Moving Pics

Another video of Paradox starting to properly exploit the stable foiling setup.
As you can see by contrasting this vid from those of earlier sessions, stability is heavily influenced by the relative lift contribution of rudder winglets and main foils.
We now set up the rudders to provide some upward lift when the boat is at neutral trim. If driving force from the sail increases, causing the bow to dip, rudder lift decreases as the rudder winglet AoA approaches neutral. If trimming moment should keep increasing (this would only happen if a gust an order of magnitude greater than the average wind speed is encountered), rudder winglet AoA would become negative, pulling the sterns down.
When the setup is correct, crew weight can be placed surprisingly far forward. This is more efficient as it puts more mass over the main foils, reducing the burden on the rudder winglets which are smaller and so have to work harder to support a given weight.
Even though speeds are significantly higher than in displacement sailing, the feeling of losing the bow 'down the mine' disappears completely. If anything the instinct to shed power must be reprogrammed as the limit is much, much further away. Easing sheet in a panic just causes ride height to momentarily increase and then settle again.
We are now confident that this mode is significantly faster in a straight line at least in winds over 10 knots.
The next question that must be answered is whether it is faster around the course when tacking and jibing are considered...

Pilotcam

A short video from a recent testing session.

Our understanding of the settings necessary for sustained stable foilborne sailing is steadily improving.

It is worth re-iterating the definition of stable flight with reference to the feedback loop that arises when external forces upset pitch angle and ride height. A stable setup settles on an attitude and altitude without input from the crew.

We announced that Paradox could foil in a stable mode only when we were sure we had proven that it could. Stability comes at some cost and we are open about the uncertainty regarding whether the benefits outweigh the costs. I believe we are close to finding an answer and I will describe our findings in detail in later posts.

Recent experiments by other manufacturers have shown that an unstable setup can be 'tamed': a well practiced skipper on a small boat can anticipate departures from the desired attitude and altitude given certain provisos, and make corrections, akin to balancing a ball on top of an inverted salad bowl. In a racing context the conditions when this becomes unmanageable may not occur very often so overall an unstable setup can be competitive. Think of it as riding a unicycle instead of a tricycle. Obviously humans are capable of learning to ride unicycles so the question becomes one of costs vs. benefits. Exploiting an unstable platform is a muscle memory skill that can be learned 'by feel' with practice and is arguably more 'natural' once mastered than the mechanical and intellectual skill of adjusting foils for optimum trim.

In any case, our conclusions will reflect what we learned in testing. We will adopt the fastest configuration for getting around a course. Since we have been learning from our testing it will be different from the original setup.

A few notes on this video:

The discontinuities in the editing correspond to where Tom backed off to make adjustments using a control system that we would like to keep to ourselves for now. The 'flight' was reliably uninterrupted for the whole run. The boat was safe and controllable throughout.

Looking at the wake carefully you can see the occasional disturbance due to ventilation of the surface piercing foil. This is an issue inherent in highly loaded surface piercing foils and we are experimenting with devices to mitigate it. Fences are an obvious solution but have practical drawbacks as the foils must be retracted through the bottom bearing. More promising options are leading edge discontinuities and boundary layer turbulators...

Output

Productive times with new A Cat platforms and next generation foils all under build.
More details coming soon...

Setup

As already mentioned, we have spent lots of time on the water recently testing, evaluating and tuning. Certain tests with Paradox sailing alone and some in the company of  other known fast A Cats. I think it is safe to say that we are getting a handle on the issues and how they will be addressed on the production boat.

Two boat testing session

As a general observation, we are in unexplored territory for this class and arguably for this type of boat at this scale simply because the relative effect of foil setup on overall performance is much greater when the foils are working hard enough to support most of the mass of boat and skipper most of the time (and all of it some of the time).
To put it simply, when the foils are doing most of the work, getting the settings right is much more influential than if they were only helping out a little.
In hindsight this should be no surprise. Ask any 'Mothista' about the effect of a small fraction of a degree of foil angle and they will say it is like night and day. When the foils are the only part of the boat actively interacting with the water (in the case of Paradox the hull may still be 'skimming' but our measurements tell us it is supported by the foils, not by the water) their effect is dominant.

The saving grace is that the correct setup is mostly related to crew weight and remains constant for different conditions. Once the correlation is understood, it should be easily duplicated.
Now that we understand the (far reaching) effects of main foil toe-in and rake, the key is getting the right amount of 'lift share' so that the sterns are supported by the rudder winglets but a step back can still raise the bows up sufficiently to 'pop' the boat up onto the foils.
This is a function of some combination of winglet Angle of Attack (AoA) and winglet area.

Lets say we want X amount of lift from the rudders such that they will support enough weight to keep the sterns 'flying' but not so much that the stern cannot be made to sink somewhat when the skipper takes a step aft.
We could obtain the desired lift with small winglets at a big AoA or with big winglets at a smaller AoA.
Assuming aspect ratio can be optimised in both cases, the lowest drag solution will come down to the chosen foil section and the lift coefficient (Cl) it is happiest at.
However the choice will also have an effect on stability: If the AoA is larger, then the boat will trim down further before the winglet goes through a neutral AoA and begins pulling down to restore the desired pitch attitude.
In reality having the winglets actually pull down will only happen in rare 'extreme' situations. However it is a helpful way to visualise the dynamics at play.
Simply reducing the AoA with bow-down trim is enough to introduce a stern-down restoring moment.
The vital part is the rate at which this moment increases since its rate of change is key to stability in pitch.

Optimum ride height with skipper not all the way aft and correct lift sharing by the rudder winglets.
As the bow pitches down, rudder winglet AoA decreases.
The boat happily sits in this attitude when set up correctly. Notice the absence of wake other than spray

We are cristallising a useful map of how this foil system works and how it can be exploited.
It appears that performance is good when it is set up correctly.
The most impressive aspect has been the utter predictability and controllability when pushing hard downwind. That is definitely an aspect of the brief that was met successfully.

