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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?

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