Stability Principles

Time to answer some questions about stability in pitch. 

Over the past few months of testing we have found some very interesting things worth sharing.

Stability as an Alternative to Active Management

Without going into the maths, stability in pitch has a strict definition in aircraft theory and is a requirement for what I would consider ‘sustained foiling’.

Meaning the ability of a boat to remain ‘balanced’ on foils without continuous corrections in the form of course changes, weight shifts, and adjustments to power settings (sheet tension).

It is possible for a boat to sail with the hulls clear of the water in spurts without being stable in pitch and/or heave. Even sustained ‘bursts’ of a few hundred metres are feasible. 

This is what is happening in the majority of As with C and J foils, as well as in the NACRA 17. 

When you compare these sporadic foilborne tracts (that are becoming more prolonged as sailors master new techniques) with the ‘rock steady’ sustained foiling of a Moth or AC72, the difference is obvious.

Stability at a Price

The interesting thing is that stability necessarily involves a drag penalty. 

Some stable setups also have additional drawbacks, such as the need to ‘tack’ the foils (retract the windward one as is necessary with the 'acute L' concept pioneered by ETNZ).

In the A Class, the drawbacks of stable foiling make the choice rather marginal:

-          Sail area and power are limited

-          The hulls have an extremely low displacement to length ratio

-          Simplicity is paramount as there is only one pair of hands on board

-          Maneuverability is a priority because racing takes place on relatively short windward/leeward courses.

On larger boats stability is vital for control. 

On a small boat such as an an A, the centre of gravity (CG), heading and sheet tension can all be altered very quickly in a coordinated way by the skipper: A step back, a pull on the tiller, letting out an armful of sheet… It can all happen in less than a second in response to a feeling in the inner ear. 

People learn to ride unicycles, so mastering a small unstable vehicle is not outside the realm of possibility. 

When the top skippers in the A Class today speak of learning to foil, they are referring to mastering the technique of prolonging their stints of balancing on an inherently unstable platform.

The evidence on the racetrack shows that this solution, when mastered, can be competitive since bursts of unstable foiling can offer gains compared to more conservative foil-assisted sailing.

The risks involved are higher because a mistake is more likely to end in capsize, but taking risks to win a race is nothing new.

Experimentation

As our followers know, we believe in sharing what we learn, explaining the reasoning behind our development choices and, always, following an objective evidence-based process. 

If theory disagrees with measured findings, then the theory must be revised.

In our early development of Paradox, we found that the original stable configuration brought unacceptable penalties in terms of drag and maneuverability. 

Stable full foiling was slower around the course than unstable ‘jumping’. 

In response we tested a few alternative configurations and came up with the current setup that is ‘just on the stable side of neutral’, but has much lower drag. 

We accepted a higher takeoff speed and more moderate ride height in exchange for simplicity, maneuverability and, above all, reduced drag. 

We started out 2013 with a deficit of boatspeed and ended the year with some outstanding upwind pace and a small edge downwind that we are confident we will be able to build on. 

Much will be learned at the Worlds and we will continue development after that.

The fascinating question in the A class at the moment is about striking the optimum balance between stability and drag.

Mental Model

The illustrations below aim to explain the key factors affecting pitch-stability. 

The simple way to think about it is this: A stable system will return to the initial state after being upset by an outside force.

When you consider a system made up of a main lifting foil, a rear foil, and a CG, it is easy to see that the relationship between these three objects will determine system behavior.

Think of the two foils as supports at either end of a plank. Then the CG is a person standing on that plank.

If the person stands right at one end of the plank, then the support at that end will be taking all his weight and the support at the far end will be taking almost no weight.

If the person stands exactly half way along the plank, then both supports will be sharing the weight equally.

Now imagine that the supports are not solid and immovable. 

Instead they are peculiar springs that can only push back so hard before giving out. 

The main foil has a higher threshold (maximum absolute lift) than the rear foil. 

The forward foil could take all the weight unassisted, but the rear one can only help up to something like, say, 35%. 

If the CG moves too close, the rear foil will at first attempt to push back harder. 

But eventually it will be unable to keep increasing its lift and will subside. 

Here some dynamic factors come into play: As it subsides, the ‘apparent’ Angle of Attack (AoA) changes. But we will ignore dynamic effects for now.

Key to understanding this system is the concept that as the AoA of each foil increases, so does the lift contributed by that foil.

When the whole system pitches up, lift will increase for both foils. 

The rate of change for each foil depends on initial loading (lift coefficient), section shape, aspect ratio and initial AoA. 

The lift generated by a foil will change a different amount when going from, say, 1 degree to 3 degrees, compared to when going from 4 degrees to 6. In both cases the change was 2 degrees, but, since the changes happened at different points on the graph of Lift Coefficient vs. AoA, the change in total lift force was not the same.

Now you can see that, all other things being equal, the relative angle of the main foil and rudder foil is very important to foiling behavior. 

