Engineers can fix the wobbly bridge for £5m. Now there's a row over who will foot the bill

If there is a place in history for the most expensive idea sketched on the back of a napkin, the Millennium Bridge in London - the "blade of light" from St Paul's to Southwark - will surely wobble its way into the running.

If there is a place in history for the most expensive idea sketched on the back of a napkin, the Millennium Bridge in London - the "blade of light" from St Paul's to Southwark - will surely wobble its way into the running.

After five months of analysis, the engineering company Ove Arup finally announced yesterday that it had chosen the method by which it hopes to stop the bridge's notorious shaking. It will brace the minimal "deck" of the bridge, on which people actually walk, and fit "dampers" beneath - rather like the shock absorbers on cars - to mop up the potentially dangerous movement that occurs when large groups of people walk on it.

The cost - on a bridge that has already cost £18m (of which £7m came from lottery funds) - is estimated at £5m, "plus the additional costs of long-term maintenance". And there is not much chance it will open to the public again until midsummer.

The debate has already begun about who should pay - the designers, the Millennium Commission, the Corporation of London (on the north side of the river) or Southwark Council (on the south)? Yesterday, none was willing to volunteer, although David Bell, chairman of the Millennium Bridge Trust, said in a statement that "everyone involved with the bridge is committed to a permanent opening at the earliest possible date" and "discussions about the funding of work have made good progress".

Southwark Council is believed, however, to be utterly against putting in more money, while Ove Arup can claim that its design was not negligent (even if it is a little wonky), and it is thus not liable for any extra costs.

The engineering work to fix the bridge will be complex and difficult to test - as indeed the bridge itself was. Even assuming that those tests meet their six-week timetable (unlike everything else to do with the bridge since it opened in June), fitting and testing the solution will mean an entire year of the bridge's life will have been wasted. The organisers had hoped that four million people would have crossed it in that time. Instead the number will remain at 160,000 - those who showed up on its opening weekend.

Those eager first weekenders immediately exposed a design flaw which had never been expected. When people began to walk over the bridge it started swaying faintly from side to side, and the pedestrians started stepping in time with the movement - exaggerating the sway. The bridge was closed on the evening of 12 June, just two days after its public opening.

Since then, only engineers and a few groups sent out by Ove Arup to test how and why the swaying occurs have been across it. "It's cost far more than a simple bridge crossing the Thames," said Robert Benaim, a consultant and former chairman to Robert Benaim and Associates, who has long experience with bridge design. "But it's a symbol, isn't it, not just a bridge; it symbolises London and the millennium and ambition."

Certainly, like London's other principal millennium attractions, the bridge has been cursed; the Dome also ran into problems, while the difficulties of the London Eye wheel mostly preceded its erection. It has been a classic case of ambition overreaching itself - even among civil engineers, usually the most cautious designers to be found.

The Millennium Bridge, however, was born out of a sense of excitement. The "ray of light" design began in mid-1996 with a quickly drawn sketch on the back of a napkin in a wine bar called Zelda's on Charlotte Street, central London. Chris Wise, then at Arup, was talking to colleagues about their potential entry, together with Foster & Partners, and the British sculptor Sir Anthony Caro, to design a new bridge across the Thames for the prestigious competition.

It would span the Thames from the north bank to the new Tate gallery on the south side. A suspension bridge would have needed towers - which would have obscured the view - so Mr Wise and his colleagues hit on a "flat" solution, later called the "blade of light", which in December 1996 won the competition. Later Mr Wise (who has since left Ove Arup) said: "We went home that night tremendously excited about the purity of the diagram, and petrified that the bridge might shake itself to bits." A remarkably prescient comment.

The bridge design was an innovation. Unfortunately there was no way to test for every interaction; there never is with innovations. Ove Arup insisted two weeks after the bridge's closure that it had tried every known test before building to see if there was vertical resonance, which designers have known about for centuries. But it had no way of predicting sideways resonance.

"When you innovate you take risks," Mr Benaim said. "It's right to innovate, but once you do there's always the chance of something you haven't spotted cropping up. When the designer of the Tacoma Narrows bridge [which shook itself apart in 1940] innovated by using a box construction rather than steel girders, it didn't occur to him that this could cause wind effects which would tear the bridge apart." Nobody died on the Tacoma bridge in Washington state. Was it just luck that nobody died on the Millennium Bridge? Ove Arup refused to comment beyond its written statements yesterday, in which it said there was "a small risk perceived to pedestrians".

At its largest sway (exaggerated in the diagrams on this page) the bridge moved about one metre to the side at its centre. Ove Arup did consider limiting the number of people allowed on the bridge, or forcing them to undergo an obstacle course with "street furniture" so they could not walk in step. But that seemed unsuitable. Stiffening the bridge would only work if it could be made nine times stiffer - which would be "obtrusive and expensive" (even more so than the proposed method). So bracing (to limit the sway slightly) and damping have been proposed.

Even so, Ove Arup was still insisting yesterday that the movement was "unrelated to the innovative design". Instead, it claimed, it was the combination of the low weight of the bridge, its natural sway frequency, and "the large number of people that used the bridge over the opening weekend".

Cursed by success? If so, it can only be a matter of time before the Dome's managers are ringing Ove Arup to ask for a bridge inside the Greenwich structure. And the "blade of light", meanwhile, will remain unsullied by footfall, and a symbol of what can go wrong when engineers take too giant a step for mankind.