Dear EASD community,

In the never ending EASD quest for unique knowledge and experience in surfing medicine, we connect state of art sciences. This effort is a key step to the EASD product development program, based on medical and scientific knowledge.

The global surfing community has so many talented people. Right across this community we find unique characters, supporting the EASD. We call these special persons “The EASD Scouts”. They are neither MDs nor Allied Health Professionals (AHP), but they are professionals in other topics, like physics for instance.

It is our pleasure to present the second article from our fellow scientist, physicist, and author Chris Woodford, who has worked out an interesting article for scientific and non-scientific viewers explaining the energy and power in the waves we love to ride. In doing so he has touched a medical topic related to surfing, Trauma. Trauma will also be one of the topics at The EASD Conference 2015 in Anglet/Biarritz, leading to great discussion and knowledge exchange. The international scientific effort on surf trauma is progressing. We are excited to hear more state of the art knowledge on this topic from our vast community of Surfing Doctors at the coming Conference from the 29th Septembers until the 2nd of October 2015 in Pays Basque, France.

See you in the water,

O. Markovic

EASD Board Member | Outreach, Sponsorship, Education


“Motion in the ocean: the energy in waves”

By Chris Woodford

Blame the Sun. When you fail to take off or painfully wipe out. When you wake up the day after a stunning surf, horribly aware of muscles you’ve not seen since med school. When (much less luckily) you strain your back or break your leg and have to spend gloomy days or weeks watching from the shore. Blame the Sun for all your surfing-related problems—because that giant nuclear fireball, 150 million km (93 million miles) away, is surely to blame.

Like almost everything else on Earth, surfing is solar-powered: the energy that shoots you over the sea comes indirectly from the Sun. And what a lot of energy beams our way: theoretically, up to 1000 watts of solar power per square metre of land.[1] But the interesting thing is not where this energy comes from, but where it goes. Earth’s lopsided tilt means the planet cooks unevenly in sunlight, like a spit-roasting joint we’ve stupidly propped at the wrong angle. The tropical bits can blacken and char to the point of forest fires while the polar caps (for now, at least) stay locked in ice. Because energy likes to even itself out, Earth has a turbulent atmosphere and an equally dynamic ocean. And where the howling winds meets the tumbling water, we get waves. Lots of waves.


Credit: Waves: Woodcut by Konen Uehara (1878-1940), courtesy of US Library of Congress, Japanese Prints and Drawings Collection (public domain).

What are waves anyway?

You know the answer to this question both in theory and in practice. In theory, because you can still remember flipping through the pages of your old school textbook: amplitude, wavelength, and frequency—those are officially the measure of waves. Now you’re older and a surfer, and you spend a significant part of your life bouncing up and down the sea surface, waves mean something different: breaking waves make your day. They’re no longer two-dimensional scientific abstractions—wiggly black lines drawn on white paper—but colourful, three-dimensional memories, vividly tied to places and times, burned in your memory till the day you die. Every science book explains waves the same way: as energy in motion, shooting from place to place while the medium (water, air, or whatever it might be) goes nowhere. But every surfer—even every beach-bound wave watcher—knows better than to reduce practical waves to a simple theory. Because, in glorious surfing reality, every wave is slightly different from every other wave that has ever broken in exactly the same place.

The waves surfers care about happen at the interface between the atmosphere and oceans, although they’re not the only waves you’ll find in either the air or the water. High above your head, there are waves shooting through the sky; that’s one of the reasons you’ll sometimes see cool, repetitive patterns formed in clouds (instead of the random lumpy cotton-wool you might be used to).[2] There are also waves that travel deep underwater, never breaking the surface, never kissing the board of a single surfer, but—intriguingly—often visible from high up in space.[3]

How do waves form?

We all know the simple answer is “when the wind blows across the sea”, so the energy that was in the air is systematically transferred to the water. But how does that transfer take place? Is it like slowly running a knife over butter, when that nasty, yellow, artery-clogging fat magically springs into a curl? Is it like stirring a cup of coffee, except with friction from the wind dragging the water surface and tugging it along? Or brushing leaves off a garden path, where you slowly heap the water into a pile? It’s not hard to think of all kinds of ways the wind might stir up the water—but what does the science say?

