## the bulbous bow

Article 2. 5

This section of my site is an explanation of the modes of operation of the conventional wedge bow and of the relatively recent bulbous bow.

Contents

Introduction

Surface waves created by ships, models and ducks

The test boat- Arcboat

The wedge shaped bow

The bulbous bow

Controlling the bow wave

Introduction

My interest in the bulbous bow started at least ten years ago when I started to look more carefully at the bow waves produced by ships moving slowly on the Thames. The pattern of waves is so ubiquitous that it seemed to me that it must have an explanation. It took me a long time to make any progress but when I started to look at bulbous bows I knew how to think about them. This article is the outcome.

In my experience people do not even look at the wakes produced by bodies moving across the surface of water. I enjoy looking at wakes and every one gives me some new aspect to decipher.

My cover picture may seem to be unrelated to the bulbous bow but it is the starting point because it shows clearly where the energy required to propel the boat goes. Sculling boats are about 25 feet long and 1 foot wide. It is hard to imagine a reason for making a boat with a higher slenderness ratio than this. The bow is producing a set of surface waves that are superimposed on the ripples. They spread out and carry away energy as kinetic energy in the rotation in the water near the surface of the water. The hull is dragging water along with it by friction and this water has no flow pattern and forms a wake in the water that moves in a confused manner and, in the picture, suppressing surface ripples into its motion. It can be seen in the middle of the picture. The water in this wake is moving in the same direction as the boat and has kinetic energy that it did not possess before the boat passed as well as random kinetic energy in the eddying motion. On the right there are two circular waves moving radially from the point where the blade of the scull entered and then left the water.

I am beginning to think that it is time to recognize that the hull that developed by cut and try methods has reached the end of its days and that hulls with completely new shapes at the front will replace them. The traditional hull took its form from the constructional materials and the constructional methods used to make it. The early hulls were made from wood or wood and skins. In both cases wood was cut to shape and bent to form a hull and not much has changed since. Constructional methods developed into plank on frame for wood and plate on frame for metal but the shape was still largely determined by what could be made by these methods and no one seems to have stopped and said “is there a better design?” When Froude did his celebrated work on the prediction of ship resistance he took the hull shape as given and the resulting wave patterns as inevitable. (This is not a criticism, Froude achieved more in one lifetime than most would achieve in several.) One must remember that ship design is ultra-conservative because ships need to be safe to operate.

I am not a historian and so I do not know when people began to look at the wakes from ships and see that there were two processes at work to produce the resistance to motion. When Froude set out to find a way to predict the resistance to motion of ships from tests on scale models he either knew about, or observed, the two processes. His great insight was to see that if the two are regarded as operating independently there is a practical way of predicting the resistance. He studied wave-making and frictional resistance separately. We still use the same method.

Now I want to look at the waves produced by moving floating bodies to see whether they can be manipulated to reduce the loss of energy to wave-making. Before I can do that I need to find out how water moves round ordinary floating bodies so that I might be able to think of practical changes that might be improvements.

Surface waves created by ships, models and ducks

It is evident from figures 1, 2 and 3 that the frigate, the model boat and the duck produce very similar patterns of surface waves.

The dominant feature is clearly the line of short waves coming off the front of the moving objects that look rather like the overlapping tiles on a gable end.

However there is another feature that is present and not so obvious. It is shown more clearly in figure 4. Those short waves are joined by waves that appear to be at right angles to the course of the boat. They are shown even more clearly in figure 5.

Once this has been noted, the pattern is also evident in the wake from the naval vessel. I have to account for it and there must be some simple explanation for this. It has taken me a very long time to find a mechanism that gives all the common features and fits in with the laws of physics. In the end I found that the best starting place was the flow at the front of a swim-headed barge.

Figure 6 is of a swim headed sailing barge. The section of the hull is everywhere trapezoidal and the bow is simply an angled plate.

Its most simple form is shown in the next diagram figure 7.

The hull is now free from complications and I can consider what happens at the forward end as it makes way.

It is impossible for the water to just flow under the barge because there is no force in existence to permit this. The water in front of the moving barge must split in some way. No one would, I think, dispute that, somewhere, the water will divide so that the total momentum per second flowing upwards equals the total momentum per second flowing downwards. This is one of the well-tried “laws” of dynamics put forward by Newton. Then the two streams are driven by equal and opposite forces.

I have shown the split in fig 8. It must be below the free surface, the split may not take place in a plane as I have shown it and this is clearly not the whole flow pattern.

