Model–Ship Correlation (Scaling)

Extrapolate model test results to full scale using ITTC ’57 + correlation allowance. Includes Prohaska k-estimator.

Method

Pick direct scaling or estimate k from two low-speed points.

Model L (m)

Ship L (m)

Model S (m²)

Ship S (m²)

ρ (kg/m³)

Density (model & ship assumed equal).

ν (m²/s)

Kinematic viscosity (≈1.19e-6 seawater).

η_D

Propulsive efficiency.

C_A

Correlation allowance (default 0.0004).

A) Direct scaling (known form factor k)

Form factor k

Model speed Vₘ (m/s)

Used to get Fn & matching ship speed.

Model RTₘ (N)

or C_Tm (–)

If both RTₘ and C_Tm are provided, C_Tm is used. C_Tm = RTₘ / (0.5 ρ Vₘ² Sₘ).

Scale ratio λ = Ls/Lm: —

Froude (model) = Froude (ship): —

Ship speed V_s: — m/s

k (form factor): —

R_T,s: — kN

P_D,s: — kW

Provide model data and geometry; we compute C_R on model, carry it to ship at same Froude, and add C_A.

Report: Model–Ship Correlation (Scaling)

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Notes

ITTC ’57 friction: \( C_f = \frac{0.075}{(\log_{10} Re - 2)^2} \).

Prohaska: linear fit of \( y=\frac{C_T}{C_f}\) vs \(x=F_n^4\), intercept = \(1+k\).

Ship total: \( C_{T,s} = (1+k)C_{f,s} + C_{R,m} + C_A \); \( R = \tfrac12 ρ V^2 S C_T \).