How to Think Like a Naval Architect
Naval architecture is the engineering of floating structures. Everything in this field flows from a handful of physical ideas:
- Archimedes' principle: a floating body displaces a weight of water equal to its own weight. If the seastead weighs 27,500 lb, it must push aside exactly 27,500 lb of seawater (about 430 ft³, since seawater weighs ≈64 lb/ft³).
- Stability: when tipped, does it return upright? This depends on the geometry of buoyancy versus the height of the center of gravity.
- Seakeeping: how the platform responds to waves — a matter of natural periods, damping, and the wave climate it will live in.
- Resistance & propulsion: how much force it takes to push the shape through water and air at a given speed, and whether the propulsion can supply it.
Key idea: everything oscillates
A floating platform is a mass attached to a "spring" (buoyancy) moving in a forcing field (waves and wind). Almost every seakeeping question reduces to: what is the natural period of the motion, how much damping does it have, and does the ocean contain energy at that period?The figures below show the design concept used as the running example throughout this page: an equilateral triangle superstructure 44 ft on a side and 7 ft tall, supported by three vertical legs, each a NACA 0035 foil section with an 8.5-ft chord (≈3 ft maximum thickness), half-submerged, with heave plates, ladders, rim-drive thrusters, a solar roof, and a small RIB tender aft.
About the numbers in this page: worked examples use the stated design (44-ft triangle, three NACA 0035 legs with 8.5-ft chord ≈ 3-ft thickness, 27,500 lb displacement, half-submerged legs) plus standard textbook approximations. They are back-of-envelope estimates for learning — a real project needs formal hydrostatics, seakeeping analysis, structures, and review against standards such as ISO 12217, ABS or DNV rules, and local maritime regulations.
1. Resonant Roll Period
A vessel that rolls is a rotating mass held by a restoring "spring" — gravity pulling it upright. Every such system has a natural (resonant) period at which it "wants" to oscillate. Roll is the most familiar motion because it is the most uncomfortable and the most dangerous.
I44 = roll moment of inertia (weight × radius of gyration²); Δ = displacement (weight); GM = metacentric height (the stiffness measure); k44 = roll radius of gyration; g = 32.2 ft/s²
The formula tells a simple story: heavy and far-from-axis mass (big k) makes the period longer; strong stability (big GM) makes it shorter. Sailors call a large-GM vessel stiff — it snaps back quickly with a short, jerky period. A small-GM vessel is tender — slow, lazy rolls, but if GM gets too small or negative, the vessel capsizes.
Why resonance matters
Waves rolling a boat apply a forcing push once per wave (strictly, once per encounter period). When the encounter period matches the natural roll period, each push adds to the previous one — synchronous rolling — and amplitudes can grow several-fold. The amplification at resonance is roughly 1/(2ζ), where ζ is the damping ratio; an undamped system would build without limit. Real vessels have ζ ≈ 0.05–0.2 in roll (often the least-damped motion), which is why roll resonance is a classic capsize and injury mechanism.
| Wave type | Typical period range | Implication |
|---|---|---|
| Wind sea (chop) | ≈ 3–8 s | Excites short-period (stiff) vessels |
| Swell | ≈ 8–20 s | Excites tender vessels, spar buoys, semis |
| Long swell / infra-gravity | > 20 s | Rare; matters for very soft platforms |
The designer's goal is either (a) place natural periods outside the band where the ocean has energy, or (b) accept resonance risk but supply heavy damping (bilge keels, hull form, heave plates, active stabilizers) so resonance cannot build.
For this seastead (illustrative estimate)
The three legs sit near the corners of a 44-ft triangle, about 25 ft from the center. Each leg's waterplane slice has area ≈ 17 ft², so the waterplane inertia is ≈ 3 × 17 × 25² ≈ 32,000 ft⁴. Dividing by displaced volume (≈430 ft³) gives a metacentric radius BM ≈ 74 ft. Even allowing for a center of gravity well above the center of buoyancy, GM is likely in the tens of feet — enormous, like a trimaran with wide outriggers.
With a roll radius of gyration of perhaps 18–22 ft (mass concentrated out at the legs), the roll period works out to roughly 2.5–3.5 seconds: short, stiff, catamaran-like. That is inside the wind-sea band, so short chop can excite roll resonance. The saving grace is damping: legs spread 40+ ft apart, shedding vortices from foil edges and heave plates, damp roll far more strongly than a single hull would. Expect quick but small-amplitude motions rather than slow deep rolls. An inclining test after assembly (tilt with known weights, measure the angle) should be done to confirm GM, and roll period can be measured directly by timing free oscillations.