Figure 9 shows what happens on the vertical centre-plane where there can be no sideways flow. The upward flowing water slows in the gravitational field, falls forward, and becomes a surface wave that remains stationary relative to the hull. This wave lifts the water ahead of the boat.

The water that goes downwards accelerates in response to the newly created force and goes under the hull. It cannot make the sudden change in direction at the joint between the sides and the swim-head and it will most likely separate forming an eddy under the hull and then come back up to the boundary layer.

In effect the water has been split horizontally into two streams at some level below the original surface level.

I have said that this diagram is for the centre-plane because the water at every other point across the front plate will move sideways towards the outer edges of the plate. This must be so because the water that starts off in line with the sides, experiences forces that tend to produce a rise in pressure without any obstruction to oppose it. As a result the water accelerates sideways and flows round the sides of the barge. This reduces the pressure sideways on all the water in contact with the flat bow and all the water will move to the right or the left by a very small amount at the middle and a greater amount at the edges. This spread will be much greater for the upper stream than the one under the hull.

But I have not said what finally happens to the water that went under the barge. This water cannot continue to flow in the same way. It is flowing from front to back relative to the hull and, at the same time, water is being dragged along with the hull by friction. Although the boundary layer has not yet grown in thickness it is inevitable that the faster flow from the swim-head will split and flow sideways from under the hull and ultimately upwards to create another wave on the surface.

Both waves are created by what amounts to linked, but separate, events and will appear as waves of finite length that are propagated sideways and left behind by the barge. The transverse waves are generated during the interaction between the down-coming water and the water moving at boat speed under the hull because the water ends up in an unstable state. These waves join the two waves that are shed by the interaction.

I have derived this for the special case of a simplified swim-headed sailing barge but it would apply to a swimming bird or to any boat with a bluff bow. (Be careful with swimming birds. They are short front to back and waves are generated from their tail ends as well and these are not far apart. They also have big webbed feet that upset things under the water.)

The test boat - Arcboat

I needed some visual evidence for the real motion round a swim-head. As it happens I built a boat with sides that were parts of cylinders. I called it Arcboat. It was built when I was designing my miniature, steam-powered, paddle steamer (See article 2.2 fig 5). I needed to keep the beam to a minimum yet to design a hull that was not too tender because paddle wheels dig in if they can. Stability is was so sensitive to beam that I could not rely on calculation to find the minimum beam that would be practical. Arcboat was pressed into service again when I thought about using a wedge rudder. I fitted a wedge rudder to Arcboat and an airscrew to drive it and tested the rudder. I took some pictures of Arcboat in action.

Fig 10 shows Arcboat under way and it was usefully fast. Figure 11 shows the two bow waves and the stern waves.

Figure 12 is very revealing. The boat had been turning to the left and, for the want of a large vertical surface under the water, slipped to the right across the surface of the water. Then the rudder was centred just before this was taken. In effect the hull has been moved out of the way to reveal the true nature of the flow under a large hull or a small smooth hull. The stem is creating a heap of water to such a height that a wave is propagated forwards at boat speed. This heap of water also propagates a wave backwards at boat speed under the hull. Of course the water will not bob up and down under the hull but the wave pattern does show up at the sides of a large boat. This wave is like the wave made by a stone dropped into still water. It oscillates up and down and produces a wave pattern of a series of waves that is stationary relative to the hull. The heap of water at the stem also propagates waves sideways on both sides. The main body of the hull has no input to this overall pattern.

It occurred to me that I could make a false swim-head bow to go on Arcboat so I made one from card and taped it on. In line with my view that engineers test easily imagined devices I made the angle of the swim-head equal to 45° and the sides vertical and parallel. Figure 13 shows unquestionably that the water rises ahead of the bow, that it spreads sideways to spill round the sides and that water goes down under the bottom to re-appear moving sideways as a second wave.

The water has been split along a horizontal line on the surface of the flat bow.

Figures 14 and 15 show other views of the effect of the swim-head with 15 showing most of the flow pattern.

In figure 15 we can see that the driving-down of the water and its subsequent re-appearance leaves the water under the hull not in equilibrium and a series of waves form under the hull and spread sideways.

There are two crucial observations to be made from my swim-headed barge. Firstly the swim head splits the water horizontally into two streams which agrees with my analysis. Secondly the laws of mechanics in this context tell us that wherever still water is made to flow upwards at a moving surface other water must flow downwards and that the two streams of water have the same momentum per second where they split and are acted on by equal and opposite forces.

