Friday, July 24, 2015

Surfboard Calculus

Surfboard Calculus
By Mike Black

Surfing is a massive part of our lives. My ideal weekday involves surfing in the morning, working through the afternoon, and ending with quality family time. Regarding work, I get paid to solve math problems. My B.S. in Math and my Master of Arts in Pure Math from the University of California set that path for me decades ago.  Often as the morning colors go through orange, light blue and violet, I find myself staring at the horizon waiting for a wave, thinking about math since it’s what my day will be about.

It was one of these mornings that the seed for this article was planted. I wanted to hear what contribution surfboard shapers and surfers from around the planet thought mathematics has made to surfboard design. The responses were varied.

In the late 70’s shaper and engineer Bill Barnfield was keeping track of numbers like length, thickness, width, and rocker. Rusty Preisendorfer of Rusty Surfboards said Bill was tracking ten or twelve numbers. Bill taught Preisendorfer the importance of tracking numbers. Preisendorfer said about his shaping before the use of machines: “I was tracking 30 or more points per board. This ensured consistency. I started getting more consistent positive feed back.“ The more points he had to hit, the more accurately he could reproduce his curves. Preisendorfer continues: “One thing that still needs some basic math skills is scaling the boards up and down. Volume is a wonderful tool. The only way to get that number before software was with a displacement tank. I don’t know of any shaper that went to the trouble to build one. Volume is a number that everyone tracks now.” 

Volume plays an important role in surfboard design. Australian Andrew Kidman was telling me about a software program: “…a friend of mine that uses computers to make his boards takes his customers’ weight and then somehow figures out the volume they’ll need using some program he has.“ I responded: “I wonder what that software is doing. How do other design elements contribute to that volume number? For example, what would the difference in volume need to be for a finless board designed for a 180-pound guy compared to a single fin or twin fin. I'm interested in the input variables and the algorithm. I’m guessing it's a regression deal. I suspect the algorithm was fed data based on surfboard designs that were known to work but I’m not sure. So the programmers put in the plan for the latest zip-zang model, then I go to order it and the machine beefs it up to compensate for my plumpness. Does this increase in volume represent a true proportional increase in every element of the shape? Or does the volume just show up in some elements of the shape? If the increase in volume isn’t proportional throughout every design element, won’t the board be different than what it was intended to be? “

This exchange Andrew and I shared was insightful, but off the mark somewhat. We are saying volume, but in this case we probably should have been saying something else. A cube that is 10’ by 10’ by 10’ has the same volume as a 3D rectangular solid that is 1000’ by 1’ by 1’. Clearly they are different shapes.

Volume, like any design element, is practically impossible to discuss in isolation. Two boards of equal volume can ride completely differently. In an example of length, my 10’ pig rides WAY differently than my 10’ Simmons replica.  That’s where other dimensions of surfboards come into play.

I asked Richard Kenvin the project director of Hydrodynamica what he thought about math and surfboard design, he wrote me a quote: ‘I went over to Simmon’s place. He had all these equations written everywhere. It looked like Chinese! –Dale Velzy’ A quote instead of an original thought surprised me given the content on the Hydrodynamica website.

Manuel Caro of Mandala Surfboards loves the book The Power of Limits: Proportional Harmonies in Nature, Art, and Architecture. This book provides examples of objects that fit the golden ratio. The golden ratio (defined as a proportion) is sometimes called Phi, a math term that represents two fractions that are equal. These fractions are built using two positive numbers, a small one, and a large one. The first fraction is the large number over the small number. The second fraction is the sum of the numbers over the large number. It works out that the large number is roughly 1.61803 times greater than the smaller one.  According to this book, if one is optimistic and keen to stretching their imagination, many naturally occurring (or man-made) objects can be thought of as fitting the golden ratio. “There’s always math underlying beautiful design, both natural or man-made.” Says Caro. “As far as mathematics is concerned, beyond the normal and obvious methods of measuring boards in terms of feet and inches, there are relatively few people using any ‘real math’ in design. I know I’m not.”

