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Illustrated tutorial: Powerboat seaworthiness
Rough water is a sly predator, and boats are a favorite prey, but the LEGO fun must go on. This illustrated tutorial is about building fast RC powerboats seaworthy enough for the rough water of a busy swimming pool and operating them safely therein.
About this creation
Please feel free to look over the images and skip the verbiage.

This tutorial is about making remote control LEGO® powerboats seaworthy enough for the LEGO®-scale equivalent of a heavy storm sea -- i.e., a good bit rougher than this...



... but not quite this rough...



In the spirit of safety first, the focus is on (i) building in the required seaworthiness and (ii) exercising due seamanship in heavy swimming pool chop. Since seaworthiness starts with hull selection, I've also posted a separate guide to powerboat-compatible LEGO® unitary hulls.

I can't do justice to performance and multihulls here but touch on both often. The ever-present seaworthiness-performance trade-off is a recurring theme. You'll find more on performance and multihulls in the pages devoted to Nadine and Trident, respectively.

On this page:


Motivation, content, and organization

Shawn Kelly and I have been avidly building, racing, and occasionally sinking LEGO® powerboats for nearly 2 years now.


Trident, a seaworthy outside-the-box power trimaran

To date, we've come up with dozens of seaworthy powerboats (mostly no-frills speedboats) based on various LEGO® unitary hulls (LUHs). We've also dabbled in heavier motorized ship models.


R/V Stormin' Norma II, a marine geology research vessel

Our boats have benefitted greatly, in both seaworthiness and speed, from a deep dive into naval architecture -- the engineering discipline devoted to the design, testing, and construction of boats and ships of all kinds. The big pay-off came when Shawn's boat Radio Flyer took 1st place at the boat drag races at BrickWorld 2015!



Two of the more important lessons learned in all of this:

You can't count on flat water, even in a swimming pool.

Anything water can do to a real boat, it can do to a LEGO® boat -- only at a much faster pace.

For the sake of your expensive LEGO® electricals, best then to understand how boats and rough water get along.

This page attempts to explain what seaworthiness and good seamanship entail in the LEGO® realm. Many of the terms and concepts introduced aking the way are standard in naval architecture, but some had to be modified a bit for LEGO® use. All terms are italicized where defined, usually on first use. SI (meter, kilogram, second) units are used throughout.



Just add water
Many aspects of the mechanical behavior of liquid water remain effectively unpredictable despite modern advances in fluid dynamics and computer modeling. Add boat-water, boat-air, and water-air interfaces to the equation and bring them all together at the waterline, and the complexity and nonlinearity of the problem goes through the roof.

Nonetheless, naval architects have devised clever and effective ways to deal with the perversity of water at a practical level, many of them semi-empirical. Scale model testing is a prime example. Indeed, much thought and experimentation has gone into the relationship between scale model and real boat behavior.


Tramontana, a nimble power catamaran

The great news: Scale effects -- i.e., phenomena that don't scale well between model and ship -- are generally of little practical importance in LEGO® naval architecture. We consistently find (i) that the issues we encounter have already been addressed in real boats, and (ii) that the same solutions work at LEGO® scale.

The upshot: Everything here applies equally well at LEGO® and supertanker scales.




Safety first

The most important definition on this page deserves a special place right up front: Our working definition of a seaworthy LEGO® powerboat is one that's buoyant, stable, controllable, maneuverable, and powerful enough to...
  • Ply the chop of a busy swimming pool with little risk of water damage to the electricals onboard
  • Move out of harm's way quickly and decisively
  • Return to shore on demand

Laverne, a seaworthy twin-screw monohull

To meet these criteria, a LEGO® speedboat needs
  • One of more unitary hulls with buoyancy and stability to spare
  • An adequate propulsion system
  • A reliable control system
  • Lightweight structures strong enough to hold propulsion and control components and all hulls firmly in place in waves
  • An operator alert to the hazards involved


General tips from hard experience:
  • Better to start with a seaworthy boat and make her fast than the other way around.
  • Swimming pool waves can easily build to the LEGO® equivalent of a heavy storm sea -- especially if there's a busy diving board.
  • Learn from others' mistakes -- no shortage of object lessons on YouTube.
  • Water's usually quick to punish unsafe designs but isn't above waiting for the most inopportune time. Best to take the punishment while the boat's well within arm's reach -- e.g., in a tub trial. Test the seaworthiness of every design change thoroughly and move to open water only when comfortable with the odds.
  • Choose your hull(s) conservatively. The surest way to lose a boat is to ask too much of her hull(s).
  • Make sure the hull attachments and cross-structures holding your multihulls together are up to the repetitive wave loads they'll face in rough water. When the only hull attachments available are studded (the usual case), recruit more studs than you think you'll need and reseat them before every launch.
  • LEGO® electricals usually survive brief immersions in fresh water if disconnected immediately and allowed to dry out thoroughly before reuse. Salt water's a very different story.
  • Controllability, maneuverability, and speed are every bit as important to seaworthiness as buoyancy and stability -- especially in rough water.
  • Expect the unexpected and build in appropriate margins.
In our experience, reliable remote control (RC) is essential to seaworthiness. Unfortunately, the Power Functions (PF) infrared RC (IRRC) system hardly qualifies.

Your LEGO® powerboat will be much better off with a reliable, long-range RF-based RC system like the third-party Bluetooth-based SBrick or the all-LEGO® RF system from the long-discontinued RC Race Buggy (RCRB) line.




Radio Flyer uses RC Race Buggy remote control

I generally prefer the SBrick, as the RCRB system has its own problems: (i) It's very rare and much more expensive than an SBrick. (ii) The handset is ill-suited to differential-drive twin-screw steering. (iii) An RCRB receiver with NiMH AAs weighs ~0.2 kg more than an SBrick and a PF rechargeable battery. (iv) The rare and expensive 74x18x7 LU City Lines hull (CLH) is the only LEGO® unitary hull large enough to carry the RCRB receiver as a monohull.

