Katana Marblehead Design – Hull

Katana has the same waterline beam as Octave. Canoe body maximum depth has increased by 2.4mm. Maximum cross section area is unchanged, staying at a value that has proven optimal.  Moving some midsection area from the turn of the bilge to the bottom of the hull gives a midsection that returns to being as close as practical to a true semicircle.

Katana in red, Octave in gray

Shaping of the ends incorporates lessons on boundary layer behavior learned in other work we have done. This new knowledge has refined our analytic tools, reducing the margin of error.
Armed with higher resolution tools, a more linear pressure recovery could be engineered reliably. The newly resolved pressure recovery rate is achieved through straighter diagonals from the mid section to the transom, combined with aft sections that are closer to semicircular. 

Straightening the run aft makes pressure recovery smoother, placing less stress on the boundary layer. In practical terms, this means not asking the water flow to follow excessively tight curves toward the back of the boat because, by the time the water reaches the back half of the boat, much energy has been lost to friction in the boundary layer.

This concept is not new, but being able to quantify how much we can 'ask the flow to do' empowers us to identify the optimum values for the conflicting requirements we are trying to mediate.
A very simplified overview might go something like this:
On the one hand we want to bring the flow back together (from max beam/draught to a point on the centreline/waterline near the transom) to
1) Make the wake as small as possible - smoothly refill the hole in the water made by the boat and
2) Get as much 'push' as we can from the water pressure on the aft surfaces of the boat - since the surfaces are angled inward, the normal pressure that acts at 90 degrees to the surfaces has a component pushing the boat forward. This component would in an ideal world be the same as that pushing back on the forward parts of the hull, but in reality is less due to energy lost through viscosity in the boundary layer.
On the other hand we want to maximise volume in the stern to
1) Get as much support as possible from the stern wave,
2) Damp pitching,
3) Avoid flow separation and
4) Maximise power.
All the while we want to keep wetted area to a minimum...
So you can see how nailing down more exact values makes our design choices much clearer!

In most conditions this particular change as implemented on Katana is near neutral. It trades the power and support of firm aft sections for reduced drag.
But in specific conditions (namely low to medium speeds, very high speeds, and in waves) our updated analyses show a small but measurable gain.
The new aft treatment has the advantage of less wetted surface area, which is a bonus at low speeds. At higher speeds the risk of laminar separation is reduced. 

The new stern treatment has the effect of reducing prismatic coefficient. In order to maintain the high prismatic coefficient of our successful previous designs, the sections in the forefoot were made even firmer, adding volume with a pronounced ‘U’ shape that transitions smoothly into the semicircular mid and stern sections. 
The forward volume distribution has been revised with a less aggressive rocker profile but more angular sections in the forefoot. 

This treatment of the forward sections has several advantages: it increases resistance to bow-down trimming moment both hydrostatically and dynamically, it keeps the entry narrow at the waterline (by pushing volume down rather than out), dampens pitching, and moves the LCB forward (also a trend in the evolution of our designs).

Above the water, the forward sections remain vertical, with a peaked foredeck for clean wave piercing and to keep added drag to a minimum when over-pressed. 

Moving aft, the topsides are no longer vertical but instead flare progressively. 

Amidships the moderate flare provides additional support, smoothing the heeled waterlines and helping to locate the heeled LCB such that trim remains neutral or slightly positive with heel. 

At the maximum deck beam location there is a subtle inflection under the gunwale to enhance water shedding when pressed and in waves, keeping aft flowing water off the sidedeck.

Finally some flare in the topsides aft has been introduced, accounting for perhaps the single largest visible change from Octave. 
In fact the new stern treatment achieves a similar effect to the characteristic soft chine/tumblehome of Octave but does away with some associated minor penalties. 

Specifically, water shedding is now done by the hull/deck joint instead of the chine. The sharp edge and acute included angle are more effective, but are higher up, so the flow remains attached a bit longer than would be ideal. 
However, since the sections are more rounded, the actual distance along the hull surface between the two separation lines is only marginally greater than before. 

Also, the new sheerline is lower at the back, reducing the distance even further and doing away with some mass in the process (the sheerline is more steeply inclined, being the same height as on Octave amidships, and higher at the front). 

As always there are compromises involved. This aspect of this particular choice is a net gain in some conditions, neutral in others and possibly a slight loss in the particular circumstances when the previous arrangement was at its best. 

To tip the scales, the principal advantage of the new stern shape is enhanced pitch damping. Marbleheads are inherently susceptible to speed sapping pitching due to their deep bulb, tall rigs, fine ends and (obviously) their small size relative to common wind generated waves. 

Our updated tools tell us that the dynamic effect of horizontal area aft is smaller than previous results showed. 

This is consistent with a more accurate understanding of boundary layer behavior. 

So the best way to damp pitching aft (over the full range of speeds/conditions) is hydrostatically, by progressively increasing waterplane area as the aft sections sink.

In summary, the new boat incorporates several small but significant changes that are all consistent with new knowledge we have acquired through other work as well as feedback from prototype development.
Major values such as waterline beam, midsection area and prismatic coefficient have not changed. 
Management of the flow has been refined whilst still achieving a 1.5% reduction in wetted surface area and an increase in power to carry sail, especially downwind.

It is worth remembering that the differences identified through more accurate theoretical analysis tools are small. But they do exist. 

And each small change cumulatively contributes to race winning differences. 

Furthermore, a deeper understanding of aspects such as boundary layer behavior enables the designer to adopt a consistent approach. The parts can be designed to work better together taking into account realistic flow phenomena. 

Quite apart from fine numerical validation, meaningful gains were made by learning from real observations of handling characteristics and other aspects of behaviour by a number of different observers, through a deliberate and structured development programme. 

This is why we are now confident to embark on series production of Katana.

Marblehead Development

A sneak preview of our next RM design: Katana.

Katana is an evolution of Octave, incorporating improvements in several key areas.

