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 wave.
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 wave.
For small displacement hulls, such as sailboats or rowboats, wave-making resistance is the major source of the marine vessel drag.
A salient property of water waves is dispersiveness; i.e., the greater the wavelength, the faster it moves. Waves generated by a ship are affected by her geometry and speed, and most of the energy given by the ship for making waves is transferred to water through the bow and stern parts. Simply speaking, these two wave systems, i.e., bow and stern waves, interact with each other, and the resulting waves are responsible for the resistance. If the resulting wave is large, it carries much energy away from the ship, delivering it to the shore or wherever else the wave ends up or just dissipating it in the water, and that energy must be supplied by the ship's propulsion (or momentum), so that the ship experiences it as drag. Conversely, if the resulting wave is small, the drag experienced is small.
The amount and direction (additive or subtractive) of the interference depends upon the phase difference between the bow and stern waves (which have the same wavelength and phase speed), and that is a function of the length of the ship at the waterline. For a given ship speed, the phase difference between the bow wave and stern wave is proportional to the length of the ship at the waterline. For example, if the ship takes three seconds to travel its own length, then at some point the ship passes, a stern wave is initiated three seconds after a bow wave, which implies a specific phase difference between those two waves. Thus, the waterline length of the ship directly affects the magnitude of the wave-making resistance.
For a given waterline length, the phase difference depends upon the phase speed and wavelength of the waves, and those depend directly upon the speed of the ship. For a deepwater wave, the phase speed is the same as the propagation speed and is proportional to the square root of the wavelength. That wavelength is dependent upon the speed of the ship.
Thus, the magnitude of the wave-making resistance is a function of the speed of the ship in relation to its length at the waterline.
A simple way of considering wave-making resistance is to look at the hull in relation to bow and stern waves. If the length of a ship is half the length of the waves generated, the resulting wave will be very small due to cancellation, and if the length is the same as the wavelength, the wave will be large due to enhancement.
The phase speed of waves is given by the following formula:
where is the length of the wave and the gravitational acceleration. Substituting in the appropriate value for yields the equation:
or, in metric units:
These values, 1.34, 2.5 and very easy 6, are often used in the hull speed rule of thumb used to compare potential speeds of displacement hulls, and this relationship is also fundamental to the Froude number, used in the comparison of different scales of watercraft.
When the vessel exceeds a "speed–length ratio" (speed in knots divided by square root of length in feet) of 0.94, it starts to outrun most of its bow wave, the hull actually settles slightly in the water as it is now only supported by two wave peaks. As the vessel exceeds a speed-length ratio of 1.34, the wavelength is now longer than the hull, and the stern is no longer supported by the wake, causing the stern to squat, and the bow to rise. The hull is now starting to climb its own bow wave, and resistance begins to increase at a very high rate. While it is possible to drive a displacement hull faster than a speed-length ratio of 1.34, it is prohibitively expensive to do so. Most large vessels operate at speed-length ratios well below that level, at speed-length ratios of under 1.0.
Since wave-making resistance is based on the energy required to push the water out of the way of the hull, there are a number of ways that this can be minimized.
Reducing the displacement of the craft, by eliminating excess weight, is the most straightforward way to reduce the wave making drag. Another way is to shape the hull so as to generate lift as it moves through the water. Semi-displacement hulls and planing hulls do this, and they are able to break through the hull speed barrier and transition into a realm where drag increases at a much lower rate. The disadvantage of this is that planing is only practical on smaller vessels, with high power-to-weight ratios, such as motorboats. It is not a practical solution for a large vessel such as a supertanker.
A hull with a blunt bow has to push the water away very quickly to pass through, and this high acceleration requires large amounts of energy. By using a fine bow, with a sharper angle that pushes the water out of the way more gradually, the amount of energy required to displace the water will be less. A modern variation is the wave-piercing design. The total amount of water to be displaced by a moving hull, and thus causing wave making drag, is the cross sectional area of the hull times distance the hull travels, and will not remain the same when prismatic coefficient is increased for the same lwl and same displacement and same speed.
