A three-part series: **Part Two**

**Naval architect Filip Sochaj explains the complexities of hull form**

For new readers just joining Ocean Sailor, this is part two of a series of articles in which we take a deeper look at the world of yacht design. We examine how statistics and ratios shape the yacht, how they affect its stability, performance and sea kindliness. As we do so we are advising readers not to take everything at face value or rely on one statistic out of context, as that will only give a partial picture.

Last month we talked about ballast ratio, sail area/displacement ratio and displacement/length ratio. This month we look at hull form stability, motion comfort and a yacht’s ability to carry sail. The subjects are determined by various formulae and statistics such as the Block coefficient, Prismatic coefficient, Brewer’s motion comfort rating and the Dellenbaugh angle. In the next issue, we will bring it all together with AVS and STIX.

My objective in writing this article is not to teach you how to be a yacht designer, but to allow you to understand the principles which need to be grasped when deciding if the type of yacht the designer has drawn is most suitable for the type of sailing you wish to do. Once again, it comes back to deciding what you want to do with your yacht and what your primary considerations are, because you cannot have it all.

This subject is quite complex, but hopefully, at the end of the series, you will have a good understanding of what we are trying to achieve. If you have any questions please email us at the address below and we will do our best to answer them.

**Brewer’s Motion Comfort**

Mr. Brewer came up with this comfort ratio in order to assess sea kindliness of yachts of the same type and similar shape. To quote the author himself:

**“Given a wave of X height, the speed of the upward motion depends on the displacement of the yacht and the amount of waterline area that is acted upon. Greater displacement, or lesser WL area, gives a slower motion and more comfort for any given sea state.”**

This ties in nicely with last month’s issue where we talked about ballast ratio and how a heavier boat will usually be better at seakeeping. The absolute champions of this metric are the heavy cruisers of old, like those from the Colin Archer design school, which sit heavy in the water while maintaining a slim underwater profile.

Brewer’s equation ranges from 0 to 80. Classic heavyweight cruising boats of 30 or 40 years ago might have sat around 40, while a modern production cruiser-racer such as Benetau, Hanse, Jeaneau or X-Yachts would be 20 to 25. We believe a well-appointed modern blue water cruiser should not be less than 30. Kraken’s range is 35 to 50 depending on size.

The aspect of speed also comes into play as sails act as a stabiliser for the motion caused by waves. This we cover in the next section dealing with power to carry sail:

**Form Stability**

Form stability deals with how the buoyancy of the hull is affected by its crossways shape or beam. As the name implies, this is simply the stability of the hull which is provided by its shape. A yacht stays upright thanks to two factors; the weight that sits below the centre of buoyancy – ballast, and the shape of the hull – its form. A more technical explanation would be that as the boat heels, the centre of buoyancy moves outboard as new areas of the hull are submerged. The further outboard it goes the better it is at counteracting the heeling arm. The principle is simple – a yacht that is wide and flat is harder to overturn than one which is narrow and round, however an extreme example would be a catamaran, which is very stable until it goes over, but then doesn’t come back.

All yachts need both. The famous Swedish warship Vasa sank because her ballast was not low enough, nor was there enough of it. This caused her to capsize as soon as she left port. Lack of form stability, and therefore hull volume, will make the yacht sink down into the waves as she gets powered up, as per the Cp discussion below.

Lifting keel designs like the Allures, Garcia, and Southerly, rely heavily on form stability. That’s because they have un-ballasted lifting keels, and all internal ballast sitting in the bilge. Because of the shorter lever arm, the righting moment induced by the ballast is smaller and must be subsidised by form stability.

This is not a problem in absolute terms as the sum result is the same, but it does matter in ocean sailing where due to heavy weather, there is a potential for a knockdown. Whilst it is true that form stability can be used to supplement keel ballast, the problem lies in that once the yacht goes past the point where form stability is holding it up, there is little keel weight to bring it back up again.

Saying that a wide hull will be just as stable upside down as it is the right way up might be true to the law of physics, but it is hardly the desired result for a cruising family!

Hull shapes with high form stability mean that internal volumes can be increased. This is Gold dust to interior designers who are trying to fit all the optional extras the sales team are selling to potential buyers, but those buyers should be careful what they wish for.

So why not have both a deep and heavy keel with a generous hull to provide all the room and form stability you might want? For that, you need to look no further than the section above where we look at Cp and the optimal band for fullness of hull which minimises drag.

Even if you do want the faster performance achievable by using a delta-shaped hull, we must consider the very negative effect that these hull shapes will have on its comfort motion, or sea kindliness, especially if the yacht’s main purpose is extended ocean passages and blue water sailing.

Bear in mind that a flat U-shaped cross-section will slam as it comes down from each wave and a vertical stem will cut into the wave rather than lifting over it. This produces a very wet foredeck which the crew must sometimes work on and requires them to endure constant slamming. This slamming is debilitating at the best of times and is extremely destructive to the yacht’s integrity and construction.

**Block Coefficient **(Cb)

Let’s make a rectangle in which the dimensions are described by the length of the waterline (LWL), breadth of the waterline (BWL) and canoe body draft (D). What we have is a trunk-shaped box with right-angle corners that encapsulate the underwater section of the hull. The relation of how much of that box is filled with the underwater section of the hull is the block coefficient.

All ratios enjoy a sweet spot, and for this one, it is usually between 0.4 and 0.7. That said, modern yachts try to stretch this as high as possible to maximise the internal volume with minimal draft.

