"Sea," said King Canute, the 11th-century Danish King of England, "I command you to come no further!"
These words were spoken to convince his flattering officers of the limits of his power: He could not control the tides. A millennium later, no one yet can rule the sea, but we can do something almost as useful: predict its behavior.
The 70th anniversary of D-Day is an occasion to remember not only the sacrifices Allied troops made on the beaches of Normandy, but the role science played in making their victory possible.
For any amphibious operation, an ability to predict the height and timing of high tides is crucial. U.S. military planners had learned that lesson at the Battle of Tarawa in the Pacific. A miscalculation in predicting the height of a high tide stranded U.S. landing craft on a shallow reef for several hours, while Japanese defenders of the island used U.S. Marines for target practice.
Predicting tides correctly is not as simple as you might think. Having taught oceanography to undergrads for many years, I can testify to just how complex, even counterintuitive, this science is.
As long ago as the 17th century, Isaac Newton divined that ocean tides are driven by distortion of Earth by the gravitational pull of the Earth's moon and sun.
These interactions are very complex. Every place on Earth has different and changing angles of position relative to these objects. Water responds strongly to the gravitational pull of the sun and moon, and its movement toward them creates a wavelike bulge on the side of the Earth closest to the moon. The solid Earth itself is pulled toward the moon as well. On the opposite side of the Earth, this planetary attraction is greater than the attraction of the thin layer of water that sits on that part of the planet. This sliver of water becomes the other tidal bulge as the solid Earth moves slightly toward the moon. Imagine these watery budges as two long waves that move over Earth as the planet rotates.
When the sun and moon are aligned, the double pull creates higher tides than when the sun and moon are tugging in opposite directions. Then the complications really begin. All three celestial bodies have elliptical orbits, which means that the distance between each of them changes throughout the year. The angle between each of them also changes, and with it the gravitational attraction and tide height.
Newton's elegant simplifications work well on a static, homogeneous Earth without continents and with a very deep ocean. But the planet is covered with continents, islands, and oceans of different depths. Then the ocean tide is created on a rotating planet. There is friction along the ocean bottom, for instance, so the ocean tide moves slowly, and it interacts with intricate shorelines. Hence ocean tides vary widely in timing and height when they intersect the shoreline. In the Bay of Fundy, between New Brunswick and Nova Scotia, the tide changes twice a day, ranging 50 feet in height. Meanwhile, a 1.5-foot tidal range changes only once a day in Texas' Galveston Bay.
The shape of the coastline creates tide height and timing differences even within a relatively small area. Long Island Sound, the watery southern border of my home state of Connecticut, is an example. A high tide passing Newport, Rhode Island, and entering Long Island Sound travels westward and reaches Bridgeport, Connecticut, about 100 miles away, three and a half hours later. The average tidal range at Bridgeport is 6.7 feet, almost double that of Newport's 3.5 feet. Predicting tides has always been important for commerce and defense, but it is not a problem for pen and paper.
The first British tide-predicting machine was constructed in 1882 by the future Lord Kelvin. His analog computer, a brass calculating machine, used gears and pulleys to represent the 10 most important tidal components and recorded the predictions on a rolling piece of paper. About the same time, William Ferrel of the U.S. Coast and Geodetic Survey, now part of the National Oceanic and Atmospheric Administration, constructed a similar machine that predicted times and heights of high and low tides. Over the next quarter-century, improvements were made in both machines, culminating in "Old Brass Brains," a tide-predicting machine built by Rollin Harris of the U.S. Geodetic Survey in 1910. His machine incorporated 37 tidal components, such as moon phase, depth and width of bay, and offshore islands, and operated successfully throughout World Wars I and II and the Korean War. (An electronic calculator replaced it in 1965.)
Brass calculators, based on prior records of tidal patterns, allowed the Allied Forces in World War II to predict tides. These crucial predictions were accurate in the English Channel, where detailed tidal records had been kept for decades. Tides there averaged 18 feet, with highs reaching 25 feet. Seven feet is a lot for a soldier.
As the complex D-Day invasion was planned, there were conflicting interests among the military forces about the ideal timing for an invasion. Aviators wanted moonlight to navigate by and to let them see where to drop more than 13,000 paratroopers behind enemy lines. The Navy wanted a low tide, exposing the extensive obstacles identified by aerial surveillance as "ski lifts" (such as large tree stumps sunk in the Normandy sand, pointing toward the English Channel) and cement bunkers. These structures were built by the Nazis, under Erwin Rommel's orders, to prevent Allied ships from landing. (Rommel anticipated a high-tide landing.) The Army favored high tides, decreasing the amount of time soldiers would be targets as they crossed the exposed beaches.
An Army-Navy compromise was struck: The invasion would begin one to three hours after low tide. The necessary tide and moon conditions in 1944 were on June 5, 6, and 7. Tides could be predicted, but weather could not. Storms and rough seas would be a disaster, but so would postponement.
Considering the size of the invading Allied force, any delay would certainly alert the Nazis to the military gathering. Imagine hiding 702 warships, thousands of ships and landing craft, 20,111 vehicles, and 176,475 soldiers.
The weather report for June 5 was not good: low clouds, poor visibility, and high winds and waves. The invasion was postponed, and ships already in the English Channel were recalled. Relatively good weather was predicted for June 6. The massive assault along 60 miles of beach began, and with it the beginning of the liberation of Western Europe.
Suzanne O'Connell is professor of Earth science at Wesleyan University and chair of the Geology and Society Division of the Geological Society of America.