There are few things more impressive than watching a big-wave surfer dropping into a monstrous "bomb" 60 or 70 feet high. Actually doing it must be quite an adrenaline rush. (I've been out in waves maybe a fifth that size and even then the energy of the wave can be, well... terrifying!) In the video we can see that the surfer gets towed into the wave with the aid of a jet ski. If you're familiar with surfing you might be aware that once waves get big enough (wave faces larger than 40 or 50 feet) it's impossible to paddle into them in the "traditional" way: you have to be towed in. Why is this? Not surprisingly, it all has to do with some basic principles of physics.
Let's examine the physics of this particular aspect of surfing -- the takeoff or the "drop-in". How do you catch the wave? Waves coming in to shore from the open ocean have speeds that can vary from 8 to 10 miles per hour for smaller waves to up to 35 miles per hour for a tow-in-sized wave. In order to catch the wave, you must paddle in front of it with sufficient speed that the wave does not pass right under you.
But paddling by itself doesn't get you into the wave, because you actually cannot paddle as fast as the wave is moving, and you need to match the speed of the wave if you want to ride with it. In order to catch up to that wave speed, it's necessary to use the gravitational potential energy of the wave. The trick is to obtain sufficient speed by paddling that, as the wave travels under you, your board begins to fall down the face. As you drop down the front of the wave, the gravitational potential energy you gain is converted into kinetic energy. Soon you are travelling as fast as the wave. In fact, if you continue to drop to the bottom of the wave, you'll be moving faster than the wave -- and if you don't cut into the face, you might temporarily outrun it.
We can use conservation of energy to calculate the approximate speed of a surfer as he hits the bottom of the wave just after take-off:
KEbottom = PEtop \+ KEtop
1/2mvs2 = 1/2mvw2 \+ mgh
vs is the speed of the surfer at the bottom of the wave,
vw is the speed of the wave and
h is the wave height. We are also assuming no significant loss of energy due to friction between the board and the water.
So why is it impossible to paddle in to a wave if it's too big? Big waves move faster, and that giant you're trying to catch up with is just moving too darn fast. You simply cannot generate enough paddling speed to get into the wave before it passes by. You need a jet ski to get the speed you need.
Finally let's calculate about how fast you would be going after dropping into a 70-foot monster wave. Solving the above equation for a wave speed of 35 miles per hour and a wave height of 70 feet, we find that you will hit the bottom at a whistling 57 miles per hour. Now you just have to pull off the turn, avoid the grinding lip, carve a "cutback" if you can, and hope the wave doesn't "close out" and drag you 300 yards under an avalanche of whitewater.
Adam Weiner is the author of Don't Try This at Home! The Physics of Hollywood Movies.