Empirical regression from Holtrop & Mennen (1982) with the 1984 re-analysis. Default early-design resistance method for most displacement hulls.
Formula
$$ R_T = \tfrac{1}{2} \rho V^2 S \left[(1+k_1) C_F + C_W\right] $$
$$ 1 + k_1 = 0.93 + 0.487118 c_{14} \left(\frac{B}{L}\right)^{1.06806} \left(\frac{T}{L}\right)^{0.46106} \left(\frac{L}{L_R}\right)^{0.121563} \left(\frac{L^3}{\nabla}\right)^{0.36486} (1 - C_P)^{-0.604247} $$
Symbol legend
| Symbol | Meaning | Unit | Source |
|---|---|---|---|
| $R_T$ | Total bare-hull resistance | kN | result |
| $\rho$ | Sea-water density | kg / m³ | 1025 default |
| $V$ | Ship speed | m / s | derived from knots |
| $S$ | Wetted surface area | m² | Holtrop S-approximation |
| $C_F$ | ITTC-57 frictional coefficient | - | ITTC-57 page |
| $1 + k_1$ | Hull form factor | - | Holtrop regression |
| $C_W$ | Wave-making resistance coefficient | - | Holtrop 1984 / simplified here |
| $L$ | Waterline length | m | hydrostatics |
| $B$ | Waterline beam | m | hydrostatics |
| $T$ | Draft | m | hydrostatics |
| $L_R$ | Length of run | m | $L \cdot (1 - C_P + 0.06 C_P \cdot LCB / (4 C_P - 1))$ |
| $\nabla$ | Displacement volume | m³ | $L \cdot B \cdot T \cdot C_B$ |
| $C_P$ | Prismatic coefficient | - | hydrostatics |
| $c_{14}$ | Stern-shape coefficient | - | Holtrop lookup (default 1.0) |
The simplified $C_W$ expression this calculator exposes is illustrative. Production work needs the full $c_1 \ldots c_{15}$ table from the 1984 paper, which covers stern types, bulbous bow, and transom corrections.
Sources
- Holtrop & Mennen - An approximate power prediction method (1982).
- Holtrop - A statistical re-analysis of resistance and propulsion data (1984).
- Molland, Turnock & Hudson - Ship Resistance and Propulsion (Cambridge).