What remains to be proven is whether the gains are exploitable around the course.
One finding for example has been that there is quite a significant benefit in raising the windward foil when sailing upwind.
In a close racing situation this can only be exploited if the system to raise and lower the foils is extremely easy and fast to use with minimal distraction.
We have therefore experimented with a series of mechanical solutions and it seems the last iteration meets the criteria.
In short it uses elastics to raise the boards automatically and a single line with significant mechanical advantage to lower them. More detail on the evolution of these mechanical systems will be released later.
As already mentioned, this is a problem that some of our competitors will also have to solve as they adopt 'S' foils with outward inflection at the top that alters dihedral angle as a function of foil vertical position.

Having explored this development path we will only adopt a system that is reliable and easy to use without distracting from 'keeping ones eyes out of the boat'.
If we are not satisfied that such a system can be engineered (meaning that, after friction is overcome and single line operation achieved, the burden on the skipper is still judged to be excessive) then we will change the foil system so that it does not need to be touched during racing.
This may involve changing foil shape and/or finding a compromise toe-in setting that is optimised for always having both foils down.

Referring to the design brief for Paradox, the final balance to be struck must be in favour of best achievable speed around the course.
If a certain setup cannot be sailed at a high percentage of its potential for a large percentage of the time around a course, then a slightly compromised variation that is more exploitable will be more competitive.
With this in mind, simplifying the boat is vitally important and what we are learning now will inform the choices for the next prototypes and the production setup.

Evaluation

Lots of testing in the 'off season'. We completed some very productive sessions over the past few days and have more planned. We are working on several areas for both numbers and feel, initially alone, later against other As as their availability permits.

The first area of investigation is properly understanding the behaviour of the foil system as the relationship varies between main foil and rudder foil force.
Rudder foil force can be manipulated by raking the rudder (tuning) and altering rudder winglet area (permanent change). The latter also influences aspect ratio which in turn modifies the overall lift-to-drag ratio at different angles of attack.
Aside from qualitative information such as visual observations and feedback from the skipper, we identified the need to work methodically through the range of possible combinations to gain quantitative 'proof' of how any concept performs.
The outcomes we are interested in are performance and stability (in that order).
We know that we can make the foils work much harder than with a conventional geometry (meaning they can be set up to carry a much higher percentage of boat weight without loss of control upon 'takeoff' - Takeoff simply being when that percentage reaches 100, keeping in mind that ride height is intended to be minimal).
What we don't know yet is whether this mode is faster in terms of VMG to the bottom mark.
The trade-off between hull drag and foil drag is a fascinating, subtle and complex one given the A Class rules. It certainly seems to be less clear-cut than in some other classes.
So we are working through a range of settings for different values of rudder area to correlate our measurements with theoretical predictions.
We started with rudder winglets with Xcm 'chopped off' and tested the full range of useful rudder rake angles. Then repeated for the same rudders with a bit more length chopped off...
At the same time we monitor the 'load share' of the main foils and the behaviour of the platform as a whole.
Obviously we want to nail the minimum foil force required for stability (as that corresponds to the smallest drag penalty) then ascertain the best combination of area and angle to achieve the desired force.
One really interesting finding has been the tight correlation between optimum rudder lift and crew weight. In short, a lighter sailor does not require as much lift as a heavier one. This seems obvious at first, but the relationship between weight and the minimum lift necessary for stability is not a linear one. A product of this methodical testing will be a reliable table connecting each crew weight to a known ideal rudder setup.

A positive finding is that once set for crew weight little adjustment is required. Fine tuning is achieved by stepping forward and aft on the gunnel. Since rudder winglet angle is always positive in normal conditions (the exception being an incipient nosedive when they can go beyond neutral and start pulling the sterns back down), trimming the bow down neutralises their effect and thus reduces induced drag.
Similarly there are various options for foil immersion (connected to dihedral) and rake (connected to up/down lift) when sailing upwind.


The second area of investigation is the optimum transition points between different modes. Such as between sailing 'conventionally' with moderate heel to reduce immersed (windward) foil area and flat with the traveller down to get both foils working and carrying the entire weight of the platform together with the rudder winglets.

Finally we are looking carefully into the 'human factors' or interface issue.
Some additional complexity is acceptable if the reward is increased performance. However we are working hard to simplify the systems to make them easy to understand and to use effectively with minimal training.
As previously described, foil rake is easily adjusted with a single line.
Foil immersion is a bit more tricky as the foil should be able to be raised and lowered remotely.
It remains to be seen whether vertical adjustment will be deemed worthwhile in terms of the cost/benefit trade-off between the workload of making the adjustment and the performance reward.
The saving grace is that vertical adjustment would only be required in sub trapezing conditions (less than 100% Righting Moment).
It is also worth noting that at least two other manufacturers have released information to the effect that they will also be incorporating dihedral change through vertical foil adjustment.
It will be interesting to see whether the predicted gains on offer can be realised in the real world during close racing.
In an ideal world the windward foil would always be fully up when sailing upwind, but the constraints of a singlehanded boat make the practical 'bancability' of that option rather finely balanced.

FAQ: Optimum Altitude

Q: "You say you are foiling yet the boat seems to be just 'skimming' above the surface. Why not fly higher?"

A: Altitude control in Martin Fischer's foil concept comes from the change in foil curvature just below the hull exit point. As the boat rises, the radius of the part of the foil immediately under the water surface changes progressively so that the immersed portion of the foil gets more vertical. This gradual reduction in dihedral of the wet part of the foil reduces the vertical lift component and encourages ride height to settle.

Maximum lift is generated just below the hull.
As the upper part of the foil exits the water, lift immediately decreases.
Paradox is designed to converge near the light blue line, with the hull just clear of the surface.
If ride height were to momentarily increase to, say, the dark blue line
(as for example when applying a vigorous steering input into the wind),
most of the lift would disappear so the boat would gently return to the design altitude.

