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[GG]

When I started in this hobby as a naive schoolboy, my first model was based on a destroyer which looked much more interesting than my "superiors" apparent preference for cabin cruisers. After several similar and successful models (including my first forays into RC) I was told that such slim models were notoriously unstable and totally unsuitable for working models without widened beams and/or external ballast beneath the hull. This puzzled me as my models had sailed quite safely without the need for these features.


Further questioning on the topic of model boat stability resulted in rather vague answers often including the term "Metacentre".  Alas, with no clear explanation of what this mystical point actually was but if you got it in the wrong place, you were in trouble and only more beam or lower ballast would magically restore stability.


Thaumaturgy (just being reading a Discworld book and this is too good a word not to use) might appeal to some but, having a reasonable science/engineering education, I'd prefer something I could understand and use.  So, after a little research the mysteries of model boat stability were understood, at least enough to keep me out of trouble most of the time!


What follows is will hopefully give a straightforwards idea of why our models remain upright and what all those funny terms mean.  There is much more to this subject but unless you want to become a Naval Architect, it ought to be good enough for our models.


Glynn Guest

[GG]

Lets consider a model floating upright and at rest.  Gravity acting on the masses that make up the model create the Weight Force that acts downwards and can be considered as acting from a single point, called the Center of Mass.


This is countered by an equal but opposite acting force (Upthrust) generated by the water pushed out of the way by the immersed part of the hull.  This being equal to weight of the displaced water and, like the weight force acting on the hull, can be considered as acting from a single point, the Center of Bouyancy.


The section of a hull containing both these points is shown in Fig 1.  It does look somewhat unstable as, although both forces are the same size and are perfectly aligned, the slightest tilt will move them out of alignment.  This being just like balancing a pencil on its point, stable until the slightest disturbance and then it falls over!
Glynn Guest

[GG]

But, things change when a hull is tilted, or more correctly "Heeled" over to one side.  The model still needs to displace the same volume of water (who's mass equals the model) so as one side rises above the waters level, the other side is more deeply immersed.  This creating the "In-wedge" and "out-wedge" shown in Fig 2.


To keep the total volume of displaced water the same as before the volume of both wedges must be the same.  Now there is more hull volume to the right of the hull center-line which means that the Centre of Buoyancy must move to the right also, see Fig 3.  As the Buoyancy force acts vertically it now does not run along the hull center-line but cuts it at some point, this being the Metacentre!


The more the hull heels, the more the Centre of Buoyancy moves away from the center-line.  You can think of the Metacentre as the point that the Centre of Buoyancy swings about as the model rolls from side to side.
Glynn Guest

[GG]

But something hasn't changed, the hulls Centre of Mass should be in the same position as before, on the centre-line of the hull.  Or, it should be if nothing has moved inside the hull when heeled (not something you can rely upon with a few modelers...!).


Since the weight force still acts vertically downwards, it is still parallel but no longer aligned with the Buoyancy force, Fig 4.  A valuable distance is also shown, that between the Metacentre and Centre of Mass, called the Metacentric Height.

These now two misaligned forces act on the hull to rotate it back upright, Fig 5.  This is a stable system as the further the model heels, the stronger will be the restoring effect.
Glynn Guest

[GG]

The Metacentric height (often abbreviated to GM) is a good way to assess the stability of a model.  Taking the position of the Centre of Mass as the zero point on the hull's vertical center-line, then any distance above this is positive and distances below are negative.  All very logical since if the Metacentre is above the Centre of Mass you get a possitive value which is good, but below produces a negative value which is bad news, very bad news...!


A models GM can be found by simple experimentation, Fig 6.  If a model of mass "M" is heeled by placing a smaller mass "m" a distance "x" from the hulls centre-line then the angle of heel can be measured, Fig6.  Putting these values into formula shown should produce a value for GM.


Measuring the angle of heel was the most troublesome part of the exercise.  I used a protractor fitted with a small pendulum installed on the model.  Nowadays, it might be easier to photograph the model from the bows, then add the small mass "m" and rephotograph the model from the bows, then compare the two pictures.


Going back to my destroyer models which started me out on the journey, and their GM's were found to be in the range 0.3 - 0.4 inches (8 - 10 mm) which might not sound much for models with beam of 3 -3.5 inches (76 - 89 mm) but never gave me a moments worry when sailing even in some quite unscale conditions!


There was even a model based on the fast minelayer HMS Manxman, which had a GM of around 0.15 inches (4 mm), always safe to sail but it kept you on your toes!


