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Monday, March 26, 2012

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.

Thursday, March 22, 2012

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?

Wednesday, March 21, 2012

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.

Tuesday, March 20, 2012

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?

Wednesday, March 14, 2012

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.

Monday, March 12, 2012

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. 

Saturday, March 10, 2012

A Class Catamarans – A Look at the State of the Art Part 3

With reference to the illustrations, I will attempt to roughly cover the progression to angled and then curved foils.
Let’s start with a conventional centerboard dinghy.
On any point of sailing except dead downwind, the sail force will have a component across the boat. This is the aerodynamic sideforce.
For the boat to sail at a constant speed, all forces must cancel out as any net difference will result in some acceleration.
The forward component of sail force is balanced by hydrodynamic drag from the parts of the boat in the water (and some aerodynamic drag of the superstructure).

At rest we have sail drive force but no hydro drag. So the boat will accelerate.
As boatspeed increases, hydro drag increases. The boat will accelerate until the rising hydro drag equals the aero drive force. This will be the equilibrium speed.

Increasing the drive force and/or reducing drag will result in a higher equilibrium speed.
At the same time, sideforce is balanced by an equal and opposite hydrodynamic sideforce generated by the hull/board/rudder system, but principally by the centreboard/foil(s).
The hydro sideforce arises because the leeway component of boatspeed (arising due to sideforce) makes the water meet the foils with an angle of attack (AoA).

Since the aerodynamic force is generated above the water, and the hydrodynamic force below, there is a heeling moment that must be balanced by moving crew weight to windward.
But for now let’s concentrate on the forces as viewed from above.

Sail force and hydrodynamic reaction force can be broken down into components across the boat and parallel with the boat.
Note that a force can be thought of as the sum of any pair of components at right angles to each-other.
For example, components can be taken across and parallel with the
actual direction of motion (including leeway) or relative to the wind...
In order for the boat to be balanced in yaw (not want to luff up or bear away), the board must be positioned along the line of action of the sail force. As a boat gets wider, the board must therefore move forward. 
This, incidentally, is also why conventional monohull keelboats require the fin to be behind the mast if they are to remain balanced when heeled.

Simplified concept of the line of action of sail force and hydro reaction force.
As the board moves to leeward it must move forward.
In reality contributions to sideforce from rudder and hull must also be taken into account,
usually resulting in the board being even further forward.
The earliest use of angled foils that I am aware of is on the floats of ORMA 60 trimarans. 
When conventional upright foils were first placed on the floats to maintain side force when flying two hulls, they were naturally positioned forward of their counterpart on the main hull. 
The move forward was due to the wide platform beam and the windward cant of the rig. 
By some accounts (I heard it from Nigel Irens) it was noticed that when flying two hulls (and hence heeled significantly for a multihull), conventional upright foils tended to give a bow-up ‘assist’ that allowed the boat to be pushed harder.

Conventional upright foils give a vertical component when heeled.
If the mast does not cant, then this vertical component is canceled by the downward component of sail force that also arises with heel. If sheets are suddenly eased on a 'conventional' beach cat when heeled, the sail force goes away and the platform may momentarily 'jump' up as a result.
The next step was to angle the straight foils, but this resulted in an awkward exit angle with high interference/junction drag at the hull. 
So the next solution was to curve the foils such that they exited the hull vertically and became more horizontal toward the tips. 
A constant radius was the simplest solution since it allowed a snug fitting case without complex bearings, a significant factor for a large oceangoing boat.

Limiting factors are the hull exit angle and the tendency for the top of the foil to exceed any beam limit when the foil is raised. Also, the whole immersed part of the foil is displaced inboard. This reduces effective platform beam.
Note that a vertical component to the hydrodynamic reaction force produced by the foils exists even with straight boards. But it is small, and largely cancelled out by the downward component of the sail force due to heel (unless the mast cants to windward).


Once the bow up ‘help’ of angled and curved foils was noted, it became a logical progression to increase this contribution so boats could be pushed harder. 

In my opinion this has been a separate evolution to ongoing attempts at hydrofoil sailing where the aim was to actually sail the boat with the hulls completely out of the water, replacing displacement with hydrodynamic lift. 
That evolution had different priorities and came up with fundamentally different configurations.
Without delving too deep into this esoteric world, true foiling multihulls tended to use ‘ladder’ foils with no regard for beam limits and no hope of being competitive at sub-foiling speeds.


