Dario's Lab

Katana Marblehead Design – Hull

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

Katana in red, Octave in grey
Shaping of the ends incorporates lessons on boundary layer behavior learned in other work we have done. This new knowledge has refined our analytic tools, reducing the margin of error.
Armed with higher resolution tools, a more linear pressure recovery could be engineered reliably. The newly resolved pressure recovery rate is achieved through straighter diagonals from the mid section to the transom, combined with aft sections that are closer to semi-circular.
Straightening the run aft makes pressure recovery smoother, placing less stress on the boundary layer. In practical terms, this means not asking the water flow to follow excessively tight curves toward the back of the boat because, by the time the water reaches the back half of the boat, much energy has been lost to friction in the boundary layer.This concept is not new, but being able to quantify how much we can ‘ask the flow to do’ empowers us to identify the optimum values for the conflicting requirements we are trying to mediate.
A very simplified overview might go something like this:
On the one hand we want to bring the flow back together (from max beam/draught to a point on the centreline/waterline near the transom) to
1) Make the wake as small as possible – smoothly refill the hole in the water made by the boat and
2) Get as much ‘push’ as we can from the water pressure on the aft surfaces of the boat – since the surfaces are angled inward, the normal pressure that acts at 90 degrees to the surfaces has a component pushing the boat forward. This component would in an ideal world be the same as that pushing back on the forward parts of the hull, but in reality is less due to energy lost through viscosity in the boundary layer.
On the other hand we want to maximise volume in the stern to
1) Get as much support as possible from the stern wave,
2) Damp pitching,
3) Avoid flow separation and
4) Maximise power.
All the while we want to keep wetted area to a minimum…
So you can see how nailing down more exact values makes our design choices much clearer!

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

The new stern treatment has the effect of reducing prismatic coefficient. In order to maintain the high prismatic coefficient of our successful previous designs, the sections in the forefoot were made even firmer, adding volume with a pronounced ‘U’ shape that transitions smoothly into the semi-circular mid and stern sections. 
The forward volume distribution has been revised with a less aggressive rocker profile but more angular sections in the forefoot. 
This treatment of the forward sections has several advantages: it increases resistance to bow-down trimming moment both hydrostatically and dynamically, it keeps the entry narrow at the waterline (by pushing volume down rather than out), dampens pitching, and moves the LCB forward (also a trend in the evolution of our designs).
Above the water, the forward sections remain vertical, with a peaked foredeck for clean wave piercing and to keep added drag to a minimum when over-pressed. 
Moving aft, the topsides are no longer vertical but instead flare progressively. 
Amidships the moderate flare provides additional support, smoothing the heeled waterlines and helping to locate the heeled LCB such that trim remains neutral or slightly positive with heel. 
At the maximum deck beam location there is a subtle inflection under the gunwale to enhance water shedding when pressed and in waves, keeping aft flowing water off the sidedeck.
Finally some flare in the topsides aft has been introduced, accounting for perhaps the single largest visible change from Octave. 
In fact the new stern treatment achieves a similar effect to the characteristic soft chine/tumblehome of Octave but does away with some associated minor penalties. 
Specifically, water shedding is now done by the hull/deck joint instead of the chine. The sharp edge and acute included angle are more effective, but are higher up, so the flow remains attached a bit longer than would be ideal. 
However, since the sections are more rounded, the actual distance along the hull surface between the two separation lines is only marginally greater than before. 
Also, the new sheerline is lower at the back, reducing the distance even further and doing away with some mass in the process (the sheerline is more steeply inclined, being the same height as on Octave amidships, and higher at the front). 
As always there are compromises involved. This aspect of this particular choice is a net gain in some conditions, neutral in others and possibly a slight loss in the particular circumstances when the previous arrangement was at its best. 

To tip the scales, the principal advantage of the new stern shape is enhanced pitch damping. Marbleheads are inherently susceptible to speed sapping pitching due to their deep bulb, tall rigs, fine ends and (obviously) their small size relative to common wind generated waves. 
Our updated tools tell us that the dynamic effect of horizontal area aft is smaller than previous results showed. 
This is consistent with a more accurate understanding of boundary layer behavior. 
So the best way to damp pitching aft (over the full range of speeds/conditions) is hydrostatically, by progressively increasing waterplane area as the aft sections sink.

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

It is worth remembering that the differences identified through more accurate theoretical analysis tools are small. But they do exist.
And each small change cumulatively contributes to race winning differences. 
Furthermore, a deeper understanding of aspects such as boundary layer behavior enables the designer to adopt a consistent approach. The parts can be designed to work better together taking into account realistic flow phenomena.
Quite apart from fine numerical validation, meaningful gains were made by learning from real observations of handling characteristics and other aspects of behaviour by a number of different observers, through a deliberate and structured development programme. 
This is why we are now confident to embark on series production of Katana.