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The days of yacht designers building scaled down models of sail boats and then bobbing them in tanks of water—to see how sleekly they moved—ended decades ago. Computers now do the same job with more finesse and detail and without any need for splashing around in waders.
Yet the mathematical equation (actually, set of equations) driving designs of the most rapid yachts on this planet is almost two centuries old. In 1821 French engineer Claud Louis-Navier built upon an existing equation that addressed the flow of fluids. In the 19th century a British physicist named Sir George Gabriel Stokes took this work and improved on it—hence the name Navier-Stokes equations that describe how fluids move. (Stokes, born in County Sligo in Ireland, graduated from the University of Cambridge and was soon conferred as a 'fellow.' Curiously—according to university regulations at that time—he had to give up that title when he got married.)
What these two individuals, combined, developed are known as partial differential equations. This name sounds somewhat mysterious and the formulae, seen written on a blackboard, may raise your eyebrows with intimidation. However, their premise is quite straightforward.
A differential equation incorporates some rate of change. Consider ocean water flowing over the hull of a boat. Changes in speed (velocity) of flows will vary along different sections of a hull. Navier-Stokes equations can approximate rates of fluid flow over boat (or sail) segments. Obviously, faster flow with less friction results in a more rapid yacht.
Complex differential equations can be used to model relationships between velocity, pressure, temperature and density in moving fluids. In designing a yacht, the ultimate purpose is to develop shapes and balances that allow it to slice rapidly over seas. This entails not only generating an efficiently designed hull, but figuring out where to locate masts and sails, and how to distribute interior weights.
To do this, computer software generates multiple ‘simulations’ of flowing air and water. These help determine how much power a sailboat needs, how it will act in waves and how structurally strong portions of the craft must be. Such simulations—many of which utilize Navier-Stokes—are based on the field of study and application known as 'computational fluid dynamics,' or CFD.
Consider this: In the 2017-2018 Volvo Ocean Race, after sailing 20,550 nautical miles over a period of more than three months from Alicante in Spain to Hong Kong (equivalent to sailing three and a half round-trip voyages from Saint Malo in France to Newport, Rhode Island), the time difference between the top two contenders—Dongfeng and MAPFRE—was only 7 minutes and 29 seconds. That’s the amount of time it takes to hard boil an egg.
(One reason for this temporal proximity was that all boats in the race were designed by the same manufacturers to identical specifications; differences in speed were therefore—theoretically—due to each crew’s navigational prowess.)
Back to that equation.
Many equations relating to fluids work best not in popping out the simplest first answer, but in providing an approximation that improves the more times the equation is run. This method is called 'iterative,' which basically means repetitive. Repetition takes time. Not only that, if you want to design a rapid yacht, you desire information not just about a single point on its hull, but perhaps a million points. (The more data—used appropriately, the more accurate and precise your final design.) This need for both iteration and for analyzing multiple data points requires serious computational power.
Designing a modern yacht using CFD can require hundreds of computer cores running for weeks or months at a time. The process—obviously—also requires experienced engineers setting up and coordinating each operation. Because time, precision, equipment, talent and experience all add to costs—this process is not inexpensive.
Two sister companies that design some of the fastest yachts on the planet are based in Valencia, Spain. The company Juan-K Naval Architects and associate company JYDCFD (run by Juan’s brother, Gonzalo) depend on a suite of CFD and other programs—some licensed commercially—to provide yachts with a competitive edge. JYDCFD was launched in 2007, after its founders pioneered CFD methods to design the 70 foot (21.5-meter) ABN AMRO 1 yacht that won the 2005-2006 Volvo Ocean Race. They later designed the Perpetual Loyal, a 98-foot (30-meter) winner of the 2016 Sydney-Hobart race.
To perform computational work, JYDCFD owns more than 500 computer cores—each capable of running independent processes. (A central processing unit, or a CPU, typically includes several cores.) This assembly of cores forms what is known as a cluster, which is housed in a temperature and noise-controlled facility. Using multiple computer cores to run calculations is known as High Performance Computing (HPC).
Gonzalo Kouyoumdjian is the Chief Executive Officer of JYDCFD. (An article about his brother Juan and the company Juan-K Naval Architects is here.) Gonzalo and I met some months ago when he was visiting Bordeaux on vacation to sample wines. He shared reasons why their companies maintain strong reputations.