Glynn Guest
[size=78%]  [/size]

[rcboater1]

This is a great explanation of the concept!


If you think about it, it explains why a wider vessel will be more stable-   The center of buoyancy will move farther to the right (as shown in Figure 3) with a wider hull.  The resulting GM will therefore be higher = more righting force!


Same thing goes for  adding ballast in the bottom of the narrower hull.  That lowers the center of mass, which again increases  the metacentric height.


Thanks for sharing this!

[Tug Fanatic]

Glynn

Good explanation of a fairly difficult subject but do you use it?

We know to keep weight low, make anything high up as light as possible etc. This is an explanation of why that is true but I cannot see that I can use this it to help make my models better or am I missing something?

On a different subject can we expect to continue to see your models & articles in Model Boats or does the recent flow of very good "articles" published here indicate a change? I seem to remember you replying to someone that there would not be any more models of the type that you were discussing.

[GG]

Yes Tug Fanatic, I do use it.


I've always favored understanding why things work rather joining those who believe in "magic".  You know the type who keep on repeating the same actions time and time again and expect a different outcome. 


This has proven to be very handy as I do try to work new ideas into models rather than just building basically the same thing, not that there is anything wrong in that but I'd get bored.  Sometimes these new ideas don't work as well as I hoped and so need some puzzling out.


Understanding "GM" did help me figure out why very shallow draught models can be ultra-stable, something I might pursue further in another model.


As for further contributions in "Model Boats", you could ask the Editor and see what answer you get?
Glynn Guest

[Colin Bishop]

An excellent explanation from Glynn on a subject that is not often well understood by many people.

It does lead on to some other considerations in a practical situation. Having positive stability is not always sufficient if the righting forces are small as this can make the model very 'tender' and therefore susceptible to windage. Your boat may not capsize but it could spend a lot of its time lying at a steep angle in a moderate breeze.

Not so long ago I converted the big Revell Queen Mary 2 kit to R/C. It wasn't too difficult to get it to sit at the right waterline with a small amount of lead sheet ballast in the bottom and in the test tank (bath) it was certainly stable and quickly returned to an upright position if pushed down on either side.

On the pond it was a different story however as the high superstructure  meant that it would heel in any sort of breeze.

This is not an uncommon situation when you have a lot of upperworks and, assuming you can't lose weight up aloft then there is only one practical solution. You cannot increase the ballast significantly without raising the waterline so the ballast has to move below the hull to generate adequate righting force to combat the effect of the wind above water and this means an external keel. Yachts do it all the time!

The photo below shows what was needed for QM2. The ballast weights are door handle bars. Two are stuck to the bottom of the hull at the sides with some more in an adjustable frame amidships. They can't be seen when the model is afloat and keep it upright in most situations.

Colin

[Tug Fanatic]

Glynn
I was not implying a criticism as I also like to understand what is going on & why. How do you get the data for practical implementation before building the model that makes this a better way to design?

Model Boats magazine - Hmmmmmmm

[Tug Fanatic]

........................... Having positive stability is not always sufficient if the righting forces are small as this can make the model very 'tender' and therefore susceptible to windage. Your boat may not capsize but it could spend a lot of its time lying at a steep angle in a moderate breeze...............................


Colin

Full size cruise ships have exactly the same problem. I have been on cruise ships where the bridge has come on to the PA system to explain that there is not a problem but that a sudden squall has made the ship list as it did not give time for the ballast to be pumped to the high side!

[malcolmfrary]

Perhaps cleaned up versions of Glynn's threads should be stickied at the top of, say the begginners section?  That way, it should be easy for all of us to find them for future reference.

[GG]

Tug Fanatic,
            Sorry about the slow reply, had to visit dentists to check if I really had a problem or was I imagining toothache, apparently it's all in my imagination....?


Absolutely no offence taken.  I suppose that after designing and building a few models, I've developed a good idea of the likely stability (and performance) of the next model.  However, I'm aware that such "confidence" in a persons own skills can easily lead you in to making serious misjudgments.


So using the example of a shallow draught model, a simple experiment convinced me that not only would it be stable but it would in fact be very stable indeed.


The diagram is shown in Fig 7.  Heeling the model over at a similar angle to that used previously resulted in the transfer of a quarter of the displacement from the high to the low side.  This resulted in a massive movement of the Center of Buoyancy and an equally massive GM.