Tests on Arcboat gave a picture that gives further information. It is figure16. This is the stern of Arcboat and the wedge rudder is clear. It makes the sides cylindrical right to the end. At the aft end water moves steadily sideways and inwards on both sides to fill the hole created by the passage of the boat. Then, suddenly, the flows meet when the boat has passed. The “collision” makes water go up directly behind the rudder and two divergent waves are generated. But, as I have observed, if water goes up water must also go down and if it goes down it must come back up. The picture shows it coming back up and generating two more divergent waves. Note that these waves are very small compared with the bow waves.

The wedge shaped bow

Ships do not have swim-heads so it becomes necessary to find out about hulls with wedge bows.

These days most ships are really cuboids with a sharpened bow supposedly to part the water and a shaping aft to serve water more or less smoothly to the propeller and/or rudder. The proportion of the total length given over to shaping the bow and stern varies with the function of the ship. For battleships the need for speed led to designs with over 2/3 of the length devoted to shaping at the bow and stern. By comparison a large tanker or an ore carrier may have 80% of the hull of uniform cross-section. Recent designs of hulls for racing yachts use about 3/4 of the length to create a really sharp bow.

Hulls have many shapes but, following good engineering modes of thought, I looked at a very easily defined hull to see what could be learnt. The most simple hull to define is one having a rectangular section at every station, a flat bottom and a deck plan of two equal arcs of circles. Anyone can form a mental picture of this hull shown in figure 17. (It is not wholly hypothetical as paddle steamer “Shah” was of this shape and Arcboat shows that it is easily driven.)

Quite obviously this hull has a stem at the front of a wedge shaped bow. Universally the bow has been thought to be splitting the water vertically just as a wedge might split timber or rock and further that this is the best way to make the water divide. People also think, quite correctly, that the sharper the bow the lower the resistance to motion.

On the face of it a wedge can have a very small angle but, in fact, there are serious constraints if the boat is to have some practical use. (There have been boats with really sharp bows like Turbinia but that boat was built solely to show the potential of the Parsons’ steam turbine and had no other use.)

In figure 18 I have drawn a rectangle in which a ship’s hull must fit. I have divided the length into 10 equal parts and constructed radii that are all pass through the stem and are tangential to the outside of the box at the 20%, 30%, 40% and at 50% points. The smallest included angle at the bow in the figure is 50° which is hardly sharp yet is practically the lowest angle that can be used. It is the bow angle for my hypothetical hull.

I chose to run out a few calculations for my hull and they follow.

-----------------------------------------------------------------------------------------------------------------------------I wanted some idea about what happens when the bow of a ship that has sides that are parts of cylinders joined at bow and stern is driven through water that is effectively at rest. I looked at the complexity of the dynamics of this interaction and decided that I could not deal with a fluid medium like water but I might well find out something by treating the side of the boat as a cam and considering the dynamics of a cam follower that is constrained to move horizontally sideways. It is shown schematically in figure 19.

Initially the follower has no displacement and no velocity. This changes when the arc reaches the follower. Suddenly the follower acquires a velocity in an infinite acceleration. Then, as it follows the arc, the displacement increases and the velocity continuously falls. When the follower reaches the point of tangency the velocity drops to zero at the new maximum displacement. I ran through some numbers for a ship-sized “cam”

It comes from a Mathcad program that is not very onerous. This is my “text” of the calculation.

I want to try to calculate the order of magnitude of the acceleration imposed on a cam follower as it is displaced horizontally by a circular arc. I want the "cam" to be the size of a real boat and the arc must be defined appropriately. I have used a profile equivalent to a boat having a beam of 20 feet at a point 50 feet behind the vertical stem. This then gives a radius for the arc of 130 feet.

If I give the cam a steady speed of 20 feet per second, or about 12 knots, a time of 2.5 seconds will elapse as 50 feet of the cam passes a given point. Then a simple programme based on the geometry of the circle gives displacement against time.

This appears to give the expected graph with a maximum displacement sideways of 10 feet in a time during which the boat will have moved 50 feet. As velocity is the differential of displacement with respect to time it is easy to get the next graph.

This graph is saying that the sideways, horizontal velocity goes instantly in an infinite acceleration to about 8 feet per second and then falls off almost linearly to zero at the point of tangency.

