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Stability - how to avoid rolling upside down

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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
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