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How do I calculate the resistance of a ship hull?
The resistance of a hull is the sum of a viscous resistance (friction on the wetted surface and form drag, which depend on the Reynolds number and on roughness) and a wave resistance which depends on the Froude number Fr = V / √(g L). Friction is computed with the ITTC-57 coefficient, Cf = 0.075 / (log10 Re − 2)², multiplied by a form factor (1 + k) of 1.1 to 1.3. Wave resistance, negligible below Fr = 0.2, becomes dominant between Fr = 0.35 and 0.45 (the "hull speed", 7.7 knots for a 10 m waterline); beyond it only planing hulls keep accelerating. Example: a 10 m hull with 30 m² of wetted surface at 5 knots has a Cf of 0.0026 and a frictional resistance of 270 N, i.e. 0.7 kW of towing power, before adding form and waves.
Ship resistance formulas
- Rt, Rv, Rw: total, viscous and wave resistances, in N
- ρ: water density, 1,025 kg/m³ at sea; V: ship speed, in m/s (1 knot = 0.514 m/s)
- Sw: wetted surface of the hull, in m²; L: waterline length, in m
- Cf: friction coefficient of the ITTC-57 line, dimensionless; k: form factor (0.1 to 0.3), share of form drag
- Re: Reynolds number on the waterline length (ν = 1.19 × 10⁻⁶ m²/s for sea water at 15 °C); Fr: Froude number; g = 9.81 m/s²
- Pe: effective (towing) power, in W; shaft power is higher because of propeller efficiency
Frictional resistance of a 10 m hull against speed
| Speed | Speed in m/s | Froude number Fr | Reynolds number Re | Cf | Frictional resistance Rf | Power Rf × V |
|---|---|---|---|---|---|---|
| 3 knots | 1.54 | 0.16 | 1.3 × 10⁷ | 0.00287 | 105 N | 0.16 kW |
| 5 knots | 2.57 | 0.26 | 2.2 × 10⁷ | 0.00264 | 268 N | 0.69 kW |
| 7 knots | 3.60 | 0.36 | 3.0 × 10⁷ | 0.00250 | 498 N | 1.8 kW |
| 8 knots | 4.12 | 0.42 | 3.5 × 10⁷ | 0.00244 | 637 N | 2.6 kW |
| 10 knots | 5.14 | 0.52 | 4.3 × 10⁷ | 0.00236 | 961 N | 4.9 kW |
| 12 knots | 6.17 | 0.62 | 5.2 × 10⁷ | 0.00230 | 1,346 N | 8.3 kW |
Detailed explanations and calculation in Mecaflux
The naval hydrodynamics studies the resistance to the advancement of ships. Resistance to the advancement corresponds to the pushing force that will produce the propeller (see: Propeller calculation software). This resistance is composed of forces from several phenomena that are distinguished in the study but whose interactions are intertwined.
see also HYDRODYNAMICS OF SURFING SURFBOARD PHYSICS
Under the board, surf fins follow the same hydrodynamics: the surf fin guide (how fins work, choosing them, safety, history, shaper's guide) details their lift, drag and stall.
The results of calculations or measurements are usually given in the form of hydrodynamic coefficients Ch, relating the hydrodynamic resistance Rh, to the the weight of the volume of water displaced (Ch=Rh/Displacement)
We assume that the environment is quiet (no swell wind or current) and we limit our discussion by neglecting the resistance of superstructure (about 3% of Rh), to the study of ship resistance to the advancement bareboat, by dividing it into two parts :viscous resistance and wave resistance. (See Froude)- viscous resistance (Rv), the viscous resistance coefficient (Cv) is related to Reynolds number (Re) and to roughness (K) relating hull length (L)
- Rv= Cv . (Re . K/L)
If the object moves near the surface, viscous resistance or drag is accompanied by a resistance due to the formation of surface waves:
- resistance of waves (Rw), the wave resistance coefficient (Cw) is related to Froude number(Fr)
we distinguish different types and causes of waves (learn more about resistance waves )
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Rw= Cw.(Fr)
- Cw =Rw/(1/2)r.s.v²(r water density, S wet surface, V velocity.
