Vessel Stability

If the definition required only that an object float for it to be considered a “boat”, things would be a lot easier for the boat designer. Observe to what lengths he must go to in fact before he can claim enough proficiency in the field to be published:

Barrel Boat

Producing an attractive bow wave is the first thing he should always consider, then the flag halyard. Once these requirements have been satisfied, he can progress with confidence to considering the vessel’s stability, or its inclination to stay floating right side up. (Presenting a sober and thoughtful visage is essential at all times to reassure your backers.)

A floating oak barrel has no natural resistance to rolling around its axis: however, this example vessel has been fitted with a weighty keel and lifejackets along the sheer, demonstrating a good grasp of the requirement for transverse stability. In this regard the deckhouse is certainly also a safety positive; if the vessel inverts, it will be unstable due to the upside down deckhouse’s inclination to float. Things have every reason to promptly roll back upright, like a rescue lifeboat. Though useless in preventing a roll, the nose cone does offer some contribution to longitudinal stability, (the resistance to tumbling end over end), and its graduated entry volume will considerably reduce G forces associated with striking the waves at high speed. The use of an unfashionable square rig hints that unfortunately, this designer was perhaps slightly before his time and outside his best field of endeavour, true appreciation of his talents now being the reserve of the modern “ocean going” trawler yacht market, rather than the sailing market.

CaskThe peculiar lure that the barrel shape seems to have always had for the nautical imagination probably derives from observations made from shore in the aftermath of marine disasters. A demonstrably inadequate wooden ship’s hull contained many barrels that would be the most likely thing to bob ashore intact and serviceable, unlike the crew. It would only be natural to assume that the unfortunate souls would have fared better had their ship been constructed in like form. The contents of the surviving containers, once appraised for integrity, could of course have prejudiced the clarity of the thinking.

A few experiments would have proven that some concern for creature comforts would be desirable if one wished to attract a willing crew. The first requirement would have to been to avoid uncontrolled and excessive motions as a result of being tossed about by the waves.

Submarine Replica

One solution would be to construct a vessel, designed to operate below the sea/sky interface, the relatively easy job of resisting rolling, pitching and heaving left almost entirely up to a little ballast, the barrel then preferring to float heavy side down. (Note that in the absence of wave and wind, the prime inducement to rolling would presumably be the inhabitants running around like hamsters, and the prime inducement to pitching would be their running end to end.) In the case of the ambitious vessel above, the oars were expected to propel it at sufficient speed (underwater) for the horizontal fins to influence things, thus demonstrating the antecedents for the modern trawler yacht’s dependence on dynamic stabilizing fins. (Note how the designer has given proper attention to the flag halyard!)

Bushnell's SubBallasting, the intentional carrying of strategically placed weighty objects, is an intuitively satisfying way of exerting our determination of what will be “up” and what will be “down”. It would offend our sensibilities if an aerial balloon carried its basket above its envelope and in the same way we are satisfied that barrel with a slug of cement in the bottom will float heavy end down.

There is mathematics to prove the intuition is right, you will be glad to know, but that is not as satisfying as guessing.

If we installed something less than a maximum of ballast in our barrel we would expect it to float above the surface and still remain sunny side up and we could carry something more useful than cement; like a cargo provided it is fixed in place. (A flowing cargo like grain or oil will inconveniently rush to the “low side”, if a vessel is tipped a little, and thereby disincline it to come back up. Gawking passengers, who are likely to crowd the rail on one side of a ship in ignorance of the principles of stability, are likewise poor ballast.)

The Whaleback

This vessel appears to be a barrel derivative. It is reported that she carried more passengers in her career than any other ship on the Great Lakes. She never rolled over and was eventually scrapped in 1936, after 44 years of testing the principles underlying ship stability by staying upright.

She did drown a few passengers on her upper decks though, in the course of distinguishing herself as the only vessel in history to knock over a water tower with her wheelhouse, really.

The Whaleback collides with water tower

Our intuition suggests that in this case an extraordinary amount of ballast down in the bottom would have been needed to lever all that top hamper up to the vertical and hold it there, wouldn’t it? So much weight in fact that we would have expected her to have a lot less freeboard showing.

Yet a photo of her construction reveals a relatively shallow cheap cigar shaped hull and she floated like a duck; apparently not carrying any excessive burden of pig iron.