Now I am interested in sideways acceleration because forces are generated by accelerating a mass not velocity and this means differentiating again.

The value of 3.077 feet per sec per sec at 2.5 sec is exactly the centripetal acceleration so that is correct. I think that this graph is OK. In fact the acceleration graph starts at plus infinity, drops instantly to just less than -4 feet per sec per sec, then at 2.5 sec "rises" to zero.

So this follower would suddenly acquire a velocity of about 8 feet per second (4.3 knots) outwards and then progressively lose this velocity by the point of tangency. Throughout this time of 2.5 seconds the follower would be decelerating and a “spring” would be needed to keep it in contact with the cam. During the passage over the arc the acceleration is small in this context and the important events occur at the start and finish of the arc. There is no doubt that the mechanically serious event is the sudden acceleration as the follower reaches the cam and in a real mechanism this would be destructive. (This is the profile of many speed bumps on roads. They are designed to be destructive!)

This gives information that I did not have before and which is readily assessed because all the dimensions and speeds are comprehensible and stated. It can be used.

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Now I have to consider whether this can tell me anything about a ship. The most important observation is that the water when it reaches the stem must suddenly acquire a velocity just like the cam follower but the water can move in all directions to limit the acceleration. There is no other action that takes place on the hull that is remotely as important. Just look at figure 20. This hull is running light and the bulb is much too far out of the water to be working as intended. But it is creating a great heap of water that is lifting the surface well in front of the bulb. It is creating a rolling wave advancing ahead of the ship and water is flowing down the back of the wave and either alongside or partly, under, the ship. Inevitably, as this wave goes up another stream of water goes down and will reappear as a second wave. These two waves are parts of a greater pattern. No matter what may be done to alter the bow to make it sharp the stem will have to push water aside and a wave like the one in fig 21 will form even though it will be much smaller and a different shape. Look at the small wave generated at the bow of the frigate in fig 21 and then the second wave that has come from under the hull.

Once this phase of the flow is past the surface becomes relatively flat because the sideways movement of the water is slow, in this context, and not enough to create a wave and the acceleration is also low. Figure 17 of Arcboat shows that the sideways motion of the water to permit the passage of the hull or to fill in again has little potential for wave-making.

Any of the bow profiles shown in figure 19 will attempt to impose a sudden, infinite, sideways acceleration on the water as it is pushed forwards. Subsequently a much, much smaller acceleration will be imposed until the maximum beam is reached when the acceleration may suddenly become zero.

Of course an infinite acceleration is impossible even for solids but here, in water, the elemental forces exerted by the hull on the water are more or less normal to the elemental surface wherever it may be and this means that the force at the bow will have a forward component. (This produces the resistance to motion.)

In figure 22 I have drawn part of the bow and shown the profile of the free surface along the sides of the bow. I have picked out a small area that is under the water in the bow wave as an elemental area on which a pressure acts to produce an elemental force. The pressure will be closely equal to the static pressure and given by pressure =  where  is the density of water, and  is the distance below the surface. There will be lots of these elemental forces over the whole area above and below the level of the undisturbed free surface. Together they make up a force acting on the bow as I have shown in figure 23.

This force can be considered to have two components, one acting sideways and the other acting forwards. The forward component will be equal to about 42% of the force for a bow angle of 50°. This corresponds to the sharpest of the bows in figure 18 so one must accept that a sharp bow still splits the water horizontally. This is counter-intuitive and most would reject the whole idea.

Nevertheless I have found that it explains all the bow waves for a displacement hull.

igure 24 shows the contours of the surface from a computer simulation and figure 25 shows the wave pattern produced by a real ship. They are strikingly similar. The two pictures appeared independently. It is clear that this pattern matches that of the frigate in having a small wave at the stem and the main wave from some way back from the stem. However figure 3 shows that the main wave on the rather less sharp bow of the model is relatively nearer to the stem and is in fact in front of the swimming duck.

The bulbous bow

It seems to me that a pertinent question is whether the whole idea of modifying an existing hull by the addition of a device at the forefoot is the correct approach. The simple analysis of the cam above shows that the principal aim of good practice in hull design must be to avoid sudden changes in the radius of curvature of the hull in the direction of flow of water over the hull. No matter how one struggles there is no way that this can be implemented over the whole hull and it seems that the hull must be treated as two parts, the bow section and the stern section with an inevitable sudden change in radius of curvature where they join. Then the hull becomes two separate design exercises.