The relative angle influences the differential in the rate of change of lift. 

In other words the initial setting will affect the difference in rate of change of lift as the whole system pitches.

When the CG is forward, the rear foil has a long lever arm and is therefore most effective at restoring neutral trim. It will naturally tend to restore level trim. 

As the CG moves back, the rudder foil must share more of the weight so it cannot be set to neutral.

Instead it will be sharing vertical load.

This reduces drag but makes the choice of rudder foil section and area crucial: Its rate of change of lift must be greater than that of the main foil if it is to maintain stability (Note that to make the rudder share vertical load, its AoA has to be increased relative to that of the main foil. If the rudder is left 'neutral' and the whole boat is pitched up, then the increase in lift for the main foil will tend to up ride height and the rudder will still want to restore level trim). 

The final complicating factor is the bow-down trimming moment exerted by the rig. 

This has to be taken into account when designing and setting up, but conceptually it does not alter the basic understanding of the system: adding a moment is equivalent to moving the CG so that it puts more pressure on the support that would be forced down by that moment.

We found that mast rake angle has an important effect on handling. Raking the mast shortens the lever arm between the drive force (green arrow) and the CG. It also vectors some of the drive force upward (blue arrow) 

Foil set at a 'cruising' AoA, rudder foil neutral (no AoA therefore no lift). CG is just far enough aft of the main foil to counter the bow-down moment from the rig (red arrow). Rudder foil is contributing only drag!

Same setup as above. When perturbed, lift on both foils increases. Since equilibrium was at zero rudder lift, this configuration is very stable: rudder foil has a lot of leverage to restore level trim.

When this same system pitches down, main foil lift drops to zero and then becomes 'negative' (pulling down). All along rudder foil force is increasing, exerting leverage to restore level trim.

The above three diagrams show the same foil setup as the first ones, but with the CG shifted aft. This represents what happens when you step back on an A that has small rudder foils sized/angled as 'pitch dampers'. It is obvious that the further back one stands, the more unstable the system becomes. The rudder foils have less and less leverage while the main foil has more and more.

A more stable setup uses the rudder foils to share lift at optimum trim. By selecting the appropriate rudder foil size, section and AoA, the rate of change of rudder lift can be made greater than that of the main foil. This setup is more tolerant of shifts in the CG location.

FAQ: Optimum Altitude

Q: "You seem to be just 'skimming' above the surface. Why not fly higher?"

A: Altitude control in Martin Fischer's foil concept is supposed to come 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.

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 significant 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...

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.
So spray only adds drag if it strikes the front half of the boat while moving back. If it strikes the back part of the boat while moving forward it can be ignored...
The ideal solution would be to fence the foils to suppress/redirect the spray in the first place, but this is not practical since the foils must pass through the bearings at the hull surfaces.

It may be that in 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 tradeoff 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 appears that it 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 initial 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. With the initial Fischer S foil solution full foiling is proving just too expensive in terms of drag.

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 mass.

Regardless of whether that goal has been achieved (still being evalusted), the bottom line is that overall drag around the course is what matters.

We will continue to experiment until this crucial value has been reduced below that of other designs.
At the same time the drag reductions must be exploitable: the boat must be simple and intuitive to use so the single-handed skipper can look 'out of the boat' and concentrate on the race.

Now we are working to establish the best settings to get the most out of the first generation 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.
After that we will play with different concepts and draw some informed conclusions.

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 interesting though more work still lies ahead.
Stability is unaffected but the boat is more responsive to changes in longitudinal trim.

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, L 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 less 'wildly' to upsetting trimming forces.
One drwaback of having the lift just under the surface, however, is that the foils ventilate quite easily. A problem that could be solvable by optimising foil section and/or adding boundary layer devices to keep the flow attached...

To be clear, these are handling issues, not performance issues.
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 weighing the drag penalties associated with maintaining stability, and determining whether they are worth accepting in 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.

To exploit the gains, one must understand the way the foils work. The boat must be kept flat so both foils can work together. The traveler seems to work best slightly lowered to direct the sail vector forward.

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 other configurations that have most of the advantages of the S foils but require 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/span.

Hydrodynamics

A single bent foil has no intersections so there is no interference drag (strictly speaking there is still some interaction between the pressure fields, 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 (in three dimensions) with surfaces locally orthogonal to their respective spans.

An assortment of Moth horizontal T foils with junction bulbs.
The bulbs smooth out pressure peaks and may even be designed to create destructive interference:
A high pressure area in the bulb can be made to coincide with a low pressure area in a foil.
The two pressure fields cancel in a way not dissimilar to the waves behind the bulbous bow of a ship.
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. Also foil assisted multihulls optimised to have the windward rudder winglet 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/construction, 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 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.

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 since 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 transverse '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 top bearing that only moves fore-and-aft is a much lighter solution.
Pulling the foil up and down in this laterally 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.