With the largest shed in Christendom and a debt the size of Brazil's, Boeing's staff sketched an outline on the back of an envelope; 75,000 engineering drawings later ... and the rest is the sort of history that comes to life in Seattle's Museum of Flight.

"These men will not be hindered from accomplishing at their best speed the distance which they have to go, either by snow or rain or heat or darkness of night." When Herodotus wrote these words, around 450BC, he was referring to the Persian postal system. Nonetheless, the world's biggest plane maker has pinched the lines to set the tone for its corporate history.

You probably arrived in Seattle aboard a 747 - homeward bound to the city of its birth. If you were lucky enough to secure a window seat, you may have noticed an extra runway. Busy with executive jets and planes straight off the production line, this is the Boeing test facility. Between it and the Pacific stands a big, bright building, as clean as a new Jumbo. Return your seat to the upright position and stand by for the Museum of Flight. (That's its official name, though everyone calls it the Boeing Museum. The absence of any reference to Boeing's main competitor, Airbus, emphasises that this is a one-company venue.)

If any innovation has defined our epoch, it is surely air travel. Until three years into the 20th century, powered flight was a dream. Yet three years from the end of the millennium, flying has become both humdrum and thoroughly liberating. The average British worker needs to labour for a mere fortnight to fly clean around the world - an achievement which is technologically and socially amazing, but which has become so commonplace that airlines are reduced to competing against each other on the quality of their in-flight films and the width of their stewardesses' smiles. The company that helped bring this about is based a handy 10-minute bus ride from Seattle's international airport. With the small change from selling a few Jumbo jets, Boeing has helped to establish the Museum of Flight.

The American brothers Orville and Wilbur Wright may have pioneered powered flight, but after their achievement at Kitty Hawk in 1903, Europe accelerated in the race for the skies. So the first tranche of the museum's chronology is Eurocentric, and reveals secrets such as that the Dutch aircraft firm Fokker was first based in Schwerin, eastern Germany; it moved to Holland after the Second World War.

US civil aviation really took off 70 years ago this month, with the first international flight by an American airline. Pan Am took off from Key West, Florida, destination Havana. Amid the many competing aircraft manufacturers, Boeing made its name with the 247, and its first manufacturing facility was right here, in the carefully preserved Red Barn. Today, it looks barely large enough to assemble an Airfix kit.

Regular, reliable transoceanic travel began in 1939 with scheduled transatlantic flights. However, the two most obvious and glamorous destinations, London and Paris, were not on the route map. Instead the flight began in Marseille, hopped down to Lisbon and then across to the Azores before reaching New York.

The first commercial jet flight by a US airline, Pan Am, took place 20 years later, when a Boeing 707 flew from New York to Paris. By this time Britain's disastrous first-generation Comet had suffered a series of fatigue-related crashes. The British retired hurt from the cutting edge of aviation.

The fickle nature of air travel was demonstrated when, two decades later, that same Boeing 707 was pressed into service for British package tourists travelling with the budget airline Dan-Air. It is rumoured that Pan Am tried to buy the 707 back from Dan-Air to put it into its own museum. The British charter airline refused. Both airlines then went bust.

If you have visited the air museum in Duxford, Cambridgeshire, you will know that crawling all over the aircraft is part of the fun. At the Museum of Flight, the planes are mostly kept at wing's length. Cold War relics such as the B-52 are fenced off. As on the average flight, the intention seems to be to maintain a feel-good, no-fear ambience. So the thousands killed in air crashes hardly figure, nor do the hundreds of thousands massacred in bombing raids. There is mention of a Kamikaze plane, but this one does not indicate suicidal tendencies when applied to air travel. In 1937, the name (which translates as "Divine Wind") was applied to a Mitsubishi Ki-15, a civilian aircraft that flew from Tokyo to London in 51 hours in 1937.

The museum is not without humour. It reveals that the first 747 simulators were mounted on top of a truck to get pilots used to the extra height of these revolutionary aircraft. The most amusing relic is the Aerocar, a Fifties idea to make a plane that converts to a car (or vice versa). Wings, tail and propeller are bolted on to what looks strangely like an aeronautic Renault 5. It does fly, but commercially the concept never took off.

Besides the collection of aircraft (and imposters), the Museum of Flight has a livelier repertoire of films than any in-flight programme. Many of them are techy, Technicolor tearjerkers from the pull-focus school of cliches; the strongest suit is devoted to the exploration of space. "The dream of flight" is a triumphalist yet witty look at the space race, and touches upon the extraordinary spirit of the Sixties, an era in which almost every scientist and engineer appears to chain-smoke.

Early footage takes you through Sputniks to Muttniks, as the early Russian space experiments using dogs were called by Nasa. The Soviet Union won the opening heats of the space race, with the launch of the first manned space flight in 1961. "I looked and looked, but I couldn't see God," Yuri Gagarin said when he returned from his day trip to space. Scientists working for Nasa were deeply alarmed. "When we land on the moon, we'll have to go through Russian customs," commented Wernher von Braun. Facing headlines such as "Reds beat US into space", President Kennedy made his reckless promise to get a man on the moon by the end of the decade.

"We were heroes because we volunteered to take the place of chimpanzees," observes one astronaut wryly. "In my book that doesn't make me a hero." The fact that the Apollo XI astronauts had only seven seconds of fuel in reserve when they landed on the moon in 1969 persuades you that heroism was as important as oxygen for the space pioneers.

Shortly before Neil Armstrong took his small step came the first commercial flight of a 747. A month after the moon walk, Seattle lad Jimi Hendrix terrified the Woodstock crowd with a particularly angry version of "Purple Haze". It's not yet the company song at Boeing, the aircraft maker based in his home town, but it should be - if only for the perfect tag: "'Scuse me while I kiss the sky".

Simon Calder paid pounds 275 for a return flight to Montreal on Air Canada, booked through Quest Worldwide (0181-546 6000) and reached Seattle on a Canadian airpass, pounds 199 from AirPass Sales (01737 555300). The Museum of Flight (001 206 764 5720) opens daily; admission $8 (pounds 5), free on the first Thursday evening of the month.