A special type of bow, called a bulbous bow, is often used on large power vessels to reduce wave-making drag. The bulb alters the waves generated by the hull, by changing the pressure distribution ahead of the bow. Because of the nature of its destructive interference with the bow wave, there is a limited range of vessel speeds over which it is effective. A bulbous bow must be properly designed to mitigate the wave-making resistance of a particular hull over a particular range of speeds. A bulb that works for one vessel's hull shape and one range of speeds could be detrimental to a different hull shape or a different speed range. Proper design and knowledge of a ship's intended operating speeds and conditions is therefore necessary when designing a bulbous bow.
If the hull is designed to operate at speeds substantially lower than hull speed then it is possible to refine the hull shape along its length to reduce wave resistance at one speed. This is practical only where the block coefficient of the hull is not a significant issue.
Since semi-displacement and planing hulls generate a significant amount of lift in operation, they are capable of breaking the barrier of the wave propagation speed and operating in realms of much lower drag, but to do this they must be capable of first pushing past that speed, which requires significant power. This stage is called the transition stage and at this stage the rate of wave-making resistance is the highest. Once the hull gets over the hump of the bow wave, the rate of increase of the wave drag will start to reduce significantly. [1] The planing hull will rise up clearing its stern off the water and its trim will be high. Underwater part of the planing hull will be small during the planing regime. [2]
A qualitative interpretation of the wave resistance plot is that a displacement hull resonates with a wave that has a crest near its bow and a trough near its stern, because the water is pushed away at the bow and pulled back at the stern. A planing hull simply pushed down on the water under it, so it resonates with a wave that has a trough under it. If it has about twice the length it will therefore have only square root (2) or 1.4 times the speed. In practice most planing hulls usually move much faster than that. At four times hull speed the wavelength is already 16 times longer than the hull.
A hull is the watertight body of a ship, boat, or flying boat. The hull may open at the top, or it may be fully or partially covered with a deck. Atop the deck may be a deckhouse and other superstructures, such as a funnel, derrick, or mast. The line where the hull meets the water surface is called the waterline.
A multihull is a ship or boat with more than one hull, whereas a vessel with a single hull is a monohull.
A ship is a large watercraft that travels the world's oceans and other sufficiently deep waterways, carrying goods or passengers, or in support of specialized missions, such as defense, research, and fishing. Ships are generally distinguished from boats, based on size, shape, load capacity, and purpose. In the Age of Sail a "ship" was a sailing vessel defined by its sail plan of at least three square rigged masts and a full bowsprit.
A yacht is a sailing or power vessel used for pleasure, cruising, or racing. There is no standard definition, so the term applies to such vessels that have a cabin with amenities that accommodate overnight use. To be termed a yacht, as opposed to a boat, such a pleasure vessel is likely to be at least 33 feet (10 m) in length and may have been judged to have good aesthetic qualities.
A catamaran is a multi-hulled watercraft featuring two parallel hulls of equal size. It is a geometry-stabilized craft, deriving its stability from its wide beam, rather than from a ballasted keel as with a monohull boat. Catamarans typically have less hull volume, smaller displacement, and shallower draft (draught) than monohulls of comparable length. The two hulls combined also often have a smaller hydrodynamic resistance than comparable monohulls, requiring less propulsive power from either sails or motors. The catamaran's wider stance on the water can reduce both heeling and wave-induced motion, as compared with a monohull, and can give reduced wakes.
In fluid dynamics, a wake may either be:
In continuum mechanics, the Froude number is a dimensionless number defined as the ratio of the flow inertia to the external field. Named after William Froude, the Froude number is based on the speed–length ratio which he defined as:
In fluid dynamics, a wind wave, or wind-generated wave, is a water surface wave that occurs on the free surface of bodies of water. Wind waves result from the wind blowing over a fluid surface, where the contact distance in the direction of the wind is known as the fetch. Waves in the oceans can travel thousands of kilometres before reaching land. Wind waves on Earth range in size from small ripples, to waves over 30 m (100 ft) high, being limited by wind speed, duration, fetch, and water depth.
A sea anchor is a device that is streamed from a boat in heavy weather. Its purpose is to stabilize the vessel and to limit progress through the water. Rather than tethering the boat to the seabed with a conventional anchor, a sea anchor provides drag, thereby acting as a brake. Normally attached to a vessel's bows, a sea anchor can prevent the vessel from turning broadside to the waves and being overwhelmed by them.