The Whaleback hull

Obviously some other forces must contribute to holding a vessel upright in addition to the effects of simply making the bottom side heavier than the top.

These other forces are the effects of what is referred to as “form stability”. It is what causes a plank to float on its back, rather than doing the side stroke, and our intuition tells us that this is as it should be. There is reassurance in mathematical abstraction to prove our intuition correct, though the math is a not as much fun as pictures.

Girl riding on bikeForm stability is a little like not riding a bike; when you stop, just as you are about to fall over, your leg spontaneously cocks out to plant your foot and restore your transverse stability, (unless your foot is entrapped in a clever must-have pedal contraption).

You may note that the bicycle/girl combo is obviously heavier above than below, yet we sense that things are under control, sort of. It must be hoped that some unidentified physical forces and the mathematics are also her friends.

Einstein on a Bike

It appears to be so.

A floating body (in the physics sense rather than the forensic) may be shaped such that if it begins to tip over, a fresh section of its volume that was previously aboveboard becomes immersed, thereby exerting an upward buoyant force to push back and hold things up; (the vessel sticks its leg out to prop itself up). This stolen diagram has “CB’s” marked for us, these are the “centres of buoyancy” and are the balancing points through which the submerged shapes make their upward push. (You may imagine that the circle and rectangle are cross sections cut through a plank and barrel, floating things being 3D in the real world.) The CB always pushes straight up and is defined only by the submerged shape; projections above the water and the contents of the shape have no influence on its location.

CB diagram

rectangle is demonstrating the principle of form stability though it makes a lousy cross section for a boat hull, unless you require a barge. As some imaginary force tips things to the right, the CB obligingly moves over as well. The circle is showing us that in the case of a barrel, the CB stays put even if the barrel rolls, providing no shift to set things straight, so it has no form stability to help us.

thinking outside the box

Thinking outside the box, these examples are blissfully ignorant of our “form stability” mathematics.

If tipping is caused by a temporary force like wind or wave, our corrective buoyant force, in the case of form stability, will find itself acting alone, by and by, and as its efforts succeed in righting things, the helpful section will resurface, and the original floating state will be restored.

If the tipping was the result of a permanent shift of weight, (like you looking over the gunnel), the floating body will stay in its cockeyed state, reflecting a new state of balance.

In this way a floating body will arrive at a state of equilibrium and thereby display stability, though it may be quite precarious.

IcebergIcebergs are noted for their tendency to spontaneously roll over with no warning. They are merely showcasing the underlying principles behind stability, centres of gravity and buoyancy shifting as the ice melts or pieces fall off. The laws will be obeyed.

If you now look back now at the picture of the cigar ship under construction, you may note that the hull is not as round as it looked and in fact has the shape of a cigar that has been stepped on, The bulged out sides are what gave it form stability and kept it upright.

I’m sorry to say that to think about this much farther, we need to address the concept of “centre of gravity” to go with “centre of buoyancy”.

We must now enter the world of the abstract:

Testing gravity

The force of gravity may be considered to always act in the true vertical direction, downward. You can usually agree on where down is, even when everything else is in dispute.

A bit of confusion

The pull of gravity is proportional to the mass of an object which may vary throughout its geography; sections with different density being pulled down more or less respectively. The total effect of all these mini-forces is thought of as a single pull downward through a “centre of gravity” that may in fact be a long way away from the apparent geographical centre of an object. In this sense the CG is unlike the CB.

The daredevil’s wagon below is demonstrating some landward implications of the centre of gravity. The C to the right indicates the wagon’s centre of gravity when the load is composed of feathers, whereas the C to the left is its centre of gravity with a load of manure. The U stands for “Unfortunate place to stand” in the case of manure presumably and the L for a mysterious term lost in history. You may want to try this at home.

You may want to try this at home

Returning to the marine element we can see another drawing (not cadged this time) to show a simple CG / CB relationship when a catamaran tips a little, (you see, this is a catamaran site after all).

CG / CB

In Levelword, (left diagram), the centre of buoyancy (B) is comprised of two equal submerged hull sections and as a result it is located in the middle of the cross section. The centre of gravity (G) for the vessel is also in the middle thanks to the thoughtful placement of weights by the designer. The fact that they are directly above one another indicates that things are static, the boat is just sitting there in a millpond.