Experiments in 'pure' hydrofoil boats:
Specialist solutions included 'ladder' foils designed so that the total lifting surface
becomes smaller with increasing ride height and speed. Image source: www.foils.org
Hydroptere’ style angled foils bear a superficial resemblance to angled foils on displacement boats, but the physics are different.
To allow hydrofoiling, they work against each-other, the windward one providing half the sideforce plus some downward pull while the leeward one contributes the remaining half of the sideforce plus the necessary upward lift. For takeoff, the windward foil may actually be pulling up and to leeward. This is necessary when sideforce is too small to give sufficient vertical component to support all the displacement.
This configuration uses very large foils, spaced far apart, to achieve takeoff, with a large drag penalty at lower speeds.
The drawbacks would be crippling to time around a windward/leeward course.
A boat with a 'pure foiling' configuration of this kind would stand no chance in anything but fresh reaching conditions.
The vast majority of the time, a slender displacement hull has less drag than a true foiling configuration when averaged around a windward/leeward course.

Here the lee foil provides upward force and some side force.
The windward foil provides the rest of the sideforce and pulls down.
But for takeoff the windward foil may be configured to pull up and to leeward, with an associated induced drag penalty.
Note the extremely wide beam, surface interference, and spray.
This 'pure hydrofoiling' configuration evolved for specialised applications.
Image source: www.adriaan.com
Pure hydrofoil machines have tended to specialise in high speed straight line applications, falling outside established class rules. 
The Moth really brought full foiling to the racecourse within a 'box' rule. We will be looked later at the special circumstances that made this possible.
On the other hand, conventional multihulls to the ORMA 60 rule were foil assisted, using foils to help keep the bow up in hard reaching conditions. 
Angling or curving a foil that was already necessary to provide sideforce meant that very little drag penalty was incurred in more moderate conditions. 
This is very important because boats that have to race within a class around a course in varied conditions cannot afford to specialise. They cannot carry around additional foils (or extra foil area) only of use in some conditions on some points of sailing.

In the next post we will look at why outright foiling does not yet pay on an A cat that has to race on upwind/downwind courses in varied conditions…

Friday, March 9, 2012

A Class Catamarans – A Look at the State of the Art Part 2

   Understanding hull cross section shape independent of foils

In the following discussion we will look at the principles influencing cross section shape. 
As mentioned in Part 1, the extremely high length to beam (slenderness) ratio of each A Cat hull reduces the relative importance of wavemaking drag as a component of total drag. This is equivalent to saying that friction drag due to wetted surface is more dominant. 
In very simple terms, the hulls are so long and skinny that they push very little water out of the way for their weight. So friction due to wetted area accounts for more of the total drag than on less slender types.

Ideal underwater cross-sectional shape would therefore be a semicircle because it gives the least wetted area for a given volume. 
Strictly speaking, a semicircle gives the shortest perimeter to the cross section, the cross section being a two dimensional shape.

Think of the units:
Waterline Beam (m) X Depth (m) = Area (m2)
Area (m2) X Waterline Length (m) X Prismatic Coefficient (dimensionless coefficient) = Volume Displacement (m3)


Underwater cross section shown in red. Waterplane in blue.
The perimeter of the cross section is the edge of a slice through the surface of the hull at any given longitudinal location.
Think of a string placed on the hull along the edge of the cross section.
For a given volume, a semicircular cross section will give the shortest string.
When multiplied out by length, that gives the smallest wetted area.
The width of the cross section at the waterline determines the waterplane area.
In this diagram the cross section is approximately semicircular (twice as wide as it is deep).
A given cross-sectional area can be obtained with a range of shapes.
   Trends

The generation of boats immediately before the current one tended to semicircular sections but the latest boats have moved to more rectangular sections. 
On the face of it this is counter intuitive, but it makes sense when viewed together with the fact that overall volume has been increasing. 

As rigs have developed and sailing technique has improved, boats are spending more time on one hull. 
It follows that hulls are being optimised for taking more of the total displacement. 

Waterplane area influences the amount of ‘sink’ required to go from 50% displacement (upright) to 100% (flying a hull). 
Since length is constant, waterplane area in this context can be thought of as proportional to waterline beam. 
Wider hulls have more waterplane area so sink less for a given increase in displacement.
The amount of ‘sink’ affects:
- The ultimate waterline beam to hull depth ratio (remember that the ideal for minimum wetted area would be two to one).
- The amount of additional wetted area of the leeward hull at 100% displacement.
- The amount of heel required for the windward hull to clear the water. 
Roughly speaking, less ‘sink’ means less heel to fly a hull.
Less heel means earlier hull flying with more righting momenta and a smaller vertical component to the sail force since the rig stays more vertical.

Previous generation: waterplane area does not increase with sink,
beam to depth ratio departs from ideal as displacement approaches 100% .
The bits of flat vertical side panel that sink into the water
account for significant additional wetted area
In the absence of foils, the ideal hull shape would have a semicircular cross section with the centre of the semicircle somewhat above the upright waterline and near the 100% displacement waterline.
It would be wider than the previous generation of boats since the ideal semicircle is bigger - it needs to be because it has to displace more volume without sinking as far.

