The Science of Surfing
by Paul Doherty

Waiting for a wave.

S itting on your board, you look behind you and spot an oncoming wave. Your eyes and brain and body have learned to judge the timing so you can catch that wave and ride it. You paddle hard, then feel the acceleration as the onrushing mass of water boosts you to its speed. Then you stand in balance on the board and savor the forces you feel as you crank off some turns. When you decide to end your ride, you step back on your board to drop the tail into the water, putting on the brakes.

The Joy of Physics
You didn’t need to whip out a calculator to figure out what was going to happen as you surfed—but there’s a great deal of physics behind riding a wave. Let’s take a look at a few places where physics and surfing meet. We’ll start as the surfer starts, waiting on the board between sets of waves. Then we’ll examine the acceleration as the surfer catches the wave. Finally, we’ll look at the forces on the surfboard as it turns.

Waiting to Go
When you are lying on your board in still water waiting for the next wave, there are two important forces at work: gravity and buoyancy. Luckily, these forces are pretty easy to understand.

As the surfer paddles out, she is floating almost level with the surface of the water. Note the gentle wave passing the middle of the surfboard.

At rest, the gravitational force and the buoyant force are equal and opposite. The net force on the surfer plus the board is zero.

Gravity
This force pulls on every atom in you and in your board—yet it behaves as if it were acting just at your center of mass. For most people, their center of mass is conveniently located behind their navel in the middle of their body when they’re standing up straight. Your center of mass is your balance point. Place a support under your center of mass and you can rest in balance. (We’re ignoring the surfboard for the moment. The board isn’t massless, of course, but physicists tell these little lies all the time to help them get to the heart of a problem.)

Buoyancy
This is an upward force created by the still water pushing up on the board and is known as a hydrostatic force (a force exerted by a liquid at rest). The water exerts its force on every part of the board that it touches, yet the buoyant force acts as if it were pushing up on the board just at the center of buoyancy, which is the center of mass of the water displaced by the board. (When Archimedes, a mathematician of ancient Greece, discovered the mathematics of buoyancy while bathing, he became so excited that he jumped out of the bath and ran naked through the streets shouting "Eureka!—I’ve found it!"—or so the legend goes.)

Net Force
Since you’re staying in one place, you are not accelerating. And, thanks to Sir Isaac Newton, we know that the sum of all the forces acting on you—the net force—is zero. No acceleration means no net force. It’s great to know the answer before you start to look at the physics. (Note, however, that you can be moving at a constant velocity even when the acceleration is zero; acceleration produces changes in velocity.)

Move back on a surfboard, behind its center of mass, and the nose of the board tilts up until the buoyant force aligns with gravity once again. As this surfer moves to the right, the tail of the board pushes hard on the water it’s moving through, bringing him to a stop.

Balance
The most important thing for a beginning surfer to learn about is balance. If the downward force of gravity and the upward force of buoyancy are in line, they add to zero and things are stable. Slide backward on your board, though, and the downward force of gravity moves behind the upward buoyant force. When these two opposing forces get out of line, the board will experience a torque, or twisting force. When you move backward, the torque twists the board so that the nose begins to go up and the tail begins to go down. This changes the position of the water displaced by the board and also changes the position of the buoyant force. The board rotates until gravity and buoyancy come into line again. By shifting your weight relative to the center of mass of the board, you can tip your board nose down, nose up, right-side down or left-side down.

The Physics of Turning

First the surfer moves back.	Then the board responds by rotating.
When the surfer moves back on the board, gravity and buoyancy move out of alignment and create a torque—a twisting force—on the surfboard. The board rotates until the forces are realigned.	The surfboard rotates until the buoyancy force through the center of mass of the displaced water is aligned with the gravity force on the surfer. As the board rotates, the center of buoyancy—the center of mass of the displaced water—moves toward the back of the board. When buoyancy and gravity are again in alignment, there’s no longer any torque.