The prismatic coefficient of various vessels, from the full volume of a cockle barge (far left) to the slender lines of a sailing yacht (far right)
'Two years ago,' says Peter Bouma, a naval architect at Vripack in Holland, 'we had a Brazilian owner who wanted a displacement trawler. During our initial talks about the design, he put to us a requested design speed that was 2.5 knots above the design's hull speed. For us naval architects, this is a terrible speed to design to. Not only is it complex to get a good estimation for, it's also not an efficient speed from a fuel economy point of view. His reasoning was logical he wanted to sail in quite heavy seas, but his typical weekend trip was going to an island and back in a day. He wanted that particular speed to be able to have dinner at a certain time and still get back before nightfall. The answer was to install a big, expensive engine and to burn a lot more fuel on that specific trip a compromise that, once explained, he decided he was prepared to make.'
I am sitting in Vripack's offices in the Dutch town of Sneek to talk about the basic elements of naval architecture that every owner should know. With me are Bart Bouwhuis, director of design; Ierring Faber, manager of the naval architecture side; and Aleksandr Markov and Peter Bouma, both Vripack naval architects. Bouma's example of the Brazilian owner's request highlights the importance of understanding what you require from your new yacht, and therefore what compromises you might have to make. It's a key aspect of the concept design phase, and a key element to ensure your dreams can, in fact, become reality. And for all the styling up top, naval architecture is still king. 'For sure, you can create a body under any object,' says Bouwhuis, 'and it will float and have the right stability, but how will it behave in a seaway? Well, that's a different matter, so it all really depends on the operational profile.'
Design revolves around a golden triangle that must always be in balance speed, weight and power. Whenever you alter one of these factors, the others must also change to keep the triangle balanced. So, for example, if you add weight, you also have to add power, or lose speed; if you want more speed, you have to add power or reduce weight; and if you reduce power, you either have to reduce weight, or lose speed.
'There's no magical solution to break this triangle,' explains Bouma, 'and when a client comes with an idea that apparently does break the triangle, there's always an explanation perhaps a different material has been specified so the overall weight is less, for example.'
If you look at the three general hull forms available for yacht design, they all demonstrate the different solutions of this balancing act. A displacement hull has a limited top speed (more on that shortly), and within the speed range if you want a high volume, heavy displacement boat, you need to add more power. Similarly, if you want smaller engines for the same size yacht, you either accept that you will go slower, or will have to compromise on volume and weight lessening the displacement, in effect. Displacement, of course, is simply the weight of the water that is displaced by the yacht the hole in the water, if you will. We have Archimedes to thank for that discovery.
An underwater view of a typical planing yacht hull
A semi-planing or planing hull requires a different balance of the triangle. In these cases, your power requirement goes up with the speed for a given weight, or you have to reduce weight in order to get the higher speeds. Naturally, it is never quite as simple as this, and there are some key factors that determine what can and can't be done with a hull design. It is these factors that show why you can't have a large, high-volume and heavy displacement steel yacht that planes at 60 knots, for example. If you've ever talked to naval architects about the design of your new project, it is likely you will have heard them bandy around arcane terms such as prismatic coefficients and Froude numbers. But what do these mean? Having a basic grasp of these concepts means that you will not only have some idea of what the naval architect is talking about, but will also help at the concept stage in realising why your 60-knot planing steel giant is just not possible.
The defining characteristic between different hull forms, particularly between displacement hulls and semi-planing or planing hulls, all revolves around theoretical hull speed. Many of us will know the standard, simple formula for working out the theoretical hull speed in knots of any given yacht it's nothing more than the square root of the waterline length in feet multiplied by 1.34. So a yacht with a waterline length of 150 feet (45.14 metres) will have a theoretical hull speed of root 150 x 1.34, or 16.4 knots. But what does this mean, and why is there a boundary here?
