Holtrop & Mennen Resistance Solver

Hydrodynamic Analysis Method

Holtrop & Mennen Resistance Prediction

Statistical regression method — J. Holtrop & G.G.J. Mennen (1982 & 1984)

The Holtrop–Mennen method is a widely-adopted statistical regression technique for estimating the total calm-water resistance of conventional displacement ship hulls. Derived from model tests and full-scale trials, it decomposes total resistance into physically meaningful components:

Total Ship Resistance

$$R_T = R_F(1 + k_1) + R_{APP} + R_W + R_B + R_{TR} + R_A$$

Each term represents a distinct physical contribution to bare-hull and appendage drag in calm water.

Frictional Resistance ($R_F$)

Based on the ITTC-1957 friction correlation line applied to the wetted surface area $S$, with form factor $(1+k_1)$ capturing the viscous pressure resistance of the hull form:

ITTC-1957 Correlation Line

$$R_F = \frac{1}{2}\rho V^2 S \cdot C_F$$

The friction coefficient is driven by: Cf = 0.075 / (log(Re) − 2)², and $k_1$ from $L$, $B$, $T$, $L_{CB}$, $C_P$, $C_M$.

Wave-Making Resistance ($R_W$)

The most complex component, valid for $0.10 \leq F_n \leq 0.55$. It captures the hull's bow and stern wave interactions through empirical regression coefficients:

Wave Resistance (Holtrop Form)

$$R_W = c_1 c_2 c_5 \nabla \rho g \, e^{\,m_1 F_n^{d} + m_2 \cos(\lambda F_n^{-2})}$$

Coefficients c₁–c₅, m₁, m₂, λ, d are regression functions of principal dimensions and form coefficients.

Additional Components

Appendage resistance $R_{APP}$ uses equivalent flat-plate drag with individual $1+k_2$ form factors. Bulbous bow ($R_B$) and transom ($R_{TR}$) are optional additive corrections. Correlation allowance $R_A$ covers hull roughness and scale effects.

Component Breakdown

Physical Decomposition

Six independently computed drag contributions

Viscous Rf(1+k₁)

Frictional drag amplified by hull form factor. Dominant at low Froude numbers and for full-form vessels.

Wave-Making Rw

Grows steeply with speed. Principal component for slender, fast ships. Highly sensitive to Fn and Cp.

Appendages Rapp

Rudders, bilge keels, shafts, bossings and fins — each with individual 1+k₂ form factors.

Bulbous Bow Rb

Pressure resistance from bulb emergence and its interaction with the bow wave at the free surface.

Transom Rtr

Pressure resistance of an immersed transom stern via the effective transom area coefficient c₆.

Interactive Tutorial

Simulation Guide

Operational Control Workflow

Hull Geometry

Set waterline length, beam, forward & aft draft, LCB, and form coefficients (Cb, Cm, Cwl). The container-ship hull updates live inside the WebGL canvas as you adjust the dimensions.

Configuration & Appendages

Toggle bulbous bow, transom stern, and afterbody form. Enable appendage checkboxes to include their drag contributions; they appear on the 3D model where relevant.

Analyse Results

Switch to Analytical Plots to inspect Rf / Rw / Rt curves across the Froude range, filter individual components, or open the Data Table and export the full matrix as CSV.