The position of this change in foil curvature determines ride height.
It would be possible to position it further below the hull. However the span under the inflection would have to remain the same as it is sized to provide sideforce when foiling. Therefore the whole foil would have to be longer. This would make the span excessive at sub-foiling speeds so would bring a drag penalty upwind and in light winds.

Actually, to be technically correct, such additional span at the top (aimed only at increasing ride height when foiling) would need to be 'washed out' to stop it making any sideforce. If the additional top part did provide sideforce, it would effectively reduce overall dihedral angle: Its sideforce would subtract from the contribution to sideforce by the rest of the foil. So the vertical component of the remaining span would also shrink...

Visualisation of how ride height might be increased by adding 'stilts' as extensions above the curved portion of the foils.
This would make our foiling appear more spectacular but would surely be slower when racing.

Q: "Would flying higher have any advantages?"

A: Flying higher would require some additional foil span that would add only drag at sub-foiling speeds. In a racing context this penalty would be present more than 50% of the time.

Spray drag is an interesting consideration: Though it looks messy, the spray being thrown up by the foils does not cause additional drag when it hits the hulls. The reason is that energy had already been transferred to the water in the spray when it was directed upward by the foils. If anything, redirecting the spray down and back returns some energy to the hulls.
Think of the exchange of energy in terms of equal and opposite reactions: When you push water up and forward it pushes you down and back which slows you down. When you push it down and back it pushes you up and forward, a form of energy recovery.
The ideal solution would be to fence the foils to suppress the spray in the first place but this is not practical since the foils must pass through the cases in the hulls.

It may be that in the future it will pay to foil all the time as rigs get more powerful, sailing techniques develop, materials get stiffer and our understanding of hydrodynamics evolves.
If that happens then considerations such as wave clearance and amplified shifts in the CG due to heel will come into play.
It should be noted that, as long as two foils are being used, the dynamics of heeling to windward are not analogous to those on a Moth. If it were possible to fly on the leeward foil only (as the AC72s are doing) then flying higher might allow some windward heel which may have some advantages. If that is the case then foiling higher still could amplify those advantages.
Finally there would be a trade off between raising the rig into better wind and losing some end-plate effect from the water surface.

But in the A class, with current technology and within the present rule restrictions, it certainly does not pay to foil all the time. The long slender hull combined with a low displacement is very efficient at low speed and even more so when foil assisted. The limited sail area and constrained foil horizontal span also contribute to make foil assisted sailing the most attractive option at intermediate speeds before stability becomes an issue.
The solution chosen for Paradox is therefore to make the necessary compromises for what is effectively a foil assisted boat that can transition fully onto the foils and become dynamically stable when certain conditions are encountered.

Blue lines show how dihedral reduces as the foils are fully lowered
from the reaching position down to the upwind/light airs position.
This is an example of how the concept does not assume full foiling all the time.
Rather, foiling is a mode that can be 'dialed in' when conditions render it appropriate.

This is an example of how a clear brief is vital in guiding the assessment process during development: The brief called for a boat that could be pushed hard through being dynamically stable as the foils begin to generate enough lift to support 100% of the mass.
This goal has been achieved.
We know that because our measurements show that the foils have been carrying the entire mass of the boat and crew (only after having recorded those measurements did we announce that we had been foiling). And the boat has certainly been stable, inspiring more confidence in its predictability than any contemporary.

Now we are working to establish the best settings to get the most out of the concept.
The next step will be to assess whether the configuration is in fact faster around the course in a wide range of conditions.
This includes straight line speed, maneuverability and ergonomic aspects such as ease of handling and making adjustments.

We will continue to be open and honest about our findings and to share the process as we learn more along the way.

Stable

We tested over the weekend with reduced horizontal surface area on the rudders and the results were very interesting.
Stability is unaffected but the boat is more responsive to changes in longitudinal trim.
This gives the skipper the ability to 'pop' the boat up onto the foils by taking a step back and momentarily raising the bows a few degrees vertically.
Once fully foilborne the weight can go forward again to load up the foils.
The rudder Ls then support a bit less weight and maintain stability in pitch.

In the following sequences Tom Stuchbery is deliberately 'provoking' the boat with aggressive steering inputs to get a feel for how it responds.
Existing foil assisted A Cats with C foils would continue in a 'pitch-up' feedback loop until the foils stall, making it very hard for the skipper to stay in control.
The pitch up is initiated by a slight downward component in the steering force generated by the rudders (this is present due to heel and is independent of any T or + foils on the rudders).
The pitch-up feedback loop is not just due to pitch instability. It is due to heave instability inherent in C and J foils: Even if the C or J foils are combined with rudder winglets to give pitch damping, heave instability remains because all the lift is generated at the bottom of such foils (this is where the horizontal area is concentrated) so the lifting area stays fully immersed. Therefore an increase in ride height does not cause a decrease in lift so it is not automatically corrected.
Our S foils differ by having the horizontal lifting part close to the hull so that this area immediately decreases as ride height goes up (the lifting segment of the foil immediately comes out of the water as ride height increases).
Paradox responds to upsetting trimming forces by momentarily rising then then very gently and predictably settling back on the optimum ride height with no appreciable loss of speed.
It was quite startling to see how much 'abuse' one could get away with while remaining upright, on board and in control!

To be clear, this is a handling issue, not a performance issue.
In most conditions C and J foils can be managed by setting them up so that their lift does not exceed the weight of the whole boat.
As long as the hull takes some weight (even if just the stern is 'skimming'), heave and pitch stability are not an issue.
However if such speeds are reached that foil lift exceeds boat mass (and corrections are not made such as partially raising the foils to reduce dihedral angle), then a loss of control will be inevitable.

Our future testing will be aimed at determining whether there are any drag penalties associated with maintaining stability and, if so, whether they are worth accepting for normal racing situations.
Right now we are foiling but not claiming definitively that this is faster than foil assisted sailing in the A class. That remains to be seen.