How to evaluate
- Estimate GM and Troll; compare with the wave-period table for the intended cruising area (trade-wind Caribbean: lots of 5–7 s energy).
- Identify the damping strategy for roll (here: leg spacing, foil edges, heave plates).
- Check that GM is not merely large but that the range of positive stability (how far it can heel and still recover) is adequate — big GM alone is not the whole story.
- Plan a post-build inclining test and motion measurements; compare with predictions.
- Consider crew comfort metrics: people are most sensitive to accelerations around 0.1–0.3 Hz (3–10 s periods) — exactly the band a stiff small platform lives in.
2. Small Waterplane Area
The waterplane is the shape of a vessel's intersection with the water surface. Its area, Aw, controls vertical stiffness:
ρ g ≈ 64 lb/ft³ for seawater; m = vessel mass; ma = hydrodynamic "added mass" (water that must move with the body)
Intuition: a canoe (large waterplane relative to its weight) sinks and rises with every ripple — it is "welded" to the surface. A spar buoy or a semi-submersible (tiny waterplane for its weight) barely notices individual waves; between waves it has nothing to push against. Smaller waterplane → softer heave stiffness → longer natural period and less wave-following.
Heave is also the motion most tied to seasickness (vertical acceleration) and to slamming loads, so minimizing it is central to any "soft ride" claim.
Small waterplane as a design family
- SWATH (Small Waterplane Area Twin Hull): thin struts pierce the surface; the fat buoyant hulls hang deep below, under the most energetic wave motion.
- Semi-submersible platforms: the same idea with 4–8 columns (see Section 6).
- Spar buoys: one deep cylinder, tiny waterplane, very long periods.
For this seastead
Each leg's waterline slice is a NACA 0035 section of area ≈ 17 ft², so Aw ≈ 3 × 17 ≈ 52 ft². Vertical stiffness ≈ 64 × 52 ≈ 3,300 lb per foot of immersion (≈275 lb/in) — about 12% of displacement per foot, matching the designer's own note ("a 1-foot change is about 1/7 of total buoyancy"). Consequences:
- Payload sensitivity: adding 1,000 lb of people and stores sinks the platform only ~3.6 in. Comfortable margins; also means small weight growth does not sink it.
- Heave period: with mass ≈ 854 slugs and no added mass, T ≈ 3.2 s; added mass from the plate-like legs and heave plates (realistically 50–150% of the vessel mass) pushes it to roughly 4–5.5 s. That overlaps common wind-sea periods — so this is a moderately soft design, not an extreme SWATH. The designer is right to say so.
- The mitigation is damping: heave plates dramatically raise both added mass (softening) and damping (preventing resonant buildup). They are the single most important ride-quality component on this design.
- A deeper draft (more of each leg submerged) would lengthen the heave period and reduce excitation — but costs draft, trailering depth at the yard, and packability. The 50/50 split is the compromise.
How to evaluate
- Compute Aw and lb-per-foot of immersion; compare with displacement to get "sinkage per added ton."
- Estimate Theave including added mass; where does it sit versus local wave statistics?
- Size the damping plan (heave plate area is a known art from spar and offshore design — plates of roughly one column-diameter radius are typical).
- Check freeboard and down-flooding margins: how many feet can it sink before waves reach the walkway or door sills?
3. Drag for Something Moving Through the Water
Total resistance is the sum of physically distinct parts, each with its own physics:
| Component | Physics | Depends on |
|---|---|---|
| Skin friction | Shear stress of water sliding along the surface | Wetted area, speed, surface roughness (Reynolds number) |
| Form (pressure) drag | Flow separation and pressure differences front-to-back | Shape and orientation (drag coefficient) |
| Wave-making drag | Energy radiated into surface waves the body creates | Speed vs. size (Froude number); depth below surface |
| Induced drag | Lift-generating surfaces (e.g., struts resisting side-slip) trail vortices | Sideways forces — wind, current, turning |
| Appendage drag | Ladders, plates, conduits, sensors, fouling | Often 20–100% on top of the "clean" estimate! |
| Air drag | Wind on superstructure (Section 4) | Area and shape above water |
ρ = 1.99 slug/ft³ (seawater); S = reference area (be consistent!); η = overall propulsive efficiency (rim drives + electrical ≈ 0.4–0.6). Note D grows with V² and power with V³ — doubling speed costs ~8× the energy.
