatively small angles of heeling but there should not be more than 3-5 degrees during the test. Helps you sleep better when at sea


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## CAPTAIN JEREMY

Ineteresting. In my time on container ships, the heeling tanks for keeping the ship upright were a closed system so you were just moving water laterally. At the end of the operation, the mean C of G of the two heeling tanks would be the same as before. Surely the issue is not about moving the ballast from one side to another, but the addition or removal of weights that caused the change in the angle of list.


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## John Cassels

For a proper rolling period test to estimated , ballast cannot be used.

It must be an addition of weight placed on the vessel and then removed , 
therefore keeping the displacement the same .
Also there is no way to suddenly introduce an amount of water to initiate a
roll in the first place.


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## Michal-S

Ballast water transferred from side to side (laterally) can be used for heeling test same way as adding and removing weights. it is done, similarly, in the shipyard during inclining experiments when known weights (solids) are transferred on board to determine CoG of the vessel (same calculations apply).
For all in doubt, let's consider the case (with ballast water):
vessel with displacement of 20000 tonnes, transferring 50 tonnes of ballast water laterally from tank with TCG (transverse centre of gravity) of +13 metres(SB) to tank with TCG of -13 metres (PS), i.e. heeling lever equals to 26 metres. Resulting heeling angle is 2 degrees (tangent 2=0.035). From formula quoted in my previous post one can obtain easily GM of value, approx. 1.86 m. It is not black magic or anything, isn't it?


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## Koymann

I think maybe what has happend here is that Sydney is one of the ports, among many others that demands an compleet stability calculation on the table uppon departure without, the ship is simply held back until the officer in charge of the calculations has produced one. Normaly this is all done on an computer, but i have been in ports where auto soundings of tanks have had to be checked mannualy and compared, all this things takes time and depending on the port autorities the ship may as a result be delayed.


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