With the right technique we have found that it is possible to fully foil in as little as 14 knots of wind.
One must understand the way the foils work to fully exploit them so it does require some unlearning of habits built up when racing conventional boats.
In short the boat must be kept flat so both foils can work together and the traveller slightly lowered to direct the sail vector forward. Once learned, the results are exhilarating and do seem to result in much improved VMG because the reduced drag when foiling allows a much deeper course to be sailed. More testing will show how often this is true.

At about six seconds in the following video we are beginning to get it right though there is still much room for improvement.

We are confident that we can regain our upwind superiority by incorporating an automatic toe-in adjustment in the foil bearings.
The aim remains to simplify the systems and evaluate whether Martin's ingenious foil configuration is exploitable around the course.

As already mentioned, we are also exploring a simplified configuration that has most of the advantages of the S foils but requires less 'retraining' to exploit.
Our focus is sharply on getting around the course as quickly as possible. That is the basis for every design choice. It is important to keep an open mind so testing will inform our understanding regardless of the attractiveness of each initial theory.
The process is about testing the theory with a view to refining it to gain an understanding of its validity.

More FAQs

This is the second post in response to questions we are receiving frequently, mostly in connection with design choices on Paradox and how they may compare to developments seen elsewhere.
I have added 'FAQ' as a label so in future these posts can be filtered out by those (fellow sailing nerds) who are interested...

Why Ls on the rudders instead of Ts or '+' s?

Here are some of the considerations when designing complex foils made up of more than one surface.

Hydrodynamics

A single bent foil has no intersections so there is no interference drag (strictly speaking there is still some interaction but it is much smaller since the transition is very gradual).
Crossing two foils is very costly in terms of drag because of the way the pressure gradients combine and interact.
Basically, the low pressure peak near the main foil leading edge combines with the corresponding similar peak on the intersecting second foil and the two amplify.
Since flow speed is related to pressure, this spike in the pressure distribution is also a radical change in flow velocity.
Accelerating the mass of any fluid involves an expenditure of energy (F=ma) that comes from the total kinetic energy of the boat which is therefore diminished... In other words redirecting water around an intersection between two bodies is draggy. The tighter the included angle the worse the drag penalty.

In some applications intersections are unavoidable so to minimise the damage designers arrange them with intervening bodies that basically smooth out the transition by spacing the working sections of the intersecting foils apart with surfaces locally orthogonal to their respective spans.

An assortment of Moth horizontal T foils with junction bulbs.
Image source :http://mothbodensee.files.wordpress.com/2012/04/2012-04-08-14-25-531.jpg 

Inverted gull wings on F4U Corsair meet fuselage orthogonal to its local surface,
minimising junction drag without the need for fairings.
Landing gear is placed at the kink so it can be shorter for a given prop clearance.
Image source: http://www.airliners.net

T foils are less penalising than '+' foils as only three bodies intersect instead of four.
In some applications + foils are warranted when other advantages are sought. Examples of this are 14' skiff rudders where the distance from the foil to the water surface (the stern wave) is critical. And foil assisted multihulls optimised to have the windward rudder exit the water at small heel angles. Though in the latter case a different area distribution is usually a better solution.

T tail bulb visible on an Ilyushin Il-62. Image source: http://www.airliners.net

Another way to minimise interference drag where intersections are unavoidable is to stagger the two foils longitudinally. Especially if the foil chord dimensions are different, this can help to make sure that the pressure peaks on the two foils do not coincide. This solution requires a good understanding of the operating envelope of the foils because the pressure peaks do move around with varying speed and AoA.

Horizontal tail surface staggered ahead of vertical. Image source

Structure

For relatively lightly loaded applications, an L is structurally much more efficient since the fibres are continuous across the two foils.
In theory a T can be engineered with very little bending moment if the horizontal foil is symmetrical about the vertical. However, on a boat that sails with heel and leeway, the load will not always be identical for both sides. Any difference will impose a bending stress on the junction which will have to be engineered accordingly.
It is possible to engineer the junction to withstand the uneven forces however for a given material an L will always be lighter and cheaper to build accurately.

Geometry

For a given span, the L solution allows the rudder to be placed further outboard, leaving the horizontal foil as an uninterrupted span (all the way in to the centreline exclusion zone in the A Class).
Placing the horizontal foil entirely on the low pressure side of the leeward rudder (the one that does more work to resist leeway) actually increases the efficiency of the rudder, partly offsetting the drag penalty associated with winglets at upwind speeds, when they are not vital to longitudinal stability.

Blended winglet on a commercial airliner.
Image source: http://www.boeing.com/commercial/aeromagazine/articles/qtr_03_09/article_03_1.html

Rule

The bend at the bottom of our rudders is not 90 degrees. The primary reason is consideration of three dimensional effects to do with stability. There is a coupling of rudder sideforce and vertical lift, tuned to help maintain stability at all times, especially when bearing away.
As a secondary benefit the leeward winglet remains horizontal even when heel angle exceeds hull cant angle (when the leeward hull is heeled to leeward).
Since the winglets are not horizontal when the boat is level, the rudders are legal when pulled right up behind the hull.
Even if optimum area turns out to be much smaller than expected, angling the winglets allows a longer span and thus a higher aspect ratio for the same area.

Practical Considerations

We found that it is easier (still not easy but easier) to shed seaweed from the L rudders than from intersecting T rudders. The debris has some chance of slipping off the end of the L rudder while it is much more constrained on a T or + arrangement.
Using Ls combined with cassettes has several advantages such as constant compensation, precise control over winglet AoA and the ability to partially retract (and now reverse) the rudder while maintaining efficient steerage.

A Different Look

Some quick snaps of the last shell just out of the mould.
We are building a series of 10 Katana Marbleheads using a special hybrid cloth.
The red bits are Kevlar.
No change in structural properties, just a different and unique look.
We will keep the boats in stock so grab yours today!

