A Question About Hull Characteristics

[Cloroxbottle]

Would these statements be true?

(1) As displacement of a vessel increases, so does the stability in the pitch axis (less likely to hobby horse).
(2) As the B/D ratio increases, so does the stability in the roll (side to side) axis.
(3) As the keel length increases, so does the stability in the yaw axis (less likely to get knocked off its heading by wave action).

If not, why?

If not, what measurements could serve as a proxy for these characteristics?

[PerfectPirate]

Well, yes and no. It all depends. Let's look at each assumption in turn.

Originally Posted by Cloroxbottle

(1) As displacement of a vessel increases, so does the stability in the pitch axis (less likely to hobby horse).

A longer, heavier yacht has more inertia, so it is inherently more resistant to being bounced around by waves. However, the location of the weight is very important. More weight in the centre of the boat provides central inertia which resists movement. Having more weight in the ends of the boat, front and back, can increase movement by pulling either the bow or the stern down as the wave crest passes along the hull. This is why good designers try to locate as much of the tankage as possible low down in the centre of the boat. It is also why heavy installations like engines tend to be as close to midships as is feasible.

Originally Posted by Cloroxbottle

(2) As the B/D ratio increases, so does the stability in the roll (side to side) axis.

This is a favourite bugaboo of mine, since ballast ratio is touted in so many specifications. Ballast ratio is just a number, the effectiveness of ballast depends on where it is located. Context is everything. You can have a racing boat of 10,000 lbs displacement which has a daggerboard and 4,000 lbs of ballast inside the hull. That's a 40% ballast ratio, but the weight is within the shallow, rounded bottom of the hull, which moves the centre of gravity up and reduces the righting arm, meaning that the boat is relatively tender. Now, you can take that same hull and put a five-foot-long 4,000 lb keel on it, with 2,500 lbs of the weight in a bulb at the bottom of the keel. Suddenly the boat becomes quite stiff, because the centre of gravity is now very low and the righting arm is much longer. But it's still only a 40% ballast ratio.


My own boat has a 40% ballast ratio but is stiffer than similar vintage boats of similar displacement, from the same builder, which have a 50% ballast ratio. It's simply a matter of where the centre of mass of the ballast is located and how that affects the righting arm. Also my boat is slightly wider, which introduces greater form stability. Ultimate form stability is achieved by catamarans, which are very wide, but have little to no ballast.

Originally Posted by Cloroxbottle

(3) As the keel length increases, so does the stability in the yaw axis (less likely to get knocked off its heading by wave action).

Yes, a longer keel does improve tracking ability. However, greater control is supplied by having the rudder as far aft as possible. It's a simply a matter of leverage. But, being able to move the rudder further aft is sometimes compromised by also wanting to have it attached to the aft end of a full keel. Separating the rudder from the keel to increase control and maneuverability is what has led to the rise of the fin keel/spade rudder generation of boats, especially in racing circles. Ted Brewer tried to achieve the best of both worlds with his trademark "Brewer Bite", which shortens the keel slightly and moves the rudder further aft on a skeg, allowing him to reduce wetted surface. Longer keels can also impede the ability to go to windward, since it is difficult to create a true NACA foil shape and achieve lift, especially with a shallower keel.

So, yacht design, like any engineering design, is all about trade-offs and compromise, which is what makes it such a fascinating subject. The points which I have mentioned above deal with just a few of the basic issues. How is the boat going to be used, and in what conditions? What vulnerabilities are being introduced? Does the buyer value comfort over speed? How large and luxurious do the interior amenities need to be? Is it feasible to manufacture the design for a reasonable cost?


If you want to achieve a deeper understanding, I suggest reading Ted Brewer's "Understanding Boat Design" as a primer in the basic concepts. You could follow this with "Yacht Design Explained" by Steve Killing and Doug Hunter. The ultimate reference is "Seaworthiness: the Forgotten Factor" by C.A. Marchaj. All books worth reading, although Marchaj requires a bit of effort to fully comprehend (which I don't yet claim to do).

