Chapter 19        The bulb

 

The bulb is the weight that is attached to the end of the fin of a model racing yacht to improve the stability. The bulb serves also to increase the total weight of the yacht so that at the normal sailing speeds the yacht will have enough kinetic energy to pass through head to wind without stopping[1]. Given the necessity for the bulb, the overall goal is to minimise its effect on the racing performance of the yacht. This means that normally we want the bulb to have a shape that causes the minimum drag.

 

The first step is to make the bulb from a material of high density. Platinum(!) would be best but class rules limit us to lead. If you look up the density of lead you will find it quoted as 0.41 lb /cubic inch (11,340 kg/cubic metre). Unfortunately lead is an extremely soft metal with the lowest mechanical strength of all the common metals. Consequently it is normally alloyed with other metals to give it the mechanical properties that are desirable for some purpose. For instance type-metal contains tin and antimony in various ratios to make up over 20% of the total weight, the rest being lead. Then the density of the alloy is about 0.37 lb/cubic inch. Type metal is a very suitable alloy for bulbs because it is quite hard and will resist scratching. Most people do not specify the material for their bulbs and are likely to use scrap “lead” and this will also be an alloy of unknown density. It is best to work on the lower density figure as it is much easier to drill a hole in an over weight bulb than to add to it if is under weight.

 

Presumably the designer of a yacht will know the weight of the bulb. Dividing the weight by the density will give the required volume of the finished bulb and all that remains is to find a shape having this volume. However we want the bulb to offer the least resistance to moving through the water when it is totally submerged. If there were no other constraints, such as the severe draught restriction for A boats, this would not be a new problem requiring a new answer because the best shape was found during the Second World War for long-range fuel tanks for exactly our purpose.

 

Low drag profile for round bulbs

Text Box:  Picture 19-1We should have some idea of the guidelines for designing a shape with low drag. For low drag the flow must not break away from the profile. It will never break away over the front of the bulb but it could easily do so over the rear part if it has an unsuitable shape. In suitable shapes the front will blend smoothly into the rear and the rear will have “easy” curves. We must set against these requirements the need to have the minimum surface area. The bulb must also be smooth to avoid localised break-down of the boundary layer.

 

The usual shape for bulbs is shown in picture 19-1. It looks very like the shape that would be produced by rotating an aerofoil of symmetrical section about its axis of symmetry. Long thin shapes would preserve the flow but only at the expense of a large surface area. A compromise must be made and the best shape has a maximum diameter of between 15% and 20% of the length. It has been found that for smooth bodies of this shape the drag is about 1/30 of that of a circular plate having the same frontal area.

 

It is one thing to propose a profile and another to realise it in lead. Somehow a shape must be made for the plug needed to make a mould.  If a circular section is acceptable then making a mould by “plank on frame” methods is just ordinary modelling although the result will only be as good as the accuracy of the frames. This does mean that dimensions must be put to the profile before the plug can be made. These days easily-used computing programmes[2] take the hard work out of this but only if we use simple geometrical shapes. The obvious shapes to use are an ellipse for the front and an arc of a circle for the rear. The resulting profile is shown in Figure 19-2

Text Box:  
Figure 19-2

Figure 19-2 has been drawn to scale for a bulb of 10² overall length, of 1.5² maximum diameter at 4² from the nose. The radius is 24.375². The volume of the first 40% is 4.71 cubic inches and for the other 60% is 5.68 cubic inches. The total volume is 10.4 cubic inches. If this were to be of lead alloy of density 0.37 lb/cubic inch its weight would be 3.85 lb.

 

Radii are required for making a plug and the table below is for the 10² by 1.5² diameter profile. Scale them up as required.

Co-ordinates of nose section.

0

.25

.5

.75

1

1.25

1.5

1.75

2

2.25

2.5

2.75

3

3.25

3.5

3.75

4

0

.261

.363

.437

.496

.545

.585

.62

.65

.674

.695

.712

.726

.737

.744

.749

.75

Co-ordinates of rear section.

 4

 4.5.

 5

 5.5

 6

 6.5

 7

 7.5

 8

 8.5

 9

 9.5

10

.75

.745

.729

.704

.668

.621

.565

.497

.42

.331

.232

.121

 0

Text Box:  
Graph 19-3

If this profile is acceptable it can easily be scaled up by reference to Graph 19-3. There are five solid lines for lengths of 10², 12², 14², 16² and 18². For a required weight read from the weight scale across to the appropriate length and down to find the diameter. There are two dotted lines for bulbs with ratios of diameter to length of 15% (the lower one) and 20%. Any combination of length and diameter falling between these dotted lines will have a hydrodynamically acceptable shape.

 

 

 

 

 

 

 

 

 

Bulbs for yachts with draught restrictions

Where the draught restriction is severe such as for A boats the use of a circular bulb and a fin calls for another compromise. A bulb will weigh typically in excess of 20 lb and, for this weight, a of a bulb having the profile above, may be as much as 17² long with a diameter of 2.7². This is a substantial piece of lead. Unfortunately the 2.7² is occupying a space which we would really prefer to use for the fin (see Picture 17-2). If the circular bulb is to be used then the fin must be of greater chord.

 

However the bulb constitutes about 2/3 of the total weight of the yacht and if we could reduce the maximum height of the bulb to, say, 1.7² we could lower the centre of gravity by nearly half an inch that makes a useful addition to the stability. So we look to ways of making bulbs that are thinner top to bottom and necessarily wider. This requires a new shape for which “delta” bulbs have been designed. The disadvantage is the increase in the wetted surface area.

 

The same rules apply as for the round bulb. We can use the same profile for the side elevation, half an ellipse for the plan and elliptical cross sections to give a bulb like that in Picture 17-6. If the bulb has a length of 10², a thickness of 1.5² and a width at the trailing edge of 2.5² it would have a volume of 16.45 cubic inches. These proportions give a good compromise between thickness and wetted area and if it were to be made of lead alloy of density 0.37 lb/cubic inch the weight would be 6.1 lb. The weight would scale directly with changes in these three dimensions.

 

Surface finish

Only the best finish possible will do and every attempt should be made to preserve it. Bulbs can be coated with glass fibre tissue to give a base for paint and some protection.

 



[1] Model catamarans do not need bulbs and do not pass head to wind very easily.

[2] “MATHCAD” will do this job very quickly and easily goes on to give the wetted area and the position of the CG. .