Hollenbach (1998) updated the Holtrop & Mennen regression with modern hull data, separating single- and twin-screw cases and giving better results for high-Cb container ships and ro-pax.
Formula
$$ C_R = a_1 + a_2 F_n + a_3 F_n^2 + a_4 C_B + a_5 \left(\tfrac{L}{B}\right) + a_6 \left(\tfrac{B}{T}\right) + \ldots $$
$$ R_T = \tfrac{1}{2} \rho V^2 S (C_F + C_R), \quad P_E = R_T \cdot V $$
Symbol legend
| Symbol | Meaning | Unit | Source |
|---|---|---|---|
| $C_R$ | Residual-resistance coefficient | - | Hollenbach regression |
| $a_1..a_k$ | Regression coefficients (full table 20+) | - | Hollenbach 1998 |
| $F_n$ | Froude number | - | $V / \sqrt{g L}$ |
| $C_B$ | Block coefficient | - | hydrostatics |
| $L$ | Waterline length | m | hydrostatics |
| $B$ | Beam | m | hydrostatics |
| $T$ | Draft | m | hydrostatics |
| $C_F$ | ITTC-57 friction coefficient | - | ITTC-57 page |
| $S$ | Wetted surface area | m² | Hollenbach S-regression |
| $\rho$ | Sea-water density | kg / m³ | 1025 default |
| $V$ | Ship speed | m / s | from knots |
| $R_T$ | Total resistance | kN | result |
| $P_E$ | Effective power | kW | result |
The full regression distinguishes single-screw vs twin-screw cases and covers both design-draft and ballast conditions. Hollenbach is preferred over Holtrop for the Cb > 0.75 container-ship and PCTC hulls where Holtrop drifts high.
Sources
- Hollenbach - Estimating resistance and propulsion for single- and twin-screw ships (STG, 1998).
- Molland, Turnock & Hudson - Ship Resistance and Propulsion.