This is the sixth summer in a row that Ralph L. Wilbanks has been in Whitby, focusing on an 18th century naval hero and his ship. In these parts that can mean only one thing, can't it? Captain James Cook and Endeavour.

Wilbanks means no disrespect, but no, that is not the reason he is here. It's a question of practicalities. The harbour is a convenient place to take stock – and take refuge when the North Sea is playing up – during his own voyage of discovery. Wilbanks is a marine archaeologist. He's grizzled, paunchy, and, having recently turned 60, knows it would sensible to be relaxing at home in South Carolina. Instead, he's off the Yorkshire coast
again, trying to uncover an elusive nugget of maritime history before others beat him to it.

His quest has particular significance for his countrymen. It involves locating, beyond dispute, the remains of the vessel on which John Paul Jones established himself as an American hero.

The Battle of Flamborough Head, seven months after Captain Cook had been killed by natives in Hawaii, was a humiliation for the Admiralty at a time when it was still feeling the loss of its greatest explorer.

The swashbuckling Jones not only outwitted superior Royal Navy firepower, he did it with a converted vessel given to him by the hated French. He forced the surrender of the captain of HMS Serapis, and as a final insult captured the British frigate and used it to escape, as his own crippled vessel succumbed to the ravages of a prolonged battle which drew sightseers to the Flamborough clifftops.

But where exactly did Jones' ship, the Bonhomme Richard, come to rest? It's become one of those seafaring intrigues that, 229 years later, still fascinates historians and those who challenge untidy, inconclusive endings.

The assumption is that her remains lie somewhere in Filey Bay, at a depth of between 100ft and180ft. Timbers, possibly from the 900-ton, triple-masted East Indiaman, were found in 1974. The immediate area became a designated wreck site and six years ago an archaeological survey was commissioned by English Heritage.

It failed to confirm the presence of the Bonhomme Richard, partly because of the competition down there. The seabed is cluttered with the relics of subsequent wars and storms, the consequences of decades of commercial fishing, and shifting sands sometimes disturbed by divers seeking evidence.

For Wilbanks that means everything is still to play for. He's come back armed with charts, advanced technology, hunches, possibly some secrets, and the continuing support of one of the world's most successful novelists.

His annual pilgrimmage, with six crewmates – another American, two Brits, two Poles, and a Scot – on a Panamanian-registered former Dutch beam trawler, the Ocean Dancer, is financed by author Clive Cussler, for whom real life now imitates his art.

He founded the National Underwater Marine Agency (NUMA), a non-profit body named after the fictional government organisation that employs his hero Dirk Pitt in high-tech maritime thrillers like Raise the Titanic.

Cussler and Wilbanks are a formidable team. They've worked together on many of the 60-plus shipwreck sites discovered by the author.

Wilbanks has also been hired by the US government to survey the D-Day beaches in Normandy and look for lost fighter aircraft, and he's still searching for an airliner which went down in Lake Michigan in 1950. For Cussler, their collaboration has had two main goals. One has been achieved.

In 1995, off Charleston, they located the wreck of a Confederate submarine which during the American Civil War became the first in the world to sink a surface ship.

But the Bonhomme Richard still eludes them and all the other searchers, including a rival American group.

There is no submerged treasure at stake, but a great deal of prestige, which explains why responses are guarded, and fingers are occasionally put to lips when a stranger is on board the Ocean Dancer.

Wilbanks says in six years he's surveyed about 1,000 square miles of coast off Yorkshire, and there's much more to do. Drift studies they've carried out – how far the frigate's wreckage might have been swept along the seabed, perhaps before sinking beneath it – could put its location way beyond Filey Bay, north or south. He may, though, be saying that to startle his competitors.

So what are Wilbanks and his team doing exactly? "We are surveying up to 40 miles offshore. We run lane after lane establishing a grid. Everything is run by a computerised programme. Sonar equipment takes electronic pictures of the seabed."

They show anything that's there. A magnetometer evaluates what might be under the sea's floor. It provides pointers, like maybe a significant shape. The skill is in knowing how to evaluate the information we receive. "There's plenty of metal from the Bonhomme Richard somewhere down there. She was carrying the goods of war – muskets, pistols, cannon, cannonballs – but also domestic material such as inkwells, plates and jars. The trouble is there's also stuff from a lot of other wrecks, like steam trawlers from the late 19th century, and marine casualties of the First and Second World Wars. We know what we can discount. We're not interested in anything with a boiler. On the other hand, wooden shipwrecks have been around for 10,000 years."