The RCRB system's added mass cuts into top speed, responsiveness, and stability, but its reliable control link makes following a specific course a lot easier. That last benefit helped Radio Flyer take top honors in the BrickWorld 2015 boat drag races.

Operate boats relying on IRRC with its short range and seemingly random intermittency firmly in mind.




Hulls

Although it's certainly possible to make working LEGO® powerboats with brick-built hulls, we haven't pursued that approach. Rather, our boats use a small subset of LEGO® unitary hulls (LUHs) that we consider safe for powerboat use.


Celine, a seaworthy monohull based on the Cargo Carrier hull (CCH)

These 8 powerboat-compatible hulls (PCHs) are discussed extensively at the link just given. Here, I address the aspects most pertinent to seaworthiness.

We define a PCH as an LUH capable of supporting a 0.35 kg no-frills speedboat load in a seaworthy manner -- either by itself or joined to another copy of itself to form a twin-hull catamaran.1

To be fit for multihull use, a PCH must also have an adequate number of secure cross-structure attachment points.


Dubble°°Bubble's cross-structure is exceptionally strong

Bare hull refers to what's left after removing everything from a PCH other than the deck pieces specifically made for it. The unitary part is the one-piece bottom. The decking is never watertight but can be made so in the 4 PCHs that have weather decks.

Weather decks cover the unitary hull bottom completely and overhang it all the way around. They're easily sealed with electrician's tape or silicone caulk, both easily removed. Tape seals require careful maintenance to prevent slow leaks.


Dubble°°Bubble's taped black weather decks

Unfortunately, most weather decks have open-top deck wells large enough to trap dangerous volumes of water above decks.
Laverne's large deck well

Covering deck wells with plates effectively slows water accumulation, but the added weight is often prohibitive.


R/V Stormin' Norma II's large deck well is fully plated over



Displacement and load
LEGO® unitary hulls are displacement hulls in that they push through the water rather than skim over it. Lacking hydrodynamic lift at attainable speeds, they support the boat's weight by buoyancy alone.

That weight (W) is of course just the local acceleration of gravity (g) acting on the boat's displacement (total mass, Δ):

W = Δ g.

At sea level, g ≈ 9.81 m s-2. (Recall that weight is a vertically downward force expressed in Newtons (N). Scales with readouts in grams or kilograms report mass, not weight.)

The hull of a boat floating freely at rest occupies a hole in the water's surface. Displacement volume (∇, in m3) refers to the volume of the hole -- i.e., the combined volume of her underbody and submerged appendages.

Per Archimedes' principle, the displacement of such a boat equals the mass of the water that would otherwise have occupied the hole -- i.e.,

Δ = ρ ∇,

where ρ is the density of water (~1,000 and ~1,025 kg m-3 for fresh and salt water, respectively).

Importantly, if nothing falls off or comes aboard a boat in a particular body of water, ρ, Δ, and ∇ will all be constant at rest, regardless of how the boat sits in the water.

Displacement is the sum of bare-hull mass and the mass of the boat's load. The latter refers to everything added to the bare hull(s) to complete the powerboat as operated. Our typical no-frills twin-screw monohull load comes to ~0.35 kg with twin L motors.

This speedboat load breaks down as follows:
  • Propulsion system: Batteries, propulsion motors, props, and all the shafts and gears in between, excluding supports. Our twin-screw propulsion systems come to about 0.23, 0.25, and 0.38 kg with twin M, L, and XL motors, respectively.

  • Control system: RC receivers, steering motor and mechanism if any, and any extension cables, excluding supports. (Twin-screw boats seldom need separate steering systems.)

  • Structure: Attachments and supports keeping load components firmly in place WRT the hull. Stiff supports promote propulsive efficiency and steering accuracy. A multihull cross-structure must resist flexure and breakup in rough water and minor collisions.
Seaworthiness and speed depend critically on displacement and load distribution over the bare hull or hulls. The distribution determines the all-important KG, the height of the boat's center of mass above her keel.

The structural strength-mass trade-off forced by the seaworthiness-speed trade-off tests engineering and construction skills -- especially in multihulls. Better to err on the side of seaworthiness here, as repeated flexure in waves progressively weakens studded multihull cross-structures, and multihull break-ups invariably lead to drowned electricals.



Hull symmetry and axes
The submerged part of the hull -- the underbody -- is arguably its most important part WRT seaworthiness and top speed. Describing and visualizing the underbody in motion is a lot simpler with hull symmetry and 2 useful reference frames in mind. One frame is tied to the hull itself; the other, to local gravity.


Triton, looking down the centerline plane

Every bare LUH (and nearly every real hull) has a centerline plane dividing it into mirror-image port and starboard (left and right) halves. A centerline follows the centerline plane across an intersecting surface like a deck. Keel refers to the important but often imaginary centerline running along the bottom of the hull.

To define the hull (xyz) frame, we take as our reference a well-balanced LEGO® powerboat like Nadine with a single, flat-bottomed PCH and a center of mass G in the centerline plane, where it belongs.

The positive-forward x-axis coincides with the keel. The z-axis runs through G perpendicular to the x-axis and is positive in the direction intended to be upward. The intersection of the x- and z-axes defines the origin O. The y-axis passes through O perpendicular to x- and z-axes and is positive to port.

Hence, O, G, and the x- and z-axes lie in the centerline plane, while the x- and y-axes parallel the flat bottom of the hull in directions respectively parallel and perpendicular to the keel.

Longitudinal and transverse refer to hull-based directions parallel to the x- and y-axes, respectively. Any plane perpendicular to the centerline plane is a transverse plane, aka section. The important midship section divides the hull into equal lengths at waterline. In LUHs and real cargo vessels and warships, the hull's widest section is generally near the midship section.