True Flight

Those of you who want to see more sneak previews of the revolutionary EkranoCat, as featured on Sailing Anarchy, check out the exclusive gallery on our Facebook page: 

http://www.facebook.com/pages/Carbonicboats/276925825701235

Remember to follow us and like the page!

EDIT: Just to be absolutely clear, this was a First of April prank. Some people out there seem to think we really can do anything...

On any other day...

Illustrated

A few images to further explain some characteristics of our S foil configuration. Posted in response to questions sent in by some of you.

Firstly the effect of foil rake on the angle of attack of the horizontal part of the foil, the part that provides lift in the up/down direction:
In the first picture the foils are in the fully aft position in the top bearing.
This is the 'max lift' position, resulting in the lowest takeoff speed for transitioning to full foiling.
With the new foil bearings this will also correspond to max toe-in, further augmenting lift.
Full scale testing will confirm the optimum angle (both rake and toe-in) for lowest overall drag.

Yellow lines show foil leading edge angle to vertical and the Angle of Attack (AoA) of the lifting portion when set as pictured.
Orange lines show position for windward foil when sailing upwind.
In this position the foil will pull down, adding 'weight' to the windward hull

The trade-off is that more lift increases the drag of the foils. This additional foil drag buys a reduction in hull drag since less of the hull is in the water thanks to the lift from the foils.
If the reduction in hull drag is greater than the additional foil drag, then there will be a net gain.
Since hull drag and foil drag rise at different rates with speed, the exact 'crossover' (think of it as the optimum takeoff speed) remains to be seen. On an A, with current foil technology, it is somewhere in the teens when measured in knots. At lower speeds the efficiency of the slender leeward hull is formidable. Since sail area is limited, the option of increasing power is precluded so drag reduction becomes imperative.

Tuning the foil angles is key to assessing the true potential of this configuration. It is easy to do by simply swapping out the centre element of the top foil bearings. The difference in observed performance with different angles is significant. Getting these angles wrong means the true performance available is not realised.

Dihedral angle (and hence vertical lift fraction) is set by foil depth. It is zero with the foils fully down and maximum at the 'reaching position' as seen in the image below. This is the position always used except in consistently light ('sub-trapezing') conditions.
When underway, the effective dihedral angle is self regulating through the variation in curvature of the S foils. As ride height increases, the part of each foil that remains in the water becomes progressively more vertical, reducing dihedral.

The role of the rudder 'L's is to control pitch angle. Our new rudders will maintain stability in pitch with a considerable reduction in drag.
Remember that stability in pitch only comes into play when fully foiling. If full foiling proves to only pay in extreme conditions, then the Ls can be made even smaller (it would not make sense to carry the associated drag penalty, however small, at speeds where stability is not critical if such speeds are relevant most of the time). Since the effective split of vertical lift between foils and rudders changes with sail force, it is relatively straightforward to hone in on a winglet area that begins providing negative feedback only when the hulls leave the water completely.

Positioning the foils forward (ahead of the sidestays) has the principal advantage of reducing induced drag by letting the rudders share sideforce with the main foils.
A secondary advantage is that the Ls on the rudders have more leverage to control pitch attitude.

I have stated repeatedly that my aim (and our company policy) is to share findings as we learn new things and develop new products.
The reason is simply that all the work we do is motivated by passion for the sport. Sharing this passion is profoundly rewarding.
Our customers realise why we do what we do. That is why they decide to become our customers.

In light of this, no sweeping claims have been or will be made. Martin Fischer's stable foiling configuration makes sense and we are working to unlock its potential.
At the same time we are prototyping a less extreme arrangement that will be simpler to use and have a less critical performance profile.
This alternative arrangement will be unveiled very soon and will give buyers the option to specify a less technical boat. Meaning one with fewer adjustments and less sensitivity to settings, trim and steering inputs, with a 'conventional' feel familiar to current A Cat sailors.

Much of the thinking behind the S foil arrangement will still be applicable and the simpler alternative will also benefit from our extensive R&D process that used the very best tools.
Making both options available gives customers a way to match the boat they are buying with the style of sailing they prefer.

As the simpler alternative is going through the final analysis stage, it appears that it will have a slight edge in light and moderate conditions. This makes sense as it will have less wetted area, simply because the emphasis is on drag reduction at moderate speeds before dynamic stability becomes dominant.
In the top end of the wind range, performance should be comparable but the sailing style will be more conventional. Safety margins will still be higher than existing foil assisted designs and full foiling will still be possible, albeit with higher takeoff speeds.
This may yet prove the fastest way around a course most of the time in a class where the displacement to length ratio is exceptionally low and sail area is limited.

The reason to buy a Paradox remains the same: carefully researched design, build quality that goes beyond mere performance into aesthetic excellence, personal customer support and, most importantly the driving passion we want to share with our customers.

Versatility

This week we started production of tooling for an improved rudder design for Paradox.

Martin identified a considerable drag reduction available through increasing the efficiency of the ‘L’ surface. 

This is achieved by improving the aspect ratio of the horizontal surface. Increasing the aspect ratio dramatically reduces induced drag. The new design achieves 80% of the theoretical maximum efficiency. This is in the realm of competition sailplane wings. 

Careful structural optimisation has allowed us to exploit this solution with no cost or weight penalties.

Mk1 rudder shown yellow, new version in red

At the same time we have confirmed that the actual force the winglets have to generate is considerably less than initially predicted: As Martin explained in a recent interview published on the CSN blog, the theoretical size of the rudder winglets is determined by calculating the minimum force required to achieve the negative feedback that maintains stable flight, then adding a safety factor. In the case of the A, the safety factor seems to have been too generous.
The boat has always behaved very predictably, never giving the impression of being even close to the edge of control. We will test progressively smaller winglets to validate the new calculations. 

When you add together the increased efficiency and the smaller force required, the size of the winglets reduces dramatically (close to 40%) giving a significant drag reduction.

Mk1 rudder shown yellow, new version in red

The new rudders are designed to be versatile in two ways:

1) The winglets have an untapered portion near the tip so they can be trimmed off at any length and still maintain an efficient planform shape. 

