MN Ch. 4 — Ship Resistance and Flow: Decomposition of Resistance

1. Overview — from two main components to a full breakdown

Chapters 2 and 3 derived the governing equations and the similarity laws; it was in Chapter 3 that the total resistance was first split into just two main parts: wave resistance and viscous resistance. This chapter turns to the physics of the flow and subdivides those two parts further. Understanding the physics is what later allows hull-shape optimisation and the design of experiments; the detailed treatment of each component then follows in Sections 5, 6 and 7.

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 4 — Decomposition of Resistance.

Edital: Anexo 2-A, Área I, item 1 (Resistência do Navio — friccional, às ondas, perturbações devido à forma, wave-breaking, ar/vento, adicional devido às ondas) e item 5.4/5.7 (tipos e formas de resistência) · Anexo 2-B, Área I, item 3 (Larsson & Raven), Chapter 4.

2. Resistance on a straight course in calm, unrestricted water (§4.1)

2.1 Four vessel types and the resistance coefficient (§4.1.1)

To show how the breakdown changes from ship to ship, the chapter follows four very different vessels running at Froude numbers from 0.15 to 1.4. The first three operate in the displacement speed range (below 0.5); the fastest is a fully planing hull. Their main dimensions, Froude numbers and total resistance coefficients are typical of each class — note that even within a class the values vary a lot.

Force coefficients are defined, here and throughout the book, by dividing the force by the dynamic head ($\tfrac{1}{2}\rho V^2$) times the wetted surface $S$:

$$ C_{TS} = \frac{R_{TS}}{\frac{1}{2}\,\rho\,V_S^2\,S_S} \tag{4.1} $$

2.2 The detailed decomposition (§4.1.2)

In Figure 4.1 the total resistance of each ship is drawn as a bar of length 100%, split into its components in percent of the total; the total resistance coefficient is written above each bar to remind us that the absolute total differs between ships. The figure shows the viscous resistance subdivided into four components and the wave resistance into two. Each is introduced below.

The four viscous components

• Flat-plate friction — since William Froude's days, the friction of an "equivalent" flat plate has measured the hull's frictional resistance. "Equivalent" means a plate of the same wetted surface, run in water of the same density, at the same Reynolds number and speed as the ship. It is still used to extrapolate model data to full scale, and is due exclusively to tangential forces (skin friction).
• Roughness allowance — if surface roughness exceeds a certain limit it increases skin friction. Models are usually smooth enough for this to be insignificant, but full-scale ships always have roughness, raising resistance. The allowance shown is for a ship without fouling; for fouled surfaces it is much larger. In extrapolation it is computed from a simple formula.
• Form effect on friction — because the hull is a 3-D shape, the flow has to go around it, so the local velocity outside the boundary layer differs from the undisturbed flow (unlike a flat plate parallel to the flow). At bow and stern the velocity is reduced, but over the main part of the hull it increases, raising the friction relative to the plate. This extra friction is the form effect on friction.
• Form effect on pressure — caused by a pressure imbalance between fore- and afterbody. By d'Alembert's paradox, a body without lift in an inviscid fluid with no free surface has zero resistance (the longitudinal pressure forces cancel exactly). In a viscous fluid the boundary layer displaces the streamlines outward at the stern, reducing the pressure aft, so the pressure forces no longer cancel. This is the only viscous component due to normal forces (pressure), all others being tangential.

The two wave components

• Wave pattern resistance — as the vessel moves, surface water particles are pushed from their equilibrium position and waves are generated. The energy radiated away from the ship through this wave system gives the wave pattern resistance.
• Wave breaking resistance — if the disturbances are large, the waves may be steep enough to break into eddies and foam. The energy thus removed is found in the wake of the ship; the corresponding component is the wave breaking resistance.

"The grouping of the resistance components into viscous and wave resistance is the one normally used in ship hydrodynamics and adopted in this text." (Larsson & Raven, §4.1.2)

2.3 Comparing the four vessels (§4.1.3)

• Flat-plate friction dominates the two slowest ships (tanker, containership), which have very small wave resistance — the two wave components sum to only 7.5% for the tanker.
• Roughness resistance increases with speed, so it is a larger share of the viscous resistance for the fast hulls than for the slow ones.
• Of the two viscous form effects, the one due to pressure is considerably larger than the one due to friction. The total viscous form effect is about 30% of the flat-plate friction for the bluntest hulls (tanker, fishing vessel), about 20% for the containership, and practically zero for the planing hull (its thin boundary layer near a submerged transom causes very little displacement).
• Wave breaking is the largest wave component for the tanker, but considerably smaller than wave pattern resistance for the containership and the fishing vessel. For the planing hull, wave breaking is replaced by spray.
• The planing hull alone has appendage resistance (propeller shaft, brackets, etc.) — of viscous origin, discussed later.

3. Other resistance components (§4.2)

Beyond the ideal straight course in calm, unrestricted water, several further components appear once the conditions change — a turn, a wind, appendages, restricted water, or a seaway.

• Induced resistance — when the vessel moves with leeway (in a turn, or under a sideward wind component), a lift force (sideward) develops. High pressure builds on the leeward side and low pressure on the windward side; the difference drives a flow from high to low pressure, normally under the bottom or the tip of keel and rudder, generating longitudinal vortices. These vortices carry energy left behind — the induced resistance. It can be considerable, especially for sailing yachts and vessels.
• Appendage resistance — mainly of viscous origin, so it could be lumped with the viscous resistance, but it is treated separately for two reasons: (1) the Reynolds number of brackets, struts, etc. — based on their chord length — is much smaller than the hull's, so it needs separate scaling; (2) appendages are usually streamlined sections with their own empirical relations. For sailing yachts the appendage shape is crucial, as these appendages usually operate at an angle of attack.
• Wind resistance — can be considerable, e.g. for fully loaded containerships: the frontal area facing the relative wind is large and the containers are not aerodynamic, so strong winds generate large forces.
• Air resistance — even in still air there is a (small) resistance component. It is accounted for in the model-ship extrapolation procedure of Section 8.
• Blockage effect — in restricted waters, the flow around the hull and the wave making are influenced by the confining surface (the seabed in shallow water, or canal banks). All components may be affected; the effect is often modelled as an additional resistance component due to blockage (see Section 5).
• Added resistance in waves — a seaway causes extra resistance, mainly from the waves generated by the hull when set in motion by the sea waves, and also from wave reflection in short sea waves. It is treated in the seakeeping volume of the Principles of Naval Architecture.