[Don C L]

I'm not a naval architect but I'll take my own stab at it.

Consider one boat, let's say an old Pearson Vanguard. Narrow beam and a good deal of overhang. In that boat let's suppose you add 1000 lbs of ballast vs. adding 500 lbs to the bow and 500 lbs to the stern. I am confident the latter will hobby horse more. In both cases you'll be displacing 1000 lbs more water.

Now, same boat, with the 1000 lbs added to the ballast will she be more "stable?" Depends on what you mean by stable. Will she be less tender? Probably yes, but the round narrow hull still offers little in initial stability. The effect will be more noticeable once sailing. She will probably do better upwind. But as was mentioned, the location of the added weight makes a big difference too. Added at or above the waterline won't offer much more in the way of stability.

As far as tracking, that one is not as clear to me. I guess one might guess that fin keels with spade rudders should not track well, and should be more likely to be thrown off by wave action, but I doubt you'll find consensus on that. I think you'd have to define wave action. The times I have sailed fin keels (Catalina 27, 30, 32, 36) they tracked well until the waves were steep enough to launch the bow or stern out of the water and they lost traction. (The CLR changed) Even the Frers 65 I crewed on tracked well even after we lost the rudder!

[Lee Jerry]

While nothing PP said is wrong, I think I can provide a little more direct set of answers to your questions. These are based on the "all else being equal" premise (as far as that is possible).

1 - Yes, as mass goes up, the mass moment of inertia in pitch goes up too. Therefore, for a given speed and sea state (i.e. same pitch forcing function), the motion will be reduced. *

Note that the mass itself is the least significant factor in the equation. As mentioned, mass distribution is more important, and so is the shape of the waterplane, particularly length. (And I suppose the distribution of the buoyancy too, but that may be secondary, especially considering small changes to a general shape.)


2. Yes, as B/D goes up, initial form stability increases. However, the governing parameter is the beam, the draft is secondary (or even tertiary). Again, it's the waterplane area and shape. For illustration, the inertia of a rectangle about its long axis is 1/12*L*B^3; note the beam is cubed.

Another note, the initial stability is not the only measure of stability. Other measures include: the range of stability, when maximum righting arm occurs, and the total area under the righting arm curve (or total energy before capsize). Range of stability (how far a vessel can heel and return to upright) is often reduced as beam increases - cats have a range of 90 deg, or slightly less, where monos are typically in the 110 - 130 deg range.


3 - Yes, a longer keel will have a higher resistance to yawing. But that also means it will be harder to yaw back onto course. The hull shape also factors significantly into it, both in creating the yawing moment and in resisting it (no, I don't think this is a contradiction - the former is largely the stern shape/waterplane while the latter is largely the forefoot).


As for your last question (measurements to serve as proxies?), I'm not sure what you're asking. Maybe if you could rephrase or otherwise explain.

Originally Posted by PerfectPirate

Longer keels can also impede the ability to go to windward, since it is difficult to create a true NACA foil shape and achieve lift, especially with a shallower keel.

There's nothing special about the NACA foils. Those are just the shapes tested by the committee (so we have good data on them). There are other foil families with data available, and any foil-ish shape, even a flat plate, will develop lift. But your point is still taken...

[s/v Jedi]

I’m not a nautical engineer, but I know that length of a boat helps more against pitching than displacement.

Also, a sailboat without it’s mast will rolls violently even though it has the same ballast. Roll is not related to ballast, it is countered by inertia and active stabilization.

Not a fan of long keels, I prefer the NACA foils. Also, a large rudder but still a foil without a skeg. Our boat is like if it’s on rails and it’s designed to be like that while planing as well.

[Adelie]

Originally Posted by Cloroxbottle

Would these statements be true?