In the diagram to the right, the designer has chosen to rock the boat and see what happens. This has not apparently been done by an adjustment of weight as we see that the G is still in the middle, so we must presume the wind has pushed the boat over, or perhaps someone of substantial mass has just stepped off onto the dock. Form stability has now come in to play. The low side of the vessel has a substantially increased immersed volume at the expense of the high side. The total volume remains the same, (it is all that is required to float the vessel , see hydrostatics diatribe), but the centre (B) has moved substantially to the right. The two forces are now misaligned and will each exert themselves to rotate the boat to the left until they are once again directly opposing one another, in equilibrium. Any time you see a diagram with the arrows misaligned you may assume something will happen.

BalloonYou will have noted that our catamaran’s centre of gravity is located higher than the centre of buoyancy, (as it is for almost all ship and boats other than monohull sailboats and laden barges). Our balloon of intuition is upside down, we just know they badly want to swing around and switch places, form stability is preventing it from happening.

This balloon has its G over its B but has no form stability and its pilot is presumably stoned. It can’t stay very long in this position.

Many vessels do not rely entirely on form stability. Sailboats of all stripes are subject to disproportionately high wind heeling forces due to their sails which try to push them over. Like the balloon, most monohull sailboats have their centre of gravity below their centres of buoyancy to help keep them upright, the job being shared though with their form stability.

form stability

Their centre of gravity is artificially lowered by swinging a large weight under the vessel in the form of a heavy keel. The rest of the vessel is relatively light so when all the weights and their locations are totalled up, the resulting CG is conveniently slung below the CB. This is well and good for remaining upright but means we must maintain a substantial amount of buoyancy to avoid the keel dragging us to the bottom. The intuition keeping the sailboat upright and afloat resembles that of the balloon except the sailboat may benefit from a substantial form stability contribution.

Unlike the balloon a boat may be reasonably stable upside down, in spite of having a low CG, the form stability now working against our interests.

monohull stability

As you may have noticed, the diagram on the right displays a remarkable resemblance to the catamaran diagram in regard to the forces at work to stabilize things with the G over the B, recovery is not a given.

Rollover capable rescue lifeboatsIt is possible to build in form stability for all occasions; paradoxically you begin to come back to the old comforting shape, (but notice the neglect to design in a flag halyard).

Rollover capable rescue lifeboats have voluminous monster deckhouses that actually make them unstable if upside down by exerting so much buoyancy that the hull is hoisted up out of the water and heaved right side up as quickly as possible. This configuration is not designed to be aesthetically pleasing, so you may see it mimicked in the trawler yacht market from time to time.

If you have persisted to this point you may have gleaned that in calm water at least, a vessel’s inclination to come upright will be purely the result of a battle between its centre of gravity and its centre of buoyancy. It’s always good if the buoyant effort to float has reserves over the gravity effort to sink. The addition of ballast of any kind is counterproductive in this regard and in the case of heavily ballasted craft, the ultimate winner will sooner or later be gravity.

sinking

By design, a monohull sailboat almost invariably has to carry ballast well in excess of its ability to float it in the worse case. Ballast in itself is a useless lumpen cargo that strives to sink the boat from the moment it is launched. The decision to purchase it and float it around has to be counter-productive, if you have a choice. The nice thing about sailing catamarans is that they manage to stay upright by cheating, (all form stability, no ballast) so; you do have a choice.

The wider the distance between the catamaran hulls the greater will be its inclination to stay on the level. Considerations such as; seeing the corners, conducting pithy exchanges with the line handlers, and paying the docking fees will limit the practical over all beam of the vessel however. Also, in cruising catamarans the hulls are tied together with an accommodation deck suspended above the waves. This bridge deck influences the practical spacing distance of the hulls as it should be kept high enough to clear almost all wave action. In order to do that, it must get higher as the space gets wider. This idea seems to cause a lot of confusion. Try imagining this;

pinnacle or bridge deck clearance

As long as the lad in the picture keeps his feet together, he has an excess of bridge deck clearance. If his feet were to slide apart about a foot, he wouldn’t have enough. The comfortable bridge clearance is dictated by the height and shape of the pinnacle (wave).

A catamaran with a useful bridge deck is thus limited to practical widths by the necessary proportional bridge deck height and the relative size and choppiness of the waves anticipated.