Credit: Wind makes waves, so it's no surprise that the biggest waves are in the windiest places. This image of wave heights around the world was snapped from space by the TOPEX/Poseidon satellite in 1992. The red and yellow areas show that wave hotspots occur in places like the Roaring Forties where the winds are strongest. Photo courtesy of NASA Jet Propulsion Laboratory (public domain).

Credit: Wind makes waves, so it’s no surprise that the biggest waves are in the windiest places. This image of wave heights around the world was snapped from space by the TOPEX/Poseidon satellite in 1992. The red and yellow areas show that wave hotspots occur in places like the Roaring Forties where the winds are strongest. Photo courtesy of NASA Jet Propulsion Laboratory (public domain).

Imagine the surface of the ocean is flat and glassy with not a wave in sight. Peer close enough and the water-air interface you see is no different from the mirror surface of a pond, where cunning insects float and scamper on invisible skin. Water has surface tension, just like a drum, and if you deform it slightly, the pulling force between neighbouring water molecules will spring it rapidly back again. Closely related to capillary action (the power that pumps water up trees or blood through capillaries), this is the first key bit of science in a glorious sequence of events that builds the waves for surfing. Because as the wind starts to blow over water, it creates minuscule ripples called capillary waves, barely a millimeter high. The water’s own elasticity—surface tension—tries to destroy them immediately by tugging them back into place.

But with a steady wind blowing, it’s already too late: the water surface is roughening up. Now friction kicks in and the wind can get more of a grip, systematically building up the ripples to make wind chop and swell that will eventually clean itself up into perfectly formed surf in a voyage that could last hundreds or thousands of miles. Once waves grow beyond capillary size, surface tension can’t stop them. Now they’re at the mercy of the most persuasive long-range force in the Universe: gravity. Where surface tension does its best to rid the ocean of puny capillary waves, gravity is responsible for wrecking every surfer’s fun by cleaning away the bigger waves: it’s the force that determines the life and death of every ocean wave as it constantly tries to smooth out the sea.

Waves without wind

Ocean waves happen when there’s a big enough input of energy to deform the water surface. Water’s dense and heavy stuff, don’t forget: a mere litre weighs a kilogram. Lifting a wave’s worth of water a metre in the air, across the entire width of that wave requires a massive input of energy and force (we’ll do some simple calculations on that in a moment). Wind supplies the energy slowly and systematically and if you’ve got something like a hurricane to hand, feeding energy to the waves over days or weeks, you can certainly lift enough water and accelerate it fast enough to generate some spectacular swell.


Credit: Pacific nuclear tests were a particularly unnatural way of making waves without wind. In 1946, as part of Operation Crossroads, the Baker Test at Bikini Atoll detonated a nuclear bomb 27m (90ft) underwater, producing a giant water column powerful enough to sink the USS Arkansas. Watercolour by war artist Grant Powers courtesy of US Naval History and Heritage Command (public domain).

But that’s not the only way to make waves. Tsunamis, usually set in motion by underwater earthquakes, cause what used to be called tidal waves by adding vast amounts of energy to the ocean in a matter of seconds. The water surface is dramatically deformed; gravity tries to restore it—and that process gives an outward transport of energy we see in waves. Explosions at sea can make smaller tsunamis. In December 1917, an accidental detonation onboard an armaments ship in the harbour at Halifax, Nova Scotia thundered out what was then the world’s biggest explosion (3000 tons of TNT), rumbling 10m-high (30ft) waves out across the sea. The atomic bomb tests that happened in the Pacific, between the end of World War II and the early 1960s, were thousands of times more powerful (equivalent to megatons of TNT).[4]

The biggest waves ever recorded on Earth have been caused not by hurricanes, tsunamis, or nuclear bombs but by rocks impacting the sea. In 1957, a giant rock-fall at Lituya Bay, Alaska dumped an estimated 90 million tons of cliff into the sea, creating waves accurately measured (from marks left on the land) to be an astonishing 530m (1750ft) high. According to geologists, the biggest wave that’s ever happened on Earth was caused by a meteorite smashing into the ocean around 65 million years ago, producing the world’s most impossibly unsurfable wave, a staggering 914m (3000ft) high (over twice as tall as the Empire State Building). Try that for size, Kelly Slater! [5]

