When a ship moves through water, its hull pushes water aside and creates waves at the bow and stern. Those waves are not just a visual effect, they carry energy away from the vessel. The engine must supply that lost energy, so wave-making resistance acts like an extra drag force.
This is why faster ships often need much more power than slower ones of similar size.
Wave-making resistance grows strongly when a vessel moves fast enough that its wave pattern becomes large compared with the hull length. A surface ship is affected most because it travels at the air-water boundary where waves can form easily. A deeply submerged submarine produces far less wave-making resistance because it is away from the free surface.
Naval architects reduce this resistance by shaping hulls, controlling speed, and choosing lengths that manage the bow and stern wave system.
Understanding Ships and Submarines: Wave-Making Resistance
A moving hull creates a pattern of crests and troughs that spreads outward behind it. The pattern is controlled by the length, width, and shape of the hull, plus its speed. A longer wave travels faster in deep water than a shorter wave.
As a ship speeds up, the waves it produces become longer. At certain speeds, a crest made near the bow can line up with a crest near the stern. Their effects add together, making a larger wave system.
At other speeds, a crest can meet a trough, which reduces part of the wave pattern. This interference explains why resistance does not rise in a perfectly smooth way as speed increases.
Hull length has an important effect because the distance between bow and stern sets the spacing of the two main wave sources. Designers compare speed with the square root of hull length times gravitational acceleration. This comparison is called the Froude number.
It helps engineers compare a small boat with a large ship without using speed alone. A short vessel reaches troublesome wave conditions at a lower speed than a long vessel.
This is one reason long passenger ships and cargo ships can travel efficiently at speeds that would be difficult for a shorter hull. Length alone is not enough, since width, draft, mass distribution, and hull shape change the result.
A traditional displacement hull must push water aside rather than climbing over it. Near its practical speed limit, the ship can appear trapped between its own bow wave and stern wave. More engine power then gives only a modest increase in speed because much of the extra energy goes into larger waves.
Fast planing boats behave differently. Their hulls are designed to rise partly out of the water at high speed. This reduces the amount of water displaced, though it can introduce other forms of drag and instability.
Students often meet the same idea when comparing a rowing boat, a ferry, and a speedboat. Each has a different hull form because each operates in a different speed range.
Submarines show why the water surface matters. A submarine close to the surface can still make waves, even if its hull is fully underwater. The pressure changes around the moving hull reach the surface and disturb it.
As the submarine goes deeper, those pressure effects become much weaker before they reach the surface. Its resistance is then mainly due to skin friction and pressure effects around the hull, not visible waves. When studying this topic, separate the different kinds of resistance instead of treating drag as one single effect.
Notice that power depends on both resistance force and speed. A small rise in resistance at high speed can demand a large increase in engine power.
Key Facts
- Wave-making resistance is the drag caused by energy carried away in water waves.
- Total resistance = frictional resistance + pressure resistance + wave-making resistance.
- Power needed to overcome drag is P = Fv, where F is resistance force and v is speed.
- Wave speed in deep water is approximately c = sqrt(gλ / 2π), where λ is wavelength.
- Froude number is Fr = v / sqrt(gL), where L is hull length and g is gravitational acceleration.
- Wave-making resistance becomes more important at higher Fr, especially near Fr = 0.4 to 0.5 for many displacement hulls.
Vocabulary
- Wave-making resistance
- The part of a vessel's drag caused by creating waves that carry energy away from the hull.
- Bow wave
- A wave produced near the front of a moving hull as water is pushed outward and upward.
- Stern wave
- A wave produced near the rear of a moving hull as water flows back together behind the vessel.
- Froude number
- A dimensionless number that compares a vessel's speed with the natural wave speed set by gravity and hull length.
- Displacement hull
- A hull that moves through the water by displacing water rather than mainly riding on top of it.
Common Mistakes to Avoid
- Thinking waves are only a side effect, not an energy loss. Waves carry kinetic and potential energy, and that energy must come from the ship's engine.
- Assuming all drag increases in the same way with speed. Wave-making resistance can rise much more sharply than frictional drag at higher speeds.
- Ignoring hull length when comparing ships. A longer hull can have a different Froude number at the same speed, so it may create a different wave pattern.
- Treating submarines and surface ships the same. A submarine near the surface can make waves, but a deeply submerged submarine has much less wave-making resistance.
Practice Questions
- 1 A ship experiences 80,000 N of total resistance while moving at 6 m/s. What power must the engine deliver just to overcome this resistance, using P = Fv?
- 2 Calculate the Froude number for a 100 m long ship traveling at 12 m/s. Use g = 9.8 m/s^2 and Fr = v / sqrt(gL).
- 3 Explain why a surface ship moving faster may need a much larger increase in engine power even if its hull shape does not change.