Hull speed
Encyclopedia
Hull speed, sometimes referred to as displacement speed, is the speed of a boat at which the bow and stern waves interfere constructively, creating relatively large waves, and thus a relatively large value of wave drag. Though the term "hull speed" seems to suggest that it is some sort of "speed limit" for a boat, in fact drag for a displacement hull increases smoothly and at an increasing rate with speed as hull speed is approached and exceeded, with no noticeable inflection at hull speed. Heavy boats with hulls designed for planing generally cannot exceed hull speed without planing. Light, narrow boats with hulls not designed for planing can easily exceed hull speed without planing; indeed, the unfavorable amplification of wave height due to constructive interference diminishes as speed increases above hull speed. For example, world-class racing kayaks can exceed hull speed by more than 100%, even though they do not plane. Semi-displacement hulls are intermediate between these two extremes.

Hull speed can be calculated by the following formula:

where:
"LWL" is the length of the waterline in feet (or metres), and
"" is the hull speed of the vessel in knots (or km/h)

The constant may be given as 1.34 to 1.51 knot·ft in imperial −½ units, or 4.50 to 5.07 km·h–1·m in metric.

The ratio of speed to is often called the "speed-length ratio", even though it's a ratio of speed to the square root of length.

The concept of hull speed is not used in modern naval architecture
Naval architecture
Naval architecture is an engineering discipline dealing with the design, construction, maintenance and operation of marine vessels and structures. Naval architecture involves basic and applied research, design, development, design evaluation and calculations during all stages of the life of a...

, where considerations of speed-length ratio or Froude number
Froude number
The Froude number is a dimensionless number defined as the ratio of a characteristic velocity to a gravitational wave velocity. It may equivalently be defined as the ratio of a body's inertia to gravitational forces. In fluid mechanics, the Froude number is used to determine the resistance of an...

Background

Wave making resistance
Wave making resistance
Wave making resistance is a form of drag that affects surface watercraft, such as boats and ships, and reflects the energy required to push the water out of the way of the hull. This energy goes into creating the wake.-Physics:...

begins to increase dramatically in full-formed hulls at a Froude number
Froude number
The Froude number is a dimensionless number defined as the ratio of a characteristic velocity to a gravitational wave velocity. It may equivalently be defined as the ratio of a body's inertia to gravitational forces. In fluid mechanics, the Froude number is used to determine the resistance of an...

of about 0.35, which corresponds to a speed-length ratio of slightly less than 1.20. This is due to a rapid increase of wave-making resistance due to the transverse wave train. At a Froude Number of 0.40 (speed-length ratio about 1.35) the wave-making resistance increases further due to the increase of the resistance caused by the divergent wave train which is added to the transverse wave train resistance. This rapid increase in wave-making resistance continues up to a Froude Number of about 0.45 (speed-length ratio about 1.50) and does not reach its maximum until a Froude number of about 0.50 (speed-length ratio about 1.70).

This very sharp rise in resistance at around a speed-length ratio of 1.3 to 1.5 probably seemed insurmountable in early sailing ships and so became an apparent barrier. On the other hand, these values change dramatically as the general proportions and shape of the hull are changed. Modern displacement designs that can easily exceed their 'hull speed' without planing
Planing (sailing)
Planing is the mode of operation for a waterborne craft in which its weight is predominantly supported by hydrodynamic lift, rather than hydrostatic lift .-History:...

include hulls with very fine ends, long hulls with relatively narrow beam and wave-piercing
Wave-piercing
A wave-piercing boat hull has a very fine bow, with reduced buoyancy in the forward portions.When a wave is encountered, the lack of buoyancy means the hull pierces through the water rather than riding over the top - resulting in a smoother ride than traditional designs, and in diminished stress on...

designs. These benefits are commonly realised by some canoe
Canoe
A canoe or Canadian canoe is a small narrow boat, typically human-powered, though it may also be powered by sails or small electric or gas motors. Canoes are usually pointed at both bow and stern and are normally open on top, but can be decked over A canoe (North American English) or Canadian...

s, competitive rowing boats
Rowing (sport)
Rowing is a sport in which athletes race against each other on rivers, on lakes or on the ocean, depending upon the type of race and the discipline. The boats are propelled by the reaction forces on the oar blades as they are pushed against the water...

, catamaran
Catamaran
A catamaran is a type of multihulled boat or ship consisting of two hulls, or vakas, joined by some structure, the most basic being a frame, formed of akas...

s, fast ferries
High-speed craft
A high-speed craft is a high speed water vessel for civilian use, also called a fastcraft or fast ferry.The first high-speed craft were often hydrofoils or hovercraft, but in the 1990s catamaran and even monohull designs have become popular.Most high-speed craft serve as passenger ferries, but the...

and other commercial, fishing and military vessels based on such concepts.

Since the wave amplitude increases the energy transferred to the wave for a given hull length the wave drag can be very sensitive to the vessel's weight.