Engineering & Technology · Marine, Ocean & Offshore Engineering

Resistance, propulsion, waves and hydrodynamic response

A small speed increase can demand a much larger power increase. Meanwhile, two waves of similar height can produce different vessel motions because their periods and directions differ. Marine hydrodynamics connects these effects through defined models rather than one general performance number.

Use Fluid Engineering, Civil & Structural Engineering and Materials Selection & Degradation for balances, structural response and environmental mechanisms. Physics fluid dynamics and continuum materials provide further preparation. No example supplies a marine operating procedure, stability certificate, mooring design, electrical architecture approval or environmental permission.

Back to the chapter

After reading, you can

Separate resistance, delivered propulsion power, wave properties and vessel response, and explain the limits of a simple speed-scaling rule.

Resistance and useful power have different units

Resistance is the force opposing a specified vessel motion through water. Viscous effects, wave making, appendages, wind and operating condition can contribute. Effective towing power in steady straight motion is resistance R multiplied by speed U. Delivered shaft power also depends on the hull–propulsor interaction and losses represented by a defined efficiency account.

A simple relation R=aU² can be useful over an expressly assumed range, but its coefficient need not remain constant as speed, draft, fouling, water depth or sea state changes. It is not a universal ship-resistance law. Propellers accelerate water and exchange momentum; thrust, shaft torque, rotation rate and vessel speed must be compatible with the actual operating condition.

Water motion drives several body motions

An ideal regular wave has amplitude, wavelength, period and direction. Amplitude is half its crest-to-trough height in the sinusoidal model. Wave phase speed describes the travel of a crest; group speed describes energy propagation and need not be equal to it. Real seas combine components, so one regular wave is a selected representation.

A floating body can translate in surge, sway and heave and rotate in roll, pitch and yaw. Fluid acceleration contributes added mass; waves radiated by the moving body can contribute damping, alongside other dissipative effects. A response model connects a defined wave input to a motion or load output. Wave height alone cannot specify every response or whether equipment can continue working.

An original quadratic resistance example

Supply an imaginary resistance coefficient a=100 N/(m/s)² and a constant effective-to-shaft power ratio of 0.50. At U=4 m/s, resistance is 1600 N and effective power is 6400 W. The delivered shaft-power requirement in this model is 12.8 kW. At 5 m/s, resistance is 2500 N, effective power 12.5 kW and shaft power 25.0 kW.

The plotted shaft-power curve is Pshaft=0.2U³ kW with U in m/s. Increasing speed by 25% nearly doubles the supplied power account: (5/4)³=1.953125. This conditional cubic result follows from the chosen resistance law and fixed efficiency; it is not a guarantee about a vessel’s attainable speed.

For U in m/s, R=100U² N and constant ratio 0.50 give shaft power 0.2U³ kW. At 4m/s, 12.8 kW; at 5m/s, 25 kW. Common axes speed 0–6m/s, power 0–45 kW. This cubic curve follows explicit assumptions; no universal ship law or equipment rating.

Recognise what a smaller physical model preserves

A common gravity-wave scaling parameter is Froude number U/√(gL). If prototype length is 16 times model length, equal Froude numbers require prototype speed four times model speed. With the same fluid viscosity, Reynolds number UL/ν is then 64 times as large in the prototype. Gravity and viscous similarity are therefore not both preserved by that choice.

Towing-tank or numerical evidence needs a stated scaling and correction basis. Separately, a wave-response prediction needs the relevant mass, restoring, damping and excitation assumptions. Calm-water power, a scaled wave test and an equipment motion limit provide complementary evidence; none should silently replace the others.

Try the reasoning

Why is towing power R U rather than R/U?
Show the answer and reasoning
Power is force multiplied by velocity in the force direction; its units are N·m/s, or watts.
Does a 25% speed increase always require 95.3% more shaft power?
Show the answer and reasoning
No. That result depends on this invented quadratic resistance law and constant efficiency; actual resistance and efficiency can change.
Can equal Froude number and geometric scale alone guarantee identical viscous effects?
Show the answer and reasoning
No. In the same fluid, the Reynolds numbers generally differ, as the 16:1 length example shows.

What to carry forward

State the resistance, power-conversion, wave and response models separately, then connect their assumptions and evidence.

References

Teaching resources and research supporting this lesson’s explanations and examples.

Massachusetts Institute of Technology4 sources