The individual changes are small, but sufficiently numerous to cumulatively warrant a new designation.

This decision has been made with existing customers in mind as it will give them a clear option when placing an order. Those who have ordered recently were naturally briefed on the upcoming transition so they could make an informed choice based on the characteristics of the two boats.

As always, we make a clear distinction between development work that we carry out in house or in collaboration with like minded skippers, and commercial series production.

Committing to production involves significant investment in tooling on our part and requires a high level of confidence to guarantee a known performance profile to the customer who does not wish to risk investing in an unproven design.

The nature of our business is such that we are always developing and looking to the next performance gains. We must therefore be disciplined in structuring R&D with respect to value for money from the point of view of the customer. 
There are several key tests that we apply to a new idea as it progresses from intuition, to vague notion, to sketch, to virtual model, to quantitative analysis, to prototype... 
At each stage the value of the idea must stand up to tests which cover performance as well as reproducibility, cost, compatibility with existing items, durability, and especially the relationship between these key attributes.

Over the 18 years that we have been developing RC yachts, we have been careful to structure development and series production accordingly, and our repeat customers are a testament to the effectiveness of our approach. 
In competitive performance applications, risk cannot be eliminated, but it should be estimated and managed. 
There are always compromises to be made with respect to performance in different conditions and circumstances. We therefore make an effort to narrow the uncertainty so that we can inform the customer of the characteristics and suitability of each product.

It is fascinating to study the overlap between the passion for that elusive perfect design and the real world constraints of technology, cost, and commercial consistency. 

As I have stated previously, successful projects incorporate such real constraints in the design brief and in the project management process to create the best result in the real world.

Weighing the Options

As mentioned previously, the choice of tooling material and shape depends on the construction process of the parts to be moulded.

To decide on construction method we look at the desired properties of the finished product.

The hull can be thought of as a box girder that has to resist global bending loads and other localised forces at specific points such as stay attachments, beam junctions, foil housings and where the crew stands.

In a box girder the outer edges take tension and compression and the connecting faces work mainly in shear, preventing the load bearing edges from moving relative to each-other. 

This is an efficient arrangement because the corners are furthest away from the neutral axis so can be thought of as having the best leverage. 

The curvature of the edges also makes them less prone to local buckling.

The concept is similar to a truss such as you might see on a construction crane. 

The members that make up the long edges of the truss are substantial but the diagonal members are comparatively dainty. 

To build on the analogy, an A Cat hull relies on additional unidirectional fibres running along the turns of the bilge and the gunnels to take global bending loads efficiently. 

The panels between the four outer edges will have fibres running diagonally between the edges in a pattern similar to the diagonal elements of a truss.

Truss boom on an IACC yacht. To resist global bending loads, the long outer edges take tension and compression.
The connecting panels use diagonally aligned fibres to prevent relative movement of the edges.
Image credit unknown. 

Where forces are applied at a mechanical connection point such as a stay attachment or beam junction, the load path can be resolved locally with additional reinforcement and possibly a bulkhead or ring frame. 

Where the load is hydrostatic or hydrodynamic, panel stiffness needs to be considered more globally. 

In both cases, if the panels are inherently stiff, then less additional support is required for a given deformation.

Panel stiffness is therefore important to global stiffness as well as to maintaining the local design shape. 

Thickening a panel increases its stiffness. 

For reasons similar to those governing material distribution in a truss, the material furthest away from the neutral plane of the panel works most efficiently. 

This is why a comparatively weak material such as foam or a low density material such as honeycomb can be used in the middle of the panel in conjunction with strong/stiff materials such as carbon fibre for the skins.

So stiff is good and thick is stiff. 

Thickness is best achieved using sandwich construction. 

This brings us to our first major decision: what core material to use in the sandwich. 

The two candidates are foam and honeycomb…

A Cat RANSE

Graphic visualisation of hull wave height around a candidate shape.
These simulations are very intensive in terms of processing power, so must be used selectively to keep time frames realistic.
Fortunately we are in good hands. More will be revealed soon.

A Cat Update

Just a quick progress report for those of you who are regular followers.
Design work is going well with some very interesting insights already in the bag.
A promising hull concept has been identified and tests have started on a family of variants.

The opportunity came up to run some more advanced simulations than we had originally hoped for.
This will add four weeks to the schedule but will give even greater confidence in the final design choices.

While the design work continues we have been evaluating options for tooling and construction methods as well as choosing suppliers for materials and parts.

The first choice regards which parts and stages to machine using CNC/CAM technology vs. traditional pattern/mould making and hand finishing.
This decision is about striking the right balance between machine time cost and labour cost.
Interestingly, the optimum strategy will differ depending on local labour rates, competitiveness in the CNC/CAM market, and the complexity of each part.

Early in the project we decided that investment in tooling is warranted where it will reduce the time required to assemble/finish each boat to the desired tolerances.
Though the exact shapes have not yet been finalised, it is safe to assume that the foil tooling will have a non planar geometry requiring high precision (fine tolerances) whilst being difficult to build using traditional methods owing to the lack of a flat reference plane.
Finally, it makes sense to include in the tooling certain details to optimise beam junctions, stay attachments, and fitting mounting features, again to reduce time spent hand finishing each boat.

With all the above considerations, and given availability of competitively priced CNC/CAM service providers in Australia, the numbers come out decidedly in favour of automated machining straight from the digital 3D model. This approach is consistent with our standard practice of fully modelling all assemblies before manufacturing.

Initially we looked at machining female tools out of solid material (alternatives included tooling board, modelling foam with machinable putty skins, or MDF with a glass skin).
This would eliminate the step of laying up female tools over traditional male 'plugs', but would have the drawback of constraining the temperature and pressure we could apply during the curing of the final parts.

Traditional composite female moulds laid up over computer machined male plugs seem like the way to go. They give the freedom to use prepregs at reasonable temperatures and pressures to obtain better compacted and more stable finished parts.

