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Friday, May 4, 2012

Katana Marblehead Design – Foils

Marblehead foil design presents an interesting challenge because the maximum permitted draft is extremely generous.
In most monohull keelboat classes, maximum draft is well short of the crossover where additional righting moment gained becomes outweighed by hydrodynamic and structural considerations. 
For most classes, draft can therefore be regarded as fixed (always go to maximum).

In a rule such as the old International America’s Cup Class (IACC), where speed producing factors could be traded, it was even warranted in some conditions to exceed maximum draft and take a draft penalty (in the form of reduced sail area or measured length) because the increased righting moment was far more beneficial than the associated drawbacks. 

More often draft is taken as mandated by the rule maximum so it ceases to be a variable in the optimisation of appendages.


At this size, tall rigs are advantageous because the wind speed gradient (slowing near the surface) is very significant. 
Righting moment is therefore important if sail force is to be maintained. 
Again due to size (more precisely to Reynolds Number – the relationship between speed and length), wetted area is a dominant contributor to hull drag, so stability generated through hull beam is expensive in terms of drag. 

So far, maximising draft seems like a no-brainer because it gives more righting moment for a given heel angle and ballast mass. But what are the downsides?

This is an example of a complex design space where multiple variables are interrelated. 
Making the fin deeper increases bending moment for a given bulb weight. If this results in more fin deflection, it will reduce the gain in righting moment by allowing the bulb to move inboard more than it could if the fin flexed less. 
Note that there is the option to keep righting moment constant by increasing draft and reducing bulb mass (smaller force, longer lever). But for now we are assuming that optimum displacement must be maintained.
Assuming also that fin construction already maximizes stiffness, the only way to address the extra bending loss is to make the fin thicker. This in turn increases the thickness to chord ratio for a given fin chord. 
To compound this effect, the deeper fin actually needs to have less chord if area is to remain constant as draft increases… 
You now begin to see the fine tensions involved.

The low Reynolds number makes RC yacht foils particularly sensitive to laminar separation because the flow running along their surface is not very energetic. 
It therefore cannot be called upon to follow steep curves, especially after it has already traveled some length along the surface and has therefore lost some energy. Unfortunately this is also the point where we want the flow to follow the section in toward the trailing edge.

Increasing foil chord can help by making the Reynolds number for the whole foil higher. A longer chord also decreases thickness to chord ratio for a given fin stiffness. Decreasing thickness to chord ratio helps to keep the flow attached (by basically straightening the section lines the water has to follow), but also affects lift characteristics and possibly stall angle. 

The price for extra draft has to be paid in some combination of greater bending losses, increased thickness to chord ratio, and additional foil area.
Secondary considerations come into play for upwind sailing: Increased fin aspect ratio reduces lift induced drag. 

Moving the bulb down (and away from the CG) may increase pitching moment, a potential drawback when sailing in waves.

Without wading into the maths, we have identified the interrelated variables that make up this particular design space. 
The designer has to trade draught (good for righting moment) against fin bending losses, fin area, section thickness to chord ratio, Reynolds Number, aspect ratio and pitching moment.

Finally there are less constrained decisions such as chord distribution along the fin and rudder (basically the taper ratio), foil positioning, and lift sharing between fin, rudder and canoe body. Sharing of lift by the rudder can be controlled through rudder size, placement and angle. Hull lift is indirectly controlled by leeway angle and is therefore influential on fin section design which is usually done with reference to an optimum range of angles of attack.

Plugging in the numbers, the optimum balance usually comes out well short of maximum draught for a Marblehead that is to be competitive around a course in a range of conditions. 
Our previous work confirmed this consensus. 
The constraining factor was the ability of the section to retain efficiency with reduced chord and increased thickness to chord ratio. 

For Katana we paid a lot of attention to the section shape and were able to identify a small gain by basically smoothing out thickness distribution. This allowed us to push to a slightly shorter chord with similar drag characteristics to the previous generation. 

Improvements in construction allowed us to slightly reduce thickness for a given bending moment. However with the new section we could accept a slight increase in thickness to chord ratio (from 6.25% to 6.5%) which also makes the fin more forgiving in down speed situations. 

Taking advantage of the improved section and construction, we increased draught for the same foil area and deflection.

The bulb was revised, incorporating the improvements in foil section (that translate to bulb thickness distribution) and adding a beaver tail as successfully used on our IOM designs.

Elliptical chord distributions were chosen for both fin and rudder. This option was made practical and economical by the CAM technology being used to cut the moulds.

The new fin mould is machined over-length to permit experimentation with even deeper draughts and to allow use of the fin in bigger classes such as 10 Raters. 

The foils and bulb are also available separately so contact us to find out if they are suitable for your boat.

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