Let me concentrate on the bow section. We have a choice; do we regard the best approach as an addition to an existing hull or do we think of redesigning the whole hull? It is obvious from the many shapes of add-ons that no one shape is dominating design but it is equally clear that the rush to add bulbs to hulls of all sizes must be because almost any sensible shape gives a monetary return as a result of either an increase in speed or a reduction in fuel costs. I am not in the ship business and have no constraints on what I choose to think. In my view the best return for my effort will come from thinking about a redesign.

So how can we modify the wave pattern at the bow?

Figure 26 points us in the right direction. This is a model submarine running partially submerged. It is a model of a nuclear submarine that would have been designed to run deeply submerged. We can see that the hull is effectively a tube with an end cap like one half of a hen’s egg. It is doubtful whether this design gives the lowest resistance to motion when submerged but no one can doubt that the most important factor of the submarine hull is that it should withstand the pressure forces exerted on it at depth. For this the cylindrical tube is by far the best solution. As it moves under water the hull will part the water making it speed up in the vicinity of the hull and then close again once the hull has passed. No doubt the flow breaks down near the stern just as it does for the rowing boat but there is a propeller to complete the process of forming a confused wake.

This model is running on the surface and the pressure forces that prevailed at depth to keep the water in contact with the hull are not now present. Instead we have the small pressures that prevail at, and just below, the level of the free surface. They are small and the flow is now much changed with undulations in the surface. A wave forms ahead of the boat almost at right angles to the direction of travel just as it did for the bulb in fig 20. (In the model surface tension is sufficient to hold the flow together and suppress the breaking wave. For real nuclear powered submarines on the surface the wave breaks on the hull.) The flow has broken away because there is no sideways force being generated towards the blunt nose by the water to keep it in contact with the hull. In this wave water generally flows sideways and upwards to pass through the crest and then down into a trough. In the middle the water is lifted by the nose to flow more steeply upwards. Water cannot flow upwards like this without losing speed so it also flows sideways and down into that deep hollow behind the first crest.

Water must flow under the nose and speed up as it does so. This cannot last for long because there is slow moving water under the main length of the hull. The result is that the swiftly flowing water under and behind the nose must part and flow sideways and inevitably upwards. It comes up at the back of the first hollow to form the second crest. The downward-flowing water from the top and the upward-flowing water from under the nose combine to give that eddying wake alongside the hull.

Here, instead of the sudden acceleration produced by a sharp stem, we have much more gradual accelerations all round the nose. The water has undergone a process that first parts it horizontally and then recombines it alongside the hull at its original level or very nearly.

If this submarine ran with the top of its hull just at the surface it would have a similar flow pattern but the positions of the two combining flows from over and under the nose would be different. It turns out that fitting a nose with a more appropriate shape than that of a model submarine to the forefoot of a ship significantly affects the flow and, if it is carefully designed, there will be one wave at the front of the bulb and a second where the two flows combine and no more, only the eddying wake. This appears to reduce the resistance to motion.

I looked on the internet for explanations of the action of a bulbous bow. There seemed to be no agreement amongst who should know. However it did strike me that the seminal design is that of the Yamashiro Maru shown in figure 27. This is from Japan, goes back to 1963.

The text with the picture is as follows:-

A bow designed with a bulb under the water creates another wave that has a phase difference of 180 degrees against the ships original wave. The new technology enabled YAMASHIRO MARU to achieve a fully-loaded service speed of twenty knots with an engine power rating of only 13,000 to 13,500 max. horsepower, while a similar size of ship to the YAMASHIRO MARU without a bulbous bow required 17,500 to 18,000 max. horsepower to achieve the same speed. “

The performance is or was astonishing. If you argue, as Froude did successfully, that there is advantage in treating the resistance to motion of a ship as the sum of two components due to wave making and skin drag it would not be unreasonable to suggest that these might be about equal. If the bulb on Yamashiro Maru reduced the wave making drag by about 4,500 hp the percentage reduction in wave-making drag is about 50%. No matter how you choose to split the total drag this performance is certainly extraordinary and from an engineering point of view not open to much improvement. The bulb on Yamashiro Maru has gone a long way towards completing the job.

But how the web site claim that it works? The explanation is very limited and I need to interpret a phase difference of 180 degrees”?