A swell party

If you’ve ever played at making surf in your bored, Sunday afternoon bath-tub, by flipping your hand back and forth in the water, you’ll have figured out that there are three ways to make bigger waves: you can flip your hand faster, further, or for longer. The wind in a storm zone works exactly the same way when it’s making waves. If it blows faster, longer, or over a greater distance (technically called the fetch), it creates bigger waves. Why? Because bigger waves need more energy to create them (you have to lift more water up against the force of gravity, for one thing) and a faster wind blowing for longer, or over a bigger area of sea, is the way to get that energy into the water. That’s one key reason why open coastlines are so much better for surfing. The best surfing in England happens on the exposed north coast of Cornwall and Devon, in places like Newquay and Croyde, because wind-borne waves arriving there have had an opportunity to build power and clean themselves up as they thunder across the Atlantic: the fetch is much greater. On the South Coast of England, the fetch is limited to the relatively puny distance between England and France so the waves are rarely so good. The simple rule is that it takes energy, time, and distance to make great surf. The 6m (20ft) waves that delighted southern California’s surfers in August 2014, courtesy of Hurricane Marie, had had 1300km (800 miles) to get their act together.[6]

That begs another interesting question: just how big can waves ever be? If a hurricane blew for weeks or months over a long enough fetch of open water, would we get ridiculously big waves? “Yes” is the simple answer, but there’s still a scientific limit to how much waves can grow. Like houses of cards, waves are unstable structures that gravity is determined to collapse, sooner or later—with the added complication that they’re moving in the turbulent interface between the atmosphere and the ocean. Seven decades of oceanographic research has determined that waves don’t build beyond a certain steepness: the ratio of their length (measured between one wave crest and the one following behind) to their height (measured from crest to trough, or maximum to minimum) can never be more than seven to one. Waves break on the shore when the rising slope of the beach (or reef) increases their steepness beyond that critical ratio; out in the open ocean, the same limit applies, and we get white horses (white caps) forming as gravity forces excessively steep waves into premature collapse.

In practice, when the wind blows across the water in a perfect-surf-creating storm, we reach an equilibrium. The wind keeps on adding more energy to the water, but the waves keep collapsing. At this point, we have what the oceanographers call a fully developed sea. The waves are as big as they’re ever going to get. All they have to do now is get themselves to the shore, where the surfers are waiting.


Artwork: Skill in the Surf, published in February 1945, was one of the world’s first surfing manuals—aimed at troops “surfing” to the shore in landing boats. You can read the fascinating document in its entirety courtesy of the The Naval History and Heritage Command (public domain). Most interesting to surfers is Chapter 1X, Where the Sea Meets Land, which describes the tactics of making a military landing through surf.

The birth of surf science

Surfing is essentially a 20th-century invention, and so is surf science. But who first had the idea to turn the wonder of waves into a scribble of maths—and why?

Just as the wetsuits I explored in our previous article were essentially a Navy invention, so surf science owed its birth to military manoeuvres. As Stephanie Pain recounts in a fascinating popular science book called Farmer Buckley’s Exploding Trousers: And Other Odd Events on the Way to Scientific Discovery,[7] the pioneers of surf forecasting, Norwegian oceanographer Harald Sverdrup (head of the famous Scripps Institution) and his young American student Walter Munk, figured out how to predict wave heights from the wind speed, fetch, and duration while working for the US military during World War II. Fortunately, they also had loads of data to test their theory and quickly honed their equations enough to make accurate predictions. Although no-one knew it at the time, this crucial work was used by the Allied forces to select the best days for the famous beach landings. It was first used to pick a calm day for an assault on North Africa on 8 November 1942 and, subsequently, for the D-Day landings in Europe in June 1944. Surfing science, in other words, changed history.

Sverdrup and Munk completed their work in 1943, but it remained classified until after the War, finally appearing in March 1947 as US Navy Hydrographic Office Publication Number 601, “Wind, Sea, and Swell: Theory of Relations for Forecasting”. Later refined and extended by Charles Bretschneider, the revised theory became known as the SMB (Sverdrup, Munk, Bretschneider) model. Though it’s only a basic explanation of how wind makes waves, it’s still widely referred to today, especially in simpler articles like this, but it’s now been superseded by decades of more detailed research. If you’re interested, check out the more detailed explanation in Tony Butt’s excellent Surf Science book (see Further Reading below).

