Congratulations, Mr. President, and Bon Voyage!

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Looking for President Obama over the next few years? You should start at the White House, of course, and then try Camp David. But if you can’t find him there, you’d be wise to look overseas.

According to new research, U.S. presidents—at least in recent decades—take far more trips out of the country during their second term in office.

“A liberated president tends to spend more time abroad,” according to scholars Kathryn Dunn Tenpas of the University of Pennsylvania, Emily Jane Charnock of the University of Virginia, and James McCann of Purdue University. They outline their conclusions in a paper prepared for delivery at the 2012 annual meeting of the American Political Science Association.

The researchers looked at both domestic and international travel by two-term presidents Dwight Eisenhower, Ronald Reagan, Bill Clinton and George W. Bush. Not surprisingly, they found domestic travel peaked in Year Four of their respective administrations, as they campaigned for reelection.

International travel was a different story. The presidents barely left the country during their first year, and did so sparingly during their second, third and fourth years. (One exception: Bill Clinton, who made more than 30 overseas trips in his second year in office.)

But things rapidly began to shift once they were reelected, with the number of trips rising on average in Year Five, and then increasing further in Years Six, Seven and Eight. Clinton made more than 50 overseas trips in his sixth year in office; Bush made close to 50 during his final year as president.

The only exception to this pattern was Reagan, who, the researchers note, “was bogged down by the Iran-Contra scandal and increasing health concerns” during his second term.

The researchers suggest that “the goal underlying second-term presidential travel appears to be legacy building.”

“Presidents often shine more brightly and are perceived as more statesmanlike when representing the United States abroad,” they note.

Chief executives tired of squabbling with Congress, and looking to secure a place in the history books, often turn their attention to diplomatic challenges. The researchers point to Clinton’s final-year attempt to forge a peace agreement between the Israelis and Palestinians.

OK, that one didn’t work out so well, as Mrs. Clinton can attest. But such initiatives got him out of the house—and the country. Don’t be surprised if President Obama follows suit.