ship-resistance

name	ship-resistance
description	Ship resistance and propulsion — total resistance components (friction, wave, form, appendage, air), Froude number, Frictional resistance (ITTC-1957 Cf, form factor 1+k), wave resistance (Michell-Hogner thin ship, Kelvin wave pattern), model testing (Froude similarity), Holtrop-Mennen statistical method, propeller design (Wageningen B-series, KT-KQ charts), effective power PE, delivered power PD, propulsive efficiency, and MARPOL EEDI.
metadata	{"priority":7,"promptSignals":{"phrases":["ship resistance","Holtrop-Mennen","Froude number ship","propeller design","ship propulsion","Wageningen B-series"],"minScore":3}}

Ship Resistance and Propulsion — Complete Skill

Resistance Components

Total Ship Resistance

Total bare-hull resistance: R_T = R_F + R_W + R_F_form + R_APP + R_AIR [N; all at ship speed V_s]

Resistance breakdown (typical for cargo ship at design speed): R_F (friction): 60–80% of R_T (dominant for slow/medium ships) R_W (wave): 10–25% (dominant at high Froude numbers) R_APP (appendages: rudder, bilge keels, shaft brackets): 2–5% R_AIR (above-water windage): 1–2% R_F_form (form pressure): included in friction correction via form factor

Frictional Resistance (ITTC-1957)

ITTC Line

Coefficient of frictional resistance: C_F = 0.075 / (log₁₀(Re) - 2)² [ITTC-1957 correlation line; Re = V_s × L_WL / ν]

Reynolds number: Re = V_s × L_WL / ν [ν = kinematic viscosity of water; ν_SW ≈ 1.19×10⁻⁶ m²/s at 15°C, salinity 3.5%]

Frictional resistance: R_F = C_F × (1/2) × ρ × V_s² × S_WET [N; S_WET = wetted surface area [m²]; ρ_SW = 1,025 kg/m³]

Form factor (1+k): corrects friction for three-dimensional hull form R_F_total = (1+k) × C_F × (1/2) × ρ × V_s² × S_WET 1+k = 1 + 0.93 + 0.487118 × (1+0.011 × C_stern) × (B/L)^1.068... [Holtrop; detailed Eq. 12] Practical values: full hull forms C_B = 0.80: 1+k ≈ 1.20–1.30; fine hulls C_B = 0.60: 1+k ≈ 1.05–1.10

Wetted surface area: S_WET = L × (2T + B) × √(C_M) × (0.453 + 0.4425C_B - 0.2862C_M - 0.003467B/T + 0.3696C_WP) + 2.38A_BT/C_B [Holtrop formula; C_B = block coefficient; C_M = midship coefficient; C_WP = waterplane coefficient; T = draft; B = beam; A_BT = transverse bulb area]

Wave Resistance

Froude Number

Ship Froude number: Fr = V_s / √(g × L_WL) [dimensionless; g = 9.81 m/s²] Low Froude number (Fr < 0.25): wave resistance small; friction dominant High Froude number (Fr > 0.45): wave resistance significant; hump and hollows in R_W curve

Speed-length ratio: V_s(kn) / √(L_WL(ft)) = 1.34 = transition hump (wave resistance rapidly increases) V_s(kn) / √(L_WL(m)) = 0.74 (same Froude number)

Wave resistance humps and hollows: At Fr = 0.5, 0.4, 1/√3 = 0.577: wave troughs between bow and stern waves → relative hollows At Fr = 0.45, 0.57: wave crests coincide → humps (maximum R_W) Design: place operating speed at hollow if possible

Holtrop-Mennen Method (Statistical)

Industry standard for early design estimates: Developed from model tests of 334 ship hulls; valid range: Fr = 0–0.52; L/B = 3.9–9.5; C_B = 0.55–0.85; B/T = 2.1–4.0

Wave resistance (Holtrop 1984, R_W Eq. 7–14): R_W = C₁ × C₂ × C₃ × exp[m₁ × Fr^(d) + m₂ × cos(λ × Fr^(-2))] × (1/2)ρ × V² × L × B [N] [C₁, C₂, C₃, m₁, m₂, λ, d = functions of hull geometry parameters; see Holtrop 1984 Table 1]

Total resistance (simplified Holtrop-Mennen): R_T_total = (1+k) × C_F × (1/2)ρV²S + R_W + ΔC_F × (1/2)ρV²S + R_APP × (1+k_APP) ΔC_F = roughness correlation allowance = 0.0004 (typical for painted steel hull)

Example (container ship): L_WL = 200 m; B = 30 m; T = 10 m; C_B = 0.65; V_s = 12 m/s (23.3 kn); ν = 1.19×10⁻⁶ m²/s Fr = 12/√(9.81×200) = 12/44.3 = 0.271 (moderate; wave resistance ~15%) Re = 12 × 200 / 1.19×10⁻⁶ = 2.02×10⁹ C_F = 0.075/(log₁₀(2.02×10⁹)-2)² = 0.075/(9.305-2)² = 0.075/53.4 = 0.001404 S_WET ≈ 7,200 m² (estimated) R_F = 0.001404 × (1/2)×1025×144×7200 = 744 kN (bare friction) R_T ≈ 1.15 × 744 + R_W + corrections ≈ 850 kN + R_W (need Holtrop for R_W)