How much energy is there in waves?

That’s a fascinating question with all sorts of answers, ranging from the dreamily poetic (like the Japanese woodcut that opens this article) to the studiously scientific. It’s worth quantifying the energy in waves for all kinds of practical reasons. From an environmental point of view, it tells us how feasible it is to build things like renewable wave-energy systems—and whether we can harvest more energy from the hidden heat in ocean water (the temperature difference between the ocean surface and its depths) than from its mechanical energy (the back-and-forth, up-and-down movement of water caused by tides and waves). From a surfing point of view, asking this question tells us exactly which waves are rideable and what you can do on them. Everyone knows you can’t catch a small wave on a surfboard (or even a boogie board)—and the simple scientific reason for that is that a rideable wave needs to contain a minimum amount of energy to lift your body against the force of gravity and accelerate you to its own speed.

It’s also interesting to ask the question from a medical-physics point of view: the force that breaks a surfer’s bones or mashes her muscles comes from the energy hidden in a wave. Is there really enough energy in a typical wave to do that much damage?

Go figure

Let’s try to guess-timate how much energy there is in a medium-sized wave crashing down on top of us as we stand in the surf. I must emphasize that this is “back-of-the-envelope” physics and not in any sense rigorous or correct oceanography. It’s what’s technically referred to as “just a bit of fun”! I’m not going to attempt to use the complex equations that are really needed to do this properly, but if you want to have a go, I’ve given some pointers in the references down below.[8] For now, let’s see how far we can get with the kind of basic science we learn at school.

We know the total energy is the sum of the wave’s kinetic energy (because the water is moving) and potential energy (because the crest is lifted up above the mean water level). Let’s not get too bogged down, though: let’s simplify everything as much as we can to the point of basic, school-level physics.

Picture5Suppose we have a 1m width of a wave that closes out completely, with the water coming to an impossible, screeching halt (so effectively it loses all its kinetic and potential energy when it breaks). According to Willard Bascom (one of the founding fathers of surf science), the speed of a decent surfing wave is about 40 km/h (25mph or 11 m/s).[9] For easy sums, let’s assume the wavelength (the distance between one wave peak and the next one) is 2m and the amplitude (the height of the wave) is also 2m, so the volume of water above the mean sea level that we’re interested in (the dark grey bit in the figure I’ve drawn here) is roughly 1 x 1 x 0.6 = 0.6m3 = 600 litres, which weighs about 600kg. Simplifying very greatly indeed (I know, I know… but bear with me), that gives us potential energy of mgh = 600 x 10 x 1 = 6000 joules and kinetic energy of ½mv2 = 300 x 11 x 11 = 37,000 joules, making a grand total of about 43,000 joules—or call it 50 kilojoules to keep things simple. This is a rough estimate of how much useful (non-heat) energy there is per metre of a simple breaking wave—and the actual value is likely to be less than this because of all the simplifications I made (a real wave isn’t this steep; it doesn’t stop completely when it breaks; it has an ever-changing, irregular volume; its total mass is not all concentrated at exactly the same height; and so on—this is back-of-envelope, guerilla physics!). Remember that this is the energy in a single meter width of water—so a stupendous wave shattering into sand across 1km (0.6 miles) of a bay could theoretically deliver 1000 times more energy than that: a wave like that breaking each second could theoretically make 50 megawatts of power (equal to about 25 very large wind turbines).

How accurate is my guesstimate? I’ve seen a few textbook estimates of the energy in waves that run between 10–100 megawatts per kilometre of shoreline [10], so even if my assumptions and calculations are extremely rough and ready, my final figure isn’t too bad. Shore-mounted wave energy harvesting devices (which work by using the wave’s energy to push a column of air back and forth past a turbine, making what’s called an oscillating water column or OWC) also quote figures roughly in this ballpark. The LIMPET wave energy harvester in Islay, Scotland can make a maximum of 500 kilowatts; a similar water column generator that operated in Toftestallen, Norway in the late 1980s managed 1 megawatt for three years until storm waves smashed it to pieces.[11]

Credit: Except for the A you provide with your own muscles, everything you can do on a wave is determined by the A that wave picked up on its way across the ocean. Photo of the Red Bull Rivals International Surf Competition, 2014, by Sgt. Derrick K. Irions courtesy of US Marine Corps (public domain).