Catamaran heeling

Having decided on a suitable hull spacing, and a few other things, you can try a mathematical exercise to see how things look, a simplified version of some typical results herein provided. There is a noticeable difference between the 90 deg. diagram here when compared with the 90 deg diagram for the ballasted monohull. By the time the catamaran has reached this state, gravity is not helping us recover, in fact it has been running out of positive attitude since its peak at about 20 deg. for this particular hull. This is in contrast to the monohull sailboat whose gravity induced recovery force is at its most robust at 90 deg. (This is a “real life” floatation diagram; note the small volume that has to be immersed in order to support the vessel in absence of ballast weight.)

Tipping the catamaran is something like moving a heavy refrigerator on a dolly, really. You have to tug like crazy to get it to tip up initially. After a certain point, it becomes easier until it is balanced. If you tip it too far, it overdoes things itself and finds a new equilibrium in your lap.

Tipping point

Tipping the ballasted monohull sail boat is like spending your spare time on of those machines designed to make your front thigh muscles as thick as the ones in your head. Swinging the (keel) weight up starts off easy, and ends up toughest at the horizontal, if your knees bend both ways, things get easier again until the weight lands in your lap and is tough to dislodge.

Mast Loading Diagram - link to enlargeSo, catamaran sailboats can have an enormous resistance to heeling right from the start whereas monohull sailboats develop that resistance as they heel. This is why catamaran rigs have to be heavier, they are reluctant to heel over and spill the wind. Standing up to the wind is also one of the reasons they tend to be faster.

How much heeling resistance the catamaran has is proportional to its weight and the spacing of the hulls which define the tipping fulcrums. This diagram contains most factors of interest and then some.

Lightweight sport and racing cats, even with very wide hull spacings, tend to press the sail area envelope at the expense of stability, so may tumble about in picturesque fashion. This is as it should be for any racing craft and the more extreme versions of racing keelboats are doing their best to follow suit, keel detachment problems becoming a not uncommon occurrence.

monohull racing sailboat capsize

Pictures of inverted keelboats with their keels still on are rare, they tend to turn back upright on their own after losing the encumbrance of their masts and sails, but then unfortunately sink as a consequence of the resultant structural damage.

Cruising catamarans are in a different weight category than the racing cousins and tend to have conservative rigs, so upsetting one is an uncommon event. The conditions that it takes to jeopardize the stability of a catamaran are equally dangerous for a monohull, but at least the cat will continue to float, somehow, no matter what.

Best to stay as comfortably level as possible, avoiding gymnastics, contortions and soakings; that way you can think more rationally and casually contemplate the forces at work, while thinking outside the barrel.

One last picture that I can’t seem to tie in with catamarans, but seems to deserve a place anyway; this fellow designed his own boat and built it in his own garage, the doors were wide enough for once, and is now transporting it to the launch site. The two wheel dolly has yet to be invented at this time.

barrel design

Apologies should be offered in the memory of Alexander McDougal (1845-1924), designer of the whaleback ship, of which over 40 were built. Presumably experiments with barrels didn’t go so well and in the aftermath, McDougall’s downcast gaze fell upon a flattened cigar on the ground, giving fresh inspiration. It could be true. They are fondly remembered (even by me) because of their improbable appearance. One vessel survives as a museum piece.

So, did the girl on the bike fall over? Did Einstein use Newtonian physics in spite of its obsolesce? Or did they just enjoy things as they were and not worry too much about why things worked as long as they were having fun?

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4 thoughts on “Vessel Stability

  1. Stability. Flipping over is the only thing about Catamarans that bother me. Would not a weaker rigging make more sense? I would rather my rigging blow away than flip the boat over.

  2. I would rather my rigging stay intact AND my boat not flip over. A rig with sufficient margin of safety with respect to the calculated loads is essential. Loosing the rig in heavy seas isn’t going to make your voyage safer or more comfortable.

    Avoiding capsize in a well-engineered vessel is largely a matter of seamanship (and no bad luck):
    – have an appropriate amount of sail for the prevailing and anticipated conditions
    – keep a diligent eye on the weather and sea state as part of your watch
    – in big seas take a look from each crest at what else is coming your way
    – try to sail a course that minimizes the dangers of large breaking waves
    – when it gets seriously rough deploy a Jordan series drogue

    I would not be inclined to cross oceans in vacation boats, party boats or anything that wins all the trophies racing round the buoys.

  3. We stumbled over here by a different web address and thought
    I should check things out. I like what I see so now i’m following you.
    Look forward to looking over your web page repeatedly.

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