Hull appendages, planforms, and wing sections: what are they?

Yachts designed before the ’60s of the last century used to feature keels and rudders that were integral parts of the hull. Full keels and modified full keels were typically the standard design. Since then, an unstoppable quest for performance paired with a better understanding of the aero and hydrodynamic phenomena involved, the development of new materials, and new construction technics, have led to the emergence of separate vertical foils. These “new” types of keels and rudders are not built into the hull anymore. Instead, they are manufactured as independent pieces, which are later fastened into it. Thus, modern designs usually feature fin keels bolted into the hull and fin rudders supported by the rudderstock. Fin keels and rudders are also referred to as hull appendages.

But why keels and rudders are needed in the first place?

When a yacht is sailing in any other point of sail different to a dead run, part of the aerodynamic force generated at the sails pushes the yacht sideways. In fact, when sailing either close-hauled or in a close reach, most of the force is not directed forward but sidewise. However, the lift force generated by the keel counterbalances this aerodynamic side force allowing the yacht to move forward at the expense of a small leeway angle. Actually, the leeway comes as a consequence of the generation of lift since this process requires an angle of attack between the incoming water flow and the keel.

Due to this keel generated ‘grip’ over the water, the yacht will now tend to heel instead of moving sidewise. But the keel again plays a key role in counterbalancing the heeling force by creating a righting moment that prevents the boat from capsizing.

Besides, the combination of a keel and a rudder provides steerability and course stability or balance.

Pros and cons of fin keels and rudders

Fin keels and rudders have become the standard configuration nowadays for racing and cruising yachts and everything in between, be it inshore or offshore craft.

When compared to the “old” full keel/rudder configuration, fin keels and rudders bring significant advantages regarding performance and maneuverability:

  • they reduce the wetted surface of the underbody, which reduces, in turn, the frictional resistance to the advancement making the yacht able to sail faster;
  • A fin keel together with a fin rudder makes the yacht more responsive and easier to steer;
  • Thanks to the fin’s lift-drag characteristics, a fin keel also improves weatherliness, i.e., the ability to sail close to the wind keeping the leeway angle as small as possible. 
  • A deeper keel allows for transferring more of the weight down (keel or bulb ballast), which decreases the position of the yacht’s gravity center. A lower center of gravity increases the righting moment and the yacht’s performance since the yacht can sail less heeled (among other effects, heel reduces the effective sail area ‘seen’ by the wind).

Nevertheless, fin appendages come also with several important drawbacks when compared to “traditional” full keel/rudder configurations:

  • Grounding or hitting UFOs (unidentified flotant objects like semi-submerged containers lost overboard or marine creatures like whales) can more easily lead to hull cracks, gaps, leakages, appendage failure, and even to a complete appendage detachment. The deeper the appendage, the greater the potential damage due to the lever arm force amplification. The loss of the keel, although rare, it happens in real life, and it is, on most occasions, a life-threatening event.
  • Besides, longer appendages restrict access to shallow waters and make grounding more likely to happen.
  • Fin keels and rudders provide less directional stability than full keel configurations. The rudder has to correct more and more often to keep the course.
  • Fin appendages need a minimum forward speed to generate lift. Too small velocity, and the yacht will drift unresponsive to rudder inputs under the effect of the wind.
  • Fin rudders can more easily get entangled in fishing gear or other types of floating or semi-floating debris.
  • With their smaller lateral surfaces, yachts equipped with fin appendages display higher rolling acceleration, which, if high enough, can negatively affect the rig and the crew.

Geometry of fin appendages

The geometry of an appendage is defined by the shape of its planform and sections.

1- Planform

The planform is the shape or outline of an appendage as projected upon a vertical plane. In other words, it is the appendage seen by its side.

– Leading edge (nose)

The leading edge, also called the nose, is the foremost edge of the planform or the section. It generally has a rounded contour.

– Trailing edge (tail)

The trailing edge is the rear edge of the planform or the section.

Hull with a fin keel and a fin rudder

– Chord

It is the horizontal distance from the leading edge (nose) to the trailing edge (tail). For trapezoidal appendages, the chord length varies with the depth.

Trapezoidal appendage

– Root chord

It is the upper chord of the appendage. Usually, the root chord is the longest of the chords of the appendage, and its length is usually denoted as C1.

– Tip chord

It is the chord at the bottom of the appendage, and it is usually the shortest one. The tip chord length is denoted as C2.

Modern keels, especially those used in racing, usually display a ballast bulb either integrated into the shape or attached to the tip (torpedo bulbs). Wings are sometimes used at the bottom of the keel or integrated into the bulb (if there is one). Wings improve upwind performance and the overall hydrodynamic efficiency of the appendage.

– Mean chord (CM)

It is the average chord of the appendage and it is defined as CM = (C1 + C2) / 2.

– Draft (T)

It is the vertical distance between the root chord and the tip chord. For a keel, it is commonly denoted as Tk, while for a rudder, it is Tr

Appendage planform

– Planform area (A)

It is the the area of the lateral surface of the appendage. It its calculated as A = CM x T.

– Aspect ratio

The aspect ratio is the most important parameter regarding the efficiency of the appendage. The higher AR, the better the efficiency. It is usually denoted by AR, and it is defined as the ratio of the draft to the mean chord, AR = T / CM.

Cruising yachts usually feature low aspect ratio keels (moderate fin with a moderate draft), while racing yachts display a more extreme high aspect ratio keel (short fin with a high draft) to gain maximum efficiency.

– Taper ratio

It is the ratio of the tip chord to the root chord, i.e. TR = C2 / C1.

– Sweep angle (Λ)

The majority of appendages are not vertical but sweep backward. The sweep angle is the angle between the vertical line and a line joining the points located at 25% of the chord length measured from the leading edge at every section. Under certain conditions, the center of effort at every section lies along this line.

2- Wing/foil section

Some of the planform parameters, especially the aspect ratio, are the major contributors to the fin keel and fin rudder performance. However, the planform is fixed in most class rules and heavily penalized in different rating rules. Understanding the influence of the wing/foil section in the performance may give in those cases some advantage.

Appendage view where various sections at different keel depths are represented.

Fin appendages are designed based on principles of aircraft aerodynamics. Even though air’s compressibility is an important factor in aircraft wings’ design, the same principles can also be applied to the incompressible water flow. Most of the sections used in modern appendages are derived from the sections developed by the NACA (National Advisory Committee for Aeronautics, USA). Although the Committee was eventually integrated into NASA (National Aeronautics and Space Administration), these airfoil series/sections are still known as NACA series/sections.

The geometry of a wing section

– Nose radius

It is the radius of curvature of the leading edge.

– Mean line

It is the line situated halfway between the upper and lower surfaces of the section. Many wing sections’ properties are primarily functions of the shape of the mean line (e.g., the chordwise load distribution, the angle of zero lift, the pitching-moment coefficient).

– Thickness (t)

It is the distance from the upper to the lower surface of the section measured at right angles to the mean line. The maximum thickness is denoted as tmax and the thickness ratio of the section is tmax / C, where C is the chord length.

– Chord

Similarly to the planform, the chord of a section is the segment joining the leading and the trailing edges. Its length is denoted as C.

– Camber

In asymmetric sections, the mean line and the chord line do not match. The camber is the distance between these two lines. Both the maximum camber and its distance to the leading edge are usually given as a percentage of the chord length C.

It is very rare to use asymmetric sections in keels and rudders as the sailing craft has to perform equally well in both tacks. Thus, the most commonly used sections are symmetrical: the chord line and the mean line match. The chord is the axis of symmetry of the section, and there is no camber.

Symmetrical wing section
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