MN Ch. 1 — Ship Resistance and Flow: Introduction

1. Overview — why resistance prediction matters

Chapter 1 sets the stage for the whole book. It answers three questions: why a naval architect must predict resistance accurately, how resistance can be predicted (three families of methods), and how the book is organised. The central idea is that the resistance of a ship — together with the propulsive efficiency — fixes the engine power needed to reach a given speed, and that the resistance itself can only be understood by studying the flow of water around the hull.

Fonte: LARSSON, Lars; RAVEN, Hoyte C. Ship Resistance and Flow. The Principles of Naval Architecture Series. J. R. Paulling (ed.). Jersey City: SNAME, 2010. Chapter 1 — Introduction.

Edital: Anexo 2-A, Área I, itens 1 e 5 (Resistência do Navio e métodos para sua obtenção) · Anexo 2-B, Área I, item 3 (Larsson & Raven), Chapter 1.

2. The importance of accurate resistance predictions (§1.1)

A central problem for the practicing naval architect is predicting the resistance of a new design at an early stage of the project — before the hull exists. When a ship is ordered, the owner and the shipyard sign a contract that specifies, among the strictest clauses, the contract speed: the speed reached at a stated power consumption during a trial run before delivery.

That trial is meant to take place under ideal conditions — no wind, no seaway, no influence from restricted water or currents. In reality, corrections almost always have to be applied for those factors. If the corrected speed falls below the contract speed, the yard pays the owner a penalty depending on the difference between the achieved speed and the contract speed; if the gap is too large, the owner may even refuse the ship.

The power needed to drive the ship at a given speed depends on more than resistance. The propulsive efficiency — how well the propeller performs and interacts with the hull — and the losses in the power train both matter. Even so, resistance is the single most important factor determining the required power.

Resistance, like the other forces on the hull, results from shear and normal stresses (pressures) exerted on the hull surface by the water flow. Knowing the flow around the ship is therefore essential both to understand the individual resistance components and to design the hull well. The flow around the stern also fixes the operating conditions of the propeller — which is why the book puts heavy emphasis on describing the hull flow.

As in every design project, conflicting demands compete. The hydrodynamic qualities are only one set among many; they also include seakeeping and manoeuvring, which — together with propulsive efficiency — are covered in other volumes of the Principles of Naval Architecture series, not here.

3. Different ways to predict resistance (§1.2)

There are three families of methods for predicting resistance: model testing, empirical methods, and computational techniques. The next three sub-sections trace the history of each; the fourth explains which method is used at which stage of design.

3.1 Model testing (§1.2.1)

Because ship resistance is complicated, naval architects turned to experiments very early. Leonardo da Vinci (1452–1519) is recorded testing three models with different fore-and-aft displacement distributions. Samuel Fortrey (1622–1681) towed small wooden models in a tank with falling weights. Colonel Beaufoy, under the Society for the Improvement of Naval Architecture (founded London, 1791), ran between 9,000 and 10,000 towing experiments from 1791 to 1798 in the Greenland Dock. Fredrik af Chapman in Sweden published resistance tests on simple shapes in 1795, and Benjamin Franklin (1764) was probably the first American to test models — to confirm that resistance rises in shallow water.

The big obstacle was scaling: how to extrapolate the model's towing force to full scale, and at what speed to tow the model to represent a given full-scale speed. The French scientist Ferdinand Reech (1844) first solved the problem but never pursued it, so the solution is credited to the Englishman William Froude, who stated his law of comparison in 1868.

Froude's law of comparison (1868). "The (residuary) resistance of geometrically similar ships is in the ratio of the cube of their linear dimensions if their speeds are in the ratio of the square roots of their linear dimensions."

Put as relations between model (subscript m) and ship (subscript s) with linear scale ratio $\lambda = L_s/L_m$, the corresponding-speed condition and the residuary-resistance ratio are:

$$ \frac{V_s}{\sqrt{L_s}} = \frac{V_m}{\sqrt{L_m}} \qquad\Longrightarrow\qquad \frac{R_{r,s}}{R_{r,m}} = \lambda^3 $$

The same idea, written as a single speed parameter, is that the ratio $V/\sqrt{L}$ must be equal at both scales — the origin of the speed–length ratio (which is itself not dimensionless; the dimensionless form is the Froude number $V/\sqrt{gL}$). The residuary resistance is the total resistance minus that of an equivalent flat plate (a rectangular plank of the same area, length and speed as the hull). Froude's plan: split total resistance into friction (measured from planks, which make no waves, at both scales) and residuary resistance from the waves (found by subtracting friction from the model test, then scaled by displacement and added to full-scale plank friction).

