When a body moves relative to a fluid (either liquid or gaseous), disturbances are created in the fluid as it makes room for the passage of the body. (While the motion is relative with either the body or fluid moving, the vocabulary of the body moving will be used for language simplicity.) The disturbance can have both smooth flow and turbulence (e.g. white water). There are several different situations which will be discussed separately:
The fluid must move out of the way of the moving body. The body creates a compression wave in front of its motion. In a gaseous fluid such as air, the compression wave moves roughly at the speed of the particles in the fluid, essentially the speed of sound which shares the same mechanism. As a result the gas in front of the object has a gain in speed resulting in its moving out of the body's path. The net effect is a wave of disturbance which is deflected to either side of the body's motion. In a less compressible fluid such as water, friction prevails so that this bow wave does not precede the body very far. In general, the most efficient shape for the leading surface of a body with such motion is nearly spherical.
If the body speed is greater than that of the speed of the particles, the compression wave cannot precede the body causing the fluid to move out of the path of its own accord. Instead the fluid builds up intense pressure immediately in front of the body and must be forced to the side directly by the body. The most efficient shape for the front of the body is a narrow wedge shape optimizing the deflecting force to the side while minimizing the forward force. This builds up a pronounced shock wave to the sides such as the sonic boom created by supersonic aircraft.
In addition, the spread of the fluid as the cross section of the body increases followed by the converging of the fluid as the cross section decreases following the body's passage results in an additional wave with the speed of the body but a wavelength determined by the property of the fluid and the length of the body. In general this creates a series of regular trailing waves of diminishing intensity trailing behind the body and spreading to the side. The creation of turbulent flow greatly increases the energy required to move the body. Thus energy efficiency requires both minimum cross section and smooth flow. The most efficient shape for the balance of the body is tear shaped with the body gradually narrowing to a pointed trailing end. One might note this is the general shape of dirigibles, subsonic airliners (although modified to produce some lift), and high speed submarines.
Consider a surface vessel such as a ship with superstructure flowing through air, hull supporting by buoyancy and flowing through the water, and a disturbed interface surface between the water and air. Generally the speed through the air results in low resistance compared to that through the water. While the superstructure may be streamlined to reduce air friction, that consideration is often of lesser importance. The disturbances of the ship through the water cause pressures which distort the water-air surface into the V shaped bow wave and the gently bowed trailing wake.
The bow pressure precedes the ship and disperses water to the side. This pressure forms a series of waves which disperse to either side of the ship in a V shape. The sharpness of the V depends on the vessel speed compared to the speed of the waves. The increased pressure typically throws water up the bow of the ship which may deflect the water turbulently off to either side forming smaller, slower speed bow waves. These waves trail away in one or more often narrower V shapes to either side of the vessel. Behind the bow waves is a region of lower pressure. This is often noticeable along the side of the ship by the lower surface level. If the vessel is long enough and the speed slow enough, multiple wavelengths may be visible as the water surface meets the side of the ship. As speed is increased, a maximum hull speed is reached when there is just one wavelength matching the vessel length so that the vessel floats depressed in the wave trough it has created. The wakes travel at different speeds and initial directions so that often the trailing wave extends faster to the side resulting in a series of bow waves superimposing on top of the trailing waves as in the photo below.
At higher speeds the wake is actually simplified. The basic features of the steady wave pattern in deep water do not depend on the vessel's speed. But when a ship operates in water of finite depth H, the Froude number, Fh = V / √gH, depends on the ratio of the ship’s speed, V, compared to the water depth (and the gravitational constant, g). Shallow-water effects become important when the wavelength is approximately twice as long as the water depth. As Fh → 1, the wakes roughly converge to a single wake. (Note in computer generated wave predictions below, that at high speed, Fh = 1.2, some of the waves visible from the sailboats and predicted for low speeds have vanished.) Wave heights increase considerably as Fh → 1 and wave periods increase gradually as the ship’s speed does so.
Generally the shape of a hull is designed for a single optimum speed. A faster speed requires a greater ship length compared to cross section, to match the wavelength of the maximum hull speed. But placing a bulbous projection beyond the normal bow location has both speed and efficiency advantages. Presumably by moving the initial pressure wave further in front of the ship, the hull speed is increased by the increased wavelength. In addition, the pressure waves created by the projecting bulbous bow may partially cancel the pressure waves created by the remainder of the hull. This has been claimed to typically reduce energy consumption 5% (but in some cases as much as 25%) as long as vessel speed closely matches the optimum design.
An alternate method of increasing efficiency is to divide the hull into several parallel sections such as a catamaran, then attempt to design each hull to minimize outward wake, and to try to cancel the inward wake of one hull with that from the other. More of this will be discussed in Expt. VII-4.
Another way to minimize wake is to lift the vessel out of the water to plane across the water surface or on wing-like hydrofoils. While those approaches have potential for minimizing wake, both have high energy requirements to lift the vessel.
writing continues
Perhaps one of the more difficult aspects of ship design is understanding why a bulbous bow should be more energy efficient than a needle-nosed wedge design. Consider that the primary requirement is to move the water aside to permit passage of the vessel's largest cross section. So the issue is what bow design moves the water with the most efficiency and least expenditure of energy. One might still think a sharp wedge design which optimizes flow to the sides would always be superior to a design which bluntly exerts pressure directly ahead on the water.
You might try considering an approach of considering multiple samples of water and how each design provides for moving it aside the needed amount.
Or consider moving a fire engine down a crowded street expending the least amount of energy. Compare the following: Place a wedge shaped cow catcher on the front of the fire engine so that silently traveling down the street, obstructing people, animals and vehicles can be swept to the sides. Alternatively consider placing a loud siren on the front of the fire engine to warn people to clear a path for the fire engine. Consider which will likely result in the fire engine moving down the street the fastest with the least amount of effort.
writing continues
to next experiment
to ie-Physics menu
to site menu
