As the great British architect Norman Foster turns 75, he talks to Jonathan Glancey about flying cars, his new underground city – and how he beat bowel cancer

"The other day," says Norman Foster, "I was counting the number of aircraft I've flown: from sailplanes and a Spitfire to a Cessna Citation. By chance, it comes to 75." So Foster, who turned 75 this month, has decided to make models of all 75, to hang in his own personal museum, which he keeps at his Swiss home, an 18th-century chateau set in vineyards between Lausanne and Geneva.

These model aircraft will hover over his collection of some of the 20th-century's greatest machines, cherished for both their engineering brilliance and streamlined beauty; many of them look like winged or wheeled versions of Foster's most innovative buildings. "At the moment," says the architect, "I'm restoring a Citroën Sahara, designed to tackle north African dunes. I'm also thinking of getting a Bell 47 helicopter as a focal point. And I've had a model made of the Graf Zeppelin airship."

This last item puts me in mind of 30 St Mary Axe, aka the Gherkin, the Zeppelin-like London skyscraper that bears witness to Foster's passion for engineering marvels – a passion that began in childhood. Five years ago, I asked the architect if he had ever been a railway enthusiast. He replied by postcard, with a sketch of a Royal Scot class 4-6-0 thundering along, just as he would have seen it from his bedroom window, in the terraced house in Manchester where he grew up.

Foster has come a long way from those zinc-bath-in-front-of-the-fire days. The boy who left school at 16 to do his national service with the RAF is now – as his astronomical career shows, and as Deyan Sudjic writes in his new biography – "a phenomenon". But the lad from Levenshulme never forgot what he saw and learned as a working-class child brought up in an industrial Britain.

"There's a snobbery at work in architecture," says Foster, speaking at his riverside studio in Battersea, London. "The subject is too often treated as a fine art, delicately wrapped in mumbo-jumbo. In reality, it's an all-embracing discipline taking in science, art, maths, engineering, climate, nature, politics, economics. Every time I've flown an aircraft, or visited a steelworks, or watched a panel-beater at work, I've learned something new that can be applied to buildings. Disciplines connect, from locomotive engineering to the design of a bridge, or from a study of the way raptors and gliders soar. The most amazing lesson in aerodynamics I ever had was the day I climbed a thermal in a glider at the same time as an eagle. I witnessed, close up, effortlessness and lightness combined with strength, precision and determination. "

Foster's own rise has been no less impressive. His relentless enthusiasm and bristling energy had propelled him into the architectural stratosphere by the mid-1980s. Today, Foster and Partners is a global concern that employs 1,000 architects, working on an enormous number of projects: universities, skyscrapers, hospitals, museums, schools, production plants and entire city centres, stretching from Argentina and Brazil to Mumbai and Beijing, via London, Germany, Istanbul and the Middle East.

These range in scale from the India tower, a needle-like skyscraper in Mumbai that could end up being the world's tallest building (the height has yet to be finalised), to a sustainable school in Sierra Leone made of timber and mud-bricks. The former is an exuberant expression of the booming Indian economy; the latter a modest structure paid for by the Foster family.

Like all architectural firms, Fosters has been rocked by the recession. "In spring 2009, we had to lose 400 staff," he says. "Economic downturns hit architecture hard, but we've been recruiting again for several months. Now, we've accelerated into India, South America and parts of the Middle East, like Abu Dhabi, where economies are performing well."

Foster has, over the past decade, been criticised for building on too prodigious a scale. With so many designs on the go, and so many architects on the books, it hasn't always been possible to maintain the level of innovation and quality displayed in the firm's best works. These would include Berlin's Reichstag, a powerful remodelling of the original German parliament building torched in 1933 and now crowned with a mesmerising glass dome; the Viaduc de Millau (with Michel Virlogeux), the awe-inspiring French roadbridge over the Tarn valley with masts as high as the Eiffel tower; and the Hearst tower in New York, an eyecatching 46-storey skyscraper with a triangular exposed steel structure, rising provocatively from the top of a listed 1920s publishing HQ.

Most architects would give their souls for a sliver of his commissions. Which building is he most proud of? Always the one he is working on next, he says, although he is rightly fond of the beautifully detailed Hong Kong and Shanghai bank, opened in 1986 and built to aerospace standards of design, detailing and construction, with a budget (£500m) to match.

Essentially apolitical, Foster doesn't like to get involved in architectural spats, although he did sign a letter, along with other architects, denouncing the Prince of Wales's interference in the planning process for the redevelopment of the old Chelsea Barracks site in London. This is partly because Richard Rogers, battling the prince here, is an old friend, but also because Foster, although hugely successful, knows how hard winning major commissions can be; the wrong sort of interference can seriously damage well-meaning architectural practices.