Integral in this decision-making process was an evaluation of different core materials that led to some interesting conclusions...

A Class Catamarans – A Look at the State of the Art Part 10

Having chosen a hull and foil geometry, the next task is to execute the carefully optimised shapes accurately and efficiently.

Class rules mandate a minimum overall weight of 75Kg for the complete boat with no other restrictions on material and shape above the waterline. 

Keeping weight at rule minimum is very important for performance as carrying additional mass is slow.

It is desirable to aim for a finished boat weight around 1Kg shy of the minimum to allow for

1)      Variations in weight between different rigs, and

2)      Inevitable repairs that may be required over the competitive life of the boat. These may result from collisions during racing, filling accumulated dings and scratches, or other accidents…

When the boat is new the weight difference is accounted for by ballast that can be placed centrally to minimise pitching.

It is possible to build boats well under rule minimum weight. The challenge however is to invest the mandated weight to best advantage, taking into account stiffness and mass distribution.

Overall platform stiffness is good because

1)      It maintains the designed geometry between hulls and foils under load, and

2)      It means less of the finite energy extracted from the wind is sapped by elastic deformation.

Similarly, stiffness of each hull

1)      Maintains underwater shape,

2)      Provides geometrically consistent rig support,

3)      Minimises resonant ‘wobbles’ when loads vary upon exiting waves.

Overall platform stiffness is mostly dependent on the stiffness of the crossbeams and their connections with the hulls.

Individual hull stiffness is determined by hull shape (mainly 'boxiness'), construction material, reinforcement choices, and internal structure. 

Achieving sufficient hull stiffness is challenging because of the long cantilever ahead of the front beam. This unsupported span typically amounts to half of the overall length, more on some recent designs. 

The hulls are also typically slab sided forward, with large flat areas that need to be carefully considered in terms of stiffness and local buckling.

In essence, each hull is a box girder (or squared tube) cantilevered in bending about the front beam and reacted at the rear beam. 

In the vertical plane the load is predominantly in ‘sagging’, with the forestay pulling up from part way along the cantilevered span, and the sidestay pulling up aft of the crossbeam. Mainsheet loads are passed to the back of each hull, adding to bending and introducying a shear/twist element.

In the horizontal plane there is an inward component from the stays and there are substantial hydrodynamic loads pushing the bows sideways (alternating both inward and outaward).

Most existing boats use horizontal stringers or ‘shelves’ along the middle of the flat topside panels to increase the moment of inertia of each hull side panel. Often the shelf extends inboard to ‘tie’ together the opposing hull sides.

Hull panel laminate also has to resist ‘bruising’ from the sailor kneeling/standing on the bilge during capsize recovery. 

Some degree of tolerance to ‘real world’ conditions is important. Light contact, beaching, and occasional rough handling should be considered without unduly compromising performance.

Since material choice is unrestricted, effective constraints are to do with

-          Stiffness for a given weight,

-          Longevity and ease of repair,

-          Material availability,

-          Construction (tooling) method and cost. Especially the relationship between tooling cost and individual boat cost.

Foam and honeycomb core materials are each used in competitive boats. The optimum solution changes with the relative emphasis placed on the above factors.

I will go into more detail on the pros and cons of foam vs. honeycomb core when discussing our choices for the new boat.

Beam junction loads are usually spread into the hulls by full bulkheads or ring frames that stiffen the hull shell locally.

Typical beam solutions include

-          Filament wound (or similarly mechanically produced) round tube, typically with greater wall thickness top and bottom to increase transverse bending stiffness,

-          Similar industrially produced straight tube but with a ‘D’ cross section rather than round,

-          Custom moulded curved beams made in open (two halves cured separately then glued together) or closed (bladder/slip joint) tools.

More on the merits of different beam construction and joining methods later.

I have posted before on the value of a well defined brief where class rules impose no apparent constraint. The A Cat is a great example of an open rule where choices have to be made within a broad rule space, so it is important to evaluate and prioritise solutions with an awareness of the desired outcome.

Complete freedom in hull shape, freeboard, sheerline, and detailing, allows great innovation. To be successful, the desired outcome must be clear, and priorities must be well defined.

Just to give one example: greater hull volume (width/height) at the sheerline improves stiffness but adversely impacts windage and drag in waves. A taller hull with a broader deck will be stiffer for a given weight but will have greater aerodynamic drag and more additional drag in waves.

It is a fascinating challenge to quantify the crossovers between the various factors being traded against each-other. A challenge we are thoroughly enjoying.

A Class Catamarans – A Look at the State of the Art Part 9

I hope those of you who have had the patience to follow this series of posts now have a clearer understanding of the state of play in A Cat design.
This will be the last installment on geometry and dynamics. I will cover structures and detailing in the next post.

We saw that the boats are powered by a rig capable of large variations in lift coefficient. The cut of the sail and the flexibility of the streamlined mast are tuned with crew weight to achieve automatic gust response.

The platform is relatively narrow but is powerful due to the crew being on trapeze.
Hulls have very high length to displacement and length to beam ratios.
These characteristics make friction drag significant compared to wavemaking drag. The importance of friction drag places a premium on minimising wetted area.
Hull geometry must allow for the variation in displacement between sailing upright and flying a hull. The designer must weigh up the time spent in each mode and the exact transition speed.
A large range of positions of the centre of gravity (CG) is possible because the sailor accounts for over 50% of total displacement.

Angled or curved foils add an interesting new dimension:
They give rise to the problem of stability in pitch and ride height.
This problem has not yet convincingly been solved in a way proven on the racecourse.
It has instead been mitigated by designing in ‘reserves’ of stability and sailing the boats ‘around’ the limitations imposed by the inherent instabilities.

