Tuesday, July 01, 2014

Surfing

Jearl Walker www.flyingcircusofphysics.com

July 2014 What causes a surfer (on a surfboard) to move toward the beach or along a wave? Can you surf on top of the wave or on the backside? Here are two video examples:

http://www.dump.com/tallestwave/ surfing on a wave 26 meters high, a record

http://www.wimp.com/giantwave/ 21 meters high, beautiful

Here is what I wrote in *The Flying Circus of Physics *book:

In open water, far from shore, waves travel at identical speeds. However, near the shore, the speed of a wave decreases as the water depth decreases. Thus, when an ocean wave travels through progressively shallower water as it approaches a beach, the bottom of the wave tends to slow. The top of the wave does not slow and so it tends to outrun the bottom of the wave, causing the wave to lean forward. The height of the wave can also increase. If the wave simply collapses or surges, it spreads in the forward direction, becomes less high, and thus is useless for surfing. However, if the wave spills (the top outruns the bottom) or plunges (the top outruns the bottom so much that the top plunges over to hit the base of the wave front, forming a tube of water), then a surfer can ride the wave.

The ride involves an interplay of three forces on the surfer. (1) Buoyancy, which is perpendicular to the water surface, occurs because the surfboard is partially submerged. (2) Gravity, which is downward, attempts to slide the surfer along the wave face. (3) Drag, which is along the water surface, opposes the motion of the board through the water and is due to the water pressure in front of the board and the friction between the board and the water as they slide past each other.

By paddling to get up to speed, a kneeling surfer can move from the back face, over the crest, and to the front face. Once positioned, the surfer stands and waits for a free ride (no more paddling). By adjusting the orientation of the board in the water, the rider can adjust the drag and the board’s position on the front face. The three forces can cancel out (the surfer is in equilibrium) somewhere along the lower part of the front face. There, the buoyancy force is tilted in the wave’s direction of travel and thus tends to propel the surfer. Gravity tends to pull the surfer down the slope but the water drag tends to oppose that motion, so the surfer rides the wave. To move around on the wave face or to move along the length of the wave, the surfer changes the board’s orientation and thus the water drag. Generally, shifting the stance backward causes the rear of the board to dig more into the water, increasing drag and slowing the board, so that the rider climbs the front face. Shifting the stance forward causes the rider to speed up and move down the face.

**Sample Problem**

I also wrote about surfing in a Sample Problem in the 8^{th} edition of my textbook *Fundamentals of Physics* Halliday, Resnick, and Walker. (The international version, in English, is known as *Principles of Physics.*)* *Here I have retyped that Sample Problem, complete with its calculations.

A surfer rides on the front side of a wave, at a point where a tangent to the wave has a slope of *θ* = 30.0^{o}. Let there be an *x *axis up the slope and a *y *axis perpendicular and outer from the slope.

The combined mass of surfer and surfboard is *m* = 83.0 kg, and the board has a submerged volume of *V* = 2.50 × 10^{-2} m^{3}. The surfer maintains his position on the wave as the wave moves at constant speed toward shore. What are the magnitude and direction (relative to the position direction of the *x* axis) of the drag force on the surfboard from the water? Let’s first apply Newton’s second law to the surfer and then see how the surfer can adjust the board to ride up or down the wave, avoiding a wipeout.

**Key Ideas**

The buoyancy force on the surfer has magnitude *F _{b}* equal to the weight of the seawater displaced by the submerged volume of the surfboard. The direction of the force is perpendicular to the surface at the surfer’s location.

By Newton’s second law, because the surfer moves at constant speed toward the shore, the vector sum of the buoyancy force *F _{b}*, the gravitational force

**Calculations**

The gravitational force *F _{g}* is downward and has a component

*F _{b}* =

= (1.024 × 10^{3} kg/m^{3})(2.50 × 10^{-2} m^{3})(9.8 m/s^{2})

= 2.509 × 10^{2} N.

So, Newton’s second law for the *y* axis,

*F _{dy}* +

becomes

*F _{dy}* + 2.509 × 10

yielding

*F _{dy}* = 453.5 N.

Similarly, Newton’s second law *F*_{net} = *ma* for the *x *axis,

*F _{dx}* –

yields

*F _{dx}* = 406.7 N.

Combining the two components of the drag force tells us that the force has magnitude

*F _{d}* = [ (406.7 N)

= 609 N

and angle

*ϕ* = tan^{-1}[(453.5 N) / (406.7 N)]

= 48.1^{o}.

**Wipeout avoided**

If the surfer tilts the board slightly forward, the magnitude of the drag force decreases and angle *ϕ* changes. The result is that the net force is no longer zero and the surfer moves down the face of the wave. The descent is somewhat self-adjusting because as the surfer descends, the tilt angle *θ* of the wave surface decreases and thus so does the component of the gravitational force *mg* sin *θ *pulling the surfer down the slope. So, the surfer can adjust the board to re-establish equilibrium, now lower on the wave. Similarly, by tilting the board slightly backward, the surfer increases the drag and moves up the face of the wave. If the surfer is still on the lower part of the wave, then both *θ* and *mg* sin *θ* increase and again the surfer can control the forces and re-establish equilibrium.

http://www.wimp.com/bigwaves/ surfing big waves

**References**Dots · through ··· indicate level of difficulty

Journal reference style: author, title, journal, volume, pages (date)

Book reference style: author, title, publisher, date, pages

··· Hornung, H. G., and P. Killen, “A stationary oblique breaking wave for laboratory testing of surfboards,” Journal of Fluid Mechanics, 78, part 3, 459-480 (1976)

· Wolkomir, R., “The mechanics of waves---and the art of surfing,” Oceans, 21, 36-41 (June 1988)

··· Vanden-Broeck, J. M., and J. B. Keller, “Surfing on solitary waves,’ Journal of Fluid Mechanics, 198, 115-125 (1989)

· Anderson, I., “Let’s go surfin’. Imagine a beach where perfect waves break as regularly as the rhythm of a Beach Boys song,” New Scientist, 151, 26-27 (27 July 1996)

· Anderson, I., “Surf theories wiped out,” New Scientist, 155, 22, (6 September 1997)

··· Sugimoto, T., “How to ride a wave: mechanics of surfing,” SIAM Review, 40, No. 2, 341-343 (June 1998)

·· Edge, R., “Surf physics,” Physics Teacher, 39, 272-277 (May 2001)

··· Walker, J.,

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