(The word 'appendage' relates to appendices and protrusions that stick out of a boat's hull, such as a dagger board or keel.)
We were pioneers, and we want to keep developing our capabilities, to stay ahead. In comparing differing features in hulls and appendages, sometimes differences are quite subtle. To quantify which is best and worth keeping, we need to be able to simulate with a certain accuracy. I think this is where we are better than competitors.
The first step in designing a yacht is generating a conceptual ‘geometry’ based on information from a database. Meaning: let's figure out the general shape. Historical data, assembled by an experienced engineer, will help determine the ultimate shape of a hull and help identify where to place masts. Next, geometries are broken down into a series of components represented by a ‘mesh.’ This mesh is digitally represented within a computer by perhaps tens of millions of different points, known as 'cells.' Similar to how strings of bulbs outline the shape of a Christmas tree, a mesh of cells encompasses the geometry of a ship. For any specific design, an appropriate mesh density is first determined by experts based on experience: this decision is crucial, because it involves a trade-off between desired accuracy and final costs.
Gonzalo stressed the importance of such accuracy.
From the very beginning we have focused on accuracy. We have always been on the side of using more time and being more precise, rather than making fast calculations with less precision. We are quite meticulous.
Designing a yacht requires looking at two fluids—both water passing over the hull, as well as wind slicing over sails. Because of this, hull and sail geometries are generated separately and subjected to individual hydrodynamic and aerodynamic simulations. Specific parts of a yacht—such as the hull or appendages—are individually simulated for improvement over a period of perhaps several months. The results are then sent to a shipyard, where the yacht is physically fabricated.
Gonzalo works with Patrizia Izaguirre-Alza. This sailor and mother has a PhD in Naval Architecture and Marine Engineering. Patrizia is responsible for the day to day running of CFD simulations. She spoke with pride about her work.
Mostly the projects we are involved with are high performance boats, and we want them to be the best. We have a huge database, programs, and knowledge from many years and projects. We have a lot of information about high performance boats we simulated that are now sailing, and winning.
What gives me satisfaction is to touch the hulls and appendages afterwards in the real world. I’m an engineer and love what I do. Boats measure 20 or 25 centimeters [8 to 10 inches] on my computer screen. But then I’m able to go to a shipyard or yacht club and touch what I’ve been working on for two or three years, and see the client who says thank you very much—because they are satisfied, and are winning races. That’s the best thing.
Coordinating the computer clusters for JYDCFD is Richard Ems, from Buenos Aires in Argentina. Richard first calculated the cooling requirements of the custom building that now houses 500 computer cores. On a daily basis he ensures that dozens of terabytes of data remain organized and accessible. He spoke about the joy of efficiency.
We should be using our brains for thinking, not just clicking on computers. So, I try to program everything that can be automated so it runs faster. Satisfaction comes from investigating where any problem is, finding it, solving it so computer users can continue working, and providing a solution so that it does not happen again.
Assisting Gonzalo and Patrizia is Rafael Carro—rock climber, surfer, and naval engineer. Rafael spent summers sailing off the coast of Tenerife in the Canary Islands while growing up. This influenced his eventual career choice.
What we are doing here is at the forefront of research. Now we are trying to go from more static problems to more dynamic problems with boats that ‘fly.’ That’s super challenging and motivates me.
‘Flying’ boats basically spend a critical bulk of sailing time with most of their structure elevated out of water. This is advantageous because moving a craft through air instead of water means it encounters less resistance, thereby reducing travel time.
The scope for CFD goes beyond sailing. It is used in other maritime fields that include analyzing impacts of ocean waves on container ships and drill platforms. Outside the maritime world, CFD is also used by aerospace industries, in the design of building ventilation systems, for combustion analysis and within the field of environmental engineering.
The next time (whether in person or on screen) you see a gorgeous, sleek, handsomely designed yacht zipping to victory, consider that the physics and mathematics underlying its prowess originated before the proliferation of fiberglass or carbon fiber hulls, before nautical radio existed and when it took six weeks to cross the Atlantic Ocean by ship.
Although it may receive little media hype, the technology of transportation is rapidly delivering larger and more complex yachts with improved speeds and comfort. It also delivers, from time to time, victory.