Hull shapes have been increasingly adapted to provide buoyancy and dynamic lift in the stern. Big sterns provide the bow down moment necessary to ‘store’ reserve bow up moment required to delay terminal feedback loops caused by instability in pitch and ride height.
In other words the bow down moment provided by wide, flat, buoyant sterns gives something to ‘trade’ when additional driving force needs to be reacted.
The price of this solution is additional wetted area.

Despite such adaptations, current designs must limit foil lift by increasing the foil radius (making the boards straighter) and/or partially retracting them at high speeds (reducing effective dihedral).

If the boat were stable in pitch and ride height, reserves of trimming moment and AoA would be unnecessary. The drag penalty associated with providing these reserves could be avoided.
The foils would automatically provide the necessary restoring moment (bow up or bow down) to counter perturbations caused by external forces such as waves and gusts.
There would no longer be a need to curtail foil lift at speed. Maximum advantage could be had from foil assistance.

The following diagrams illustrate conceptually the difference between stable and unstable systems.

Above left is a representation of an unstable system: any disturbance (such as the arrow shown) will cause the red ball to roll down the curved hill further and further away from the starting point.
It is analogous to a situation where increased angle of attack (AoA) causes a pitch up which in turn increases AoA... Giving rise to a feedback loop that takes the system further and further away from the starting point.
Above right is an unstable system with a small neutral zone rather than a single equilibrium point.
Some force will displace the ball toward runaway instability but there is time to react.
The flat area represents the reserves of trimming moment and foil AoA provided by wide sterns on current A Cats.
Notice that when the force is removed the ball does not automatically return to the centre of the neutral zone. It must instead be returned there 'manually' or it will remain closer to one unstable limit than to the other. In this representation, actively keeping the ball away from the edges of runaway instability is equivalent to the active crew movements and changes in heading and sheet tension required when pushing hard downwind.

Above left is a representation of a stable system. The harder the ball is pushed away from the equilibrium point, the harder it pushes back.
When the upsetting influence is removed, the ball will return to the unique equilibrium point.
To the right we see a stable systems within limits.
This represents a conventional hull: It will resist changes in trim and sink by generating progressively more restoring force. But at a certain point it will give up and 'flip'.
In the case of a conventional hull, this limit is approached when the bow is completely buried and the crew is right at the back.
The ideal foiling or foil assisted boat would also behave according to the last diagram.

If the reader will indulge me, I would briefly take a highly simplified look at aircraft theory to convey in more practical terms the idea of a dynamically stable system.

Above you can see the effects of varying pitch angle on the balance of forces on a conventional aircraft.

If the nose is pushed down, the initial small negative AoA on the tailplane increases. This pushes the back of the aircraft down harder. Thanks to the long lever arm provided by the fuselage/empennage, a level attitude is restored.
Conversely, if the nose were pushed up, the tailplane would be projected down. AoA on the horizontal tailplane would go through zero, then turn positive and continue to increase until sufficient upward lift is generated to automatically pull the tail back down.

This self leveling is completely automatic without pilot intervention and arises from the geometry of the flight surfaces.
It is distinct from manipulations of the control surfaces that the pilots may affect in order to change flight direction.
Stability can be calculated taking into account the relationships between wing area, tailplane area, and CG.
It is easy to see that the tailplane has sufficient leverage to control pitch attitude even with a modest area compared to the main wings.

In level flight the tailplane actually pulls down slightly. Small nose up perturbations at first cause this downward pull to go to zero. Further perturbations pushing the nose up then progressively increase positive angle of attack on the tail plane, pushing the back of the aircraft up harder and harder.
The reason for the initial downward pull of the tail plane is that the aircraft CG is forward of the centre of effort (CE) of the main wings. Conventional aircraft are set up this way to provide stall recovery. Meaning that if the critical AoA were exceeded, causing the wings to stall, the nose would automatically drop, reducing AoA and enabling the flow to re-attach to the wings.

Note that stall happens at a critical AoA, independent of speed. Yet aircraft manuals refer to stall speed. This is because as an aircraft slows down, it must fly at a higher angle of attack to generate the same amount of lift it was making at the previous faster speed.
If the plane keeps slowing down, eventually a speed will be reached where AoA cannot be increased without stalling the wings. That is the stall speed.

Transferring these principles to existing successful foiling sailboats, we can look again at the Moth case.

Armed with our knowledge of aircraft stability we can see that the Moth is indeed stable in pitch.

You will notice that as pitch attitude varies, the AoA on the main wings/foils also changes.
Stability in pitch is governed by the relationship between the main wings/foils, tailplane, and CG.
Ride height is connected to pitch angle in the sense that an increase in pitch angle will make ride height want to increase.
But stability in ride height can be considered quite independently.
Aircraft analogies are less useful here because planes are not restricted to the interface between two fluids. They can pull up or nose down at will. If they are stable in pitch they will want to fly straight along their longitudinal axis. If the axis points up they will climb up as they move forward provided sufficient energy is available to keep them moving faster than stall speed.
Foiling and foil assisted boats, on the other hand, require an automatic way to maintain ride height somewhat independently of pitch attitude.

Looking again at the Moth, we can see an effective mechanical solution.
The bow wand senses the water surface and adjusts the camber of the main foil by actuating its flap through cranks and push/pull rods.
At lower ride heights it increases the camber and hence the lift.
At higher ride heights it reduces camber by aligning the flap closer to the chord line of the foil.

Fully foiling multihulls such as the Hydroptere are stable in pitch because they use a T foil on the rudder(s).
They have some stability in ride height by virtue of the fact that less and less of the main foils is in the water as ride height increases.

Foil assisted A Cats without a horizontal surface on the rudder cannot be stable in pitch.
Curved foils also cannot be stable in ride height because their dihedral angle increases with ride height.

Angled foils could possibly be stable in ride height in a way analogous to the Hydroptere setup but they have higher interference drag and it would be difficult to get sufficient horizontal projected area within the inboard bounds of the ‘foil box’ mandated by the A Cat rule. Though this is certainly an avenue worth exploring.