In the hull frame, the z-coordinate of the center of gravity G is simply KG, the height of G above the keel. This all-important quantity is central to stability and seaworthiness. In our properly balanced reference boat, the x- and y-coordinates of G are both zero.

The geographic (XYZ) frame (aka Earth frame) takes advantage of the fact that Earth is for all intents and purposes flat at boat scale. Its origin coincides with that of the hull's xyz-frame and moves with the boat.

The positive-upward Z-axis parallels gravity's local line of action, which fixes the direction we call vertical. Any direction perpendicular to the vertical is by definition horizontal. The horiztontal X- and Y-axes are positive toward true north and true west, respectively.

In the absence of waves or other disturbances, the surface of the water near the boat would be perfectly horizontal in all directions. Her waterline -- i.e., the closed line of intersection between the hull and the water surface -- would also be horizontal. In a properly balanced boat, the y-axis would be horizontal as well.

Under such circumstances, the centerline plane would be vertical, and the zZ-plane -- i.e., the plane containing the z- and Z-axes -- would coincide with it. However, the z-axis would be vertical -- i.e., coincident with the Z-axis -- only if the x-axis happened to be horizontal as well. The angle between the x-axis and the horizontal may deviate from zero by circumstance, design, or both.

Attitude refers to the orientation of the hull frame relative to the geographic frame. A boat is upright when her centerline plane is vertical with her z-axis pointing out of the water and in normal attitude when upright with her z-axis tipped forward or aft of the vertical at the intended (small) angle.

One could also think of attitude as (i) the angle between the z- and Z-axes, and (ii) the angle between the zZ-plane and the boat's direction of motion relative to the geographic frame.

The orientations and motions of a freely floating boat and the water surface around it vary on a wide range of time scales. An entity like attitude or displacement volume is said to be static when refered to a freely floating boat at rest in calm water. Should the same entity come to vary rapidly in time, as in a heavy storm sea, it becomes dynamic instead. A quasi-static entity varies slowly enough to be considered static for the purpose at hand.



Hull dimensions
We now have the language needed to define the hull's most important dimensions.

Depth (D) is broadly defined as the height (z-coordinate) of the upper edge of the bare hull above the keel. Depth typically varies fore to aft, as it does with Nadine's CLH, the deepest LUH available.

A single figure quoted for depth refers to the freeboard depth taken at the lowest point on the hull's upper edge, usually near midships. Freeboard depth sets a firm upper limit on draft and hence on load.

The hull length that counts WRT seaworthiness and performance, hereafter designated L, is the one taken at load waterline (LWL) -- i.e., the static waterline at operating displacement. Breadth (B) is conventionally taken at the widest transverse diameter on the LWL.


Earline with her LWL showing

Every waterline, static or otherwise, encloses a waterplane of area AWP serving as the underbody's virtual upper surface. In practice, ∇, L, B, and AWP vary as the underbody changes with draft and attitude via direct wave action or the gain, loss, or redistribution of onboard mass -- including that due to water taken on.

Importantly, a boat's overall stability -- i.e., ability to right herself after an attitude change forced by, say, a wave impact -- varies directly with the area and area moment of inertia of her waterplane.

Notable reductions in both occur when a wave crest is at midships, or when a wave tosses a trimaran side hull out of the water. Hereafter, stability used alone will refer to roll stability (aka tranverse stability), as that's the kind most critical to seaworthiness.

Draft (T) is just the vertical distance between the waterplane and the lowest point on the underbody at the time, appendages excluded. In practice, T varies with water density, displacement, attitude (especially pitch and trim), and even speed. A single figure quoted for T refers to the static LWL. A boat with a draft of T meters is said to draw T meters of water.

Freeboard (F) is simply the difference between depth and draft -- i.e., FD - T. A single figure given for freeboard refers to the height above the LWL of the lowest point on the upper edge of the hull. At a given displacement, freeboard varies for all the same reasons draft does, though one always at the other's expense.


Nadine, Δ = 0.855 kg, T = 15 mm


Test boat for the egg-beater-like Voith-Schnieder propellers (VSPs) hanging over the sides, Δ = 1.62 kg, T = 30 mm

The 2 CLH-based boats above show how displacement, depth, breadth, draft, freeboard, and stability interrelate. The much greater KG and much lower B/T ratio of the VSP test boat make her noticeably less stable than Nadine, but she's still more stable than any non-CLH boat on this page.




How to sink a LEGO® powerboat

Luckily, we've had only 2 sinkings so far. Both involved multihulls with sudden cross-structure failures in moderate swimming pool chop. The separated hulls capsized instantly and were dragged to the bottom in seconds by the attached electricals.

These 2 spectacles left no doubt that multihull break-ups were to be avoided at all costs. The salt water case yielded our only electrical casualty to date -- a PF receiver with instantly corroded contacts that died a week later.

We've also had some 8-10 near-sinkings -- but "near" only because the boats happened to be within arm's reach from poolside at the time.

Three near-sinkings were directly attributable to IRRC failures. The first left Trident adrift right in front of a large swimming pool side drain. By the time Shawn got to her, she was already inside the drain and headed for the pump room.

Our 2nd near-fatal IRRC failure caused a collision that left one hull of an SBH catamaran like Dubble°°Bubble perched on the stern of an FFH catamaran. The SBH cat couldn't pull free. Its cross-structure took the brunt of the wave loads on both boats but held. Meanwhile, water poured in over the FFH cat's sterns. The latter was seconds away from going under when snatched from the water.

The 3rd IRRC-related close call allowed wind and waves to push the disabled boat onto the rung of a swimming pool ladder. As the boat dangled from the outdrive hooked on the rung, wave after wave spilled over the submerged bow. Thank goodness the weather deck was sealed.