Cutting them off 180mm from the root gives equivalent area to the “+” winglets being offered by other manufacturers (typically a pair with 100mm span each, giving 200mm total span). 

However the L solution is free of the interference drag created by the intersection of three separate foils. Any intermediate area can be chosen to suit the preferences of the user.

2) The top of the rudder is tapered such that the whole blade can be reversed. This gives the option of eliminating the winglets all together in light conditions while having them 'on standby' ready to deploy if the weather changes.

The compensation has also been refined (increased and redistributed vertically) to give a lighter feel on the tiller.

The new rudder will come standard with every Paradox. 

We are preparing a simpler alternative foil package as an option for those buyers who prefer it. For boats ordered in the alternative 'foil-assisted' configuration, the rudder will be trimmed leaving similar horizontal area to existing foil-assisted boats (around 180mm total span).

The versatility of the new rudders allows us to confidently offer them for sale separately to customers who want to retrofit them to existing boats, with or without our cassette and gudgeon system.

Mk1 rudder shown orange, new version in red. The gray part of the L foil is trimmed off when the rudder is used on boats with foil-assisted configuration

Mk1 rudder shown orange, new version in red with wire-frame highlighted in yellow

Sweet Spot Part 2

RERUNNING THE NUMBERS

In light of observations collected over the season, Martin has been busy checking and optimising the foil setup on Paradox.

Using updated software he has compared optimised setups for our S foils and for C foils similar to ones used by the current generation of A Cats. 

The calculations were set up to arrive at the lowest drag combination for a given sideforce.

Interestingly, vertical lift as a percentage of boat mass (lift fraction) was left as a variable. 

The calculations were repeated for several boatspeeds. The result for each boatspeed was the lowest drag combination of foil immersion, toe-in angle and lift fraction. 

Computing a series comprising different boatspeeds (sideforce values) for each foil type gives a level comparison between the two configurations over a range of conditions.

Since lift fraction was a free variable, the calculations effectively compare total drag for foil assisted sailing against full foiling. Foil assisted will naturally have a bit more hull drag as the lift fraction will be smaller. However the number that interests us is total drag - being made up of both hull drag and foil drag. For the same speed the lowest drag combination for C foils might involve carrying, say, 50% of displacement on the foils while, at the same speed, the S foils would be happier carrying 60% of total weight. If foil drag is higher, the gain to be had by lifting the hulls out of the water will be more expensive so carrying a lower lift fraction on the foils will give a lower total drag value.

What interests us is how that optimised lower total drag figure compares to the analogous lowest number for the alternative foils at the same sideforce value, even if the lift fraction might be different.

As described in part 1, the second round of calculations will be closer to representing reality as it is informed by observations on the water. 

The numbers again came out in favour of the S foils.
Leaving aside stability when foiling, the span-wise lift distribution on them is inherently less biased toward the tip so their induced drag is less. This incidentally explains why it does not pay to set up C foils with aggressive rake (large angle of attack at the tip). Something many sailors have observed on existing boats.

TOE-IN ANGLE

The biggest question mark right now is toe-in angle.
As explained previously, toe-in is an important variable as it has two effects:

1) Upwind it ‘feathers’ the windward foil which is surface-piercing so less efficient. At the same time it loads up the leeward foil which is working under the hull so effectively has a rigid ‘end plate’ above it. To understand this effect, think of the angle of each foil with respect to leeway. Toe-in aligns the windward foil with the true course through the water and gives the leeward one more 'bite'...

2) Downwind toe-in causes the windward foil to pull up and to leeward, contributing additional vertical lift and, crucially, adding sideforce to allow the leeward foil to make even more lift.
This effect is similar to the ‘acute’ L foil being used by ETNZ (and now OTUSA) on their AC72s.

More toe-in effectively decreases the ‘takeoff speed’. The question is whether taking off ‘early' gives a net gain. Meaning whether foil drag is in fact less than the hull drag reduction it buys us. 

It now appears that foiling on an A starts to pay above around 18 knots of boatspeed - A bit faster than the original expectations of 12 to 14 knots. But the exact number is still being ascertained.

We found that aggressive toe-in is definitely slow upwind (slower than initially predicted) but can be helpful downwind above about 12 knots of boatspeed. 

So toe-in should change at the end of every leg! In fact it should increase with increasing speed downwind.

Rather than adding another control, we will solve this conflict by machining new foil bearings with an angled slot: When the foil is pulled back the slot in the top bearing will guide the trailing edge outboard. When eased forward the leading edge will rotate outboard. The range is from 0.5 degrees when fully forward to just more than 2 degrees when fully back so this can easily be accommodated in the existing bearing holders.

This solution will add no cost and in theory should give us the best of both worlds (swapping out the centre bearing elements is how we had always planned to adjust toe-in angle). 

More importantly, it will not require an additional control.

EXPLOITABILITY

The only extra control on Paradox (compared to other As) remains the foil fwd/aft line. 

You pull it and cleat it to move the top of the relevant foil aft, or release it to allow the top of the foil to go forward (it goes forward automatically, aided by a bungee and by the drag of the foil in the water).

When the top of the foil is all the way back, the horizontal part below the hull is at the greatest angle of attack so lift is maximised. 

When the top of the foil is forward, the lift is actually pulling down (this can help upwind by sucking the windward hull down, giving a bit more power). 

Half way along and the foil is neutral.

Going upwind it is simple enough to ‘tack’ the foils every time you tack the boat: Just tug on the windward foil control line as you come in off the wire, then release the new windward one as you complete the tack.

Downwind both foils are set with the top fully aft to give maximum lift (and now max toe-in) so you don’t need to do anything with them between top mark and bottom mark.

Foil depth is set for the conditions: In anything over 8 knots TWS they are cleated in the ‘reaching position’. This is when the top part sticks out about 150 mm (as you can see in most pictures of the boat underway). In this position dihedral angle is maximised. 