Spectacular flat water capsize. Probable cause
is a sudden loss of foil lift due to dynamic instability.
Image credit unknown

Addressing the issue of dynamic stability is the key to unlocking the next step in performance.
Some experimentation in the class is already bearing fruit: novel foil geometries and different shapes and sizes of horizontal surfaces on the rudders are becoming an increasingly common sight.
We are looking carefully at some very promising alternatives as we develop our new A Cat.

A Class Catamarans – A Look at the State of the Art Part 8

When we looked at influences on hull shape we concluded that minimum wetted area is a priority.

Minimum wetted area for a given prismatic coefficient is obtained by using semicircular cross sections. 

Prismatic coefficient in turn is driven by resistance to bow down trimming moment and by operating speed.
Both are essentially functions of the wind conditions that a design is being optimised for: fuller ends are more suited to higher speeds and also offer greater resistance to bow down trimming moment. 

Semicircular sections require a beam to draft ratio of 2:1. Considerations of rocker depth may push the optimum to a slightly flatter shape. 

Some fore/aft symmetry in volume distribution is desirable to minimise wetted area. A balanced shape is also more responsive to shifts in crew weight. A higher aft prismatic with some transom immersion is more suited to higher speeds. But very wide transoms carry a net drag penalty.

When weighing all these considerations, one should also take into account that the modern A cat spends a lot of time sailing on one hull, especially at higher speeds. 

It was noted that this theoretical optimum shape does not agree with what can be observed in the trends set by the winning designs in the class. 

There is a definite progression to flattened ‘U’ shape sections and wider (and wider!) sterns.

We then looked at the effects when foils support part of the weight of the boat and provide bow up trimming moment to counteract the bow down moment arising from the sail drive force. 

We saw how the instantaneous desirable effect of vertical lift generated by foils gives way to runaway feedback loops making the boat as a system unstable in pitch and ride height.

Finally we discussed how sailing technique evolved to delay the inherent instability of conventional foil assisted geometries: the boats are sailed with reserve pitch attitude and rely on quick reactions from the skipper to accelerate ‘away’ from a takeoff/crash sequence.

All these elements give clues to the reasons for the deviation of successful hull shapes from the theoretical optimum. 

Put simply, wide sterns allow the boat to be sailed with greater additional reserve angle of attack (AoA) on the foils.

There are different equivalent ways to think about the dynamics of the system, ranging from a purely mathematical description to conceptual models involving different elements. 

For clarity I will use here a crude description showing only key elements to convey the basic concept.

The first diagram in this post shows the situation when the boat is sailing with significant weight on the foils and the crew positioned right at the back. 

The foils are providing a bow up moment about the centre of gravity (CG). 

Also with respect to the CG, the stern is providing a bow down moment.

The available ‘reserve’ AoA can be thought of as proportional to the bow down moment provided by the buoyancy in the stern. 

The two moments are represented in the diagram.
Notice that the bow up moment is greater than the bow down moment. 

The difference between the bow up moment provided by the foils and the bow down moment provided by the stern is equal to the bow down moment generated by the rig at that instant.

Think of the bow down moment generated by the stern as a ‘reserve’. 

As rig force increases the stern progressively comes out of the water so the bow down moment from the stern decreases. 

At the same time the boat accelerates so foil force decreases only marginally (angle of attack decreases but speed increases to compensate). 

The difference between the bow up moment from the foils and the bow down moment from the sterns therefore increases. 

The increased difference between the foil bow up moment and hull bow down moment gives a net increase in bow up moment. 

This net increase in bow up moment resists the additional bow down moment arising from the added sail drive force.

From the point of view of the sailor, the wide stern makes the boat more forgiving. 

It allows the skipper to trapeze downwind with weight right aft and have some chance of reacting to a gust in time to avoid a rapid takeoff/crash feedback spiral.

The limitations of this system now become obvious: As sail force increases, at some point the bow down moment from the stern will go to zero. 

At that point all the bow up moment from the foils will be in use to counteract the bow down moment from the sail. 

If sail force were to increase beyond that point (or even if some external perturbation such as a wave were to momentarily alter trim), there would be no reserve available to delay a runaway feedback loop.
Another way to picture this limiting condition is to imagine the boat teetering on the foil with no way to apply additional stern down pressure.

Interestingly the instability is both in pitch and in ride height:
A change in pitch leads to ever greater change in the same direction because pitch angle affects foil AoA. 

A change in ride height also leads to further change in the same direction because effective foil dihedral increases with ride height to give more lift at greater ride heights.

So foil assisted boats are fast but have tricky handling characteristics at speed, and well documented inherent limitations. 

Much of the performance available from curved foils cannot be accessed because of control issues.
The foil assistance must necessarily be 'dialled down' at speed, just when it could be of greatest benefit.
It is quite common to hear skippers say after a race "I had too much lift for the conditions".

Sailing technique has expanded the performance envelope but the limits are inherent in the configuration and cannot be circumvented without an evolution in boat geometry.

Big sterns with broad sections and wide waterplanes are necessary to exploit existing constant radius curved foils. 

They allow the boats to be sailed with reserves of bow down moment that can be ‘traded’ for bow down moment associated with additional sail force. 

This also explains the expanses of flat area in the run aft: They give some dynamic bow down moment in addition to the buoyancy in the stern. 

But there is a significant cost in the form of additional wetted area and reduced responsiveness to fore/aft shifts in crew weight.

It would seem that this trend is well entrenched as the only way to exploit foil assisted performance. Several manufacturers have updated their hulls with wider sterns and these changes have uniformly been found beneficial. 

But is there a better alternative?

A Class Catamarans – A Look at the State of the Art Part 7

We saw in the last post that current foil assisted A cats are inherently unstable in pitch.

As sail force and hence bow down trim increase, the angle of attack (AoA) of the foils decreases resulting in less bow up trimming moment.

