# On bulbs (and keels)

Keels distinguish motor boat hulls from sailing yacht ones. As discussed in “Hull appendages, planforms and wing sections,” they perform two main functions: to counteract the aerodynamic force that pushes the boat sidewise and to help provide the required stability. Besides, they also help to damp rolling (especially full keels) and provide steerability and course stability together with rudders.

Bulbs are **ballasted**, **non-lifting bodies** attached to the tip of keels used to improve stability. Additional stability does not only enhance the safety of a particular boat. It also has performance implications. Keeping everything equal, bulbed boats can sail upwind with less heel angle. That means they will be able to expose more sail area to the wind (i.e., the projection of the sail area to a plane perpendicular to the wind direction will be more significant). More sail area translates into a larger driving force.

Modern racing rules based on velocity prediction programs do not penalize stability as much as the older ones did. As a consequence, more and more boats are equipped with bulbs today.

But, bulbs also impact the hydrodynamic performance. They come with additional viscous drag due to the extra wetted surface (frictional drag) and the development of pressure differences over their surface (form drag). They also modify the lift and induced drag profiles of the keel. Moreover, wave-making resistance should also be considered, especially when the bulb is brought nearer to the air-water interface as the boat heels. In this situation, the pressure field created by the bulb and keel–bulb junction can add up to the generation of waves.

## Bulbs and stability

The righting arm for a given heel angle is the horizontal distance between the boat’s center of gravity and a vertical line through the center of buoyancy (see figure 2). The greater the righting arm, the greater the righting moment.

As the boat heels, the center of buoyancy moves further to the side, increasing the righting arm. But this has a limit. If it keeps heeling, the boat will arrive at a position where the righting arm will start to decrease (see figure 3). In fact, for heel angles greater than the **angle of vanishing stability** of the boat, the boat will develop a “negative” righting moment that will make it capsize.

To achieve a greater righting arm (or righting moment), we could lower the position of the center of gravity (i.e., increasing the “**weight stability**“) and/or shift the position of the buoyancy center when heeled further away with an appropriate hull shape (i.e., increasing the “**form stability**“).

Bulbs help in lowering the position of the center of gravity by adding weight at the bottom of the keel. By doing this, the righting moment increases. But not only, when comparing the same boat with and without a bulb, the bulbed one has a greater range of positive stability, i.e., a greater **angle of vanishing stability**, or still, in other words, a smaller range of inverted stability. All of this means that the energy necessary to knock it down will be higher, and the energy required to get it back to the upright position when inverted smaller.

## Bulbs and induced drag

As stated before, bulbs are non-lifting bodies. Yet, they work in proximity of (attached to) keels which, unlike bulbs, are devices that generate lift. The lift force generated at the keel (and at the hull and rudder to a lesser extent) is the force that will counteract the aerodynamic side force. But the generation of lift comes at a price: induced drag. There cannot be lift without induced drag.

#### – Downwash

Due to pressure differences between the surfaces of a lifting body (also called lifting surface), vortices are created at its tips. These vortices develop a downward velocity component called **downwash** and an upward one called **upwash** (see figure 4).

The downwash decreases the actual **angle of attack** (see figure 5), thus reducing the amount of lift the three-dimensional lifting body generates. But not only: the downwash also rotates the lift vector backward, causing an additional drag component called **induced drag**.

#### – Effective aspect ratio

While the lift and aspect ratio relationship is direct, the induced drag depends inversely on it. For the same amount of lift, lifting bodies with higher aspect ratios will produce less induced drag than lifting bodies with smaller aspect ratios operating at the same angle of attack.

Provided there is no gap and flow separation at the junction, lifting bodies attached to walls of infinite dimensions will operate as if their aspect ratio was twice the real one (see figure 6). Keels attached to hulls that operate close to the free surface of the water work this way.

The aspect ratio with which the keel actually performs is called the **effective aspect ratio**. As it is twice the keel’s geometrical aspect ratio, the value of the induced drag and the induced angle of attack (see figure 5) will be half of the ones experienced by the keel when working on its own (i.e., without a hull).

#### – Elliptical lift distribution

For completeness, we will also mention that the induced drag depends too on the **spanwise lift distribution** (see figure 4). In fact, for a given total amount of lift and a given aspect ratio, the elliptical lift distribution is the one that minimizes the total induced drag.

An elliptical spanwise distribution of lift can be obtained by having a planform with an elliptical spanwise distribution of chord lengths. But also by modifying the taper ratio, the sweep angle, and/or the spanwise variations of foil sections and twist angles (as keels must operate similarly on both sides, they are usually untwisted).