Ideally the waterline beam at 100% displacement would be exactly twice the hull draught and the cross section would be a semicircle.
This shape would minimise ‘sink’ by virtue of its increasing waterline beam (and therefore waterplane) with sink, keeping wetted area down to a minimum through the displacement range.

Current generation (exaggerated for illustrative purposes):
larger waterplane, less sink, significant wetted area penalty
The latest A Cat hulls have a wide waterplane and large overall volume to minimise 'sink'. However, they depart significantly from the minimum wetted area ideal.
Departing from the ideal minimum wetted area shape can be justified in terms of other factors. For instance, if the waterline beam to hull drought ratio is constrained at two to one, the rocker depth is effectively 'pegged' to waterline beam. Due to dynamic factors, it may be better to flatten somewhat the bottom of the cross section, reducing rocker at a small cost in wetted area.

The current trend deviates significantly from the minimum wetted area ideal by being wide, very flat, and having a hard turn of the bilge.
This is often attributed to the prevalent foil setup.
To understand the influence of angled and curved foils, we need to look first at their basic principles and then at history. Part 3 is coming soon…


Theoretical ideal for minimum wetted area:
wider than older generation, increasing waterplane with sink,
semicircular cross section at full displacement
   A technical point regarding comparing like with like

Note that making the ends of the boat fuller will reduce the cross section area for a given displacement. However the merits of different cross section shapes remain valid when comparing hulls with similar total volume (displacement) and fore/aft volume distribution. 

The expression for the fullness of the ends is the Prismatic Coefficient (Cp). 
Cp can be thought of as simply the ratio of the actual volume of the hull to that of an imaginary prism of the same length with a cross section equal to the largest cross section of the hull. 

Cp = Actual Volume / (Midsection Area X Length)

A barge with untapered ends would have a Cp of 1 since actual volume would be the same as the theoretical prism defined by cross section X length. 

Sailboats usually have a decimal Cp since they have tapered ends.

To understand the effect of Cp on total volume, imagine increasing Cp by simply making the ends fuller.

Since
Cross sectional Area X Waterline Length X Cp = Volume,
if Cp increases then cross sectional area must decrease to keep volume constant.

Think of it too in terms of the units
Area (m2) X Length (m) X Cp (dimensionless coefficient) = Volume (m3)
Volume in turn has to be equivalent to a mass of water weighing the same as the boat. 
Hence the interchangeability of the terms 'weight' and 'displacement'.

Increasing the Cp and keeping volume constant effectively requires taking volume out of the middle and putting it in the ends. 
In this discussion we are concerned with the effect of cross section shape for a given cross section area. Meaning the same area distributed differently within the cross section shape.
The conclusions remain valid for different shapes at any given cross sectional area.
For those of you who are interested, there is a detailed explanation of Cp on our press/articles page.

Thursday, March 8, 2012

A Class Catamarans – A Look at the State of the Art Part 1

   Key dimensions
   
Length: 5.49m (18’)
Beam: 2.3m (7’ 6½”)
Weight fully rigged: 75Kg (165lb)
Sail area: 13.94m2 (150ft2)
Crew: One person

   Rig and power management

Though relatively narrow for a catamaran, righting moment is good thanks to the skipper being on trapeze. 
The wide staying base and lack of a jib (no need for great forestay tension) result in low stay tension/mast compression. This allows the use of streamlined masts that rotate about the vertical axis, reducing aerodynamic drag and increasing sail efficiency. 
Masts have evolved to interact with the fully battened square top sails in sophisticated ways: Fibre distribution in the carbon spar is tuned to optimise bend properties with these interactions in mind.
The current generation of masts is more flexible across the long (fore/aft) axis than in the short (port/starboard) axis of the cross-section.
They can be set up to flex significantly under mainsheet and downhaul (cunningham) tension going upwind, when the long/soft axis is closely aligned with the centreline of the boat.
Downwind, when the mast is rotated approaching 90 degrees (so the long/soft axis is across the boat), and mainsheet and downhaul tension are less, the mast remains straighter, making the sail deeper.
The deeper sail allows an increased lift coefficient. This is important for downwind sailing since sail area cannot be increased. 

In other words, the upwind/downwind transition involves altering the lift coefficient of the rig rather than the sail area. 
In contrast to boats where additional sail area can be hoisted downwind, the A cat single sail rig must be very versatile. 

The mast bend characteristics are also tuned to automatically depower the sail by ‘spilling’ the square top and opening up the leech from the top down at maximum righting moment. 