Conversely, if drive force decreases and the bow comes up, the AoA increases and a runaway feedback loop arises: More bow up trim results in a greater AoA that gives more bow up trim… 

Until either the boat jumps out of the water or the foils stall. 
Both possible outcomes happen quickly and are slow in terms of time around the course!

Bow up feedback loop being allowed to continue.
Image credit unknown

The problem is compounded by the fact that effective foil dihedral INCREASES with ride height. 
So as the boat comes out of the water, the vertical component of the foil force INCREASES, causing the boat to want to rise further.

Instability in pitch is combined with instability in ride height
due to the foils effectively becoming more horizontal with increasing ride height

In the real world the twofold feedback loop resulting in pitch instability is mitigated by the following factors:

-          When trapezing downwind, the boats are sailed with ‘reserve’ bow up attitude so there is some margin before the angle of attack goes negative, flicking the bow down suddenly. Even so, the angle of attack does decrease instantly as the sail force increases. Incidentally this explains the sudden and spectacular ‘tripping over pitchpoles’ that are often seen when foil assisted A cats are sailed at speed, even in flat water, and with the bows seemingly clear of the water. If the foils suddenly switch from producing a significant bow up moment (positive AoA) to pulling down (negative AoA), the limits are reached suddenly and spectacularly. The stern plays a role here but more on that later.

-          When sail force increases, whilst the bow up ‘margin’ is being used, the boat also accelerates. The increased speed means the foils can generate more lift for a given angle of attack. If there is enough reserve pitch angle to keep the foil angle of attack positive, then the bow up moment can remain sufficient provided enough additional speed is obtained in time. 
In other words acceleration replaces pitch angle as the determining factor in the amount of lift produced.

-          As sail force increases, the skipper steers to pull the apparent wind around and sheets on. This redirects the sail vector more across the boat and reduces the apparent wind speed, moderating the sail force.

Sailing downwind with an AoA 'reserve' allows the boat to accelerate.
Higher speed and course/sheet adjustments can compensate for the reduction in AoA caused by increased drive force.

Sailing technique has evolved to deal with the limitations of existing curved foils, and foil assisted sailing is winning A cat races convincingly. 

In moderate conditions this requires very fast reflexes and agile shifts in crew weight. 
It can be thought of as analogous to riding a unicycle: It can be difficult to master and laborious but it is possible within limits. 

Time and again one reads in forums and hears sailors comment that in certain conditions the foils need to be partially retracted to limit the amount of vertical lift and bring the boat back under control. 
This is a serious limitation: retracting the foils simply reduces dihedral angle, giving up the full benefits of vertical lift just at the speeds where the greatest advantages occur (remember that as speed rises foils get more effective and hull drag becomes more expensive).

Retracting a curved foil (constant radius) reduces effective dihedral

Yet this limitation is accepted as inherent in the current winning configuration.
One manufacturer has even increased the radius of curvature of their updated foils.
They have made the newer foils straighter partly because they were getting 'too much lift'.
Surely a better solution would be to improve dynamic stability and avoid giving up the advantages of foil assistance, just as speed rises sufficiently for the advantages to become significant.

One way to push the limiting conditions further up the speed range is to increase volume and flat area in the stern. 
That is the current trend and will be the subject of the next post.

A Class Catamarans – A Look at the State of the Art Part 6

Let’s take another look at the figures in the previous post, this time considering stability in pitch.

What happens when we introduce two real world factors: drive force and changes in pitch attitude? 

Stability in this context simply means the tendency to return to a level attitude when perturbed by some external force (in conventional naval architecture righting moment is sometimes referred to as ‘stability’ - hence the need for this premise distinguishing the meaning of the term in the context of dynamic foiling). 

Positive stability means that the system (boat) will want to return to a level attitude if disturbed. 

Negative stability means that it will want to keep deviating further away from a level attitude in the direction of the disturbance.

Referring to the first diagram in Part 3, the drive force from the rig is the component of the total sail force pushing the boat forward. It is at right angles to the side force that we have been looking at so far in connection with hydrodynamic reaction force and foil lift. 

Because it is generated by the sails some distance above the water, this drive force will give rise to some bow down trimming moment. 

Upwind the side force is much larger than the drive force. 

Downwind the sail force points more forward so the side force component is smaller and the drive component is bigger. 

Hence more bow down trimming moment when sailing off the wind.

As bow down trimming moment increases on a conventional displacement boat, the forward sections of the bow immerse progressively. This gradually increases the displacement at the bow, effectively moving the centre of buoyancy (CB) forward.
Now the CB and the CG are separated by a horizontal distance creating a bow up moment that opposes the bow down moment from the rig.
When the bow down moment goes away, the bow up moment pushes the bow up to its lines, displacement there decreases, and the CB moves aft until it is again under the CG.

As bow down trimming moment increases, the boat trims bow down.
More volume is displaced in the bow, the CB moves forward, and a bow up trimming moment results.

This process is sufficient in light winds. At some higher wind speed the bow will submerge to the point where either drag rises steeply or there is no more volume to add (runs out of freeboard).

Older Tornado style hull shapes attempt to increase reserves of buoyancy in the upper part of the bow through flared sections (widening waterplane) and high freeboard.

Sink in the bow moves the CB forward. Since the aim is to increase the separation between CB and CG, moving the CG aft also helps. On a small boat moving the crew aft has a very significant effect in moving CG back. On larger boats stacking and water ballast have similar effects, though usually not as pronounced.

Moving weight back shifts the CG aft, increasing longitudinal separation between CG and CB.
Since the forces remain the same, increasing their separation increases the moment they generate

Newer piercing bow designs rely more on shifts in crew weight (or on foils in the case of larger boats) whilst keeping additional drag when trimmed down by the bows to a minimum. Keeping extra drag to a minimum pays because it allows higher speeds and because it lets the boat accelerate, reducing apparent wind and hence sail force.

