Sailing seems simple enough.
The wind blows. The moving air bumps into the sail and pushes the boat ahead of it. You are sailing. So what's the big mystery?
What's hidden from the shore birds who watch the pretty sails go by is the physics of sailing.
Sailing is awash in science that most sailors - unless they're designing an America's Cup racing yacht - have no time to contemplate.
"They're too busy pulling on ropes," says John Kimball, a physics professor at the State University of New York at Albany, a sailor on Saratoga Lake and the author of a recent scientific paper on the physics of sailing.
Sailing science generates waves of books, papers and computer analyses, replete with graphs and formulas describing lift forces and Froude numbers, vectors and vortexes, airfoils and the Bernoulli Principle.
Some of it is counter-intuitive. Singer-songwriter Christopher Cross concluded that "the canvas can do miracles." Sailing science explains how.
How, for example, can sailboats sail into the wind? And how is it that some of them, sometimes, can sail faster than the wind?
It turns out that sailing exactly with the wind slows you down. As the boat's forward speed increases, the wind it "feels" goes down. A boat sailing 3 mph with a 10-mph breeze from the stern feels an "apparent" wind of just 7 mph. If it motored up to 10 mph, it would feel no apparent wind, and its sails would go limp.
So, downwind at least, "you can't sail as fast as the wind," says Lt. Cmdr. Warren Mazanec, director of sail training at the U.S. Naval Academy.
And just as the apparent wind is falling, the fluid drag is climbing. Fluid drag is the combined force of all the collisions of water molecules directly on the hull, and of all the water molecules that jam up behind them.
Water molecules pile up ahead of the boat's hull, creating the bow wave. The boat rides in the wave's trough, and the next wave peaks just off the stern.
The longer the boat's hull, the shallower the wave's slope, and the less energy is drained from the boat's sail force to pile it up, says Paul H. Miller, assistant professor of naval architecture at the Naval Academy. The longer the hull, he says, "the faster the boat will go."
Fluid drag increases with the square of the speed, however, so as speed doubles in one direction, the drag quadruples in the opposite. Just as our downwind sailor feels the apparent wind drop, the fluid drag beneath his hull climbs. And when all the forces reach equilibrium, he can sail no faster.
Sailing science is full of this kind of balance, Ross Garrett explains in his book on sailing physics, "The Symmetry of Sailing."
"One can think of a yacht as a sort of analog computer that automatically adjusts its speed so that the water forces and the wind forces are always exactly equal and opposite," he writes.
Fortunately, the combined physics of wind and water also work to help the sailor "beat" upwind. But it took millennia for people to devise boats to do it well.
Even in 1492, ships had little ability to sail to windward - no closer than 80 degrees. (Directly into the wind would be zero degrees; broadside to the wind would be 90 degrees off the wind - called a "beam reach.")
Columbus relied on tropical trade winds from the east to blow him across the Atlantic Ocean to the Caribbean. The Nina and Pinta rode the North Atlantic's westerlies to get back home. (The Santa Maria sank.)
"They used to think you could not sail upwind," says Chris Rowsom, executive director of the 1854 sloop-of-war Constellation. A ship trying it stalls; it is said to be "in irons."
Effective upwind sailing had to await the development of more efficient sails and hulls in the late 18th and 19th centuries.
Seated on the deck of the square-rigged Constellation, Rowsom says, "A ship like this one can sail about 68 degrees off the wind." That means 68 degrees to the right or left of the direction from which the wind is coming. Windward progress required laborious zig-zag maneuvers, called "tacking." Or a lucky wind shift.
Modern racing yachts, he says, have pushed the limits to 30 degrees off the wind. But most pleasure boats can get no closer than 45 degrees. And that's possible only because of the "airfoil" effect.
A modern sail, especially the familiar "fore-and-aft" triangular sail, is crafted with a graceful curve, like an eyelash, from front to back. Its shape mimics - actually it foreshadowed - the curve on the top of an airplane wing.
Such a sail is, in fact, an airfoil - a kind of vertical wing. And just as the flow of air over and under an airplane's wing provides the vertical "lift" needed to get the plane off the ground, so the flow of air past a sail provides horizontal "lift" to propel the boat on an upwind tack.
Wing and sail both work because of the Bernoulli Principle. Named for the 18th-century Swiss physicist who discovered it, it states that the pressure of a fluid - in this case, air - decreases as its speed increases.
Because the airfoil's shape forces the air to move faster on the sail's convex side, the air pressure is lower on that side of the sail. And because air wants to move from high pressure to low, it exerts forces against the high-pressure side of the sail.
The sum of those forces is exerted at nearly right angles to the wind direction, when the sail is properly aligned, or trimmed. That means the wind does not have to come from behind the boat. A breeze blowing in from somewhere to the left of straight ahead will push the sail toward a point somewhere to the right of straight ahead.
That doesn't mean the boat moves smartly off in that direction. The boat is sitting in water. The force on the sail is transmitted down through the boat, to its hull and fin-like keel, and presses them against the water.
Together, hull and keel resist the boat's tendency to drift downwind. As soon as the wind begins to move the boat, however, the water begins to flow against the hull and keel like the wind against the sail. And it exerts a force on the boat almost directly opposite to the force exerted on the sail by the wind.
The geometry of the hull and keel, Garrett writes, leaves just enough of a forward component in those forces to move the boat forward. And that force grows as the boat accelerates - squirted forward between the converging forces of wind and water.
The boat will continue to accelerate until all forces - wind, water and hull drag - reach an equilibrium.
But here the canvas does another miracle. A sailboat that isn't sailing "dead" downwind feels the breeze get stronger as it moves ahead. And the sails, thanks to that airfoil effect, begin to add more power. Here's how it works:
Imagine standing next to your bike, in a 20-mph breeze. Now get on and start pedaling into the wind. When you're going 10 mph, the "apparent" wind you feel is moving at 30 mph - the 20-mph breeze, plus your 10-mph movement directly into it.
Likewise, a sailboat gets a bonus "driving force" to its sails from the apparent wind - the additive effects of the "true" wind, plus the wind created by the boat's forward speed, all acting on its airfoil sail.
At certain angles to the wind, with efficient sails and hull, some sailboats - sailboards and iceboats, too - can actually sail faster than the true wind.
"And if the wind is right," as in Christopher Cross' song, "you can sail away, and find serenity."