Froude ran his first model experiments in 1863 in a rainwater tank with a falling weight, then persuaded the British Admiralty (1868) to fund a proper tank, completed near Torquay in 1871: 85 m long, 11 m wide at the surface, 3 m deep, with a mechanically propelled towing carriage — the forerunner of today's towing tanks.

By the early 1960s, very high block-coefficient ships made a finer split necessary: not all viscous effects fit into plank friction, so a second viscous component — tied to the three-dimensional (3D) shape of the hull — had to be added. This "3D extrapolation" technique was proposed for general use by the ITTC in 1978, giving the "ITTC-78" procedure, used by most tanks today for normal displacement hulls.

3.2 Empirical methods (§1.2.2)

Model tests are time-consuming, especially when many alternative designs must be screened very early. Hence the need for fast, if less accurate, estimates. These come in two types: systematic series and statistical formulas from unsystematic data.

The crucial contrast is in the last column: Doust & O'Brien's formula involves no physics — it is merely a polynomial in the tested parameters — whereas Holtrop & Mennen built a physical wave-resistance expression into the regression and split resistance by the 3D extrapolation procedure. That physical grounding is why Holtrop–Mennen remains the standard rapid method.

3.3 Computational techniques (§1.2.3)

Thanks to fast computer development over the past ~50 years, computational ship hydrodynamics matured over a shorter span than the experimental methods. The history runs along two tracks — first inviscid (potential-flow) methods, then viscous (boundary-layer → RANS) methods.

Inviscid track. The first method that counts as computational hydrodynamics came in a landmark paper by the Australian mathematician Michell (1898), over a century ago. Neglecting viscosity, he derived the inviscid flow around a "slender," narrow-beam ship in a uniform stream and integrated the fore-and-aft pressure components to get total wave resistance. To make it solvable he linearised the boundary conditions — applying the hull condition to the centreplane (so the result held for a vanishingly thin ship) and the free-surface condition to the flat undisturbed surface. Havelock and coworkers (early 20th c.) instead measured wave-making resistance from the energy of the wave system, and introduced sources and sinks distributed on the centreplane (positive forward, negative aft, proportional to local waterline angle). Inui and coworkers (Japan, 1960s–70s) advanced hull optimisation for wave resistance; in the same period, methods for experimentally determining wave resistance from wave cuts near the hull were developed — the landmark paper being Eggers, Sharma & Ward (1967).

Panel methods are now used extensively, but the assumption of zero viscosity is an inherent weakness, so agreement with measurement is unlikely to improve much further — to go beyond, viscosity must be included.

Viscous track. Computational viscous-flow methods also appeared with the computer. The 1960s brought several 2D boundary-layer methods; 3D boundary-layer research ran through most of the 1970s. A 1980 Gothenburg workshop concluded that the boundary layer was well computed over the forward and middle hull, but the stern flow could not be predicted at all by the boundary-layer approximation — that needed RANS (Reynolds-Averaged Navier-Stokes) methods. RANS had just been applied to ship flows by Spalding's group at Imperial College (1978).

Better resolution of RANS solutions can keep improving accuracy, but the turbulence-modelling problem cannot be avoided. To beat it, far more expensive methods — Large Eddy Simulation (LES) or Direct Numerical Simulation (DNS) — are required, which demands very large increases in computer power.

3.4 Use of the methods (§1.2.4)

The three methods serve different stages of design:

Optimisation may be done manually (systematic shape variation) or formally, linking a CFD code to a hull-shape program (often a CAD tool). With constraints, single-objective optimisation (e.g. minimise delivered power) or multi-objective optimisation (also pressure fluctuations, or different qualities like seakeeping) is possible.

4. The structure of this book (§1.3)

The volume aims to provide three things: a basic understanding of the resistance problem for ships and other marine vehicles; insight into the three prediction methods; and practical design guidelines.

The first objective is covered by the next six sections, then the prediction methods, then the guidelines: