Hull Resistance Calculator
Estimate preliminary boat hull resistance at a selected speed. Calculate frictional resistance, Reynolds number, Froude number, estimated residual resistance, total resistance, and effective power.
Hull Resistance Results
What is hull resistance?
Hull resistance is the force opposing a boat as it moves through water. The propulsion system must generate enough thrust to overcome this resistance at the desired speed.
For a conventional displacement or semi-displacement hull, total resistance can be considered as a combination of several components. The two most important components in this simplified calculator are frictional resistance and residual resistance.
$$R_T = R_F + R_R$$
- RT: Estimated total hull resistance.
- RF: Frictional resistance caused by water flowing over the hull.
- RR: Residual resistance, including wave-making effects and other components not represented by the friction calculation.
How is frictional resistance calculated?
The calculator uses the ITTC-1957 friction line to estimate the friction coefficient from Reynolds number.
$$C_F = \frac{0.075} {(\log_{10}Re - 2)^2}$$
$$R_F = \frac{1}{2}\rho V^2 S C_F$$
Here, V is boat speed, ρ is water density, S is wetted surface area, and CF is the friction coefficient.
What is Reynolds number?
Reynolds number describes the relationship between inertial and viscous forces in the flow around the hull. It is calculated from waterline length, boat speed, and water kinematic viscosity.
$$Re = \frac{V L}{\nu}$$
- V: Boat speed in m/s.
- L: Waterline length in meters.
- ν: Water kinematic viscosity in m²/s.
What is Froude number?
Froude number compares the boat's speed with the speed of gravity waves having a characteristic length equal to the waterline length. It is especially important when analyzing wave-making resistance.
$$Fn = \frac{V}{\sqrt{gL}}$$
A higher Froude number generally indicates that wave-making effects are becoming increasingly important. This is one reason why hull resistance can rise rapidly as a displacement boat approaches its practical hull-speed region.
What is residual resistance?
Residual resistance represents resistance that is not included in the skin-friction estimate. For boats, this can include wave-making resistance and other pressure-related components.
$$R_R = \frac{1}{2}\rho V^2 S C_R$$
Because residual resistance depends heavily on hull geometry, the coefficient CR should ideally come from a validated resistance prediction method, model tests, CFD, or measured boat data.
What is effective horsepower?
Effective power is the useful power required to overcome hull resistance at a particular speed. It can be calculated from resistance multiplied by boat speed.
$$P_E = R_T V$$
This is not the same as engine power. Propeller efficiency, shaft losses, gearbox losses, and other propulsion-system factors mean that the installed engine power normally needs to be higher.
How does boat speed affect hull resistance?
Resistance generally increases significantly as boat speed increases. Frictional resistance rises approximately with the square of speed, while wave-making resistance can increase much more rapidly in some speed ranges.
This is why a relatively small increase in boat speed can require a disproportionately large increase in propulsion power, particularly for displacement hulls approaching higher Froude numbers.
Does hull length affect resistance?
Hull length affects both Reynolds number and Froude number. For a given speed, a longer waterline changes the wave pattern around the hull and generally allows a displacement hull to operate at a lower Froude number.
However, length alone does not determine resistance. Displacement, wetted surface, hull form, beam, draft, appendages, trim, and many other factors are also important.
Is this calculator suitable for every boat?
It is best treated as a preliminary hull-resistance estimator. Real resistance prediction for a particular vessel normally requires substantially more hull-form information than this calculator uses.
Planing boats, high-speed craft, sailing yachts, catamarans, and vessels with unusual appendages can require different resistance methods and hull-form corrections.