Two dimensionless numbers organize the physics:
- Reynolds number Re = V·L/ν (ν ≈ 1.2×10⁻⁵ ft²/s) — ratio of inertia to viscosity. Sets the friction coefficient, e.g. the ITTC 1957 line: Cf = 0.075 / (log₁₀Re − 2)², typically ≈ 0.003 for these sizes and speeds.
- Froude number Fr = V/√(g·L) — ratio of speed to wave-making speed. Displacement hulls hit the "hull speed wall" near Fr ≈ 0.4. Deeply submerged bodies make almost no waves, which is why SWATH hulls and semi-sub pontoons are efficient at low Fr despite blunt shapes.
For this seastead — worked example at 5 knots (8.4 ft/s)
- Re per leg ≈ (8.4 × 8.5) / 1.2×10⁻⁵ ≈ 6×10⁶ → Cf ≈ 0.0033.
- Wetted surface ≈ 3 legs × (perimeter ≈ 18.5 ft) × 7–8 ft submerged ≈ 400–440 ft² → friction drag ≈ 95–105 lb.
- Form drag on the foil sections (CD,planform ≈ 0.01–0.02, planform ≈ 185 ft²) → ≈ 130–195 lb. (See Section 7 — a NACA 0035 is thick but clean.)
- Appendages — ladders, heave plates, conduit, thruster housings — plausibly add 50–150 lb.
- Total ≈ 300–450 lb at 5 kt. Power ≈ D·V/η ≈ (400 × 8.4 / 550) hp / 0.5 ≈ 12 hp ≈ 9 kW electrical.
- Battery check: 25% of 27,500 lb ≈ 6,900 lb ≈ 3,100 kg of LiFePO₄ ≈ 280–400 kWh (pack level). At 9 kW that is 30–45 hours ≈ 150–220 nautical miles per charge at 5 kt — solar then covers hotel loads and recharging. At 8 kt, power roughly triples for the same range; slow is the economical strategy, which suits this design.
How to evaluate
- Ask for a drag budget table (friction / form / appendage / air, by speed) — not a single "it's streamlined" claim.
- Inventory every appendage; ladders and heave plates are the big items here. Removable heave plates for passages are worth considering.
- Plan for fouling: marine growth can double friction drag within months in tropical water — include cleaning access (the leg ladders help).
- Verify with model tests or CFD before committing to range/speed promises.
- Sanity-check range with the V³ power law: every knot of extra cruise speed is expensive.
4. Wind Drag
Air is ~800 times less dense than water, but the seastead presents far more area to the wind than to the water — a 44-ft triangle of wall, plus railings, solar panels, and the exposed upper halves of the legs. Wind load uses the same equation with air density:
ρair = 0.00238 slug/ft³; A = projected frontal or side area; V in knots. Use gust speeds, not averages.
Wind matters three ways:
- Station-keeping and steering: thrust must counteract wind force, or moorings must.
- Heeling: wind force acts at the center of the exposed area (the center of effort), high above the center of underwater lateral resistance, creating a heeling moment that must be less than the righting moment.
- Weathervaning: if the center of effort is forward of the center of lateral resistance, the vessel turns its bow into the wind (stable and usually desirable); if aft, it falls off downwind and can become unmanageable.
For this seastead — illustrative numbers
- Frontal area: triangle wall ≈ 44 × 7 ≈ 308 ft², plus railings and exposed leg sections ≈ 370–400 ft² total. Side (lateral) area is similar.
- At 25 kt: F ≈ 0.004 × 375 × 25² ≈ 940 lb.
At 40 kt: ≈ 2,400 lb.
At 60 kt (squall/gust survival check): ≈ 5,400 lb. - Heel under wind is negligible here: heeling moment ≈ 940 lb × ~8 ft lever ≈ 7,500 ft·lb, against a righting moment of roughly 27,500 lb × GM ≈ 1.8 million ft·lb per radian → a fraction of a degree. Wind heel is not this design's problem; wind force is.