These incidents carried 3 important lessons: (i) IRRC unreliability is a hazard in and of itself. (ii) The sealing of weather decks isn't optional. (iii) Collisions, entanglements, and groundings in waves open up a world of potential attitudes, stresses, and flooding mechanisms we never saw coming.

A slow leak in Trident's center hull weather deck seal provided her with another near-death experience. By the time I noticed her motors dragging in the water, the center hull was half full. Boats with sealed weather decks are now weighed periodically to check for hidden water.

Freeboard-challenged Tramontana here found herself completely swamped but still lingering at the surface several times early on. Luckily, she remained upright, and her electricals stayed dry.



The flooding resulted from dynamic freeboard reduction aft due to a combination of squat and positive trim at speed. Adding bulwarks around her sterns, quarters (the sides aft of midships), and bows slowed the flooding to a manageable rate.

These near-sinkings were atypical in that capsize of a freely floating intact (undamaged) boat never entered the picture. That's not the way boats usually sink.



Prelude to a capsize: Deck wetness
The rest of our close calls taught us something real mariners and naval architects have known for millenia: Freely floating intact boats usually sink by repeatedly taking on water over the sides to the point of destabilization and capsize capsize.

Deck wetness or simply wetness refers to water coming aboard via the decks rather than through a breach in the hull. Mariners refer to wetness arriving in bulk -- as in a wave coming over the bow -- as green water or a boarding sea to distinguish it from spray. The distinction is important, because green water can accumulate and destabilize much more quickly than spray. Spray can become a significant source of wetness in wind-swept storm seas, but surface tension generally suppresses spray at LEGO® scale.

Exceptional freeboard, stability, and seakeeping ability make wetness a rare event for our CLH-based boats -- even in heavy pool chop. For the rest, however, it's only a matter of how much, where it ends up, and how long it stays aboard.

Water finding its way into deck wells or below decks qualifies as flooding, as it can only be freed (removed) by hand. The rest eventually frees itself, but not before taking its own toll on stability. All wetness in a CLH, CCH, or FFH goes straight to flooding for lack of sealable weather decks.

Freeboard is usually the 1st line of defense against wetness, especially at the bow. However, Trident and all-SBH multihulls like Dubble°°Bubble simply shrug off deck wetness as fast as it comes aboard. Such boats are like submarines cruising at the surface in that their seaworthiness doesn't depend on dry decks.



Free surface effect (FSE)
Water onboard is at its most dangerous when free to wash back and forth on deck or inside the hull in response to rolling. This free water (aka loose water) constitutes a repeatedly shifting load that effectively elevates the boat's center of mass at the most inopportune time -- namely, when already rolled.

Indeed, the amount of sloshing free water needed to destabilize a rolling boat to the point of capsize can be a small fraction of the maximum volume she can take on at rest and remain afloat.

This free surface effect (FSE) grows with roll angle and the average breadth of the free water surface and decreases with the boat's dry displacement. Surprisingly, the total mass and depth of the free water are irrelevant. Nor does the FSE depend on the location of the free water within the boat.

Bottom line: A thin layer of water sloshing around anywhere onboard can be a significant capsize risk. Indeed, FSE-related destabilization turned out to be a major player in most of our near-sinkings.

If wetness results in a broad free surface above or below decks, bring the boat in and drain it while you can.



Capsize: How most intact boats sink
Capsize refers to an attitude change ending with a boat stably keel-up or on her side. Water then enters in sufficient mass to sink her. Capsize is generally both a necessary and sufficient condition for the sinking of an intact boat. Keeping a LEGO® powerboat afloat is then largely a matter of capsize prevention informed by known mechanisms.

Importantly, capsize tends to be an iterative process that begins with enough green water to reduce the boat's stability in some way. The volume need not be catastrophic. The reduction then sets the stage for more green water in a subsequent wave or roll. Nor does the offending water have to stay aboard long to keep this positive feeback loop going. A transient FSE might well suffice.

At design stage, a LEGO® powerboat's capsize resistance hinges on (i) hull selection, (ii) operating displacement, and (iii) the center of mass height KG resulting from the desired load arrangement. The design center of mass G should be in the centerline plane and as low to the keel as possible to maximize overall stability.

Problem is, water onboard inevitably increases displacement, reduces freeboard, and shifts G to a new location. Unlike the FSE, these penalties do depend on the mass and location of the water onboard and obtain whether or not an FSE results.

Odds are, the new G will only make matters worse. If it ends up off the centerline plane, the boat will develop a list with an increased likelihood of green water over or capsize to the low side. Flooded deck wells increase KG. Stability suffers either way.

If enough water comes aboard, even transiently, it's entirely possible for the new displacement, G location, or both to become grossly incompatible with the chosen hull. At that point, stability vanishes and capsize follows.

It's up to the operator to minimize that possibility by avoiding conditions, courses, or speeds promoting deck wetness and boat motions beyond the limits of stability.




Attitude, stability, and seakeeping

If a boat floats at all, stability in draft is automatic in that it will spontaneously return to its equilibrium LWL after a modest vertical displacement -- provided, of course, that nothing comes aboard or falls off in the process.

However, there's nothing automatic about stability in attitude. It's entirely up to the designer and operator to respectively build in and maintain safe margins of attitudinal stability under credible conditions with generous allowances for the unexpected. Ditto for seakeeping ability -- i.e., overall operability under foreseeable conditions.



Attitude
Attitude strongly influences both seaworthiness and performance. The complex terminology surrounding attitude reflects its freedom to vary in 4D -- i.e., in time and all 3 spatial dimensions.