'It's just physics,' says Faber. 'It's just how water behaves. It's the speed a wave propagates through the water, and that depends on its wavelength. At theoretical hull speed, the length of the wave created by the hull equals the waterline length (essentially, the hull is the same length as one peak and one trough of a wave). Above this theoretical hull speed you have to climb the hill of the wave created. The behaviour of the boat at this point is that it trims aft and gets sucked down effectively creating even more displacement and more drag. So it's a very steep part of resistance you encounter exactly at this point.'
As the Froude number increases and the yacht's hull form moves from displacement to planing, the dominant type of resistance acting on the hull also changes
If you want to see this effect in action, hold the end of a spoon between your thumb and forefinger and let it hang in a stream of water from a tap, so the water passes over the convex curve of the spoon. You will notice that the water curves around the spoon, but also that the spoon is drawn into the flow of the water. The same thing happens with the underwater body of a yacht it doesn't matter whether it's the water moving or the object.
This is why a standard displacement hull finds it impossible to climb over the wave, no matter how much power you try to pack in engine room. The only way to break through the wave the so-called 'hump' is not only to increase the power, but also to modify the hull shape, in effect designing a semi-displacement or a planing hull form, or one of the specialist hybrid hulls like the LDL or Fast Displacement Hull Form (also known as its acronym FDHF).
Froude for thought
While theoretical hull speed is fairly common knowledge, the Froude number is not, yet is directly related and far more relevant in determining what sort of hull is required.
The Froude number (Fn) was invented by a 19th Century British naval architect called William Froude as a way of measuring and analysing ship resistance in towing tanks. Rather than rely on specific dimensions (such as a given length) to calculate, for example, hull speed, the Froude number is a coefficient a dimensionless number that can be applied to any size of vessel, so what applies to a small-scale towing tank model will also scale up to apply to a full size version. So essentially, while hull speed is just one number, the Froude number is a speed:length ratio. The formula for Fn is V divided by the square root of (g*L), where V is speed in m/s, g is gravity and L is waterline length in metres.
But why is it useful to know this? 'When you think about hull speed, the Froude number around 0.4 is a good value to have in your head,' says Markov. 'This is the point it becomes very power inefficient if you want to go faster. And at Froude numbers of 0.3 and 0.5 you have your humps. These are major numbers. For yacht design, Fn 0.3 is largely irrelevant it's the point at which the hull length equals two wavelengths but at Fn 0.5 hull length equals one wavelength, the big hump. For Fn between 0.5 and 1, you are looking at semi-displacement hulls, and at Fn 1 dynamic forces start lifting the hull. At Fn 3 you are fully planing. When an owner comes with a request for a boat and having a certain speed in mind, in practice the first thing a naval architect does is basically put that speed in relation to the length and that's what the Froude number is, a relationship between speed and length. That's what gives your basic hull form displacement, semi-planing or planing.'
When plotting the resistance curves for the key yacht hull types against the Froude number, the boundaries between each hull type can be clearly seen
Vive la resistance
As mentioned above, one of the key factors determining speed is the increasing resistance the hull experiences around the hump that point at which the yacht is trying to climb up its own bow wave, around that Froude number of 0.5. But what is resistance?
'Resistance,' explains Bouwhuis, 'is the force required to pull the boat through the water nothing more, nothing less!' If you were to tow a yacht through the water and measured the weight on the towing line, this effectively gives you a force the amount of resistance the hull is encountering. This resistance is primarily broken down into two key types: wave resistance (largely a function of the weight of the vessel) and frictional resistance (related to the wetted surface of the vessel essentially, all the things you've stuck anti-fouling paint on). 'Wavemaking resistance is the resistance to generating waves,' Markov continues, 'so the more waves you generate the more your resistance is. You use your power to generate waves. It's essentially the time that the water needs to adjust to the speed of the object that is passing through it.' For semi-planing and planing hulls, wave resistance is a major characteristic to optimise. Frictional resistance, on the other hand, is somewhat more linear it just increases as you go faster. How do you reduce friction and increase speed? By reducing wetted surface, and one way to do that is to put less weight in the boat and we are back to that speed:weight:power triangle again.