South African Donald Brink of Brink surfboards feels similarly: “Sure there are some rudimentary measurements and tasks of arithmetic involved for building a board or producing consistent results.“

Ryan Burch of bobbersandsinkers; who is mentioned on Hydrodynamica’s website had this to say regarding mathematics’ contribution to surfboard design: “I don't use math when I'm shaping except for when I'm trying to scale boards down just to get accurate proportions.  I never even got to calculus in school. As far as math contributing to design, I'm not too sure what others do, but it doesn't do shit for me. “

Australian mathematical thinker and surfboard shaper Pieter Stockert, figures the less tools one has in their shop the more they have in their head. He talks to a person and figures out what that person needs. He has different rail templates measured to the millimeter that have been proven through the years to be right for most people. These rail templates define the thickness each board will end up with. There are exceptions. Rarely, someone’s skill level might cause deviance from the rail template to board thickness relationship. Pieter has a continuous curve profile template that he is able to use on boards from five to eight feet. This curve was built from Pieter keeping an eye on the boards that guys (pros) brought back in the shop and said performed well. He found that these boards had an eight and a half meter radius curve on the bottom surface of the board by the tail. According to feedback from Pieter’s team riders, a surfboard with this curve won’t loose speed through the cutback.

Pieter is defining mathematics as  “human beings measuring something like when we figured out the calendar, that there is repetition and so forth.”  Pieter believes the shaping machines with all their liter calculations are rubbish. Pieter feels the machine can’t do one millionth of what a human brain can do. The shaper talks to the client and figures stuff out, the computer is just a zeros machine, a bloody copier that spits outs copies for a couple of cents each. Contrast this to a proper surfboard designer and shaper: he is making all those calculations in his head to make sure the surfer gets the best board they want.

Adrian of Fluid Juice Surfboards from Cornwall said the following regarding math and surfboard design: “An interesting little anecdote that gets people thinking is the fact that the very first board that an ancient Polynesian islander made was probably all guesswork but you could pretty much guarantee that the second one was compared to the first in which case the first was effectively used as a unit of measurement so the second board was the product of feedback and measurement, in other words, science and maths.”

Rob Wright of Slide 65 out of the United Kingdom says about mathematics and surfboard design: “For me when I am hand-shaping, mathematics allows me to replicate a shape accurately. I have figures for the outline shapes and more importantly, the rail banding which is critical to the board’s foil and functional volume. Thickness measurements at the nose, tail and centre give me accurate reference points for replication. Once I have roughed the blank out using figures I then shelve the mathematics and take on the role of sculptor. This is where the figures are blended and the board comes alive. I see my hand shaping as a combination of figures (mathematics) and sculpting. Without the figures replication would be impossible.”

Ricardo Muniz shaping RickyMuniz surfboards out of Puerto Rico said: “I only involve math when I get specific about measurements regarding templates or rocker of a specific shape or model. There is no equation or technical mathematical analysis that helps me define those curves. Most of the process is more of a creative and artistic nature; like sculpting.”

Ryan Lovelace out of Santa Barbara, Ca. mentioned the boat designers when asked about math and surfboard design: “…the main users of the number game are guys who look after boat design generally, as boat hull design has drawn heavily from math over its history.”

Ricardo Muniz echoes Ryan Lovelace’s statement: “After reading a lot about physics of sailing and hull design I can say that in the boat design industry mathematics has contributed a lot to the design process, development and maximizing performance of sailing and motorboats with technical mathematical analysis.  In contrary to that, surfboard design I think has come more from the soul than from mathematical analysis. Backyard shapers and professionals alike work mainly on the power of feeling and observation, and by keeping notes and template reference of what has worked and what didn't.” 

Dr. Lindsay Lord author of the famous book regarding math and boat hull design: Naval Architecture of Planing hulls, demonstrated how a boat’s performance can be modeled in a laboratory and how you can modify isolated elements and observe the results. You can apply physical principles and feel confident the theory matches the end product. Boats have a throttle; Kelly Slater and I push a throttle forward similarly. Surfboards don’t quite fit this idea of modeling. There are general design principles that are true: flat is fast, wide is stable. However, a magic board for me might or might not be a magic board for you. Consider a surfers stance. Each surfer has a different stance, height, and each carry their weight differently.  Along with other variables this affects a riders’ center of gravity.

