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Flying circus of physics


Tuesday, July 01, 2014


Jearl Walker
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: surfing on a wave 26 meters high, a record 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 8th 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 = 30.0o. 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 m3. 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 Fb 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 Fb, the gravitational force Fg, and the drag force Fd must be 0.


The gravitational force Fg is downward and has a component mg sin θ down the slope and a component of mg cos θ perpendicular to the slope. A drag force Fd from the water acts on the surfboard because water is continuously forced up into the wave as the wave continues to move toward the shore. This push on the surfboard is upward and to the rear, at angle ϕ to the x axis. The buoyancy force Fb is perpendicular to the water surface; its magnitude depends on the mass mf of the water displaced by the surfboard, as given by Fb = mf g. From the definition of density ρ = m/V, we can write the mass in terms of the seawater density ρw and the submerged volume V of the surfboard: mf = ρwV. The seawater density is ρw = 1.024 × 103 kg/m3. Thus, the magnitude of the buoyant force is

Fb = mf g = ρwVg

= (1.024 × 103 kg/m3)(2.50 × 10-2 m3)(9.8 m/s2)

= 2.509 × 102 N.

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

Fdy + Fbmg cos θ = m(0),


Fdy + 2.509 × 102 N – (83 kg)(9.8 m/s2) cos 30.0o = 0,


Fdy = 453.5 N.

Similarly, Newton’s second law Fnet = ma for the x axis,

Fdxmg sin θ = m(0),


Fdx = 406.7 N.

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

Fd = [ (406.7 N)2 + (453.5 N)2 ]0.5

= 609 N

and angle

ϕ = tan-1[(453.5 N) / (406.7 N)]

= 48.1o.

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. surfing big waves

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., Fundamentals of Physics, 8e, John Wiley & Sons, 2008 pp. 369-370
Pub Tricks
If you would a list of the links to all the pub tricks I have posted, go here and then scroll down to "Pub physics".


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