(1) As displacement of a vessel increases, so does the stability in the pitch axis (less likely to hobby horse).
(2) As the B/D ratio increases, so does the stability in the roll (side to side) axis.
(3) As the keel length increases, so does the stability in the yaw axis (less likely to get knocked off its heading by wave action).

If not, why?

If not, what measurements could serve as a proxy for these characteristics?

1. No. Hobby horsing depends on the length of the boat vs wave length to drive the pitching, and the pitch moment of inertia. It depends on where the increasing mass is installed. If mass is added near the bow or at the mast head the moment of inertia will increase and it is more likely to be out of synch with waves and hobby horsing is more likely to occur. In general hobby horsing is only a significant problem if you are racing and every possible advantage is important or you are cruising and have massively overloaded the ends of the boat, especially the bow.

2. Assuming hull dimensions and total displacement stays the same and B/D increases (ballast increases same amount displacement decreases) and the increasing ballast doesn’t change the center of gravity (ie ballast gets uniformly fatter and longer but not higher or lower) then ultimate stability will increase. Initial stability will be the same as that is a function of hull shape and amount of immersion.
Keep in mind that stability and capsize resistance are different things and increasing stability does not necessarily increase capsize resistance. Things that decrease stability may improve capsize resistance.

3. I believe this is generally correct. I can see hull shape may also affect this to some extent.

[Bowdrie]

Beam becomes a bit complex, it's not as easy as just being a dimension measured across the widest part of the hull.
If we were to superimpose the plan view of the deck over the plan view of the waterplane area at the LWL we'll get a better understanding of how the "beam" of the boat affects the characteristics of how the boat rolls and how that under heeling it affects the not only the shift to leeward of the CB but also how the leeward side of the boat resists increased immersion.
Many of the more modern hulls, (and a lot of older designs,) have what might be called somewhat of a "vertical" shape, where's there's not a whole lot of difference in the superimposed views, in simple terms, not much "overhang" between deck and waterplane, particularly in the midship sections.
In such hull shape, (what is commonly referred to as "hard bilged",) the shift to leeward of the CB is more biased upon the "lifting" of the windward side, as opposed to the "immersion" of the leeward side.
Older and more traditional shaped hull were "slack bilged", with a greater proportion of "overhang", as such, a greater proportion of the shift of the CB is due to taking a larger volume of previously "above water" hull and forcing it down into the water, (adding buoyancy).
Of course, the displacement doesn't change, therefore the total amount of water "displaced" by the boat doesn't change, it's the way the hull "sits" in the water to displace that volume as the waterplane changes shape when heeled.
Each way has its pros and cons, and attributes and deficiencies shift around as the angle of heel changes.
Edit, this "overhang", if you will, (more so at bow and stern,) also figures greatly in pitch axis motion.

[Lee Jerry]

Originally Posted by Adelie

2. Assuming hull dimensions and total displacement stays the same and B/D increases (ballast increases same amount displacement decreases) and the increasing ballast doesn’t change the center of gravity (ie ballast gets uniformly fatter and longer but not higher or lower) then ultimate stability will increase. Initial stability will be the same as that is a function of hull shape and amount of immersion.
Keep in mind that stability and capsize resistance are different things and increasing stability does not necessarily increase capsize resistance. Things that decrease stability may improve capsize resistance.

There needs to be some clarification on definitions. I took it to B = beam and D = draft (of the canoe body), whereas you (and others) are using ballast and displacement, respectively, the ballast ratio. The OP needs to chime in with what he meant.

If he meant the latter, then go with what PP said, which I'll summarize as "you don't know, there are too many other variables." And for that reason, I don't think it is a particularly useful metric, which is why I interpreted it the other way.

[Fore and Aft]

Cloroxbottle one thing I will tell you is regardless of the maths once you start being seasick the vessel size, displacement or keel type doesn't matter. The boats motion all feels the same.
Cheers

[rslifkin]

Shape of the hull is a factor for pitching too. A flared bow that gains buoyancy quickly as you immerse it further will tend to pitch more aggressively than a fine, unflared bow. The second will be more likely to go through a wave, so less pitching but easier to put water over the decks.