In light winds there are two options: Pull both foils half way up so that they become upright (but each with halved immersed area) or always have the windward one up completely and the leeward one down completely such that it is vertical (no dihedral so no lift). 

Having the leeward one fully down and the windward one up gives a slight advantage in theory but requires an additional adjustment at every tack. Keeping them both half up is comparable to what you would do with C foils so should give no measurable disadvantage.

HANDLING

Our last observation is that having the foils so far forward, which must necessarily load up the rudders to keep the boat balanced, does require some getting used to. 

The reason for having the rudders hydrodynamically loaded is so they share the task of generating sideforce with the foils. 

This is a principle well proven on big boats such as CBTF maxis and is at the root of the tandem keel solution that was seen on several IACC boats. It is also why conventional IACC boats had such deep rudders.

If the rudder were completely neutral it would be ‘coming along for the ride’ contributing only drag. If the rudder is working to help resist leeway it reduces the lift-induced drag being generated by the foils. 

This hydrodynamic load is felt through the tiller as a bit of weather helm. It is something that can be learned and managed easily but it does reduce the margin for error, especially when tacking.

CONCLUSION

Martin’s analysis indicates that no changes are required to the foil shape, rudder shape or foil positioning.

At the last regatta our setup was too aggressive, taking us past the optimum lift fraction. 

With excessive toe-in the foils were working too hard, giving plenty of lift but adding more foil drag than what was being saved in hull drag.

As with any new concept, there is a process of learning to optimise both setup and sailing technique to exploit the advantages on offer. Martin points out that any comparable innovation (such as the foiling Moth) has an associated learning curve.

In summary, the S foil and L rudder solution has potential and may yet prove to be very fast. 

It is arguably more demanding to exploit fully than a conventional setup but it would be more correct to say that it requires an adaptation in technique and a deeper understanding of foil dynamics than is sufficient on boats where the foils play a less crucial role. 

It is vital to understand where the gains lie and work through the solutions without ‘throwing the baby out with the bathwater’. An objective analysis is the only way to draw meaningful conclusions and make progress.

GOING FORWARD

We will continue to tune and test the system on our existing prototype and work to fully understand what makes it tick.

At the same time we recognise that a more exploitable alternative is called for. 

A system that is not as demanding to get the most out of but offers similar performance. 

We will announce shortly how we intend to meet that demand from existing and prospective customers.

Under Lights

par·a·dox  (par-a-dks)
noun
1. A tenet contrary to received opinion.
2. A statement that is seemingly contradictory or opposed to common sense but is nonetheless true.
3. An assertion that is essentially self-contradictory, though based on a valid deduction from acceptable premises.

Sweet Spot Part 1

Optimising a system such as a sailboat is a fascinating process. Once the basics are right, picking the best settings for each set of conditions is an art in its own right. Varying degrees of scientific thinking and 'gut feel' based on experience seem to be called for and an open mind is definitely an advantage.

Even with very sophisticated tools, the core of the problem is the large number of interconnected variables. As with any endeavour involving the scientific method, all bias toward trying to prove a concept that is arbitrarily appealing must be checked at the door if the results are to be objective. Then data gathered on the water has to be sorted, filtering out extraneous noise, so it can be used to validate the initial predictions. 

If done correctly, the discrepancy between observations and predictions will illuminate the designer about where the predictions were mistaken. 

If the source of the discrepancy can be identified correctly, then the next lot of predictions should be closer to reality.

Those with an interest in such things will know that arriving at quantitative predictions requires a discipline and constraint quite at odds with the creative thinking process that generates the concepts in the first place. To get useful numbers, many assumptions must be made so that each calculation discriminates between only a small subset of variables. Getting the assumptions right is vital and that is where real observation are of great value.

As the process is repeated the calculations will get better and more predictive of actual behaviour.

On a macroscopic scale this process has been going on in each field of design over generations.

Computational fluid dynamics and tank testing are a great example of how one tool has been vital in honing another to the point where the older one is almost redundant (almost!).

On a smaller scale each individual project goes through this cycle. Each boat, once the hull shape, rig design and foil package have been locked in, goes through a process of discovery on the road to delivering its full performance potential. 

Every sailor will know an example of a boat that just seemed to respond to a certain setup that was not the obvious first candidate. A bit more rake, a bit more jib twist, traveler down a few inches... The winning teams are the ones who accept the observations and figure out how they fit in the overall model. Complaining that 'it isn't supposed to be faster like that' won't change the reality. Just replicating the fast setting without understanding why it works is dangerously limiting since its effect may vary with different conditions so the advantage it confers cannot be relied upon. 

Part of what makes our game so engaging is that there is a very stimulating interplay of different forces, at the interface of two fluids, acting on different pieces of equipment that all have multiple dimensions of adjustment.  

This post was prompted by the work we are doing now to make sense of the observations we collected when Paradox last competed.

As explained in the post following the Gosford regatta, Paradox first raced with very conservative foil settings. 

For the recent regatta we dialed in maximum toe-in angle, giving the most aggressive lift profile in the fleet. 

Now that we have tested the two extremes in the range of this important setting, we can plot how lift and drag interact, giving us an informed guess at where the optimum might be found.

During the regatta we also tested two different sails from two well known sailmakers. Since Paradox is much more forgiving than other A Cats, it does not require as much mast rake. With a more upright mast the newer high-clew sails open up an unnecessarily large gap under the foot of the sail and we suspect this leads to significant aerodynamic losses. Once we settled on the lower-clew sail (last day), we replicated known fast settings for diamond tension and spreader rake and obtained a sail shape very similar to other leading boats. 

Having eliminated the rig as a variable (with the exception of rake angle which remains an area of investigation) we could be reasonably sure that variations in performance came down to foil settings. 

Details of the degrees of adjustment of our foils and their effects on performance will be explored in Part 2.