'The chemotherapy was horrid'

As trim as ever, Foster, who has been married three times and has five children, seems fit and healthy, light on his feet and mentally sharp. So it comes as a surprise to learn of his battle with bowel cancer a decade ago, and of the fact that he can no longer fly solo, having suffered a heart attack. "For whatever reason," he says, "Deyan Sudjic played down these events in his biography. I did explain in some detail how I had worked my way through these life-threatening conditions. I certainly had no intention of letting up, neither then nor now. The day after I was told I had cancer, I had to present the Riba gold medal to Barcelona; and there was so much else to do, so many commitments.

"The chemotherapy was pretty horrid, I have to say, but I got through it by reading Lance Armstrong's book [It's Not About the Bike]. I bought a racing bike, and though I didn't quite manage to win the Tour de France [as Armstrong did in 1999, after fighting off testicular cancer], I've cycled marathons ever since." As a boy, he used to cycle to the Lakes and back to Levenshulme in a day; today, he tackles the Alps and the Pyrenees, his most memorable ride being a five-day jaunt along the precipitous Camino de Santiago, the 485-mile medieval pilgrimage route from France into Spain.

As another 75th birthday present to himself, Foster has commissioned a car from racing car restorers Crosthwaite & Gardiner. This is not any car, but a replica of Buckminster Fuller's legendary Dymaxion. US inventor Fuller, born in 1895, is best known for his geodesic domes, but he wanted to create a car that could fly, that could whisk drivers off roads and drop them at lightweight aluminium homes planted anywhere they fancied. The Dymaxion, a 20ft-long three-wheeler that looked part-airliner, part-yacht and part-whale, was the first step. "I've admired the look and the idea of these cars for many years," says Foster. "Yes, they were flawed, but they were a brave attempt to connect the car to architecture. They were just astonishing."

The zero-carbon mini-city

Foster met Fuller in the US in 1971, and the two worked on projects together until the inventor's death 12 years later. It was Fuller who asked Foster how much his hangar-like Sainsbury Centre for the Visual Arts, built in Norwich in the 1970s, weighed. Until then, this was not a question British architects, or indeed any architects, gave much thought to. What does it matter, as long as it stays up and shelters its occupants? Foster bothered to find out: the answer was 5,619 tons (the Empire State Building, by way of comparison, is said to weigh 370,000 tons).

Fuller's question has been used as the title of a forthcoming documentary, How Much Does Your Building Weigh, Mr Foster?, made with the help of his wife Elena. "One of the things it tries to say is that we should do more with less," the architect says of the film. "Today, I'm trying to get this message across not just through single buildings, but on a citywide level.

"Just now, for example, we're working on our Masdar City project in Abu Dhabi. This is an attempt to create a zero-carbon, zero-waste mini-city with a population of around 50,000 in a hostile desert climate – with, I hope, some lessons for cities worldwide. The idea is that conventional cars are housed in parking silos on the edges of what is, in effect, a contemporary walled city. Without cars, the streets inside the walls can be narrow, so they're both pedestrian-friendly and shady. But, so people can get around, there are proposals to create a level below pedestrian streets with guided electric cars. You'd call them by phone and they'd come to you; but once out of the city, they could also be driven like a conventional car. All this is based on ideas I discussed with Bucky years ago."

Masdar City, raised on a seven-metre podium so its electric cars can travel freely below the streets, recalls the fantasy future cities depicted in the pages of the Eagle, the weekly boys' comic first published in 1950, and one that Foster and other architects of his generation found compelling. Its strips were influenced by sci-fi fantasy as well as by the latest projects of Frank Lloyd Wright, whose buildings Foster visited while a student at Yale.

Where Masdar City differs is that its architecture is based on traditional Arabic precedent: it makes use of layers of sun-defeating decorative screens, cooling towers, narrow passageways, shade and oasis-like squares. If Middle Eastern cities of the future can develop along similar lines, they will be able to contain sprawl while being models of environmental good manners. It does seem a better idea to have a dozen new small walkable satellite cities close to Abu Dhabi rather than an Abu Dhabi too big for its urban robes. It's a project – the first part of which opens this year – that shows Foster and his practice still at the cutting edge of architecture and design.

For all his worldly success and professional esteem, and despite the fact that Foster and Partners is one enormous machine for making buildings (sometimes a little too slickly), Foster still exudes the curiosity of that enchanted boy looking out of his window at a world of wonderful machines. "I've never been busier," he says. "I'm amazed to be here still and doing all this. But then I look at Oscar Niemeyer in Rio, who was a hero of mine when I was a student at Manchester. Oscar's still busy at work at 102, so there's hope. In any case, I just wouldn't know how to stop."