To a good approximation, attitude changes are just rotations, often oscillatory, about various axes passing through the boat's center of flotation (F), which is just the centroid (geometric center) of its instantaneous waterplane. (A waterplane replica cut from thin rigid plate would balance perfectly on the point F.)

A boat's upright when her centerline plane is vertical. A rolling or heeling motion transiently inclines her centerline plane to the vertical about a longitudinal axis through F. Excessive rolling can bring large quantities of green water aboard as a prelude to capsize. A boat is said to list to the low side when her centerline plane is chronically off-vertical due to load imbalance -- including that due to flooding.

A boat's on an even keel when her actual and intended static waterlines are parallel. There is no implication of a horizontal keel. A pitching boat oscillates around even keel about a transverse axis through F.

Trim, a quasi-static deviation from even keel, is positive when bow-up. Warships and merchant vessels typically keep even keels in calm water, but small fast boats with displacement hulls tend to adopt increasingly positive trims as they near top speed, as seen in Trident's pool trial video. All of our speedboats trim up with speed, least of all long, heavy Nadine.

Positive trim can be beneficial if it reduces water coming over the bow to a manageable level, but too much takes a toll on top speed and risks green water over the stern instead. The fore-aft load distribution seen on freeboard-challenged Tramontana reflects these trade-offs.

A boat yaws when her heading (centerline plane azimuth in the horizontal plane) rotates away from her actual direction of motion relative to the water about an axis parallel to the hull's z-axis. Yaw is strictly a dynamic condition in the absence of currents and tends not to oscillate.



Center of buoyancy
The buoyancy force (FB)exerted on a freely floating hull is an indirect consequence of the action of gravity on the surrounding water. Like weight W, the buoyancy force always acts vertically, though in the opposite direction and not necessarily along the same line of action.

Per Archimedes' Principle, weight and the buoyancy force are exactly balanced at equilibrium draft. Hence,

FB = -W = -ρ g

where ρ is the water density, and is the volume of water displaced by the hull. At constant ρ,

Δ = ρ

Just as the boat's weight appears to act through its center of mass (G), the buoyancy force appears to act through a single point called the center of buoyancy (B).

These centers never coincide in a freely floating boat. As we'll see, the boat's stability in attitude depends entirely on their respective locations WRT the boat's keel and centerline plane.

Consider a freely floating reference boat that neither gains nor loses mass of any kind, including water. If all the mass onboard is held rigidly in place, G will have a fixed location WRT the hull at a height KG above the keel. If the boat is well-balanced, G will lie in the centerline plane.

Where, then, is B? The only certainty is that it lies at the center of mass of the volume of water displaced by the hull. In the usual case of uniform water density, B also coincides with the geometric center of the boat's underbody, and therein lies the rub: Since the size and shape of the underbody varies with attitude and draft, the location of B relative to G must vary as well.

When our reference boat's upright (roll angle 0°), B and G lie on the same vertical line of action within the centerline plane. The boat will be stable in this position if and only if B lies closer to the keel than G -- i.e., if and only if KB < KG, where KB is the height of B above the keel. Otherwise, the boat would roll over and capsize of its own accord.

When the boat rolls to one side, B shifts off the centerline plane toward the low side while G stays put relative to the hull. The vertical line through B then intersects the centerline plane at a point called the metacenter (M). When M lies above or below G, weight and the buoyancy force generate a rolling moment (torque) on the boat, as they no longer act along the same vertical line.

This moment is a righting moment acting to reduce the roll angle if M lies above G, and an overturning moment if M lies below it. In the latter case, the boat capsizes. Clearly, M is more likely to fall above G when the latter is low to the keel by design.

When M and G happen to coincide, these moments vanish, leaving the boat in a metastable state wherein even the slightest disturbance could trigger a capsize. The corresponding roll angle is known as angle of vanishing stability (AVS).



Coupling
Dynamic changes in underbody volume and shape during rolling, pitching, yawing, and heaving cause B to shift longitudinally, transversely, or both. The resulting moments couple attitude changes to one another and to heave. Hence, for typical hull shapes, a roll necessarily induces a small pitch, and a roll and pitch together induce a small yaw and heave.

These important couplings allow attitude oscillations to transfer kinetic energy accumulated from repetitive wave impacts amongst themselves in unexpected and potentially dangerous ways.

Though one often dominates, rolling, pitching, and yawing generally occur in combination in rough water, and they're always joined by heave -- the superimposed vertical motion of G as waves pass beneath the boat. The irregular nature of real waves would be enough to insure such complex motions, but as we've just seen, roll, pitch, yaw, and heave are also coupled dynamically by the boat itself.



Shallow water, squat, and sinkage
Hydrodynamically, a boat of waterline length L is in shallow water when water depth h < 5 L. LEGO® boats often find themselves in shallow water in bathtubs and wading pools like that in Earline's maiden voyage video above.

When in shallow water, don't be caught off-guard by squat, a dangerous loss of bottom clearance that grows with decreasing depth and the square of speed. Freeboard isn't a reliable indicator of squat, as the surrounding water surface is also drawn down. In 1994, Queen Elizabeth II ran aground on a well-charted rocky shoal at 24 knots due to underestimation of squat. She would have cleared the shoal by 2-3 m at rest. A shallow pool shelf we'd launched from many times before without incident gave me my first taste of squat when I decided to cross it at full speed.

Shallow-water resistance exceeds deep-water resistance at the same speed, the disparity growing with decreasing depth.

Like all displacement hulls, LUHs show both dynamic positive trim and sinkage (the deep-water equivalent of squat) above certain length-dependent speeds. This double-whammy routinely swamped freeboard-challenged Tramontana before bulwarks were added to boost effective freeboard.



Stability
A boat is stable WRT a particular change in attitude -- e.g., a 10° roll induced by a wave impact or sharp turn -- if she returns to her normal attitude spontaneously when the causative force is removed. The buoyant torques responsible for stability in roll and pitch are called righting moments.