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Rv= Cv . (Re . K/L)
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Rw= Cw.(Fr)
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Ch= Cw.(Fr) + Cv.(Re.K/L)
Different types of approaches used to evaluate the hydrodynamic coefficient (Ch):
Despite advances in computer modeling, testing models are still essential.The effects of friction measured experimentally basins hulls, are themselves subject to scaling problems, solved by the laws of similarities(See: Froude)
testing model Towing tank
Another technique for evaluating hydrodynamic behavior is to compare measured data from a series of standard forms and extrapolate the consequences of changing forms.| serie Taileur
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- series taylor by Admiral Taylor Model Basin Experimental Ashington:
The series of taylor is still regarded as the most comprehensive research into the effects on the effective power..
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- In naval hydrodynamics, to independently evaluate the viscous resistance of the surface resistance, sometimes the method of dual models is used. It consists of a towing form consisting of a model hull of the ship and its symmetrical to the waterline. The measured drag is then halved. This experiment at sea is expensive and complex, it is carried in wind tunnel. For a simple and rapid assessment, it is possible to use the software mecaflux: The ovoid profile, whose drag (Cd) is already set in mecaflux, can be used to evaluate the viscous hydrodynamic resistance:
This viscous resistance is composed of the frictional resistance and resistance of shape. It is estimated that the roughness is very low (aerodynamic polished). If the roughness is higher, the frictional resistance due to roughness can be calculated with the detailed study of flat plate in Mecaflux standard (tab drag-lift / profiles with drag):
- Calculation boat hull underwater: For a more precise evaluation of the hydrodynamic drag hull shape of a boat or submarine, the HELICIEL software allows you to choose a hydrodynamic profile and calculate its performance drag. then export the 3D geometry for a design with CAD
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wave resistance (Rw), the wave resistance coefficient (Cw) is related to Froude number(Fr)
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Rw= Cw.(Fr)
- Cw =Rw/(1/2)r.s.v²(r water density, S wet serface, V velocity.
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A body which moves over a quiet water surface produces a wave system. This system is produced by the pressure field around the body, wave energy is given by the body. This transfer of energy from the body to the surrounding system produces wave resistance. (En bref le bateau fait des jolies vagues pour le Wake surf mais ça lui coute de l'énergie et c'est pour ça que c'est cher le Wake surf...)
There are two types of wave systems produced by hull:
- A diverging wave system inclined relative to the axis of the vessel
- A system of transverse waves perpendicular to the axis of the vessel.
The transversal waves is the main actor of the wave resistance at low Froude number.it is produced by the bow (front of ship) and stern (back of the ship). The interference between the wave systems generates peaks and troughs along the sides of the hull.
For more information: the hydrodynamic hulls of boats and the calculation of the resistance to the advancement of a hull
The total hydrodynamic resistance coefficient (Ch) is defined as:
Ch= Cw.(Fr) + Cv.(Re.K/L)
(Ch=Rh/Displacement)
Frequently asked questions
What is hull speed?
It is the speed at which the wavelength of the bow wave equals the waterline length: Fr ≈ 0.40, i.e. V (knots) ≈ 2.4 √L (m). A 10 m hull meets it near 7.7 knots, a 6 m hull near 6 knots. Beyond it wave resistance grows very fast and a displacement hull gains almost no speed whatever the power; only a planing hull, light and flat enough to rise onto the water, passes this limit.
How can a boat's resistance be reduced?
By reducing the wetted surface and the roughness (a fouled or badly painted hull can increase friction by several tens of per cent), by lengthening the waterline to lower the Froude number at a given speed, by refining the entry and run of the hull, and on large ships with a bulbous bow that creates a wave in opposition of phase with the bow wave.
How do I go from resistance to engine power?
The effective power is Pe = Rt × V. The propeller returns only 50 to 70 % of the shaft power as useful thrust, and the hull slowed by the propeller needs a thrust slightly above Rt (thrust deduction). For 2,000 N at 10 knots, Pe = 10.3 kW and about 17 kW are needed on the shaft with a propeller efficiency of 0.6, plus a margin of 15 to 20 % for rough seas and fouling.
How do I calculate the resistance of my own hull and choose my propeller?
The hull resistance module of Heliciel estimates the total resistance of your hull against speed from its main dimensions, then designs the matching marine propeller with blade element theory, with cavitation checks and 3D export of the blades. For a quick estimate of the viscous share, Mecaflux Standard computes the friction of an equivalent plate and the drag of an immersed ellipsoid. For a boat, a submarine or a towed body to design, Mecaflux carries out the study of your project, or offers training on the software applied to your own project.