Modern monohulls and, to a lesser extent, some newer multihulls, use dynamic ‘planing’ forces on flat areas of the underside of the bow to generate some vertical force complementing the additional buoyancy given by bow down trim. In the case of multihulls, this is a small contribution because the hulls are narrow so the available flat surface area forward is limited.

The conventional system of separating the CB from the CG as described above has positive stability in pitch: If more trimming force is added, more restoring moment automatically arises. 

When the trimming force is removed, the system automatically returns to a level attitude. 

Clearly there are limits determined by the maximum possible bow up moment (CG right back and bow fully immersed). But within those limits the system is automatically self leveling.

When we add foils the dynamic picture changes drastically. 

Imagine a boat sailing along at a level attitude with significant vertical foil lift and the CG positioned to balance the existing bow down trimming moment (as in the previous post). 

Now add some extra trimming moment as if a gust has just hit the sail or the crew trimmed the sheet on harder.

Initially the bow will go down. The natural effect of the hull will be as for a conventional boat but less pronounced because the total displacement is reduced (some of the weight is supported by the foils). 

But the effect on the foils will be to reduce their angle of attack. 

This will reduce the amount of lift!

As the bow goes down, foil angle of attack decreases.
If AoA was initially neutral, as could well be the case for asymmetrical foils set for moderate lift and low drag,
any bow down trim would result in a negative AoA

So foils react to increases in drive force by offering less and less lift.
But how can modern A cats sail around fully powered up with most of their weight on their curved foils?

A Class Catamarans – A Look at the State of the Art Part 5

In previous posts we looked at the extremes: full ‘foiling’ and simple displacement modes. I touched on a middle way that I refer to as ‘foil assisted’. As is often the case, a compromise is preferable to either extreme. And is what the existing fleet seems to have settled on.

I mentioned that ORMA 60 trimarans progressed to curved foils in order to take advantage of a bow up moment resulting from the forward positioning of their outboard foils - Foils that were already present with the primary purpose of providing sideforce in reaction to the side component of the sail force.

Because of narrower beam, aft rig positioning, and non-canting rig, A cat foils are further aft. However, in all but the lightest conditions, they are still forward of the centre of gravity (CG) of the boat (keep in mind that the position of the skipper has a big influence on total CG of boat + sailor).

Moving a foil aft has the effect of reducing the leverage it has to push the bow up.
But it also means that more upward force can be generated by the foil for a given bow-up trimming moment. 

This can be understood by considering that the trimming moment is given by
force X distance from the CG. 

As a thought experiment, consider that if a foil were extremely far forward, a much smaller force multiplied by the much longer distance to the CG would give the same moment as a larger force applied further aft (i.e. at a shorter distance to the CG). 

The extreme opposite case would be placing the foils at the CG so that the distance would be zero. In that case the force would impart no trimming moment. Its effect would just be to push the hull up without changing its attitude in pitch.
Practicing beach cat sailors can relate to this by recalling that lifting a boat right at the bow requires less force than lifting the same boat from the front beam.

Section through lower (more horizontal) part of curved foil shown in red.
With the skipper forward in the boat, the foil has no leverage to exert a trimming moment

The modern A Cat uses curved boards to support some of the weight of the boat and at the same time help keep the bows up.
Since the foils are placed close to the CG, they can provide a large amount of vertical lift for a given trimming moment.
As speed rises, they take more and more of the weight of the boat, making the hulls more and more efficient.
The added hull efficiency comes with a small foil drag penalty, but the net effect is less overall drag. This is because the foil has negligible extra drag compared to a 'conventional' straight/uncanted foil.
Looking at the components of foil drag, there is little added lift induced drag because the extra lift is small compared to the side force that has to be generated anyway (remember that at low speeds no attempt is made to produce enough lift to support large percentages of the weight of the boat so the foils are not sized to do so). There is little extra frontal area and little extra foil wetted area so the remaining components of additional foil drag are modest.

Intermediate CG position with crew approximately at aft beam.
Now the foils have some leverage to exert a trimming moment.
Note that changes in trim due to movements of the CG are ignored here.
They will be considered in later posts

At very high speeds the foils may be taking a large percentage of the weight. Remember that the ratio of side force to vertical force is determined by foil dihedral. Since side force is a reaction to sail force, vertical force is effectively also proportional to sail force. At high speeds, when more side force is required, more vertical force is produced automatically.

Extreme aft CG (crew trapezing off the transom).
The same force as the previous figure generates a greater moment

So foil assistance by means of angled boards is great in many respects.
Curved foils are even better because they have the same effect as angled foils but with less interference drag. A constant radius is a good compromise as it makes the foils and the housings easy to build.
Both solutions are preferable to ‘J’ foils since they couple vertical force to automatically adjust with side force, with minimal additional drag.

But how do the foils affect stability in pitch, ride height and righting moment? 

Part 6 is coming next week.

A Class Catamarans – A Look at the State of the Art Part 4

In the case of ORMA 60s and A cats, the hulls have such favorable drag characteristics that 'foiling' does not (yet) pay in the majority of conditions. Instead, boards already present to provide side force are modified and 'double purposed' to complement the buoyancy of the displacement hull. This is a 'foil assisted' mode.

ORMA 60 in flat water. Notice the forward location of the foil
and the bow-up attitude it encourages.
Image source: www.sail-world.com

   Hull drag vs. dedicated foils (additional foils for generating vertical lift)

For every length traveled, a conventional hull must displace (move out of the way) an amount of water weighing the same as the boat.
A long slender hull with a fine entry angle, narrow beam, and shallow draft, can spread this displacement ‘thinly’ over its length, effectively making a very small hole in the water. 

The water pushed out of the way at the front takes energy away in the form of a bow wave. Some of this energy is recovered when the second peak of the wave system forms at the stern, effectively leveling the hull. 
The net loss of energy (wave drag) increases rapidly as speed approaches and exceeds 'hull speed' - hull speed being the speed characteristic of a wave with the same length as the hull. For very slender hulls the drag rise with speed is more linear but still steep.