If the causative force is removed abruptly, a stable boat will oscillate around her normal attitude at a natural frequency specific to both the boat and the axis of rotation. The natural frequency in pitch is much lower than that in roll -- something readily observed in the bathtub by tipping a LEGO® boat in the appropriate direction and releasing it suddenly.

Because boats are by nature much easier to capsize in roll than in pitch, seaworthiness depends critically on a safe margin of roll stability, aka transverse stability.

Shipyards determine righting moment strength as a function of roll angle in stability trials performed after launching a new design and provide owners a curve of statical stability with righting moment strength plotted against roll angle.

LUHs don't come with curves of statical stability, but you can get a good feel for the way righting moment changes with roll angle by rolling a boat back and forth with your hand in a tub. The strength of the initial righting moment near the upright condition at 0° of roll is an important standard measure of calm-water roll stability.

A good feel for the minimum initial stability required for seaworthiness is a valuable tool. I've gotten into the habit of making qualitative manual (re)assessments of initial righting moment for every newly completed boat and every design change that might affect roll stability, and I don't need to let go of the boat to do so.

Another simple measure of calm-water roll stability is the angle of vanishing stability (AVS), beyond which a boat rolls to capsize on her own. On the curve of statitical stability, the righting moment goes to zero at the AVS.

Nadine has the roll stability to beat among our boats, but I can't quote an AVS, as her righting moment is still quite strong when she reaches her 27° flooding angle (the roll angle at which water starts pouring in over the low side).

Rolling past the AVS guarantees immediate capsize. A single roll past the flooding angle may not capsize a boat right away, but the water taken on is guaranteed to reduce her stability -- in part by decreasing her righting moment and AVS. The result is an increased likelihood of flooding -- or of reaching the AVS -- on future rolls.

Some PCHs, like the long, narrow SBH serving as Trident's center hull, find use only in multihulls. The main reason is lack of adequate roll stability under a typical powerboat load. Trident's AVS of 0° without side hulls means that her load renders her inherently unstable as a monohull boat. Her AVS of ~25° with sidehulls means that she's stable enough for rough pool water.

As a general rule, the lower G is to the keel, and the greater the breadth and the breadth-draft (B/T) ratio, the greater the initial righting moment and AVS in calm water. Nadine's breadth and B/T ratio are 0.142 m and 7.1, respectively. The same figures for Trident's SBH center hull are 0.048 m and 1.33. Quite a difference.

NB: Unfortunately, these simple measures of calm-water stability are poor predictors of stability in high waves. The notion of dynamic stability recognizes the fact that a boat on a high wave crest running perpendicular to her keel is much less stable than her calm-water stability would suggest -- especially if the wave is also steep.



Seakeeping
Seakeeping refers to the overall operability of a boat under all credible conditions. Controllability, maneuverability, and speed are important here, as evasion of hazards like breaking waves and obstacles often hinges on the ability to change course, speed, or both decisively.



Twin-screw propulsion really shines here, as it largely circumvents the factors known to reduce rudder effectiveness in rough water.

Operability also demands a shipboard environment that allows crew members to perform their duties safely and effectively in heavy seas. This calls for hull shapes and dimensions that limit boat motion amplitudes and accelerations to tolerable levels.



Broad, flat-bottomed PCHs like the CLH above and the CWH in the previous photo would not score well here, but this is one design challenge that LEGO® naval architects can safely ignore. Minifigs are immune to sea-sickness, tend to stay on station once pressed into place, and aren't much help to begin with.




Waves and seas
Most of the hazards faced by a powerboat in open water surround the wind and waves encountered therein -- especially the latter.

Real waves in oceans and swimming pools are irregular in that their pattern never repeats itself in detail, and their crests are fairly short. Multiple wave sources (moving bodies) and repeated wave reflections and refractions in pools make for a chaotic water surface with very short crests known as chop.

Unfortunately, rogue waves are much more common in busy pools than on the high seas. While the root causes of natural rogue waves remain poorly understood, little mystery surrounds pool occurrences. Most of the latter come from cannonballs intentionally done right next to your boat by -- you guessed it -- unsupervised little boys.



A bad day in the Gulf of Alaska


The guy who named the Pacific must've caught it on a good day, because there was nothing pacific about it on this day in the Gulf of Alaska.

The video above shows a heavy confused, breaking sea dominated by a steady parade of high following (stern) waves with less frequent groups of even higher spilling breakers from starboard.

The lead boat is already listing to port from having taken on water. It capsizes to port suddenly at 4:38 after being struck broadside by an unusually large breaking beam wave at its least stable moment -- when on the crest of a wave from the stern.

This video is worth watching more than once, as it illustrates many of the seaworthiness issues discussed on this page. Everything seen in the video can happen at LEGO® scale -- including the loss of stability due to flooding and dynamic loss of stability on wave crests.



Sea state
Sea state refers to the statistical distribution of wave properties of practical concern in a particular patch of water. The rich terminology surrounding sea state is useful in that it helps one "read the water". Identifying developing hazards while there's still time to react takes some of the risk out of LEGO® powerboating in busy pools.

The wave properties pertinent to sea state include crest-to-trough height, crest orientation and length, direction and celerity (speed) of wave travel, wavelength, frequency, period, and the prevalence of steep or breaking waves. The higher the sea state, the more dynamic and dire the boat's situation becomes -- especially when complicated by high winds.

Wind-driven waves whipped up by severe storms at sea are the root-cause of most real-world high sea states. Wind seas -- i.e., sea states generated by local winds -- radiate waves of many different wavelengths into the water beyond the storm.

Swell, as waves from distant storms are known, can travel thousands of kilometers with little attenuation. As swell of longer wavelength travels faster and attenuates less with distance, the first swell to superimpose itself on a local sea state is generally higher than the swell to follow and has much longer crests than those typical of a (local) wind sea.

