Naval Architecture — Cheat Sheet
Hydrostatics, stability, Froude and resistance, scantlings, sea water and cathodic protection on one page.
Hydrostatics
| Volume of displacement | ∇ = L·B·T·C_b |
| Displacement | Δ = ρ∇ — mass, not force; Δ·g for weight |
| Sea water, design | 1025 kg/m³ (fresh 1000) |
| Sea water, ITTC at 15 °C | 1026.021 kg/m³, ν = 1.1892×10⁻⁶ m²/s |
| Waterplane area | A_w = L·B·C_w |
| Tonnes per cm immersion | TPC = ρ·A_w·0.01 / 1000 |
| Sinkage from a weight | δ = w / (ρ·A_w) |
| Centre of buoyancy | KB = T/2 for a box; take it from your own hydrostatics |
Form coefficients
| Block | C_b = ∇/(L·B·T) |
| Midship | C_m = A_m/(B·T) |
| Prismatic | C_p = ∇/(A_m·L) = C_b/C_m |
| Waterplane | C_w = A_w/(L·B) |
| Rectangle | Every one of them is 1 — the box is the reference, not the target |
| What moves what | C_b buys displacement; C_p sets where it sits along the length |
Initial stability
| Metacentric height | GM = KB + BM − KG |
| Metacentric radius | BM = I/∇, I about the CENTRELINE |
| Waterplane inertia | I = i_w·L·B³, i_w = 1/12 for a rectangle, less for any real hull |
| Righting moment | M = Δ·g·GM·sin θ (small angles) |
| Heel from a shifted weight | tan θ = w·d / (Δ·GM) |
| Heel from a moment | tan θ = M / (Δ·g·GM) |
| Free-surface loss | (ρ_tank/ρ)·i/∇, i = l·b³/12 — independent of how full it is |
| One baffle | Cuts the loss to a quarter; n bays to 1/n². The width is CUBED |
| Roll period | T = 2π·k/√(g·GM), k ≈ 0.35–0.40 B on a small craft |
| Measured roll | GM = (2π·k/T)²/g — the one stability number a stopwatch gives you |
| Cost of height | Lifting w by h costs w·h/Δ of GM, directly |
Speed and resistance
| Froude on length | F_n = V/√(gL) — governs wave-making |
| Hull speed, F_n 0.4 | V = 2.4349·√L knots (L in metres) |
| Froude on volume | F_n∇ = V/√(g·∇^⅓) — governs whether it planes |
| Regimes | <1 displacement · 1–2 semi-displacement · >2 planing |
| Knot | 0.514444 m/s = 1.852 km/h |
| ITTC-1957 friction | C_F = 0.075/(log₁₀R_n − 2)² |
| Reynolds number | R_n = V·L/ν |
| Coefficient sum | C_T = (1+k)·C_F + ΔC_F + C_A + C_W + C_AA |
| Resistance | R_T = C_T·½ρSV² |
| Effective power | P_E = R_T·V |
| Propulsive chain | η_D = η_O·η_H·η_R, η_H = (1−t)/(1−w) |
| Shaft power | P_S = P_E/(η_D·η_S) |
| Rule of thumb | Power goes as V³ — 10% more speed is ~33% more power |
Plating and stiffeners
| Plate deflection | w = α·p·b⁴/D |
| Plate stress | σ = β·p·b²/t², b is the SHORT side |
| Flexural rigidity | D = E·t³/(12(1−ν²)) |
| Clamped, a/b = 1 | α = 0.00127, β 0.137 centre / 0.308 edge |
| Clamped, a/b = 2 | α = 0.00253, β 0.247 centre / 0.498 edge |
| Clamped, a/b ≥ 3 | α ≈ 0.0026, β ≈ 0.25 / 0.50 — a long bay bends like a strip |
| Simply supported, a/b = 1 | α = 0.00406, β = 0.287 |
| Simply supported, a/b = 2 | α = 0.01013, β = 0.610 |
| Spacing is the lever | b is squared in the stress — halving the spacing quarters it |
| Stiffener line load | w = p·s, s the spacing |
| Continuous over frames | M = wl²/12 at the support, wl²/24 at mid-span |
| Cut at every frame | M = wl²/8 — 50% more moment for the same metal |
| Deflection | wl⁴/384EI continuous, 5wl⁴/384EI simply supported |
| Required section modulus | Z = M/σ_allow |
| The plating is a flange | Include it — on a shallow bar it is most of the section modulus |
| Effective breadth | The full spacing is optimistic below about span = 6·s |
| Shear allowable | 0.577·σ_allow (von Mises) |
| Flat-bar tripping | Watch h/t_w above about 15 without a flange or bracket |
Pressure and head
| Hydrostatic pressure | p = ρ·g·h |
| Sea water | 1 m of head = 10.06 kPa = 1.459 psi |
| Fresh water | 1 m of head = 9.807 kPa |
| One atmosphere | 101.325 kPa ≈ 10.1 m of sea water |
| Design pressure | A slam pressure is not a static head — it comes from the rule book |
Sea water and corrosion
| Resistivity, temperate | 0.30 Ω·m (sediments 1.3) — DNV-RP-B401 6.7.4 |
| Protective potential, steel | −0.80 V vs Ag/AgCl |
| Al-Zn-In anode | ε = 2000 A·h/kg, E° = −1.05 V (sea water) |
| Zinc anode | ε = 780 A·h/kg, E° = −1.00 V |
| Driving voltage | |E°_anode − E°_protect| — 0.25 V for Al, 0.20 V for Zn |
| Design current density | Temperate 0–30 m, bare steel: 0.200 initial / 0.100 mean / 0.130 final A/m² |
| Tropical 0–30 m | 0.150 / 0.070 / 0.100 A/m² |
| Anode mass | M = I_mean·t·8760/(u·ε) |
| Utilisation factor | 0.90 long stand-off, 0.85 short/flush, 0.80 bracelet |
| Anode output | I = ΔE/R — resistance is geometry, so output is SHAPE not mass |
| Galvanic rule | Area ratio decides the damage: small anode + large cathode is what kills parts |
| Aluminium hull | Al anodes only; never magnesium in sea water — over-protection makes alkali |
Sanity checks
| Is GM positive? | And does it survive the tank being half full? |
| Short side, not long | Plate stress goes with the SHORT dimension squared |
| Did the plate count? | A stiffener without its plating has half the section modulus |
| Which Froude number? | Length for wave-making, volume for planing |
| Is C_W yours? | Nothing computes wave resistance from main dimensions |
| Anode: mass or shape? | Passing on kilograms and failing on output is the usual way round |
Formula reference — verify against the governing standard. Not a substitute for engineering judgment.