A closer look at the numbers we use to predict the performance and handling characteristics of the cruising cats we choose to sail.

by Tony Grainger

"The test of a machine is the satisfaction it gives you. There isn't any other test. If the machine produces tranquility it's right. If it disturbs you it's wrong until either the machine or your mind is changed".

From Robert M Pirsig's *Zen and the Art of Motor Cycle Maintenance*

We use all kinds of numbers, ratios and formulas to get a grip on the performance potential of any given sailing yacht. Some of these numbers may be revealing about some aspects of performance but context is critical. Here's the problem; every ratio you look at is related to other ratios. Not just one or two, but a myriad of complex relationships that combine to make up a very complex machine, a piece of technology that can be fast or slow, beautiful or not beautiful, well behaved in a seaway or not, and a whole range of possibilities between the extremes.

So how can we know in advance whether the boat we build or buy will meet our expectations and gives is that sense of satisfaction?

*Robert M Pirsig*

*"If you* *constantly unpacked everything for* *deeper understanding you never get*

*anything done and if you don't* *unpack understanding when you need to* *you'll do the wrong thing."*

Microprocessor engineer Jim Keller in an interview with Lex Fridman.

It's not absolutely necessary to understand all of the technology that goes into yacht design in order to make a decision whether a particular boat is right or wrong for your purposes, but if you want to understand a boat in terms of specifications and ratios its important to understand which ones are meaningful, what they mean and under what circumstances their influence comes into play. There are three significant factors that limit our ability to use the numbers effectively and accurately in determining overall performance.

The first is that weight is a critical factor, probably the single most critical factor to most of the formulas either directly or indirectly, and most of the time we simply don't know the weight. We tend to rely on "displacement" numbers which for the most part are published without any clear explanation of how they have been derived and whether they have been verified.

The second is windage, a significant drag factor that becomes more significant as speed increases. It could be determined reasonably accurately using detailed models and fluid dynamics, but such investigation does not come easily or cheaply and accordingly is generally put aside while we attend to other things.

The third factor is the big picture. That is: how the various specifications and ratios interact with each other and where they sit in the hierarchy of importance. Which ratios are important in specific conditions, and what price is paid for optimizing one particular ratio at the price of another?

We can fixate on power to weight, but once we've reached maximum stability the excess sail area becomes a drag factor. A focus on the displacement to length ratio doesn't tell us how much driving power is at hand. Additional beam gives us stability but what has that done to drag from excess windage? A skinny hull will allow a higher top speed in fresh reaching conditions but what has the additional wetted area done to performance in light and medium air, arguably the most common sailing condition? The wing clearance specification on a cat is of little value if it has been determined on an unrealistic displacement figure or the boat is loaded below its lines. And a wing deck that extends further to the fore and aft extremities should ideally have more clearance than a short one, so the height should not be considered in isolation.

So how do we get a realistic picture of the overall performance and seaworthiness? We can look at all of the specifications and ratios one by one see if they are favorable or not, but there is no level of technology at hand that can provide a quick and meaningful answer to how these numbers work together in the big picture.

*When we think deeply, whether that be through philosophical or mathematical language, it’s a purely creative act. But reality is messy, and as the meanings
behind words and formulae get more and more detached from direct experience the more we get lost in the mess.*

Zat Rana

We can easily and accurately determine the acceleration and top speed of a car, and it will be consistent for all of the cars from one particular assembly line. For sailing yachts things are much more complicated. There is no great unifying number, no book, no tables you can look up. Figures produced by VPP software should be treated with a healthy skepticism unless or until the numbers have been validated on the water in the wind and not massaged, manipulated or simply invented by the marketing department.

Without actually sailing the boat with a competent crew (preferably a professional crew) and taking measurements in a whole range of conditions the best we can do with current technology is digest all the numbers, mull them over in the subconscious and eventually make a judgement based rather unscientifically on a whole range of factors with particular attention to their relevance to our individual requirements. The value of this judgement will be based on another range of variables including sailing experience and the ability to form a rational conclusion.

But let's not despair. The process of yacht design is a process of endlessly moulding and manipulating forms, specifications and ratios with the objective of arriving at a well resolved design. In working on Raku 2020 designs it became clear to me for the first time that there are three highly significant elements at play that are by far the most important elements that determine the overall character, the performance potential, and the suitability of the boat for its intended purpose. For an efficient working design process these big three should be largely resolved early in the process and should always remain at the pinnacle of the hierarchy of design factors.

These three big factors are Hull Form, Mast Position and the Bridging Structure which I will refer to as "bridge form" because we are talking about the wing deck, the saloon cabin and the cockpit, not just the structural aspect of the cross deck.

**Hull Form**

For a hull of a given length (and yes, the length is usually given, not the displacement, and I'm not sure this is logical), we play with displacement, beam to length ratio, wetted area, prismatic coefficient (fullness in the ends) the rocker line, the centre of buoyancy, the degree of flatness in the aft sections, and more. All of these factors are important and they are all part of design technologies that are available to us completely free of charge through the knowledge, experience and judgement of the designer.

We cannot consider any one of these technologies without considering their relationship with the others. An adjustment to any one has at least some effect on all of the others. Think of it like a balloon. You can't push in on it in any one place without it affecting the shape of the ballon in every other part of the surface.

**Bridge Form-Volume and Geometry**

This is significant for the length relative to the hulls, the beam, the water clearance, the height of the cabin and a drag coefficient determined by the profile. But none of these factors is directly determinant in the shaping of the hull form. Weight and fore and aft position of the bridge form on the other hand will determine the position of the centre of buoyancy and the displacement of the hulls.

**Mast Position**

The mast position will also be part of the centre of buoyancy equation, but more importantly it has a strong influence over the bridge form. We want to put the mast base on the deck, not on the cabin top. A deck stepped mast saves a lot of complication for the builder and the rigger. Halyards are readily lead aft to the cockpit, but can still exit to the cabin top if preferred. A mast stepped further forward will allow a longer saloon cabin and this configuration is the choice of most production catamaran builders catering to the cruising market space.

A mast stepped further aft (typically around 50% of LOA) is the preferred choice for sports cats and racing sailors. The more hull length you have forward of the centre of effort in the rig the more power you can apply to drive the boat in fresh conditions with less risk of driving the bows into the waves.

The problem is that for a deck stepped rig on a cruising cat the further aft you locate the rig the further aft you drive the saloon and cockpit, and accordingly limit the accommodation space or allow it affect the hull form, possibly paying a price in compromised hull form that is not commensurate with the benefit of moving the rig aft.

We want our boat to trim on its designed lines, so if we push weight further aft we only have two options. One is to increase the rocker in the hull to move buoyancy aft. This will compromise high speed reaching performance. The other option is to retain a relatively flat rocker line and allow the transom to be submerged at rest. This will create turbulent flow at the stern, increase wetted area and handicap light air performance. Tacking speed might also be adversely affected.

So while there are many factors at play in manipulating the complexities of the overall design it is clear that there are hierarchies in the complexities, and by studying and optimizing the big three as a first priority we are better equipped to make sound judgements about the other factors.

There's no formula for calculating the effect the volume and geometry of the bridge form is having on the hull shape, or even whether the designer has considered the issue at all. But we can use our judgement based on previous experience, and in fact that's the way most design works anyway.

Consider the three factors of hull form, bridge form and mast position like a scalene triangle. We can fix one angle, we can fix two angles, but the third and final angle will always give us a total of 180˚. If we're not happy with that third angle we can go back and start adjusting the other two - but it's much more productive to be working with all three right from word go.