Credit: Except for the energy you provide with your own muscles, everything you can do on a wave is determined by the energy that wave picked up on its way across the ocean. Photo of the Red Bull Rivals International Surf Competition, 2014, by Sgt. Derrick K. Irions courtesy of US Marine Corps (public domain).

Catching waves

Do the numbers tell us anything useful? Suppose you weigh 70kg (not including the weight of your board). If you want to travel at 40km/h (11m/s), you need kinetic energy of ½mv2 = 35 x 11 x 11 = 4235 joules. To ride a meter above the ocean surface, you’ll also need potential energy of mgh = 70 x 10 x 1 = 700 joules, so you’ll need about 5000 joules of energy altogether. Let’s say it takes you 5 seconds to catch the wave. The power your muscles and the wave need to supply for you to start surfing is the total energy needed divided by the time it takes, so that makes an average power of about 1000 watts to reach 5000 joules in 5 seconds—as much as a typical clothes washing machine. Could you get that from a 1m wave? Maybe yes, maybe no. My estimate of about 50 kilojoules was for the total energy in 1m width of a wave, which sounds like it’s 10 times more than enough—but, remember, you wouldn’t get all that energy from the wave (it keeps moving and doesn’t break) and you’re not tapping into a 1m width of water (maybe only the width of your board).

Kids, lucky things, can catch smaller waves than adults because they weigh about half as much and they can accelerate faster. The potential and kinetic energy of a surfer are both linearly related to body mass, so if you have less mass, you need correspondingly less energy—making it more likely the wave will sweep you along. By the same token, if a wave is big enough, you can (theoretically) surf it in or on whatever you like. Willard Bascom’s classic book Waves and Beaches has an amazing photo of him surfing a 4m (12ft) plunging breaker behind the wheel of an amphibious Dukw truck weighing around 5.5 tonnes (6 short tons).

How exactly does paddling help? If you’re paddling as you catch a wave, you’ve already given your body a certain amount of kinetic energy and momentum, so any oncoming wave has to provide you with less of the total energy you need to get moving: paddling, put very simply, gives you a head-start in terms of kinetic energy and momentum. It doesn’t help you with potential energy: unless you’re lying prone on a bodyboard, you’ve still got to get upright!

What about medicine? Does the physics tells us anything useful about that? From the viewpoint of materials science, bone is a material like any other: it has its limits, and it will fracture when you subject it to a certain amount of force (powered by a certain amount of energy). I’ve seen various estimates of the kind of force required to break bones—and it obviously varies according to which bones you’re talking about, the age of the person involved, the nature of the impact, and how inconvenient a trip to hospital would be right at that moment. But let’s do some more school-level, back-of-the-envelope scribbling and see what happens. Isaac Newton’s famous second law of motion (the one that says soccer balls accelerate when you kick them) tells us the force a breaking wave delivers is equal to the rate at which its momentum changes (so, mathematically, F=ma or F=mv/t). If we return to the same breaking wave we looked at a moment ago, we know m (600kg) and v (11m/s) so let’s guess that the wave breaks in 1 second (for super-easy sums). That tells us the force involved is about 600 x 11 /1 ~7000 newtons. Enough for a fracture? Certainly. A quick bit of online searching suggests a ballpark estimate for the force needed to break a bone might be several thousand newtons.[12]

But different waves deliver very different force even if they contain the same amount of energy. Why? Think of sudden-impact car crashes, which hurt you much more than slower ones: cars are designed to crumple to slow down the impact, so your body feels less force and the chance of life-threatening injury is dramatically reduced. In exactly the same way, waves that break faster produce more force, which is why a plunging wave that closes out in a shore-dump is more dangerous than a wave that peels gradually across its width. Simple physics tells us why: if two waves contain exactly the same amount of energy but one breaks five times faster than the other, it can (theoretically) deliver five times the force (because F=mv/t and if t is five times smaller, f is five times greater).

9781472912220In the last article, we looked at the heat energy in the oceans and why you need to wear a wetsuit. This time we’ve looked at the energy in waves. In the next article, I’ll be looking at how waves travel over the ocean and form themselves into perfect surf.

Check out Chris’ new book!