The flexibility of the mast can be tailored to the weight of the sailor to optimise the point at which automatic depowering occurs.
Automatic depowering is desirable because it reduces the workload on the skipper. 

Mast height is not constrained but consensus is around 9m.
One consideration is to raise the centre of effort (CE) sufficiently to induce enough heeling moment to fly a hull early in the wind range.

A cat rig ‘moded’ for height (upwind) or drive (downwind).
   Platform characteristics

The above key factors lead to a very efficient boat with some unique traits:

- The displacement to length ratio of each hull is orders of magnitude greater than most other classes.
- Hulls also have a very high length to beam ratio, so wavemaking resistance is less dominant and wetted area is important.
- The hulls have to work through a 100% increase in displacement (from taking half the weight of the boat when upright to supporting all the weight when sailing on one hull) over a wide range of boatspeeds.
- With advances in rigs and sailing technique, the boats are spending more and more time on one hull. One of the extremely rewarding challenges inherent in the class is learning to ‘do the wild thing’, sailing downwind on one hull.
- Since the weight of the crew is more than 50% of the total displacement, drastic changes in trim can be obtained by simply moving around on the boat. In strong winds, crew weight can be placed right at the back to resist bow down trimming moment. In light winds weight is moved forward to reduce transom immersion.
- Construction favours platform stiffness within the minimum weight. Beams are increasingly unsupported (strikerless) and bonded to the hulls.

   Trends

Hulls are trending to fuller and more ‘U’ shaped sections with greater maximum width, wider sterns and flatter bottoms.
This is often justified as being connected with angled and curved foils but much confusion exists regarding the physics involved.
It is therefore worthwhile to examine first the effects of hull shape and then the story of curved foils to fully understand the latest A cats.
Stay tuned for Part 2…

Wednesday, March 7, 2012

New A Class Catamaran by Carbonicboats – The Brief

In previous posts I expressed my motivation (why) and approach to new projects (how).
I stated the importance of clearly identifying the needs of the user, and talked about the effectiveness of working to a congruent brief.
These beliefs drive quality. They will be shared by all who value passion applied with focus to create things of beauty.

Now, on the practical side, here are the goals defining the new boat:

Fast around the course
Best time on a typical windward/return race course. 
May sound obvious at first, but this requirement is vital to exclude any specialist or extreme solutions
With reference to existing designs, we are investigating variables in hull form, foil geometry, aerodynamics, and structural arrangements, to identify the best compromises for winning races.

Controllable, simple, responsive to changes in trim
The boat must react positively, taking advantage of movements in crew weight. This is related to volume distribution and rocker profile.
The boat must be dynamically stable in pitch, overcoming a critical limit on existing boats. By addressing the pitch stability issue inherent in existing boats, the skipper will be able to push harder with greater safety.

Optimised for the most frequent conditions whilst remaining competitive in light wind and controllable so it can be pushed hard in strong winds
Appropriate weighting should be placed on prevalent racing conditions, taking into account accompanying wave states
Having made primary gains in the target conditions, we have identified secondary gains in light winds and in top end conditions to remain competitive at all times.

Crew weight
Account for a crew weight of 85Kg dressed. This allows enough volume for average-to-heavy sailors to be fast
One of the constraints on the hull shape is a tolerance for a range of crew weights.

Platform stiffness
Global stiffness is a high priority for two reasons: maintaining the design geometry (correct angles between rudders, boards and rig), and minimising energy losses.

Durable and easy to repair
Material selection should take into account toughness, durability, and ease of repair
Given the class minimum weight rule, the available mass should be distributed to satisfy the requirement for stiffness, but also to safeguard the longevity of the boat, thus protecting the investment of the buyer.
Under this requirement, future-proofing for foreseeable foil developments and rule changes is vital. The boat should be easily retrofitted with future generations of foils with minimal modifications. Obviously we cannot foresee all eventualities, but we should make allowances for reasonable variation.

Cost competitive
Best performance/cost relationship, achieved by investing in well thought out tooling, and optimising the production process
Solutions will be ranked according to performance criticality, so that their cost can be factored in accordingly.

Able to take existing rigs, but with provision to accommodate longer chord masts
It is common practice in the class for skippers to carry over a ‘personalised’ rig from platform to platform. We aim to allow this on the new boat by maintaining consistent the geometry of stay attachment points, mast step, and traveler location. However we envisage investigating different rig solutions in the future.

Emphasis on reducing platform drag
We have identified possible gains in crossbeam, trampoline, and deck solutions that will be investigated during the design and prototyping process.

Aesthetically pleasing and well detailed
The boat must reflect our core values expressing them in the overall shape and in the detailing. 
Styling should be elegant and use a consistent formal language
The boat should have an integrated, unitary look.  
Quality should be reflected in a pained finish to a custom boat standard.