Hull speed or displacement speed is the speed at which the wavelength of a vessel's bow wave is equal to the waterline length of the vessel. As boat speed increases from rest, the wavelength of the bow wave increases, and usually its crest-to-trough dimension (height) increases as well. When hull speed is exceeded, a vessel in displacement mode will appear to be climbing up the back of its bow wave.
A bulbous bow is a protruding bulb at the bow of a ship just below the waterline. The bulb modifies the way the water flows around the hull, reducing drag and thus increasing speed, range, fuel efficiency, and stability. Large ships with bulbous bows generally have twelve to fifteen per cent better fuel efficiency than similar vessels without them. A bulbous bow also increases the buoyancy of the forward part and hence reduces the pitching of the ship to a small degree.
The waterline is the line where the hull of a ship meets the surface of the water. Specifically, it is also the name of a special marking, also known as an international load line, Plimsoll line and water line, that indicates the draft of the ship and the legal limit to which a ship may be loaded for specific water types and temperatures in order to safely maintain buoyancy, particularly with regard to the hazard of waves that may arise. Varying water temperatures will affect a ship's draft, because warm water is less dense than cold water, providing less buoyancy. In the same way, fresh water is less dense than salinated or seawater with the same lessening effect upon buoyancy.
The bow is the forward part of the hull of a ship or boat, the point that is usually most forward when the vessel is underway. The aft end of the boat is the stern.
A vessel's length at the waterline is the length of a ship or boat at the level where it sits in the water. The LWL will be shorter than the length of the boat overall as most boats have bows and stern protrusions that make the LOA greater than the LWL. As a ship becomes more loaded, it will sit lower in the water and its ambient waterline length may change; but the registered L.W.L it is measured from a default load condition.
The International rule, also known as the Metre rule, was created for the measuring and rating of yachts to allow different designs of yacht to race together under a handicap system. Prior to the ratification of the International rule in 1907, countries raced yachts under their own national rules and international competition was always subject to various forms of subjective handicapping.
Manoeuvering thruster is a transversal propulsion device built into, or mounted to, either the bow or stern, of a ship or boat to make it more manoeuvrable. Bow thrusters make docking easier, since they allow the captain to turn the vessel to port or starboard side, without using the main propulsion mechanism which requires some forward motion for turning; The effectiveness of a thruster is curtailed by any forward motion due to the Coandă effect. A stern thruster is of the same principle, fitted at the stern. Large ships might have multiple bow thrusters and stern thrusters.
A ship must be designed to move efficiently through the water with a minimum of external force. For thousands of years ship designers and builders of sailing vessels used rules of thumb based on the midship-section area to size the sails for a given vessel. The hull form and sail plan for the clipper ships, for example, evolved from experience, not from theory. It was not until the advent of steam power and the construction of large iron ships in the mid-19th century that it became clear to ship owners and builders that a more rigorous approach was needed.
The draft or draught of a ship's hull is the vertical distance between the waterline and the bottom of the hull (keel). Draft determines the minimum depth of water a ship or boat can safely navigate.
A sailing yacht, is a leisure craft that uses sails as its primary means of propulsion. A yacht may be a sail or power vessel used for pleasure, cruising, or racing. There is no standard definition, so the term applies here to sailing vessels that have a cabin with amenities that accommodate overnight use. To be termed a "yacht", as opposed to a "boat", such a vessel is likely to be at least 33 feet (10 m) in length and have been judged to have good aesthetic qualities. Sailboats that do not accommodate overnight use or are smaller than 30 feet (9.1 m) are not universally called yachts. Sailing yachts in excess of 130 feet (40 m) are generally considered to be superyachts.
The Lürssen effect, used in the design of high-speed boats, is a reduction in wave-making resistance provided by two small rudders mounted on each side of the main rudder and turned outboard. These rudders force the water under the hull outward, lifting the stern, thus reducing drag, and lowering the wake height, which “requires less energy, allowing the vessel to go faster.” The effect was discovered by the German shipbuilding company Lürssen Werft based in Bremen-Vegesack. The Lürssen effect is best remembered for its use during the Second World War in the various classes of German "Schnellboot," or fast torpedo attack boats.