The reason I mention Cb here is that it is similar and often mistaken for the Prismatic coefficient (Cp) which is also a very important tool for designers, giving them a good indication of the sort of performance to expect from a hull’s form.

**Prismatic Coefficient **(Cp)

This coefficient deals in volume distribution. Again, let’s imagine the same trunk-shaped box as we used for Cb, but instead of taking the true underwater profile of the hull, we take the biggest cross-section and stretch it along the whole length. The equation then compares how much of the trunk-shaped box is occupied by this new “hull” and gives a coefficient that is under 1, usually between 0.4-0.7. A box-shaped barge would have a Cp of 1, a shapely yacht a Cp of 0.5.

This is because the area that dictates the bounding box is defined by the max cross-sectional area (usually midship). The way to change the Cp is to increase or reduce how full or slim either end of the hull is. In other words, the Cp describes the fullness of the body.

A low Cp indicates a hull with fine/slim ends

A high Cp indicates a hull with full ends (box barge example)

Knowing how to calculate Cp we can then focus on how it affects performance. We know thanks to thorough testing by American Admiral David W Taylor that for every Speed/Length**1** ratio there is an optimal Cp.

This coefficient deals in volume distribution. Again, let’s imagine the same trunk-shaped box as we used for Cb, but instead of taking the true underwater profile of the hull, we take the biggest cross-section and stretch it along the whole length. The equation then compares how much of the trunk-shaped box is occupied by this new “hull” and gives a coefficient that is under 1, usually between 0.4-0.7. A box-shaped barge would have a Cp of 1, a shapely yacht a Cp of 0.5.

This is because the area that dictates the bounding box is defined by the max cross-sectional area (usually midship). The way to change the Cp is to increase or reduce how full or slim either end of the hull is. In other words, the Cp describes the fullness of the body.

- A low Cp indicates a hull with fine/slim ends
- A high Cp indicates a hull with full ends (box barge example)

Knowing how to calculate Cp we can then focus on how it affects performance. We know thanks to thorough testing by American Admiral David W Taylor that for every Speed/Length**1** ratio there is an optimal Cp.

If we take the Kraken 50 as an example; she has a maximum hull speed**2** of 9.5 knots, so her S/L ratio of 1.34 gives a Cp of around 0.63. A boat will only spend a small amount of time travelling at hull speed, and therefore, it makes sense, therefore, to design for a Cp that corresponds to the actual cruising speed of the yacht, otherwise she’ll be punished by a hull form optimised for a condition that is rarely experienced.

Kraken’s designer, Kevin Dibley, set the Cp at 0.55 which corresponds to 1.15 S/L or around 8.1knts. This is the speed that this hull is designed to be most efficient at, in terms of it’s displacement.

If volume is either too high or too low—that is if Cp is too big or too small—your hull drag is going to go up. This means either the boat is going to have to push too much water out of the way (Cp too big) or it is going to sink into its own waves (Cp too small).

**1 =** Speed/Length ratio= Speed (in knots) divided by square root of waterline length (in feet) 2 = Hull speed is the theoretical max sustainable speed achieved by a hull of a given length

**Dellenbaugh Angle **

Let’s dive further into the world of yacht design and look at a metric called the Dellenbaugh angle, often referred to as ‘the power to carry sail’. This is overall a simple equation to show how much a yacht will heel in a given wind speed. Below we explore how this can be calculated:

- We can simplify and say that all of the heeling forces will act through the centre of effort of the sail plan (CE)
- The heeling will be balanced by the side force generated by hull and acting through the centre of lateral resistance (CLR)
- The distance between CE and CLR is called the heeling arm (HA)
- The heeling force will be equal to the sail area x wind pressure
- Therefore the heeling moment = sail area x wind pressure x heeling arm
- If we divide the heeling moment by the righting moment @ 1 degree we get a simple approximation of the equilibrium heel angle.

To calculate the Dellenbaugh Angle for your boat you will need its righting moment, or metacentric height. To get these, the easiest way is to perform an incline test.

The equation does have some serious limitations. It assumes the sails are flat planes and the wind is acting at a right angle to them. Neither of these conditions can be true in the strictest sense, but, the closest we are going to get to this is at relatively light winds and small heel angles.

What the Dellenbaugh angle is good at is predicting how stiff or how tender the boat will be. The lower the angle the stiffer the boat, while higher angles mean she will roll more.

It is worth noting that, with the modern design school of beamy hull forms, the yachts of today have shifted the trend lines by 15-20% towards the stiff side.

Arriving at precisely the right DA comes back to the same old issue, making sure you first determine the purpose of your yacht. A degree of stiffness is desirable, otherwise she cannot carry enough sail to drive her up wind without being heeled too far, but too much stiffness will induce an uncomfortable jerky motion. A Kraken 50 sits in mid range at 11 degrees.

“With the use of numbers and ratios (Cb, Cp, Form stability and DA), as discussed above, you can optimise a yacht to be very fast and/or voluminous, no doubt. At Kraken Yachts, where we focus purely on blue water cruising yachts, we believe that these are not as important factors as safety and motion comfort. Of course, we want Kraken yachts to sail well, and they do, but not at the cost of what we believe are the primary consideration; to deliver the crew safely and comfortably across the oceans.”

**– Dick Beaumont, Chairman of Kraken Yachts**