Hollenbach Resistance Solver

Hydrodynamic Analysis Method

Hollenbach Resistance Prediction

Statistical regression method — U. Hollenbach (1998)

The Hollenbach method is a regression-based technique for predicting calm-water resistance of single-screw displacement ships. It was developed from a larger and more recent dataset than Holtrop–Mennen, covering conventional cargo ships between 42 m and 205 m. Unlike Holtrop, Hollenbach outputs both a mean (fleet-average) and a minimum (optimised hull) resistance estimate.

Total Ship Resistance

$$R_T = \tfrac{1}{2}\rho V^2 S_d \bigl(C_F + C_R + C_A + C_{APP} + C_{env}\bigr)$$

$S_d$ is the predicted wetted hull area; each coefficient captures a distinct physical contribution.

Residuary Resistance ($C_R$)

Computed via a polynomial regression in Froude number and $C_B$, with multiplicative correction factors for geometry ($k_L$, $k_{BT}$, $k_{LB}$, …) and a high-speed amplification factor $k_{Fr}$ that activates near the critical Froude number.

Residuary Resistance Coefficient

$$C_R = 1000\,C_{R,std}\cdot k_{Fr}\cdot k_L\cdot k_{BT}\cdot k_{LB}\cdot k_{LL}\cdot k_{AO}\cdot k_{Tr}\cdot k_{Pr} \cdot \frac{BT}{10\,S_d}$$

Appendage Resistance ($C_{APP}$)

Computed from the flat-plate friction line with an area-weighted $(1+k_2)$ form factor — the same physical model used in Holtrop & Mennen — so appendage types and their $k_2$ values are directly interchangeable between the two solvers.

Appendage Resistance

$$R_{APP} = \tfrac{1}{2}\rho V^2\, S_{APP}\,(1+k_2)\,C_F$$

Dual-Curve Output

Mean vs Minimum Resistance

Two calibrated resistance envelopes

Mean Rt — Statistical Average

Represents a typical hull from the regression dataset. Includes high-speed amplification and all geometric correction factors at fleet-average values.

Minimum Rt — Optimised Hull

Lower bound for a well-faired hull. Geometric correction factors are frozen at ideal values ($k_{Fr}=k_L=1$); useful for design-space optimisation.

Appendages Rapp

Rudders, bilge keels, shafts, bossings and fins — individual $1+k_2$ form factors identical to the Holtrop solver, so results can be directly compared.

Interactive Tutorial

Simulation Guide

Hull Geometry

Set LPP, LWL, LOS, beam, draft and displacement volume. Block coefficient is derived automatically. A warning banner appears if principal ratios fall outside the Hollenbach regression limits.

Appendages

Enable appendage checkboxes exactly as in the Holtrop solver. Default wetted areas are pre-filled; the area-weighted $k_2$ is shown in the telemetry strip.

Analyse Results

Switch to Analytical Plots to see the mean / min / component curves, or open Data Table and export the full resistance matrix as CSV.