- Compare with thrust: six ~1.5-ft rim drives might deliver on the order of 600–1,200 lb combined. Holding station against 25–40 kt of wind may be marginal, and against 60 kt unlikely — which is precisely why the tension-leg mooring screws exist. The porous aluminum grating walkway is a genuine bonus: it lets wind (and green water) pass through instead of adding solid area.
How to evaluate
- Compute frontal and lateral projected areas, including solar panels and railings.
- Plot wind force vs. wind speed; overlay total available bollard thrust. Define the wind speed at which running for shelter or deploying moorings is mandatory.
- Size mooring hardware (screws, lines, fairleads) for the survival wind case plus wave and current loads, with safety factors.
- Check center of effort vs. center of lateral resistance for weathervane stability in forward and reverse winds.
- Verify wind-heel compliance with a small-craft standard (e.g., ISO 12217) even if the platform "feels" unstoppable.
5. Active Stabilizers
Passive devices (bilge keels, heave plates, hull form, flume tanks) need no power or sensing — they simply dissipate motion energy. Active stabilizers measure the motion and fight it in real time with a control loop: sensor → controller → actuator.
| System | How it works | Best at | Limits |
|---|---|---|---|
| Active fins | Rotating foils generate variable lift | Underway, at resonance | Need speed for lift; added drag |
| Gyroscopic (flywheel) stabilizers | Precessing spinning mass creates opposing torque | Zero speed, at anchor | Heavy, costly, only counteracts roll |
| Interceptors / trim tabs | Fast-moving plates adjust flow | Faster planing/semi-displacement craft | Speed dependent |
| Rudder-induced roll damping | Uses the rudder's side force | Underway | Conflicts with steering |
| Thruster-based (DP) | Thrust vectors modulate moments | Low/zero speed, heading control | Power hungry; response bandwidth |
Key concepts for judging any active system: bandwidth (can the actuator respond within a fraction of the wave period?), authority (how much moment can it generate?), energy cost, and failure behavior (what happens when the computer, sensor, or power channel dies — ideally it degrades to a safe passive state).
For this seastead
- The six fixed rim drives give, via differential thrust: yaw control (port pair vs. starboard pair; counter-rotating for zero-radius turns) and pitch trim (front leg reversing while rear legs push). Roll, however, has no direct actuator — thrusters are fixed facing fore/aft, and roll moments would need vertical or lateral thrust. Roll must be handled passively (widely spaced legs + heave plates — which is exactly what the geometry provides).
- Heading management is the real active tool: choosing the heading relative to seas, and gently repositioning with thrust, changes which motions get excited. This is how dynamically positioned vessels survive storms.
- Redundancy is genuinely good: each leg has its own battery bank, charge controller, and inverter, and its thruster pair draws from that leg — a single electrical failure strands one pair, not the platform. (This mirrors how offshore DP vessels achieve "equipment class" redundancy.)
- The two-seastead walkway idea implies relative-motion control: the two computers coordinating thrust to minimize relative surge/sway/yaw at the coupling — the same problem as DP station-keeping, one link over. It is feasible in principle with IMUs and shared data, and worth modeling before trusting people to a passageway.
How to evaluate
- For each of the six motions (surge, sway, heave, roll, pitch, yaw): what controls it — passive, active, or nothing? Is that matched to which motions the local sea state actually excites?
- Ask for the control architecture: sensors, update rate, actuator bandwidth, failure modes, manual overrides.
- Confirm the power budget includes active systems running continuously in a storm.
- Prefer systems that fail to a safe, damped, weathervaning state with no power.
6. Semi-Submersible Platforms
Semi-submersibles came from the offshore oil industry (early 1960s): put the buoyancy in big pontoons well below the surface, connect it to the deck with thin struts through the surface, and keep the working deck high above the waves. Because wave orbital motion decays exponentially with depth:
λ = wavelength. At a depth of half a wavelength, motion is only ~4% of the surface value — deep buoyancy sees a much calmer ocean.
Combined with the small waterplane of the struts, semis achieve natural heave/roll/pitch periods of roughly 20–60 s — far above storm-wave energy (5–15 s) — so they barely respond. SWATH ships (e.g., the US Navy's Kaimalino, or the later "Slice" hulls) applied the same principle to self-propelled vessels with superb passenger comfort.
The costs of the semi-sub approach
- Deep draft (often 25–60 ft operational) — limits harbors and shallow anchorages.
- Ballast complexity: they float high for transit, then ballast down to operate; stability must be safe at every intermediate draft.