He and the search team work four-hour shifts, round-the-clock, studying instruments, watching and hoping for something from "the target", as he puts it, to make itself known. Wilbanks has re-examined every piece of data they've gathered over six years to try and ensure they haven't missed a clue. If something exciting turns up, divers or a submersible will be sent down, and they'll video the scene. "We're not salvors," stresses Wilbanks. "We don't recover artefacts. We're not like
those guys looking for sunken gold and silver. We don't have anything that came from a shipwreck. What we do is locate history, and it's for others to decide what happens next.

"In the case of the Bonhomme Richard that could prove interesting. It would be a very important archaeological site, with international implications. Americans would love us to find the vessel, and so would the French because it was one of theirs, but would the British be so excited? After all, Flamborough represents a defeat for them.

"John Paul Jones lost his ship but won the battle, and it helped establish him as the father of the American Navy. An interesting man in all kinds of ways, and ahead of his time."

Cussler, who is 77 and lives in Arizona, now shares much of the work with his son, Dirk, who was in Whitby earlier this month for a progress report. The project has already cost them tens of thousands of dollars, and the bills will be coming in until the end of August, after which, assuming there are no leads, they'll call a halt for another year because the North Sea can become even more unpredictable from September on. Is it worth the effort? The question is almost ludicrous to these men.

"Clive is big on mysteries and underwater dramas. It's what he writes about from his imagination, and investigates in real life. He has to do something with all that money he's earned. This is an expensive job. He sees it as spending money for the public good." Wilbanks is driven too. "I have a wanderlust and enjoy searching. Do I think we'll find the Bonhomme Richard? Put it this way, there may not be that much left, but I'll know it if I see it.

"I've been looking for her for nine weeks a year, over six years. That's more than a year in total. I've nothing against Yorkshire, but I'm getting old and it would make a nice change not to have to spend my summers here. There's been a lot of speculation. Are the theories of the rival searchers right, and have we got it wrong? You have to back your judgment, and it's worked for us many times in the past. On this one we may reach the point where I say to Clive, 'it just ain't there. There's no place else to look'."

Seaman became an all-American hero

John Paul, (he added Jones later), was born in Kirkcudbright, south-west Scotland on July 6, 1747, the fourth of seven children of an estate gardener and his wife. Much of his boyhood was spent around ships on the Solway Firth.

At 13 he signed-up for a seaman's apprenticeship and his first voyage was to Barbados and Virginia, to where his older brother had emigrated. By 21, John was a captain. Events were leading up to the American Revolution, and letters indicate his strong support for the rebelling colonists. When Congress formed a Continental Navy he offered his services and was commissioned as a first lieutenant in December 1775.

With his reputation growing, he sailed for France and became an ally of the American Commissioner in Paris, Benjamin Franklin. In the following months he returned to his native shores to attack ports and shipping, including naval vessels.

Back in France again, he was given command of the Duc de Duras, a merchantman which he converted into a warship and renamed Bonhomme Richard – in honour of Franklin's best-selling publication Poor Richard's Almanack.

On August 14, 1779 Jones set sail as commodore of a squadron of seven ships intending to destroy British commerce in the North Sea. By now notorious, he was regarded here as little more than a pirate.

The Royal Navy was ordered to hunt him down, but their confrontation off Flamborough Head was a fiasco for his pursuers. On the moonlit night of September 23, he engaged HMS Serapis and the Countess of Scarborough and, with typical daring, Jones neutralised Serapis's greater firepower by manoeuvering his vessel alongside and lashing them together. On a mill-pond sea, amid the confusion of a savage fight which lasted more than three hours and claimed dozens of lives, the Bonhomme Richard became a victim of "friendly fire".

At one point the British captain asked his rival if he wished to surrender. Jones replied with a phrase which has immortalised him in the history books of American schoolchildren: "I have not yet begun to fight". He went on to capture the Serapis and sailed her to Holland with more than 500 prisoners.

Later he became the toast of Paris, added to his reputation as a womaniser, and was decorated by Louis XVI. In 1781, Jones returned to America a hero, and for several years advised the new nation on the establishment of its navy and the training of officers.

Briefly he was made a Rear Admiral in the Russian Navy on the recommendation of Thomas Jefferson. But back in Paris his reputation, and his health, declined, and on July 18, 1792, he died, aged 45. His rum-filled coffin lay in an unmarked grave in a cemetery for foreigners for more than a century.

Then, in 1905, America's naval expansion prompted President Theodore Roosevelt officially to recognise John Paul Jones's contribution and return him to the country he'd fought for. A flotilla of warships escorted his remains into Chesapeake Bay, there was a gun salute, and eventually he was laid to rest in a marble sarcophagus, modelled on the tomb of Napoleon, in the chapel crypt of the United States Naval Academy at Annapolis, Maryland.

Finding what's left of the vessel from which he humiliated the British would write the last chapter of a remarkable
life story.