The resulting model, based on a small cruise-liner (published in June 2018 issue), would normally have been built with a draught that resulted in a weight of some 9 pounds (4 kg) but actually weighed in at 2 pounds (0.9 kg).  This made it very easy to launch/recover and incredibly stable, you could roll it onto its "beam ends" and it still knew the right way to float.


Finding the Centre of Buoyancy is just a matter of geometry for simple shapes but for more complex underwater hull shapes you can make a flat cutout of it and find its Centre of Mass.  Do note that you really ought to consider not just the midships section, but also allow for the finer sections in the bow and stern.  But, this is more work and I've found that if the GM looks to be big enough with the midships section, the hull ought to be OK.


Thanks for your interest.
Glynn Guest

[Martin (Admin)]

Tug Fanatic,
            Sorry about the slow reply, had to visit dentists to check if I really had a problem or was I imagining toothache, apparently it's all in my imagination....?

Was it all in your head Glynn ?!   

[GG]

Yes Martin,
            I may be paranoid but that doesn't mean that they are not out to get me.


Glynn

[Jerry C]

Use Simpson’s Rules to find centre of buoyancy.
Re Passenger Ships Quote. You never pump ballast to the high side. If you need to lower G you remove deck cargo from high side or take on ballast in bottom tanks on the low side first. This makes things appear worse initially but the further away from G you take action has the biggest and quickest results. Shifting ballast should only be done in calm waters or in port to correct for uneven loading. You wouldn’t move it again until arrival. If wind causes ship to heel enough to bother passengers GM is too small.
Timber ships are a prime example. Master receive bonus from shipper for large deck cargo. During voyage fuel and water used from bottom tanks cause rise in G and reduction in GM. Deck cargo takes on water (soft wood) further raising G until G rises above M and becomes negative. The ship takes on an “ angle of loll”. The ship rolls about thi AOL which gets worse as voyage continues.   This list on arrival at the Thames can be more than 30°. We used to watch timber ships going up flop from 30° port to 30° stbd when making the port alteration on the bend above Gravesend. If the old man had got it wrong and needed to ditch deck cargo it was high side first. Counterintuitive but to get it wrong would result in capsize.
Jerry.

[Colin Bishop]

The problem most cruise ships have is that draught has to be limited to 8-9 metres to allow them to dock in popular destinations. This places constraints on the design.

Colin

[Tug Fanatic]

Use Simpson’s Rules to find centre of buoyancy.
Re Passenger Ships Quote. You never pump ballast to the high side. If you need to lower G you remove deck cargo from high side or take on ballast in bottom tanks on the low side first. This makes things appear worse initially but the further away from G you take action has the biggest and quickest results. Shifting ballast should only be done in calm waters or in port to correct for uneven loading. You wouldn’t move it again until arrival. If wind causes ship to heel enough to bother passengers GM is too small.
Timber ships are a prime example. Master receive bonus from shipper for large deck cargo. During voyage fuel and water used from bottom tanks cause rise in G and reduction in GM. Deck cargo takes on water (soft wood) further raising G until G rises above M and becomes negative. The ship takes on an “ angle of loll”. The ship rolls about thi AOL which gets worse as voyage continues.   This list on arrival at the Thames can be more than 30°. We used to watch timber ships going up flop from 30° port to 30° stbd when making the port alteration on the bend above Gravesend. If the old man had got it wrong and needed to ditch deck cargo it was high side first. Counterintuitive but to get it wrong would result in capsize.
Jerry.

Once again the obvious is wrong. I learn something most days. That is presumably why we sailed with a list for some time as throwing some passengers off the high side might have been seen as unfortunate (and unnecessary).

[RST]

 I’m a few years past this but is static stability not still ultimately defined by the GZ curve?  And class dictates a minimum* and maximum** GM (which is potentially smaller than you think!), then area under the GZ curve, then minimum angle when crosses X-Axis at which the point of no return is reached?  GZ x displacement essentially determines the righting effort?

*too small, can roll very easy, potentially unstable
**too large, very stiff, potentially causes sickness like on the Stena HSS, metal fatigue but stability can peak then diminish very quickly

2 equations I also still remember (hopefully, but never near my books and notes when I see this):
 

• GZ=GM*sin(thi) -for small angles anyway
• GM=KB+BMt-KG

• Find KB from hydrostatics (simpsons rules for curved shapes, the centre of underwater area, which if you are capable of working to real plans is not that hard)
• KG from summing up the weights onboard (I did a deadweight survey once -somewhat wild goose chase on a working installation!)