Figure 28 shows what is most commonly meant by a phase difference of 180°. There are two sine waves of different magnitudes, one red, one blue, that take their peaks 180° apart. They partially cancel out to give the smaller wave in green. I think that this idea has been extended to the two isolated, surface waves to say that they partially cancel out. Whether the surface waves around the bow of Yamashiro Maru do cancel out is another matter. Any other phase difference leads to greater value of the mean square for the green curve.

Look at the picture fig 27. Where is the point where the waves join? I think that it is fair to expect the picture to show Yamashiro Maru running at its best speed with the bulb at its best depth. So we should be able to read this wave pattern. How exactly are we to know when two flows have joined correctly? It is clear that the wave off the bulb is falling in a mass of foam to meet another coming up from under the bulb but they do not look to me to be joining to form a single wave anywhere near to the stem. When I look at the wake I see a foaming parallel wake, ie, a wake that is no longer spreading,  as if some process had been completed. So the joining is complete by the start of the parallel section of the foaming wake. We do not have the whole wake but there is just enough to see the surface wave fanning out probably in a tile pattern. So the effect of the bulb is to shed a tile pattern like any other ship but to coalesce the two waves from the bow into one foaming wave.

It seems to me, as an engineer, that a simple device like the bulb on Yamashiro Maru that, for success, must have the positions of two waves from above and below the bulb in the correct relative positions, is unlikely to behave properly at all speeds. It seems to be clear from the internet that this is the case and bulbous bows are most effective over a small range of speeds. This tells us that a bulb will produce waves that have positions on the forefoot that vary with speed. So whatever is used to reduce the resistance to motion of ships has either to be designed carefully for a specified application or be adjustable to suit the speed.

It seems to me that I should try to design a bow with a bulb and see how it compares with published designs. Then a shape is required for the bulb. The mathematics for the cam show that the best shape would have no sudden changes in radius of curvature. The cylindrical surface that is tangential to a plane surface looks to be a nice smooth shape but in fact the change in radius of curvature at the junction is very large and on a ship would lead to the shedding of a surface wave. What we want is a shape that is mathematically free from sudden changes in radius of curvature, that has a rounded front, and ends up parallel at some point. This may be possible but, if it is, I have never seen a suitable mathematical expression. This means that no hull can be shaped from continuous mathematical curves and the bow and stern will be two separate shapes blended together in some way. I am looking at the bow section. The only shape I know that might be a suitable basic shape for a bulb comes from “stream functions”. This is a collection of mathematics that gives mostly graphs of two-dimensional flow patterns for a frictionless fluid. The one we want is for a source in a uniform flow. Then we need to be able to draw the stagnation line between the source and the uniform flow and streamlines around the stagnation line. I used Mathcad again.

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Let the uniform flow be M per unit width. Let the flow from the source be U per unit angle. Let the flow-line in the uniform flow that passes though the source be the horizontal axis and the source be the origin. Let the vertical axis be x and the horizontal axis be y.

Then the flow up to level x  =  and the flow from the source to angle  = .

For the special case of the stagnation line these flows are equal. Therefore

From this . But .

Then  and

This can be plotted using Mathcad as follows

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Here is the stagnation line. I have actually seen such a line as a small ripple created on the surface of the Thames by the buoyant plume of warm water from the condensers of the Littlebrook power station at Dartford as it flowed upwards into an incoming tide. It was real and very persistent.

This curve will not be asymptotic, it will go on widening very slowly to infinity. In this respect it is not suitable but it does give a shape for the nose of a bulb that gives an excellent flow pattern and as a blend is inevitable it is worth consideration.

This is pretty obviously a good starting shape to think about. It can be manipulated to have any proportion.

Suppose that this shape were to be used to give the cross section of a bridge pier with the curved end facing the stream and the back just squared off. The flow round the pier at the surface will be complicated by waves in the surface but lower down the flow lines approaching and passing the pier will look like those in figure 29 which shows one half of the nose and the streamlines around it.

There are points to note. Where two lines diverge the water is slowing down and the pressure is rising. The water flowing along the centre line stops and so the pressure rises to its maximum.[1] The presence of the pier affects the flow a fair way ahead of the pier and it parts the flow in an orderly way. The speed of flow of the water increases as it passes the pier and this means that its kinetic energy increases. This energy has to come from somewhere and, in a river, it is obtained from a drop in the surface level. This is easily seen and studied. It is a much better shape for a bridge pier than the pointed shape that early bridge builders used intuitively.