Chris Woodford’s latest book, Atoms Under the Floorboards: The Surprising Science Hidden in Your Home, is published worldwide by Bloomsbury.

Further reading

The Wave Watcher’s Companion: Ocean Waves, Stadium Waves, and All the Rest of Life’s Undulations by Gavin Pretor-Pinney. Penguin Group USA, 2011. A wonderfully readable (completely non-technical and non-mathematical) guide to all kinds of waves we find on Earth, from Mexican waves and brain waves to the more familiar waves we find on the sea. Great relaxation for armchair surfers!

Surf Science by Tony Butt and Paul Russell. Honolulu, Hawaii: University of Hawaii Press, 2002. The most accessible introduction to surf science you’ll find. Very clearly illustrated and with a minimum of maths, this is the perfect starting place for surfers who love a bit of science.

Waves and Beaches: The Dynamics of the Ocean Surface (Revised edition) by Willard Bascom. Anchor, 1979. A classic introduction to the physics of moving water, this book covers the basics of how waves form and move, though topics like ocean energy and coastal defence also get a mention. Again, there’s very little maths here to bog you down.

Wind Waves: Their Generation and Propagation on the Ocean Surface by Blair Kinsman. Dover, 1984. This one’s for experts only. It’s somewhat dated, but well worth browsing, if only to convince yourself just how complicated wave science really is. You can browse quite a lot of it for free via Google Books (follow the link and click on the book cover).


[1]: Unfortunately, that doesn’t mean every square metre gets 1000 watts all the time: obviously, you have to be facing the sun! For a good discussion, see “Chapter 6: Solar” in Sustainable Energy Without the Hot Air by David MacKay. Cambridge: UIT Press, 2009, p.38.

[2] Kelvin-Helmholtz clouds offer the most obvious visual comparison between sky and ocean. Check out this great photograph at The Cloud Appreciation Society.

[3] Just as waves form at the interface between the atmosphere and the ocean, so they can occur at the boundaries between different layers of water deep beneath the surface. Check out this article and photo from the NASA Earth Observatory, which shows underwater waves spotted from the International Space Station!

[4] For a history of the world’s biggest waves, see The Sea: Tsunamis by Eddie Bernard and Allan Robinson (eds). Cambridge, MA: Harvard University Press, 2009.

[5] My accounts of the rockfall in Alaska and the giant Cretaceous tsunami were researched using “Chapter 8: Waves and Water Dynamics” in Essentials of Oceanography (Sixth Edition) by Harold Thurman and Alan Trujillo. New Jersey: Prentice Hall, 1999, p.244-245.

[6] Huge California waves attract US surfers. BBC News, 29 August 2014.

[7] “Chapter 8: War and Peace” in New Scientist: Farmer Buckley’s Exploding Trousers: And Other Odd Events on the Way to Scientific Discovery by Stephanie Pain. London: Profile, 2013.

[8] You can find a fairly basic—though typically unclear—introduction in the Wikipedia article on Wave power. That gives an estimate of 36kW per meter for a deep water wave well away from the shore. To see how complex this subject really gets, check out one of the classic books, Blair Kinsman’s Wind Waves: Their Generation and Propagation on the Ocean Surface, especially “Chapter 11 Energy considerations” (p.516).

[9] Waves and Beaches: The Dynamics of the Ocean Surface (Revised edition) by Willard Bascom. Anchor, 1980, p.241.

[10] Thurman and Trujillo (see note 5), figure 8–25 on p.270 gives a diagram of likely wave energy potential for different coasts around the world. Values range from about 10 kilowatts per metre (in sheltered areas) to over 60 kilowatts per metre for super windy parts of the southern continents (the south coast of Australia, South America, and South Africa) where wave heights routinely exceed 3m (10ft). That gives a broad range of 10–100 megawatts per kilometre.

[11] Renewable Energy: Sustainable Energy Concepts for the Energy Change by Roland Wengenmayr and Thomas Bührke. Weinheim: John Wiley, 2013, p.103. For a quick review of how LIMPET turns wave power into electricity, see Bath University’s Wave Power: LIMPET page.

[12] See for example Brute Force: Humans Can Sure Take a Punch by Charles Q. Choi, Live Science, 3 February 2010, which estimates 4000 newtons for the force needed to crack a rib.

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