Confused seas -- typically local wind seas with superimposed swell -- are dominated by waves coming from two or more different directions. As seen in the fishing boat capsize video above, the high, steep, short-crested waves generated by constructive interference at wave crest intersections in a heavy confused sea are quite dangerous.

LEGO®-scale high sea states tend to be confused seas generated by multiple disturbances some distance away -- e.g., by swimmers and divers in a busy pool or cove, or by wind running ahead of an approaching thunderstorm. Such disturbances are common occurrences all summer long where I live.

Just as sea state can escalate dramatically over a shallow harbor bar, an otherwise manageable pool sea state can turn ugly over shoals (shallows) less than a dominant wavelength deep, in wave-focusing pool corners, or in converging currents (e.g., near a drain).



Seas worth recognizing
Sea (also seaway) refers to the patch of rough water occupied by a particular sea state.

Chop seems to be the norm in most pool sessions, but I've seen every sea state described below in pools -- especially when the diving area gets busy or the wind comes up. Irregular seas with dominant waves coming from a single direction are more the norm in the open ocean but also occur occasionally in pools with active diving areas.

The dominant waves in a following sea, head sea, and beam sea appear to overtake the boat from the stern, bow, and side, respectively. A quartering sea is intermediate between a following and beam sea in apparent direction of wave approach.

Contrary to common belief, the order of decreasing peril is quartering > following > head > beam. Quartering and following seas are lumped as stern seas, and stern and head seas as longitudinal seas, the last out of respect for their greater capsize risk relative to beam seas.

A boat in a steep sea repeatedly finds itself badly misaligned with gravity on uncommonly steep wave faces. In extreme cases, gravity can jam the bow of a boat surfing down a steep wave face into the trough below -- a dire event known as pitch-poling.

Wind, shoals, and currents are common wave-steepening agents. All occur in swimming pools. Steep seas increase the risk of capsize in a host of mostly indirect ways -- in no small part, by promoting wave-breaking.

A breaking sea is dominated by large, steep breaking waves with numerous whitecaps. A breaking sea in deep water is a sure sign of a very high sea state.

The extreme wave loads possible when a breaking wave impacts a boat can capsize it outright, as seen here. The breaking seas I've seen in pools occurred on windy days.



Wave loads and boat responses
Boat-wave interactions are exceedingly complex but approachable if broken down into (i) wave loads -- i.e., forces exerted on the hull in wave encounters, and (ii) boat responses to the wave loads.

Boat responses represent dynamic combinations of 6 distinctly different elementary boat motions called degrees of freedom (DOFs). Each would die out at its own decay rate if another wave didn't come along.

The 3 translational DOFs are surge, sway, and heave. The first two correspond to respective displacements of the boat's center of mass G along the hull's x- and y-axes. Heave is a displacement of G along the hull's z-axis.

The 3 rotational DOFs correspond to roll, pitch, and yaw -- i.e., to respective rotations or oscillations about axes parallel to the boat's x-, y-, and z-axes. They're coupled to each other and to heave via changes in underbody shape and volume. Hence, wave energy pumped into any one of these responses can bleed into the other three, sometimes abruptly and dangerously.

Naturally, the water responds to the boat's response, and gravity acts on both the whole time.

Gravity's effect on the water is as always re-routed via water pressure into the buoyancy force supporting the hull against gravity. Boat weight and the buoyancy force are always vertical and opposed. Per Archimedes' principle, they're exactly balanced in the static case, but the boat-wave interaction is anything but static.



Resonance
Resonance is noteworthy for its ability to turn small periodic wave loads into dangerous boat oscillations.

Roll resonance, the most important case, occurs when the wave-encounter frequency ωW approximates the boat's natural frequency of oscillation in roll ωR (think metronome) or a whole number multiple thereof. Wave encounter frequency is a function of the boat's speed and direction of travel relative to those of the dominant waves.

Wave loads pump kinetic energy into roll very efficiently at resonance. Rapid growth of roll amplitude follows. DOFs coupled to roll can become strongly excited as well.

In the presence of other compounding factors like flooding, FSEs, improper loading, and loose or lost load, roll resonance can lead to capsize. However, if ωW can be altered quickly enough by a change in course, speed, or both, the resonance can be broken.



Dynamic stability in waves
Calm-water roll stability depends primarily on static waterline breadth B, draft T, waterplane area AWP, and underbody volume and shape.

Unfortunately, these factors become highly dynamic in waves, and dangerous variations in stability can result. The term dynamic stability acknowledges this fact.

The greatest departures from calm-water stability come in longitudinal seas dominated by wavelengths near boat length. AWP then becomes a function of wave crest position along the hull, with the minimum at midships. The resulting reduction in roll stability is called pure loss of stability to distinguish it from parametric roll, a coupled resonance of even greater peril occurring in the same setting.

The flat bottoms and near-vertical sides found on most PCHs reduce AWP variation, while overhanging sterns like those on the CLH and especially on the CCH amplify it.

Pure loss of stability on wave crests heightens the risk of sudden capsize. Compounding factors like resonance, flooding, FSEs, improper loading, and loose or lost load only make matters worse.

Stern seas with dominant wavelengths and celerities near boat length and speed, respectively, carry the greatest capsize risk, as the crests then pass along the hull very slowly. The long periods of time spent near minimum stability give boat responses ample time to build to dangerous levels.

A head sea reduces the time spent near minimum stability in each wave pass, but the threat of capsize due to pure loss of stability remains. The signature head sea hazard, however, is repeated green water over the bow as the boat plows into oncoming wave faces.

The CLH, CCH, and FFH exemplify the usual countermeasure -- namely, increased freeboard at the bow via a raised foredeck surrounded by bulwarks. The slight flare of the CLH bow also helps.