- Drag and propulsion: large wetted surface and bluff pontoons make them slow; most are towed or crawl at 4–8 kt.
- Cost and maintenance of many watertight compartments, valves, and monitoring — which is also why they are so safe when done properly.
For this seastead — a hybrid, and that's the interesting part
- It is a mini semi-sub with only ~7–8 ft of draft and columns that are themselves the buoyancy (foils instead of strut-plus-pontoon). Compared to a true SWATH: much shallower (great for Caribbean anchorages and shipyard assembly), but the buoyancy sits closer to the surface, so wave excitation is higher and natural periods shorter (Sections 1–2). The heave plates are the compensating trick borrowed from spar and semi-sub practice: cheap, passive, bolt-on damping.
- Streamlined foil columns plus rim drives give it a propulsion efficiency a drilling semi never needed — moving at 4–6 kt is credible.
- Tension-leg parking is textbook TLP: helical screws + taut lines pull the platform down a few feet so the tendons never go slack. TLPs are the stiffest of all: heave, roll, and pitch become almost rigid; the softness that gives a nice underway ride becomes near-immobility when parked. Good — that is the goal for living aboard. The designer's notes (small tides, protected water, 3 ft of pull-down) are the correct constraints for a small TLP; note that big swell or a hurricane will violate them, so the operations plan needs a "when do we release/move" policy.
- Warm Caribbean water means fast marine growth — on legs, heave plates, and mooring lines — adding weight, drag, and corrosion. Plan haul-out or in-water cleaning intervals and inspect the foil surfaces.
How to evaluate
- Compare draft with intended anchoring depths and shipyard capabilities.
- Ask for motion predictions (RAOs — response amplitude operators) in realistic sea states, not just "it's a SWATH-like soft ride."
- Check compartmentation, damage-floodability (one leg holed), and free-surface effects in any tanks.
- Review the mooring operations plan: deployment loads, slack-line prevention, storm/hurricane policy, corrosion of screws and lines.
7. Coefficient of Drag Due to Shape
The drag coefficient CD packages "how slippery is this shape" into one number so different shapes can be compared. But it is only meaningful when you state the reference area and the flow conditions (Reynolds number, orientation). Typical values:
| Shape (flow left→right) | CD (frontal area) | Comment |
|---|---|---|
| Flat plate, face-on | ≈ 1.9–2.0 | Worst case; full flow separation |
| Cube, face-on | ≈ 1.05 | Sharp edges fix separation |
| Circular disk | ≈ 1.17 | |
| Sphere | ≈ 0.47 (≈0.1–0.2 in the "drag crisis") | Shows CD depends on Re |
| Circular cylinder, cross-flow | ≈ 1.0–1.2 | Why round piles are draggy |
| Streamlined strut (t/c ~ 20–30%) | ≈ 0.08–0.2 | Rounded nose + long taper kills separation |
| Streamlined body, CD on planform area | ≈ 0.008–0.02 | Mostly skin friction |
The lesson of a century of streamlining: round the front, taper the rear. Drag is dominated by the low-pressure wake behind a body, so a long tapered tail matters more than a pointy nose. Cutting the tail short (a truncated trailing edge, as on these legs to fit the 8.9-ft container height) adds modest base drag but keeps most of the benefit — a standard engineering compromise, used deliberately on struts and torpedoes.
Orientation flips everything: the same foil that slips through the water end-on has a cross-flow CD of order 1 broadside. Drag you hate while cruising is damping you love when parked — heave plates are deliberately the "flat plate" row of the table.
For this seastead
- Legs: NACA 0035 is thick (35% of chord) — thick foils have extra skin friction from large wetted area, but at 4–6 kt the penalty is small, and the thickness buys structure and battery volume. Expect CD,planform ≈ 0.01–0.02 going forward — roughly 50–100× less drag than a round cylinder of equal volume pushed sideways, and dramatically better than the same shape backward. Leading-edge-forward orientation is correct.
- Ladders on the front of the legs sit in the highest-velocity, most sensitive flow. Round rungs (CD ≈ 1.2) shed vortices, add drag, and can hum. Streamlined (flat/oval) rungs flush to the surface would cut this substantially.
- Heave plates: intentionally high-drag normal to motion — the point is dissipation. Their fore-aft drag when cruising is the price; being bolt-on, they could be removed for long passages.