There are other tricks too with planing hulls, all those steps, and hydrofoil shapes and catamaran and trimaran designs are all ways of reducing wetted surface, and therefore reducing frictional resistance. Of course, weight is disproportionate to length, as length is one-dimensional whereas weight is three-dimensional. This is why the larger your yacht, the harder it is to get it planing.
The two primary resistance forces a yacht encounters are wavemaking resistance and frictional resistance
Reducing one type of resistance using a bulb on the bow, say, to reduce wavemaking resistance often impacts inversely on the other type of resistance. In the case of a bulb, you may achieve a 30 per cent reduction in wave resistance (which accounts for perhaps 60 per cent of overall resistance) but you add wetted surface area, which increases frictional resistance so your overall reduction may actually only be 10 per cent
Hull shapes are often talked about in terms of the prismatic coefficient (Cp), but what is this? In its most basic terms, it is a measure of the fullness of a hull. Think of a supertanker, with a box-like cross section and beam that is the same at the bow, midships and stern. This is a very full hull, compared to a J Class yacht, which has max beam amidships but almost no volume at all in the bow or stern. The prismatic coefficient is calculated by effectively cutting through the underwater part of the hull to find the cross section that has the largest surface area. This figure is then multiplied by the waterline length, and Cp is the ratio between the actual displacement volume and this figure. The coefficient is therefore always less than 1, and typically ranges from about 0.5 (the relatively slender J Class hull) to about 0.9 (for the extreme, very full tanker hull). In other words, it's the volume distribution through the length of the hull. Planing yachts (both sail and power) will tend to have more volume in the aft end due to higher beam, and therefore will have a higher Cp.
There are a couple of other factors that are important longitudinal centre of buoyancy (LCB) and longitudinal centre of gravity (LCG). LCB is the centre of gravity of the displaced volume of water the point where the upwards force of the water will push against the hull; LCG is the centre of gravity of the vessel on a fore/aft measure and represents the downward force of the boat. LCG should be directly above the LCB if you want to have no fore-aft trim. To imagine the impact that design has on LCB and LCG, consider an explorer-style vessel with the bulk of the superstructure located quite far forward, compared to a sleek speedboat with a long, slender nose and main superstructure aft. It is more critical on planing boats, as LCG is not just a measure of volume distribution but also has an impact on dynamic stability.
What about beam? Why isn't beam included in these basic calculations? 'We tend to look at length over beam,' says Faber, 'which has a lot of influence over resistance components discussed above. The influence of beam on resistance is more complicated and not that straightforward as it is with length. Ideally you want to have a slender boat for Froude numbers in that critical area between 0.3 and 0.5, but once you get above those numbers closer to the planing mode you would like to have some beam and waterplane area to generate lifting force in the aft ship.' Beam is usually regarded as a high resistance component. For wavemaking resistance, beam is a negative factor and the wavemaking resistance is predominantly an issue in displacement and semi-displacement hull forms hence why a slender hull can be more efficient in that speed range.
But beam has quite a different influence in planing mode, where it is very much more related to the mechanics of how a planing hull operates. It helps provide dynamic lift, and you need a certain beam to carry a certain weight, plus it's good for resistance up to a point beyond that, it becomes negative for resistance, so there is an optimum beam. If you extend the beam further, you create a lot more wetted surface and therefore more resistance. Too little beam, on the other hand, means the bottom load is too high because there is no support anymore, and with it a lot more trim, which means wetted surface and resistance
While the three basic hull types form the platform from which all yachts are built, there are of course tricks to optimise for certain speed requirements or operating conditions, and specialised hull forms that offer particular advantages for particular purposes, usually as highly optimised versions of one of the three basic hull types. We will look at these aspects in more detail when we consider the science of hull optimisation and what compromises this brings.
Stay tuned for owner's guide to superyacht naval architecture part 2, where we will look at one of the critical elements of that design triangle weight and the importance not only of controlling the overall weight of a project, but also in managing its distribution throughout the hull.