Trident's needle-like sealed center hull with narrow cambered decks and the wide stance of her sealed side hulls allow an entirely different wave-piecing approach to head seas.

A heavy beam sea can excite sustained, high-amplitude rolling, especially near resonance -- i.e., when ωWωR.

However, the associated stability fluctuations are slight, and capsize generally ensues only if the boat takes a direct hit by a steep breaking wave or has already been compromised by one or more of the compounding factors mentioned previously. (This is exactly the set-up that led to the fishing boat capsize shown in the Gulf of Alaska video embedded above.)

Unfortunately, excessive rolling only increases the likelihood that one of these compounding factors will eventually materialize.



Capsize modes
The terminal event in most capsizes is usually a sharp roll exceeding the boat's AVS, but a pitch-pole and a sharp yaw can accomplish the same thing in extreme stern seas.

A capsize mode is an identifiable sequence of events likely to end in capsize under certain more or less recognizable conditions. The events may include FSE development or operator error (often, failure to act).

The predisposing conditions typically include a characteristic sea state, a particular speed and direction of travel relative to those of the dominant waves, design choices made long before, and reluctance to to change course, speed, or both.

Capsize modes are worth knowing about, as the final flip can unfold in seconds to minutes in large ships and a split second at LEGO® scale. Best, then, to see capsizes coming and try to intervene as early as possible. At design stage, that means building in stability to spare.

Several capsize modes have already been noted in conjunction with particular sea states and dynamic stability. Two additional modes deserve mention here.

Parametric roll occurs in longitudinal seas, especially following seas, with a dominant wavelength and celerity closely matching boat length and speed. Sustained pitching at a wave-encounter frequency close to twice the boat's natural roll frequency can then trigger a sudden capsizing roll via pitch-roll coupling, even if the boat has no ostensible reason to roll.

The only way to prevent parametric roll is to recognize undue rolling in a longitudinal sea and change course and speed as quickly as possible to nip the inciting resonance in the bud.

In a broach, a more common capsize mode, the inciting event is a sudden forced yaw on the face of a steep wave in a severe stern sea -- especially a quartering sea.

The most extreme surges occur when gravity propels a boat bow-first down a steep wave face. When surge combines with loss of control due to rudder or prop emergence near a steep wave crest, the boat can enter a sharp yaw -- especially in a quartering sea or if the wave happens to be breaking on the stern at the time. At some critical yaw, the boat broaches or "broaches to", as they say, "tripping over her own keel" in a final capsizing roll.



Avoiding capsize in busy pools

Please click here to see this important final section.




Selected references

Complete list here.



Comments

 I made it 
  July 19, 2015
Quoting H a v l Fascinating reading. Thank you for sharing your knowledge and research. I'd love to build a CLH-based powerboat some day.
Thanks for the kind words, Havl. This megapage was obviously a labor of love for me. Hope you get a chance to make a CLH-based boat, too. The CLH is by far the best unitary hull TLG ever made for speedboats and working ship models alike. Really hope it reappears in another set soon.
 I like it 
  July 15, 2015
Fascinating reading. Thank you for sharing your knowledge and research. I'd love to build a CLH-based powerboat some day.
 I made it 
  November 21, 2014
Quoting Nerds forprez We may be few and far between but there are us ot there that love this stuff :) BTW... are you on Eurobricks? There is a whole community there are complete LEGO geeks like ourselves, and a healthy sample of non-purists that will extend boundaries if needed and use other elements to try and improve LEGO models.
Thanks again for the encouragement. Yes, I've stolen some great ideas from Eurobricks but should look again for the non-purist stuff you mentioned. I notice that Sariel's new book (highly recommended, BTW) showcasing selected models from builders he admires includes more than a few models with a key non-LEGO components, and he's not bashful about doing that himself. He makes that stance quite clear in the book: This building genre is primarily about functional realism and meeting LEGO engineering challenges. If it takes a non-LEGO component here and there to capture the functional essence of some gizmo, real or imagined, so be it. If it looks good, so much the better. I'm eternally grateful for the astounding array of technical parts TLG has already provided us. I'm quite sure that their designers yearn for most if not all of the new parts I do and more. However, I'd rather they stay in business and leave it to them to release new parts at a rate that makes market sense. Meanwhile, we all have building to do and can't be bound by such decisions. Hence, we'll continue to supplement the official parts inventory as needed. Good to see from his book -- but not surprising -- that some of the heaviest hitters in technical LEGO share that sentiment.
 I made it 
  November 21, 2014
Quoting Gabor Pauler Nice groundbreaking research!
Gabor, coming from the guy who's way out front on LEGO helicopters, that's quite a compliment. The selfish goal here is to stir up more interest in powerboats on MOCpages so I can learn from the boats other folks come up with.
 I like it 
  November 20, 2014
Nice groundbreaking research!
 I made it 
  November 18, 2014
Matt and Nerds forprez, Many thanks for your comments. My talent for over-complicating things knows no bounds -- especially when combined with a life-long fascination with boats and ships. Cooking up these mega-MOCpages forces me think very carefully about the overlaps and disconnects between real-world and LEGO engineering. Most gratifying to know that others find them useful as well.
  November 18, 2014
We may be few and far between but there are us ot there that love this stuff :) BTW... are you on Eurobricks? There is a whole community there are complete LEGO geeks like ourselves, and a healthy sample of non-purists that will extend boundaries if needed and use other elements to try and improve LEGO models.
 I like it 
  November 15, 2014
I'm in awe at your continued attention to every possible detail. This is amazingly thorough and enlightening. I'll need to come back for reference. Excellent!
 I like it 
  November 14, 2014
So thorough! Every post is like reading a book. I wish everyone's Technic posts were like this guys....including mine :)
 
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