The 24-year-old Scot was talking to someone else, but politely excused himself to oblige. Just as he handed back the piece of paper, curiosity made him unfold it. It turned out to be the telemetry printout of a rival team's engine performance during the San Marino Grand Prix, which had just ended. Coulthard smiled at its new owner. "Excuse me one moment." He called his Williams-Renault race engineer, Jock Clear, over, showed it to him and asked: "Do you think we should photocopy this?"
Opportunism is everything in Formula One, from grabbing a chance in the first place, to keeping it and improving it. Nigel Mansell proved that throughout his career, and Coulthard has never been a slow learner.
Bernard Dudot, Renault Sport's engine designer, once explained the complex process by which one team worked out how many revs per minute another team's engine achieved. It entailed making a recording of the rival car at maximum speed and comparing its frequency to the frequency of his own engine. Yet here he did not have to go through that palaver: one of his drivers was bringing in empirical data like manna from heaven.
Uncharacteristically for a man in his profession, Coulthard handed back the paper with a smile and a pleasant remark. "One day you'll start acting like a Formula One driver," a reporter standing next to him said. "If I do, I hope some of you guys will come and put a gun to my head," he replied.
So Coulthard is smart, obliging and personable. That much we know, and have known for several years. But some people, even within the Williams team, believe he is too good to be true - the first hermetically sealed, polished and presented Formula One driver. They speak disparagingly of the "packaging" of the protege.
There are two reasons why he can come across this way, and both are directly and indirectly linked to Jackie Stewart, the last Scot to win the World Championship and a man who played a significant role in Coulthard's development. As a climber on Stewart's "staircase of talent", Coulthard ran the Brazilian driver Rubens Barrichello very close for the 1991 British Formula Three Championship, though his Formula 3000 relationship with Stewart the next year foundered after financial differences.
"David is coming along," Stewart says with almost paternal pride. "He is one of the new generation who have come along, and who are better prepared. It's not for me to say, but I think he was brought up the right way in motor racing. He was a very easy student."
Through Stewart, Coulthard has also forged links with the management company IMG, which now handles all his affairs and which, perhaps, has been responsible for the feeling that Coulthard is being over-marketed. Cut through the hype, however, and he is still the same man who broke the lap record at Thruxton the first time he stepped out of a kart and into a Formula Ford.
"He hasn't really changed at all," says his fellow Scot and touring car racer David Leslie, who gave Coulthard his first vital break. "He's just a lot more used to the world. He's learned an awful lot. People like Jackie taught him a great deal, and now he has to learn to be bloody-minded and not just accept what some people present to him as fact. He's got to work hard to protect himself."
For all his new worldliness, there remains an engaging naivety to Coulthard who, back in his days of graduation from karts to Formula Ford took a while to realise that David Leslie was not a man of the cloth, even though he was known within the team as Father David.
When Coulthard was recruited to drive alongside Damon Hill at Williams- Renault in Barcelona last May, replacing the late Ayrton Senna, he acclimatised very well, and only mechanical failure robbed him of a podium finish. At Spa he ran ahead of Hill, and he led at Monza and Portugal. Even when Mansell came back to supplant him for the final three races, he remained phlegmatic.
But now the critics are doing their sums. In only his fourth grand prix (and just the second for Williams) Hill scored World Championship points by finishing second to Senna. In his ninth he took pole position and looked a possible winner. By his 11th he had won a race. These are impressive statistics, especially when compared with those of stars such as Senna, Prost and Mansell, all of whom have been his team-mates at one time.
While Hill might not be accorded the merit he deserves in some quarters, such figures are not lost on Coulthard, by irony a driver who has yet to match them but who is perceived by many to have a brighter future. He has now started 15 races for Williams, one in pole position, and has scored a second place. The critics are beginning to get restless, suggesting that he needs to win a race to maintain his momentum.
It so nearly came in Argentina in April as he took a convincing pole position in treacherous conditions, and led comfortably ahead of Hill and Schumacher until he was delayed by an electrical problem. But since then things have bogged him down. Before France he had troublesome tonsils removed, and raced to a welcome third place, albeit some way behind Hill. It may be a new beginning.
"For sure, I have much more energy now that I've had the operation," Coulthard said during testing at Silverstone last week. "I wake up and feel like I want to do the job, and instead of just being there I'm thinking two or three stages ahead. I can give direction again. Just recently I've been feeling as if I was competing but not challenging.
"The other thing is that your training goes to pot. Now I hope to pick it up from here, and if the car is reliable I can also use the races themselves to improve my fitness."
Hill's record of achievement does not worry him: "There was a feeling in some races last year that I might have been able to win given certain circumstances, and the closest I've yet come was Argentina earlier this year. Otherwise I haven't been that close. Naturally, I'd rather the first win came sooner rather than later, but I don't feel under any pressure because of what Damon has achieved, especially early in his F1 career, and Frank [Williams] is very calm about it all. Times have changed. We don't have the dominant car that Damon had then."
Leslie, like Stewart, maintains his faith. "David's great strength is his calmness. He has a very low heart rate. He races very well and he's good at overtaking, where many others are content just to follow. I have every confidence that he'll be quicker than Damon. Don't forget, he's still in only his first full season. I'm sure he'll win a minimum of one race this year, and if he stays in a competitive car, he can win a World Championship."
Formula One has yet to go to David Coulthard's head. Those who know him well suggest it never will. Recently, he moved to an apartment in Monaco, one of the outward trappings of his new lifestyle. "It's funny," he mused in Canada. "Ever since I moved nobody in the media seems to call me any more. It got to the point where I was wondering what I'd done to upset them . . ."
And, so far, he is cool about the prospect of racing in front of the home crowd in his second British Grand Prix. "I don't feel at the moment that there is any additional pressure because of that. I'm concentrating hard on getting a good result, and of course it would be nice if it could be at Silverstone. By the time qualifying and the race come around I may be a little more tense, because I really don't want to go off on the first lap here. But I'm relaxed about it all in my mind right now."Reuse content