BMt being moment of inertia -transverse.  For anything with free-surface (i.e. water or fuel tanks, minus the free-surface effect from each tank from BMt.  Explains why tanks onboard generally are always tried to be hard pressed or empty, and why the old ro-ro's turned over when water entered the uninhibited car deck)
 
For the cruise ship example windage must be massive on these?  I’m guessing here as was never involved in hollybob boxes but the big ones have something like dynamic stabiliser fins (retractable) as well as decent bilge keels, a good ballast system plus something like an intering system which should shift water dynamically fairly quickly up to a point.  We certainly used a compressed air intering + manual pumped ballast system offshore, both were used when we used the 150Te crane.  Pneumatic intering was a noisy ****, almost deafening near the air vent but you got used to it!!  I also worked on a vessel where a flume tank had to be introduced fairly high up to reduce stability a bit after sponsons were added to bring fatigue back into check.

Interesting subject.  I did tens of inclination trials on one offshore installation 2 decades ago when I worked a summer for a company providing live stability system on MODU's.  Not involved last time a vessel went through Inclining trials.  There's usually enough for the nominated N/A to worry about.  I just had to declare every singe nut, bolt and part installed onboard to correct KG before.

For R/C models I see no shame in deviating from builders plans to increase beam somtimes (Increased BMt or shifts the centre of the immersed "wedge" further outwards), maybe decrease draught but whatever for me always make CG as low as possible.

May your models stay dry and upright.  What Glynn Guest says is true, but don't get too tangled up like everything seems to be these days!

Rich
 

[Colin Bishop]

Interesting comment re Stena HSS. I travelled on it to and from Holland once and the motion was quite uncomfortable compared with a conventional ferry.

The sandwiches onboard gave my Wife food poisoning but that's another story.

Colin

[RST]

Interesting comment re Stena HSS. I travelled on it to and from Holland once and the motion was quite uncomfortable compared with a conventional ferry.

The sandwiches onbioard gave my Wife food poisoning but that's another story.

Colin

HSS went through waves rather than over or under absolutly what it was meant to do, longevity not so good (fatigue).  You have to understand what SWATH means also.  Not that that made any difference to passengers and when I was young SWATH was the new thingg -now SLICE, X-Bow or Axe-Bow!  Or just poor Greta saying Go Home.

[Tug Fanatic]

Interesting comment re Stena HSS. I travelled on it to and from Holland once and the motion was quite uncomfortable compared with a conventional ferry.

The sandwiches onbioard gave my Wife food poisoning but that's another story.

Colin

There was a lot of fuss at Felixstowe about the wash from these although when I have seen them elsewhere they don't seem to make much wash. Shallow water (Tsunami) effect?

[Navy2000]

When I build my Naval models I try to keep the top weight of the model down as much as I can. For example I do not use brass tubing for the mast, instead I use styrene tubing and the thin wall stuff as well. Some times I have to use a thicker wall because of tappers. When building structure components that go on top of another part of the superstructure I will remove as much of the deck that I can in which it covers to help reduce the upper weight. Any casted parts that are solid when molded I will hollow them out as much as I can to help reduce the weight, example The US CIWS gun when it is casted weighs in lets say 2 oz's times two of these now weigh in at 4 oz's, after I hollow them out they now weigh in at 1.4 oz's when done. I will also do this to the deck lockers and ammo lockers as well. Where ever I can remove material to keep the overall top weight down I will.


I hope that some of this will help you in your build. By doing this it will keep the model from rolling over during a turn.


Duane

[Martin (Admin)]

This from Marine Modelling Magazine 1986...





( Double click to enlarge )

[Allnightin]

I built a 1/200th HMS Abdiel based on the Polish card model with lite ply hull sides and a balsa hull bottom.  The superstructure was light alloy lithoplate and plastic card.  Despite keeping everything as light as I could, the completed had barely enough stability when static and needed 170 grams of extra lead ballast in the bottom of the hull (max weight was intended to be about 450 gram) to be sailed safely.  This extra weight submerged the hull appreciably deeper in the water so I changed to using a detachable bulb keel made from a brass tube filled with lead and putty ends weighing 70 grams as shown below.  This allowed a scale displacement and ample stability for tight turns at high speed.   In retrospect, I should have gouged/trimmed the hull bottom out as much as possible so that the motors and battery pack could be lower down and also made superstructure sections that wouldn't get handled (and therefore didn't need any great strength) such as the bridge from the kit card pieces to save weight.