Now I have to think about the three-dimensional flow round a solid of revolution, like that in figure 30, with the mathematical shape above. Initially I can think about it at being deeply submerged. The same things will happen in that the pressure on the nose will rise, the flow will accelerate as it passes the solid and the energy to increase the kinetic energy will come from the same source but now, because of the depth, the lowering of the surface will not be detectable let alone visible. The flow will be symmetrical about the axis of the solid.

The fact that it is a three dimensional solid will mean that the speed of the flow around the solid will not increase as much as for a two-dimensional flow but there will be no fundamental change in the flow pattern.

Can this shape be used as a basis for a redesigned front end of a hull and operate just under the free surface to reduce wave-making drag? It would make sense to see how it can form a part of a hull. In figure 31 I have added a conventional forward section of a hull to the streamlined solid in figure 30. It looks to be very practical and one might think of blending the underside of the solid of revolution into a flat bottom with curved sides.

Now I have to decide what should happen as this bulb is pushed along under the surface. There can be no question that the flow pattern will be symmetrical about the vertical centre plane. It will be grossly asymmetrical vertically. Let me look at the water that starts off in line with the lower half of the bulb. It will follow streamlines like those in figure 29 and flow all round the lower part of the bulb. In doing so the pressure will fall as the streamlines close and this lowering of the pressure will cause the stream to converge and for a depression to form at the free surface. The flow will then split into two streams that come up on either side of the bulb. The water that forms the upper stream heaps up in front of the bulb and rises up the bulb slowing in the gravitational field. The net effect will be to split the flow in an orderly way to let it flow down into the trough created by the under flow and on into the up-flowing stream from under the bulb. It seems that process requires less energy to sustain it than the conventional bow.

Having said what I think should happen I need some visual evidence. Yamashiro Maru certainly exhibits this behaviour but the extreme foaming prevents us from seeing the detail. There are often pictures of bulbs in the papers and the technical press but there is no popular interest in bulbs actually working. However, as I write this on September 11 2007, the daily paper shows exactly this behaviour as a nuclear-powered submarine runs on the surface.

If I can predict the flow the bulb is a device that is susceptible to engineering design. Unhappily I do not think that many people have even attempted to look at the flow pattern round a bulbous bow except from a cut-and-try point of view. If they have, it does not show in designs of bows.

Figure 32 shows two bulbs that are very half-hearted as if the designer could not bring himself to believe that a bluff bow would be better than a wedge bow. It is tempting to say well they are little ships so it does not matter but in figure 33 we see the bow of the Queen Elizabeth II

The wedge bow obviously is dying very slowly.

Fig 34 shows a bulbous bow that was retro-fitted to the Ronald Reagan aircraft carrier. This is a large heavy boat and the bulb was fitted by cutting off the original sharp bow to one of the hull frames and attaching the new bulbous bow. The designers were not free to produce whatever they saw to be the ideal design. The bulb appears to me to be smooth as if some suitably streamlined circular section had been distorted vertically to form an ellipse and blended into the existing bow. It satisfies all the normal design criteria. I suppose that it might have been circular had the hull not been in existence.

It turns out that one shape does not fit all hulls. The very large cruise liners are well over 1,000 feet long and weigh in excess of 100,000 tons. A very large bulk carrier of a similar length will weigh more than 250,000 tons. (Cruise liners are mainly empty space.) The cruise liner has a draught that is only 40% of that of a comparable tanker. This means that ships of the same length may vary greatly in their depth at the stem. This leads to quite different shapes for the bulb.

Fig 35 shows the bulb on a tanker. It, too, suggests that its designer did not believe in bulbous bows. The bulb is more nearly a vertical cylinder than a rounded nose.Figure 36 shows the bulb on Queen Mary II Clearly the designer has a very large hull that has a relatively shallow draught and the design is quite different. It has been shaped to facilitate the two flows over the bulb. It is a confident design and clearly an add-on as distinct from an integral part of the hull.

Figure 37 is of a similar bulb but it has the most unlikely looking flats that do not really seem to fit with the physics of bulbous bows.

Figure 38 shows a beached cargo vessel It exhibits two unlikely looking knobs on its bulb but otherwise is as one might expect from my analysis.

I am not persuaded that there is any real understanding of bulbs. Wedge bows are dying hard.

Controlling the bow waves

It must be evident that the performance of a hull fitted with a bulbous bow is much dependent on the way in which the two waves created by the bow interact especially their positions relative to each other and the hull. This, in turn, may well be dependent on speed and the trim of the hull, ie where the bulb is relative to the surface. I understand that it is now more important to trim a vessel with a bulbous bow by the bow instead of by the stern as used to be the case before bulbs were used.