Dr. Lord assumes a non-variable static load with force coming from one direction (other than the force of gravity, and the opposing force of buoyancy). How many directions does force come from when we are surfing? A surfboard is built around the function it serves. Customers seek out shapers that build boards that have a reputation for functioning a certain way. If Kelly Slater and I are the same height and weight, I am not guaranteed to surf his board the same way he does. Skill is yet another random variable that throws us off Dr. Lord’s trip.

Dr. Lord’s entire book is not off the mark regarding surfboard design. Dr. Lord states: “It was axiomatic that there could be no ‘best’ boat, only best compromise”. This is something that seems to be directly applicable to the surfboard design paradigm.

Two boards identical in every aspect except fin placement or fin shape will ride completely differently. I can test a fin in a water tank all day long. I can publish results claiming some advanced design leading to improved functioning. What meaning do those results have outside the laboratory’s specific conditions? Each surfer has a different stance; every wave is different outside a lab. This idea is relevant beyond fins. Recall my statement regarding volume and length. How many variables would it take to map surfboard design? How many differentials are there between these variables? A differential is a method of recording the change in a mathematical function with respect to one variable. The entropy that occurs when the concert of design elements play is the challenge a computer savvy surfboard designer has with mathematical modeling.

Consider a surfer’s speed on a wave. My Simmons feels way faster than my pig, and my Simmons has more extreme rocker. This seems to contradict the basic fact: flat is fast. The key is the idea of “feels”. Once someone starts telling me numbers corresponding to their speed on a wave, all I hear is white noise. Distance divided by time equals speed. According to this definition of speed, when I’m surfing a standing wave, my board has no speed. When I surf a point break, my board goes fast. Both experiences left me “feeling” like I was going fast. How could we possibly model something with mathematics if we can’t even accurately measure results?

Most shapers asked mention the idea of math being a tool to ensure consistent results. There is no doubt that math is used in surfboard design. Anyone that orders a board has undoubtedly said a number in the description of the board to the shaper they were ordering from.

It is bizarre when one looks at board and “knows” how it will ride. If you know how a board is going to ride by looking at it, then it must also be possible to predict how that board will ride by looking at some spreadsheet of numbers. The question remains, is there some mathematical function (Riemann, Euler, trigonometric, partial differential or other) that can fuel an algorithm to fill the spreadsheet with numbers that define the perfect mathematical surfboard? Can an equation dictate design? If there were some mathematical equation that gave birth to some shape, what would the shape be? Would the board have fins, would it be flexible, would it be symmetrical? How much would it weigh? What would it be made of? Would it take you different places on the wave than our current boards? What could cause us to believe that this equation is the beginning, middle, and end of all “proper” design elements? How does one quantify proper surfboard design?

Dr. Lord addresses the issue regarding a mathematical equation defining design quite eloquently: “There have been serious attempts to generate hull lines by mathematical formula, but for practical purposes it is evident that the merit of such procedures lies very largely in the resulting similitude for duplication in other sizes according to whatever shape was first worked out, rather than in achieving any possible virtue inherent in a mathematical formula.”

Greg Noll said it best when he said: “Here is how you build a good board. You build the damn thing. If you like it, it’s a good one, if you don’t, it isn’t”. Brian Hilbers updated that quote in the following way: “Here is how you build a good board. You build the damn thing. If you like, it’s a good one, if you don’t, it isn’t a good one for you.”

It is beautiful when an experienced surfboard designer navigates through what seems like a mathematical nightmare so effortlessly. All the chalkboard scribbling in the world won’t top time in the water. Matt Calvani has designed many surfboard models that work in a variety of conditions. Although mathematically modeling surfboard design might be impossible, functional designs continue to be developed. Does this make surfboard design more of an art than a science?

Mathematics, the science seemingly shrouded in mystery, is definitely a trendy way to advertise a surfboard. Mathematics is not some wizard science reserved for mousy geeks studying under fluorescent lights. It’s clear logic. A surfboard isn’t some 3D mapping of a mathematical function. It is from the hand and mind of a human. Sure a surfboard can be drawn on a computer, but that drawing is not the result of any one mathematical function (equation).

Few people interviewed diminish the importance of Mathematics and surfboard design, all thought it was necessary. One thing is certain; the surfboard has grown organically, not algorithmically. Surfboard Calculus: Ride it. If you like it, it's good.