Width of the stern affects behavior in pitch too. A wider stern will tend to reduce how much the stern squats as the bow pitches up, so the center of pitch rotation is further aft compared to a narrow stern hull.

[Cloroxbottle]

Originally Posted by Lee Jerry

There needs to be some clarification on definitions. I took it to B = beam and D = draft (of the canoe body), whereas you (and others) are using ballast and displacement, respectively, the ballast ratio. The OP needs to chime in with what he meant.

Sorry, I meant the balance/displacement ratio.

[Don C L]

The ballast to displacement ratio tells me more about the weight of the hull than anything else. Where that ballast is located tells me more about stability, upwind performance and draft.

[Lee Jerry]

Originally Posted by Cloroxbottle

Sorry, I meant the balance/displacement ratio.

Yeah, I'm not surprised.

As mentioned, the ballast ratio by itself tells you almost nothing. Probably the best quick guide to a vessel's initial stability (remembering that that is only a small part of stability) is the description of the keel underbody. For example: bulb keel, fin keel, shoal keel, full keel, centerboard, etc. Then you can consider other factors to fine tune the picture somewhat: draft, beam, ballast ratio.


Why are you asking these questions? What's the goal?

[Bowdrie]

The type of "Keel" or the ballast attached to the keel, (or its weight,) has very little to do with "Initial Stability".
Initial stability, (this means small angles of heel,) are all about hull form, (a flat-bottomed barge has tremendous initial stability, a floating log not so much),
This initial stability is measured with an "inclining experiment" where known weights are placed a known distance from the centerline and the angle of heel, (actually the horizontal displacement of a pendulum,) is used in a formula to give what is called the Metacentric Height.
This procedure is required for any vessel that carries passengers for hire, and for various commercial vessels.

[Lee Jerry]

Originally Posted by Bowdrie

The type of "Keel" or the ballast attached to the keel, (or its weight,) has very little to do with "Initial Stability".
Initial stability, (this means small angles of heel,) are all about hull form, (a flat-bottomed barge has tremendous initial stability, a floating log not so much),
This initial stability is measured with an "inclining experiment" where known weights are placed a known distance from the centerline and the angle of heel, (actually the horizontal displacement of a pendulum,) is used in a formula to give what is called the Metacentric Height.
This procedure is required for any vessel that carries passengers for hire, and for various commercial vessels.

Not exactly.

The buoyancy vector of a hull acts perpendicular to the waterplane. When the hull is heeled a small amount, say half a degree, the buoyancy shifts to the side while still acting vertically, so this new buoyancy vector will cross the centerline at some height. For a small range of heel angles, say 2-4 deg, all of these vectors will cross at the same point; this point is called the metacenter, point M. The height of the metacenter above the baseline (point K) is the distance KM.

The various distributed weights of the vessel can be assumed to act at the center of gravity (CG), point G. (This a pretty common concept, so I won't go further.) The height of the CG above the baseline is the vertical CG, either VCG or KG.

The difference between the height of the metacentric (KM) and vertical center of gravity (KG) is the metacentric height, GM.
GM = KM - KG
If GM is positive, the vessel is stable at rest. If GM is negative, the vessel is unstable and will list or capsize.

An inclining experiment measures GM. From the vessel lines plan, you can calculate KM. (This can be done by hand but is usually done by computer model these days.) You can then calculate the KG through basic algebra on the earlier equation:
KG = KM - GM

The purpose of an inclining experiment is to determine the vertical center of gravity (KG or VCG) of the vessel.

Now, the type of keel / ballast has a direct effect on the VCG. Therefore, the keel / ballast has a direct effect on the GM and the initial stability. Some might say it has a great deal to do with it, since many sailboats would be unstable at rest without it.