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.

Versatility

This week we started production of tooling for an improved rudder design for Paradox.
Design work from here on in is entirely in-house.

Considerable drag reductions should be possible through increasing the efficiency of the ‘L’ surface. 

This is achieved by improving the aspect ratio of the horizontal foil. 
Increasing the aspect ratio dramatically reduces induced drag. The new aspect ratio 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. 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 50%), giving a significant drag reduction.

Mk1 rudder shown yellow, new version in red

The new rudders are conceived 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.

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.

Balancing Act

After testing four different prototypes, here is the latest version of the rudder cassettes that we will supply with your Paradox A Class Catamaran.

Once again, the optimum choice strikes a balance between different considerations. 

In fact, the design of this component is a great illustration of how the best solutions use the most appropriate materials and techniques for a given application, regardless of trends.

The cassette assembly requires very high dimensional accuracy since it sets the steering geometry.

At the same time it needs to be light, stiff, easily manufactured to reliably tight tolerances, and economical.

This assembly determines the position of the pivot axis relative to the rudder blade (fore-and-aft) and the angle of the blade relative to the tiller (in the horizontal plane).

The position of the pivot axis is critical to the balance of the rudder: The further back along the blade (more foil area ahead of the pivot axis) the more ‘compensation’. Meaning more area helping to turn the rudder relative to the area behind the axis pushing to straighten the rudder. 

On a swing-up rudder compensation can be adjusted by ‘kicking’ the rudder forward past vertical so that the bottom tip is ahead of the pivot axis. 
This solution is fine when the rudder is fully submerged, but it has the drawback that compensation will increase as the upper part of the blade exits the water. When only the tip is left in the water, the rudder will most probably be over-balanced, resulting in a light and ‘skittish’ feel through the tiller extension. At high speeds, especially when foiling, this can be dangerous. 

A Class cats so far have not had to confront this problem because stable foiling has been impossible. But the effect can still be felt when in displacement mode as immersion of the windward rudder varies.

Our solution maintains the correct compensation regardless of ride height and heel angle. 
Actually the rudders are designed to provide a more positive feel as they come out of the water. 
This is achieved by tapering the leading edge aft toward the rudder tips… 

Another advantage over kick-up rudders is that compensation does not change as the angle of attack of the horizontal foil on the rudder is altered (rake). 'T' or ‘+’ foils on the rudders of other boats cannot be tuned for horizontal angle without altering rudder compensation. 

Coming into the beach, kick-up rudders with winglets also cannot provide any control because they can only be fully up clear of the water or fully down. Our rudders can be partially retracted to still provide steerage in shallow water.

To achieve the goal of positioning the rudders accurately, there are important material and process considerations that are not immediately obvious. 

The bearing surface needs to be precise, have a low coefficient of friction, be dimensionally stable and able to hold the rudder without damaging its surface and trailing edge. 

The connection with the pivot axis has very high point loads that need to be reacted out into the cassette. 

The tiller needs to be supported at the correct angle both inboard and upward and be tough enough to withstand the occasional abuse such as a rough tack or jibe.

Satisfying these needs with carbon mouldings requires the build-up of considerable thickness in high load areas. 
The processes are necessarily complex because the shapes involved cannot be moulded in one piece. Dimensional accuracy is not ideal because of the nature of the process and materials. 

The relationship between any weight savings and the additional cost is so disproportionate that it raises doubts about the appropriateness of the material.

A carefully optimised machined aluminium fabrication results in a very efficient structure that is competitive in terms of weight and can be made reliably at a fraction of the cost. 

As a bonus there is a certain ‘aeronautical’ aesthetic that is unique and very pleasing.

Rake adjustment is through shims between the gudgeons and the transom.
Tapping plates inside the boat mean you can replace the shims without having to access the interior.