The depart from the elliptical lift distribution is generally accounted for with the **efficiency factor**, **e**. This factor is always ≤ 1. It is equal to 1 if the lift distribution is elliptical and smaller than 1 for non-elliptical distributions. The value of the induced drag depends inversely on it.

#### – Lift carry-over

The lift spanwise distribution drops to zero at the tips (see figure 4). There, the trailing vortices occur. However, provided there is no flow detachment at their junction (see figure 8), when a bulb (non-lifting body) is attached to a keel (lifting body), **lift carry-over** occurs: the keel lift distribution extends over the bulb.

Moving the position of the vortices further down increases the **active span**, which is the distance over which the configuration carries the load (see figure 7). This, in turn, increases the configuration’s effective span and effective aspect ratio.

The lift carry-over increases the total amount of lift available by moving the original position of the tip vortices further down (see figure 7). Moreover, the lift value per unit span is also higher due to the increase in the effective aspect ratio.

Suppose the bulb is a **body of revolution** (a three-dimensional figure formed by revolving a plane area about a given axis) with a pointed trailing edge. In this case, the value by which the effective span will increase will be more or less half its diameter. Yet, it has been found that bulbs displaying flat bottoms and ‘beaver tails’ tend to move the position of the vortices still further down.

Similar to the fact that attaching a bulb to a keel will increase the effective span, a single keel will have a greater effective span than a keel-bulb assembly if both configurations have the same draft.

#### – Keel – bulb junction

The junction between the keel and the bulb has to be faired by filleting to avoid the development of a positive pressure gradient that may cause the flow to detach. A **fillet** (see figure 8) is a rounding of a corner. For the same reasons, the filleting is also done at the junction between a hull and the keel.

## Bulb design

Bulb design is a complex process. It is usually carried out by professionals, and the outcome is typically validated by velocity prediction programs (VPPs), numerical methods, and/or tests realized in towing tanks. However, we will indicate here some ideas for their design.

#### – Body of revolution

We want bulbs to generate the least amount of drag. A streamlined body of revolution with the least wetted surface possible for a given volume will reduce the viscous drag (friction and form drag). Optimal diameter/length ratio values for different Reynolds numbers have been provided, for example, in Hoerner (S.F. Hoerner. Fluid-dynamic drag. 1965).

#### – Airfoils

Airfoils (two-dimensional) can be used to design three-dimensional bodies of revolution. However, It has been found that the body obtained does not display a favorable pressure gradient similar to the two-dimensional section from which it originates. To obtain similar pressure gradients, we must first calculate the thickness at each chord position to the power of 3/2 and then scale the result down so that the new section displays the same maximum thickness as the original one. The result is a more pointed shape (see figure 9).

#### – L and T-keels

Several investigations involving wind tunnel tests and numerical computations have been carried out at Chalmers University of Technology for four different keels:

- L-keel
- T-keel
- Integrated keel
- Fin keel

The material used for all the keels was cast iron, and the bulbed keels were designed to have all the same righting moment. The fin keel, however, had a considerably smaller righting moment, and a different sail area had to be used for this configuration to achieve the same heel angle. All the keels were tested using the same hull. Unlike the shapes shown in figure 10, which are bodies of revolution, all the bulbs tested featured a more flattened bottom.

Summarizing the results:

- The fin keel performed the worst in all cases.
- The difference in performance between the bulbed keels was relatively small.
- The T-keel performed the best in all conditions except when sailing upwind in strong winds, where the L-keel obtained a similar result.

Still, it is not clear that the same results would be obtained for other hull-keel-rig configurations, and in general, each new situation would require CFD and wind tunnel tests for optimization.

#### – Further considerations

Additional considerations to have in mind are:

- A bigger righting arm is better when sailing upwind. It improves the boat capacity for carrying a larger sail area. Therefore, a bulb keel would be more suitable. However, when sailing downwind, it is preferable to have a smaller wetted surface such as the one featured by fin keels of the same draft.
- A boat with a bulbed keel can achieve with a smaller draft the same amount of righting moment as the same boat with a fin keel. This is important when considering sailing in shallow waters.
- T-keels might not be the best suitable for ocean-going sailing because they will be more prone to being entangled with nets and other debris.
- In T-keels, the Longitudinal Position of the Center of Effort (LCE) of the keel can be placed first in an optimum position. Then the bulb’s Longitudinal Center of Gravity (LCG) can be placed separately. This is not the case for L-keels, where a balance between both has to be achieved.

#### See also:

- Hull appendages, planforms, and wing sections: what are they?
- What the hydrodynamic resistance is and why it matters.
- Introducing the hull.
- Understanding the boundary layer.
- The Reynolds number.
- Surface waves.
- The air-water interface.

#### References:

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