It seems to me that there is an incentive to be able to adjust the pattern of the bow waves at any time to suit the displacement and perhaps sea conditions, especially waves. So what adaptations are open to us if a proposed bulb design based on the design above does not appear to operate most efficiently at the service speed? I see two possibilities. The first is that the whole bulb could be mounted on a pivot and trimmed for angle whilst the ship is under way the second is to fit guide blades to the bulb to control the flow as shown in figure 39. Certainly the second idea is more practical and the volume in the bulb would be usable as it is on a warship. There is plenty of precedent in stabilisers and the planes on submarines for moving guide blades.

I have no idea whether anyone has ever fitted guide blades to a bulb but I thought that it might be interesting to try it at model size and see what happens. I suppose that I could have created my hull and bulb at model size but Arcboat had already been modified to have a first attempt at a bulb and so I chose to use that in the first instance.

Figure 40 shows the bulb and in retrospect it could have been mounted on a bearings and been capable of being trimmed.

Figure 41 shows the bulb under way. It is not running deeply enough but you can see the flow off the top of the bulb and the flow coming from under the bulb. It behaved as expected and it was the basis for a bulb on my model paddle steamer. (Note that both waves are coming off the bulb so it might be suitable for trimming.)

It seemed to me that the whole idea stood or fell on whether I could control the shape or perhaps position of the bow waves coming off the bulb. If it turns out to be possible it might permit fine-tuning of its performance at a given speed. This is something that can be established with my boat.

I modified Arcboat as shown in figures 42 and 43. The blades were controlled by radio with a servo operating an internal lever. The blades had an NACA symmetrical section. I used the electrically driven airscrew to drive the boat and it moved at a useful speed.

I loaded the boat with lead to what I thought might be a suitable depth and set about taking photographs. It turned out to be very difficult to achieve. First I needed a boat driver who could keep the boat on a straight course at a set distance from the bank. This was necessary because I had to follow the boat through the viewfinder and take a picture of about twice the boat length to get the hull and its waves and the initial part of the wake in shot. This gave no time to use the telephoto. Then I wanted the surface to be flat so that the only effect was from the boat. It was difficult to get it all together and then the light was such that I could see the waves but the light coloured hull was “burnt out” in the sun and I could not see the profile of the waves on the hull. I painted the hull grey, added a grating of lines and tried again.

The result is given in figures 44, 45 and 45. The flag shows the position of the guide blades, forward for angled down, middle for level and backwards for angled up.

If you look at the shape of the trough after the first wave it changes in shape as the blade angle changes. Without doubt the bow wave and the second wave can be moved by the blades.

The level position gives the best looking result. With the blades angled up the bow wave only just clears the upper reference line. The upper wave drops sharply to give a deep hollow in the second bay and then the water emerges from under the boat to form a wave at the third reference line and then, what looks to be a continuation of the upper wave comes up behind it. When the blades are angled down the top wave climbs well above the upper reference line and then dives down sharply to come up again in the forward part of the fifth bay but now the wave from under the hull comes up behind so the two waves have swapped positions. When the blades are level the two waves combine cleanly.

Figures 47, 48 and 49 are enlargements of the first half of the boat. They clearly show the wave switching sides.

I have no doubt that guide blades can be used to change the flow over a bulbous bow but I cannot measure resistance to motion so I can take this no further.

As a tail piece figures 50, 51 and 52 show the effect on the overall wave pattern of altering the angle of the guide blades.

Using guide blades on the conventional wedge bow.

I suppose that, having recognised that the wedge bow splits the oncoming flow horizontally, I would wonder what happens if there was no bulb and only the adjustable blades at the bow. It seemed to me that I have two devices at work if I used a bulb and blades and eventually I decided to cut the bulb off Arcboat, to re-arrange the blades and try again. I am glad that I did because the blades altered the wave pattern far more than I expected.

Figures 53, 54 and 55 show the wakes for the blades angled downwards in 53, level in 54 and upwards in 55. There is no doubt that the wake from the bow is much changed in 55 when compared with the other two. Guide blades make a difference. The stern wave is unchanged and one might ask whether there should be blades at the stern as well.

[1] This rise in pressure has consequences in a bridge pier. The rise in pressure causes flow both up and down the pier. It leads to a wave on the surface and to scouring of the bed of the river in front of the pier. Piers have to be protected.