This great shot by Karen Parker

Learning Curve

All packed up after the Victorian State Championships, ready for the long drive back to Sydney.
The event was run with great efficiency so that we were able to have seven races over three days leaving plenty of time to enjoy the great atmosphere ashore.
It is interesting to reflect on the places that our sport leads us to visit and the diverse people it gives us the pleasure of meeting.

Jason Waterhouse sailed Paradox faultlessly to a standard well beyond what would be expected of someone new to the class.

It was apparent however that we simply did not have the speed to match the top boats in this very competitive fleet.

Our task now is to analyse the wealth of data we collected over the regatta and draw the conclusions that will allow us to make the necessary changes.
Initially we will check that our predictions match our measurements for the settings that had been identified as optimum. Depending on how that goes we will evaluate the possibility of making changes to some aspects of the overall geometry.
As always, the process is one of elimination given the number of variables involved.
The boat behaved well, beginning to transition onto the foils in the brief periods where the wind exceeded the predicted takeoff speed (the regatta was a light wind one overall). However our speed was not what it should have been so we must acknowledge that and proceed to address it.

As always we will share our findings as development continues.
This is the nature of the game and such lessons are steps on the path to our goal of creating a competitive, high quality production A Cat that is a joy to own at a great value price.

Memorable Times

Great interview with Martin Fischer on Catamaran Racing News and Design.
Discusses Paradox and other foiling multihull projects...

Busy Season

The end of our Southern summer season is approaching so we have been making best use of each long warm day whenever the breeze has been good.

Lots of time on the water for Paradox, putting the theories to the test and giving many interested parties the opportunity to experience A Cat sailing on stable foils.

In just a few short weeks we will be back in the office so the technical content many of you tune in for should start flowing again.

In the factory we are now building customer boats, sooner than we had expected thanks to a few early adopters who have believed in us, sharing the passion that drives us to do what we do.

Build slot number four is the next available, waiting to be filled. A few slots are still available for delivery at the AUS Nationals. Then the lead-up to the Worlds will begin.

Martin's insights and numbers have been vindicated by the behaviour of the new boat. It handles very 'un-spectacularly' which shows the foils are doing their job.
Rather than jumping and crashing, the motion is straight and level, unperturbed by external disturbances. As soon as the skipper starts to see white caps on the water, the technique is to flatten the boat out. The hulls nudge up until they are just clear of the surface and the magic carpet ride begins. Taking a small step forward keeps the foils loaded and the boat tracks straight and true with little regard for chop and wakes. All who have tried it so far have come away very excited saying stable foiling on an A Cat is a sensation unlike any other sailing they have done.
The really remarkable fact is that it all happens automatically. There is none of the 'skirting the death zone' dance familiar to those who have tried to balance on C or J boards.

Now that the basics are right, the slower process of tuning for competition begins. As with any new boat, there is a learning process discovering the quirks, optimising the systems and sniffing out the small hidden weaknesses that only pop up during the heat of battle.
Everything we are learning is informing the user manual that will come with every boat.

Interesting times indeed!

S Foils FAQ: Why the Top Bend?

The bottom inflection on the foils for Paradox is there to give stability in heave (controlling ride height). This solution is unique to our A Cat and other Martin Fischer designs such as the GC32 and Flying Phantom.

The upper inflection is a way to adjust overall dihedral angle. It has also been seen on the ETNZ AC72 and is being explored by at least one other A Cat builder in an upcoming model release.

Adjusting dihedral is simply a way to eliminate unwanted vertical lift when it is not required.
On Paradox we want to reduce lift when sailing at lower speeds such as in sub-foiling wind speeds and upwind in light to moderate conditions.
Other designs need to reduce lift at high speeds to avoid transitioning from foil assisted to fully foiling if stable foiling was not a design goal.

Dihedral adjustment could be achieved by moving the top foil bearing inboard/outboard.
This is a valid solution which would not require the top S bend and would give 'infinite' adjustment within the available deck width.
It was a solution we considered however, when carefully analysed, it had several drawbacks that made the S foil solution more attractive:

1) Low speed sailing, when we want less dihedral angle, is also the condition when we want more foil span. This is because deeper foils increase heeling moment (by moving the centre of lateral resistance vertically down away from the sail centre of effort), helping to load up the leeward hull and 'unstick' the windward one sooner. Also, increasing foil area in these conditions allows a lower loading per unit area and a higher aspect ratio, reducing induced drag.
If we used an inboard/outboard adjustment, the sailor would have to make two discreet changes each time: lower the foil, then pull the top bearing inboard to cant the bottom end outboard making the foil more upright.
With the top S bend, the foil only needs to be pushed down and the dihedral angle decreases automatically to the precise value required.

2) Mechanically adjusting the top bearing would require an arrangement strong enough to take all the sideforce (meaning maximum sideforce when sailing very fast on the foils) while maintaining manageable levels of friction when being adjusted.
This would mean making a very stiff sliding plate at the top that is supported such that it cannot skew on the two support 'rails' which are necessarily separated by the chord length of the foil plus the necessary fore/aft adjustment distance needed to control the angle of attack of the part of the foil that provides vertical lift.
This can be done but results in a heavy and complex piece of engineering that is not ideal for a production boat.
Having a fixed top bearing is a much lighter solution.
Pulling the foil up and down in this fixed bearing requires much smaller forces on the control systems, resulting in a lighter arrangement overall.

3) A 'V' shaped foil case with a wide opening at the top would hold much more water than a fitted case just big enough to accommodate an S foil.

4) The legality of an inboard/outboard adjustable system is questionable since when the foil is partially retracted the top of the foil would breach the beam restriction if the top bearing plate were adjusted to the outboard position.

For our requirements the S foil seemed to offer more advantages than disadvantages.
Other applications may lead to different conclusions.
As always our approach is to share the process and our thinking to convey to fellow enthusiasts our reasons for doing things a certain way.
This is an expression of our philosophy that a clear brief is vital to good, elegant design and the best design response is the one which on balance satisfies the brief with the smallest possible drawbacks.