- Conduit at the trailing edge: well-placed — it sits in the slow, separated wake where it adds least.
How to evaluate
- Whenever someone quotes a CD, ask: based on what area, at what Reynolds number, in which orientation?
- Every external item (ladder rung, bolt head, fairlead, sensor) is a small separation generator — tally them.
- Check that drag-critical surfaces (foil noses, plate edges) have a fouling and damage inspection plan.
- Where dissipation is wanted (heave plates), verify the shape is bluff on purpose; where speed is wanted, verify it is streamlined on purpose.
Putting It Together: A Seastead Evaluation Checklist
| Area | Key question | Tool from this page |
|---|---|---|
| Flotation | Displacement = weight, with margin? | Archimedes; lb/ft immersion (Section 2) |
| Stability | GM, range of stability, inclining test planned? | GM & roll period (Section 1) |
| Heave comfort | Natural period vs. local wave periods; damping? | Waterplane & heave period (Section 2) |
| Roll comfort | Is roll stiff or tender, and is it damped? | Resonance analysis (Section 1) |
| Speed & range | Drag budget at cruise speed; battery/solar math? | D = ½ρV²SCD; P ∝ V³ (Section 3) |
| Storm behavior | Wind force vs. thrust vs. moorings; heel; headings? | Wind loading (Section 4) |
| Motion control | Which motions are passive / active / unaddressed? | Stabilizer taxonomy (Section 5) |
| Parked behavior | Mooring concept, slack prevention, storm policy? | TLP logic (Section 6) |
| Shape efficiency | Every part streamlined or deliberately bluff? | CD thinking (Section 7) |
| Safety & compliance | Compartmentation, damage stability, redundancy, standards (ISO 12217, ABS/DNV), insurance? | Professional review — mandatory |
The described design's genuine strengths to verify and preserve: container packability, triple-redundant power and propulsion channels, no through-hulls in the legs, passive damping via geometry, tension-leg parking, and a realistic (slow-speed) propulsion philosophy. The main items to scrutinize with real analysis: stiff short-period roll/pitch in the wind-sea band, heave period near trade-wind chop periods (damping is everything), wind force vs. thrust budget, appendage and fouling drag, and storm/hurricane operating limits.
Glossary & Further Reading
| Term | Meaning |
|---|---|
| Displacement (Δ) | Total weight of the vessel = weight of water pushed aside |
| Draft / freeboard | Depth of hull below waterline / height of deck above it |
| Waterplane area (Aw) | Area of the vessel's "slice" at the waterline; sets vertical stiffness |
| Metacentric height (GM) | Stability stiffness measure; big GM = stiff, small GM = tender |
| Natural period | Period at which a motion freely oscillates; danger zone if waves match it |
| Damping ratio (ζ) | How quickly motion energy is dissipated; resonant gain ≈ 1/(2ζ) |
| Added mass | Extra water that must move with a body, lowering its natural frequencies |
| Reynolds number (Re) | Inertia/viscosity ratio; governs friction and separation |
| Froude number (Fr) | Speed/wave-making ratio; governs wave drag |
| CD | Drag coefficient — shape slipperiness, valid only with a stated reference area |
| RAO | Response Amplitude Operator: motion output per unit wave input, vs. frequency |
| SWATH | Small Waterplane Area Twin Hull — thin struts, deep buoyant hulls |
| Semi-submersible | Platform with deep pontoons on thin surface-piercing columns |
| TLP | Tension-Leg Platform — taut vertical tendons make it nearly rigid vertically |
| DP | Dynamic Positioning — computer-controlled thrusters hold position/heading |
| Rim-drive thruster | Propeller with the motor in a ring around the blade tips; no shaft seal |
| MSI | Motion Sickness Incidence — % of people sick vs. motion frequency & amplitude |
| Inclining test | Measuring heel from known shifted weights to determine GM |
Further reading
- Principles of Naval Architecture (SNAME) — the standard reference, especially the volumes on hydrostatics and seakeeping.
- Skene's Elements of Yacht Design — accessible entry to stability and drag.
- Faltinsen, Sea Loads on Ships and Offshore Structures — semi-submersible and SWATH motions.
- Fossen, Guidance and Control of Ocean Vehicles — dynamic positioning and active control.
- ISO 12217 (small craft stability), ABS/DNV rules for high-speed craft, offshore platforms, and DP systems — the regulatory yardsticks.