Lift generated by foils comes with its own drag penalty. Think of it as a cost that has to be paid to get the lift. Foil drag has several components such as lift induced drag - proportional to the lift generated - and profile drag - always present as a consequence of the foil being in the flow. 

At low speeds the drag associated with supporting all the weight of the boat with foil vertical lift is much higher than the drag of a long slender hull cutting through the water. 

As discussed previously, wave drag as a component of total hull drag is of lower relative importance in a multihull than surface friction drag - which is proportional to wetted area and rises less steeply with speed. But when comparing hull drag with foil drag, we look at the total drag for each alternative, assuming each has been optimised with respect to its components.

As speed rises, hull drag generally rises more steeply than does the drag of the ideal foil for that speed.  

This is a complex tradeoff, taking into account that a smaller foil can do the same job at higher speeds - the ideal foil size gets smaller with rising speed. 
At low speeds, foils would have to work very hard to impart on the passing water the circulation necessary to generate sufficient vertical lift to support the weight of the boat. Or they would have to be larger, with higher parasitic drag and more area than would be optimum at higher speeds.

   Crossovers

For every boat type there will be a crossover speed where foil drag goes from being greater than hull drag to being equivalent and eventually smaller. Think of it as hull drag overtaking foil drag as speed rises. 
In the case of a long, slender, light boat such, that speed may be seldom reached during racing. In any case, sizing of the foils for the ideal crossover speed may be problematic if such dedicated foils would be of little use at other speeds. 

If T or L/J foils were used, separating out the task of generating vertical lift from that of providing side force, then the sizing of the horizontal foils (or foil segment in the case of L/J foils) would be such that the parasitic drag at low speeds would be crippling, and/or efficiency at high speeds would be compromised. This is before taking into account ride height control, stability in pitch and the effects on righting moment. 

J and T foils separate the vertical and horizontal lift functions to different parts of the foil.
Thus vertical lift can be independent of side force and  only related to speed and angle of attack,
but there is a penalty in terms of parasitic drag because foil area is increased

   Using existing foils (necessary to generate sideforce) to provide some vertical lift

Using angled or curved foils results in less parasitic drag but an important constraint exists because sideforce is ‘pegged’ to sail force. 
Because vertical lift is one component of the total foil force, its relationship to sideforce is fixed. An approximation of this fixed relationship is given by the dihedral angle of the foil. 
Dihedral angle for an angled foil is simply the ratio of vertical projection to horizontal projection. 
If the foil were angled at 45 degrees, then the two projections would be equal. In this case horizontal lift would equal vertical lift at all times.
Ignoring flow peculiarities due to foil curvature, the effective dihedral angle of a curved foil can also be approximated by looking at horizontal and vertical projections.

Dihedral angle determines the ratio of horizontal to vertical component for a given foil force.
Note that since the two components are in a fixed ratio for a given dihedral angle,
and since sideforce is determined by sail force,
the amount of vertical force ftom a curved or angled foil will always be limited by sail force

   Break-even points in different cases

A long slender hull with high efficiency in terms of wave drag, and minimum wetted area, may be a better solution around a course than any hydrofoil geometry that aims to completely replace displacement with vertical lift. 

The two extremes are easy to calculate: 

At low speeds the hulls are supporting all the weight by displacing water and the foils are 'coming along for the ride', generating parasitic drag. 

At foiling speeds the hulls have zero hydrodynamic drag (they are out of the water) whilst the foils have friction drag and lift induced drag as well as losses due to any loaded surface piercing parts. 

The transition period is more complex because as lift from the foils increases, the hull has to displace less water (it gets ‘lighter’). 
This actually increases the efficiency of the hull because it makes it even lighter for its length. 
But the reduced hull drag must be weighed against the foil drag.

Forces on a foiling moth. Note that the submerged horizontal foil provides a force
with both horizontal (side force) and vertical components.
Diagram taken from www.moth-sailing.org/download/10-11-11_ThesisBoegle.pdf   

Contrast this with the case of a moth: a short relatively heavy boat (when taken with the weight of the crew) where hull drag is much more expensive, so the crossover with lifting foils happens lower down the speed range. 
Even then, compromises have to be made in light winds. 

But the contrast is even starker when you consider that foiling moths are able to heel to windward. 

This allows them to use the fully submerged horizontal foil to provide both side force (horizontal component) and upward lift (vertical component). 

The horizontal foil, free of surface interference, then effectively becomes the fulcrum and every other part of the boat is providing righting moment. 

It is interesting that even a moth does not use separate dedicated foils for vertical and horizontal lift but instead combines the components in a single efficient surface.
Such a solution probably could not work well on a multihull with foils mounted outboard (heeling to windward would be possible but it would not result in similar gains). 
Once again, a long slender hull is much more attractive in terms of drag than complex foil geometries.
Re-purposing existing foils will be better at certain speeds. The challenge is finding the crossover that gives minimum time around the course.

   What has been proven to work

Having said all the above, curved foils that assist displacement hulls do work around the racecourse.
This is mainly because they increase hull efficiency with a drag penalty that is much smaller than what would be incurred by a fully foiling arrangement.
There is a subtle 'sweet spot' where the existing board (as opposed to a separate dedicated foil) is only generating marginally more lift than it would be if it were vertical (the total foil force must increase if the vertical component is to increase) so the additional drag is small. 
In doing so, it supports some of the displacement, effectively making the hull lighter. 
The hull stays in the water so all the waterline length is still being used, but now the displacement to length ratio is even better. 
There is also a bow up trimming moment that results from the foil being in front of the centre of gravity. This is effectively like making the bow fuller without changing the hull entry angle.

But to get a better understanding of the complexities involved, we have to look at the effects on righting moment, stability in pitch, and ride height control.