Model Testing (Froude Similarity)

Scale Effects and Extrapolation

Froude hypothesis: total resistance split into frictional (Cf depends on Re) + residuary (Cr depends on Fr) Scale law: Fr_model = Fr_ship → V_model = V_ship × √(λ)^(-1) [λ = scale ratio = L_ship/L_model]

Resistance extrapolation (ITTC method): C_TM = C_FM + C_RM [model total = friction + residual] C_RS = C_RM [residual same at same Froude number] C_TS = (1+k) × C_FS + C_RS + ΔC_F [ship total; use ship Re for C_FS; add roughness correction]

Typical model sizes: L_model = 5–10 m (towing tank tests); scale λ = 20–50 Towing speed: V_model = V_ship/√λ [Fr similarity]

Propeller Design

Wageningen B-Series

Most common open propeller series: B.Z.P (Z = blade number; P = pitch ratio P/D; 0.6–1.4; AE/AO = 0.40–1.05) Blade count Z = 2–7; optimal: 4–5 blades for merchant ships Open water efficiency η₀ = f(J, P/D, AE/AO, Z) from polynomial KT-KQ charts

Advance ratio: J = V_A / (n × D) [V_A = speed of advance through water; n = rev/s; D = propeller diameter] V_A = V_s × (1 - w) [w = wake fraction; w = 0.2–0.4 for typical ship forms]

Thrust and torque coefficients: K_T = T / (ρ × n² × D⁴) [thrust coefficient] K_Q = Q / (ρ × n² × D⁵) [torque coefficient] η₀ = (J/2π) × (K_T/K_Q) [open water efficiency]

Design point (maximum efficiency): Find J, P/D, AE/AO that maximize η₀ while achieving required K_T (thrust = resistance) Use KT-KQ polynomial (Oosterveld & van Oossanen 1975; 47-term polynomial)

Cavitation check (Burrill chart): σ = (P_s - P_v) / (0.5 × ρ × V_R²) [cavitation number; P_s = local static pressure at shaft depth; P_v = vapor pressure] V_R = √(V_A² + (0.7πnD)²) [blade tip relative velocity; 0.7R reference] From Burrill chart: allowable thrust loading τ_c vs. σ; verify τ_actual ≤ τ_allow

Power Balance

Required effective power: P_E = R_T × V_s [W]

Propulsive efficiency: η_D = P_E / P_D [overall propulsive efficiency] η_D = η₀ × η_H × η_R [η_H = hull efficiency; η_R = relative rotative efficiency] η_H = (1-t)/(1-w) [t = thrust deduction; w = wake fraction; η_H ≈ 1.05–1.20 for single screw] η_R ≈ 1.0 for twin screw; η_R = 1.02–1.08 for single screw (behind-hull gains)

Delivered power to propeller shaft: P_D = P_E / η_D [W; η_D typically 0.65–0.72 for modern ships]

Shaft power (accounting for transmission losses): P_S = P_D / η_S [η_S = shaft efficiency = 0.97–0.99] BHP at engine = P_S + mechanical losses

MARPOL Energy Efficiency

EEDI (Energy Efficiency Design Index)

EEDI = CO₂ per unit capacity per nautical mile: EEDI = (P_ME × C_SFC_ME × C_F,ME + P_AE × C_SFC_AE × C_F,AE - P_eff × ...) / (C_W × V_ref) [P_ME = main engine power; C_SFC = specific fuel consumption; C_F = CO₂ emission factor; C_W = capacity; V_ref = reference speed] Target: EEDI ≤ EEDI_required (decreasing limits Phase 1: -10%, Phase 2: -20%, Phase 3: -30% vs. baseline)

Standards and References

Standard	Scope
ITTC 7.5-02-03-01	Resistance uncertainty analysis
Holtrop & Mennen (1982, 1984)	Statistical resistance prediction
Wageningen B-series (Oosterveld 1975)	KT-KQ polynomial coefficients
MARPOL Annex VI	EEDI — ship energy efficiency
ISO 15016	Guidelines for ship speed-power performance

Output

Provide: hull particulars (L_WL [m]; B [m]; T [m]; C_B; C_M; C_WP; S_WET [m²]; displacement [t]), design speed V_s [kn] and Fr, frictional resistance (Re; C_F [ITTC-1957]; 1+k form factor; R_F [kN]; method: Holtrop Eq. 12), wave resistance R_W [kN] (Holtrop-Mennen or model test extrapolation; Fr; wave hump check), total resistance R_T [kN] and P_E [kW], propeller design (Z blades; D [m]; P/D; AE/AO; J; KT; KQ; η₀; cavitation number σ; Burrill check), hull efficiency (w; t; η_H; η_R; η_D overall), delivered power P_D [kW] and P_S [kW], engine selection (MCR recommendation; fuel type), EEDI [g CO₂/t·nm] vs. Phase limit, and applicable standard (ITTC resistance method; Holtrop-Mennen; MARPOL EEDI).