Dynamic stability There are two important dynamic stability phenomena for high speed hulls. One is caused by the large centrifugal forces generated when a hull at high speed changes its direction. The other occurs due to the suction forces which may be generated near the chines due to convexity of the hull buttocks. We will deal with both in the following.
When the rudder is given an angle of attack a force is generated sidewards. This causes the hull to start moving in this direction and, since the force is aft of the centre of gravity, the hull also starts to rotate. After a short while the hull has obtained an angle of attack to the flow and a side force opposing the rudder force develops, mostly 011 the forebody. Now the direction of motion has started to change; the path is curved. A ccntrifusal force directed 'outwards', ie in the same direction as the rudder force, is now gradually built up. (See Fig 10.13.)
It is seen that the pressure force on the 'outer' side is larger than that on the 'inner' side. The difference in their horizontal components is the side force mentioned above. There is, however, also a vertical component, which is larger on the outer side and the resulting pressure force creates a moment (around the centre of gravity) that tends to heel the hull inwards. This moment is amplified by the rudder force. Taking the centre of gravity as the origin for the moment means that neither the gravity nor the centrifugal force contribute, so the total effect is a moment that will heel the hull inwards.
Fig 10.13 Forces on ¿1 turning hull
If the centre of gravity is moved upwards the resulting hull pressure force will soon pass through this point, thus creating no moment. At this stage, the rudder force still heels the hull inwards, but if the centre of gravity is moved still higher, the hull pressure forces will start heeling the hull outwards and at one position the moment from these forces will exactly balance the moment from the rudder. Now the hull does not heel at all. For any higher position of the centre of gravity the hull heels outwards.
Whether the hull is going to heel outwards or inwards thus depends on the height of the centre of gravity. Most planing hulls have their centre low enough to heel inwards, but some pleasure craft with a high flybridge may have it high enough to heel outwards, even dangerously so. For displacement hulls the pressure forces on the two sides are almost exclusively due to buoyancy, which is the same on the two sides (hull upright), thus creating no moment. The change in pressure force due to the turn is more or less horizontal and thus practically always directed below the centre of gravity. Even though the corresponding moment is to some degree compensated by the rudder, the result is a hull heeling outwards.
The other type of dynamic instability, often called 'chine walking", occurs due to convexity of the buttocks. When a flow passes over a convex surface the pressure is reduccd, and the larger the curvature, the lower the pressure. If the buttocks are too curved near the chine a suction force may develop. Of course, as long as the hull is exactly upright the effects from the two sides cancel, but if the hull sets a small heel ansle
the side that is most submerged will generate the largest suction, and the more submerged it gets the larger the suction. The situation is thus unstable; the heel tends to increase all the time, until hopefully the static righting moment gets large enough to compensate the heeling moment. Now, any disturbance may reduce the suction, which means that the large righting moment will roll the boat back, and due to its inertia it will roll over to the other side, where the process is repeated. The hull thus rolls from side to side and may in fact eventually capsize. Further, it is very difficult to steer the boat when it is rolling in this way.
Normally, the buttocks 011 the wetted part of the hull are kept relatively straight, but it is very difficult to avoid convex buttocks on the forebody. The problem therefore normally occurs when the trim gets too small, ie when the forebody goes into the water at high speed. Situations when this may happen are:
• if the boat is overloaded
• if the load is put too far forward
• if the engine power has been increased without moving the centre of gravity backwards
• if the trimplanes generate too large a bow-down moment.
Alternative propulsion Today, the most important alternative to the conventional propeller is devices the water jet. This device works like an aircraft jet engine, deriving its thrust from the reaction force when the fluid is accelerated. In the water jet the acceleration is achieved by an impeller. Water enters through an intake, normally in the bottom of the boat, and is ejected through a duct at the stern. Note that it is the acceleration of the water that creates the force, so it does not matter whether the water is ejected above or below the water surface.
The basic principle for obtaining the thrust is the same as for a propeller, and the requirements for efficiency are the same. To optimize propulsion, as much water as possible should be accelerated but the speed increase should be as small as possible. For a propeller this speaks in favour of a large diameter and a low rpm. Unfortunately this is hard to achieve in a water jet, where the flow has to pass a channel inside the hull and the space is limited. The water jet has been less popular in the past, although the basic principles have been known for a long time. In fact, a patent on water jet propulsion was granted in England in 1661!
The reason why water jets have gained in popularity for high speed propulsion is the fact that no outside appendages are required. The higher the speed of a planing hull the smaller the wetted surface to lift it. Appendages, such as brackets and open shafts, obviously have a constant wetted surface, and thus account for an increasing proportion of the resistance as the speed goes up. Although it is hard to claim that there are no corresponding losses in a water jet intake and channel they are normally smaller, particularly as the need for rudders is relaxed. There is thus an advantage from a frictional point of view, and the advantage gets larger and larger as the speed increases. An example of a water jet driven hull will be given below. For more information on water jet efficiency, see the paper by Dyne and YVidmark in the References section.
The concept of cavitation was introduced in Chapter 9. When the pressure at any point in the flow gets below the vapour pressure, the water evaporates. Bubbles of vapour and air dissolved in the water are created and these interfere with the flow and solid surfaces. Particular problems occur when the bubbles reach regions of high pressure where they may implode abruptly, causing large pressure pulses. Such pulses create vibrations and may erode the surface of, for example, a propeller. Further, the thrust of a cavitating propeller is often reduced.
When the speed goes up. the rate of revolutions of the propeller is increased, and both effects contribute to high velocities around the propeller blades. High velocities mean low pressures, so the risk of cavitation gets larger and larger with increasing speed. To avoid cavitation, large blade area ratios, as in Fig 10.9, are required for high speed boats. At speeds above 40 knots this may not help, however, and the problems with thrust reduction, vibrations and erosion may get large enough to prevent the use of conventional propellers. A possible alternative is then the so-called super-ca vita ting propellers. These are designed to have a steady cavitation bubble covering the entire suction
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