Murray warms to his task in hot-house atmosphere of Centre Court occasion

At 6ft 6in tall and weighing more than 14st Sam Querrey is big enough to look after himself, which is just as well considering the support that Andy Murray will have when the two men meet on Centre Court.

"I think it will be 99 per cent for Murray, and my mum and dad and sister cheering for me," Querrey said as he looked ahead to their fourth-round match. "As an American, I play almost half my tournaments in the US so I can't complain too much. Andy Murray has got Queen's and Wimbledon. Let him have his moment with the fans. I've got three months' worth of tournaments in America."

On the evidence of Murray's third consecutive straight-sets victory on Saturday night, when he beat Gilles Simon 6-1, 6-1, 6-4, the Wimbledon crowd are warming up as quickly as the weather. Home support for Murray has sometimes been less than wholehearted, but the intelligence and inventiveness of his play against the Frenchman, who has been recovering from a knee injury, generated an increasingly jubilant atmosphere around Centre Court. The effect can work both ways because Murray thrives in the heat of a big-match occasion.

"The tennis got better as the match went on," Murray said. "Gilles hasn't played a whole lot this year because of the injury. He started to get better as the match went on because of that. There were some really good rallies out there, and obviously when you win it's a lot more enjoyable, but at the time you're not really focusing on individual points or games. You just try and stay in the moment as much as possible. There were a lot of long rallies in the third set and it will be good for me going forward."

In reaching the fourth round of his ninth consecutive Grand Slam tournament – a record that only Roger Federer can match – Murray has put behind him some of the problems of the last few months. Since reaching the Australian Open final he has not made a semi-final anywhere, though he was not unhappy with his form at his Wimbledon warm-up at Queen's Club, when he went out in the third round of the Aegon Championships.

"I said then I didn't feel like I was that far away from playing really good tennis," he said. "Maybe it's Wimbledon that has brought it out of me, I don't know. I needed something to really focus on and winning this tournament was what my goal was. I know it's going to be incredibly difficult, so I've had to focus a little bit more because of that."

He added: "I've been striking the ball really well, not only in the matches but in practice as well. I haven't been missing much, and have been serving great, which definitely helps."

Murray came here as Queen's champion 12 months ago. This year that honour went to Querrey, who is at a career-high No 21 in the world rankings. The two men go back a long way: Murray, who is five months older, beat Querrey in the quarter-finals en route to winning the 2004 US Open junior title. The Scot has also won their three previous meetings as professionals without losing a set.

"He's got a big serve – bigger than the guys that I've played so far – and a slightly more unpredictable game," Murray said. "There are certain things that you have to try to do against big guys. You want to keep them on the move as much as possible."

How does Querrey assess his own grass-court game? "My return is getting better and better every match," he said. "I'm hitting it on both sides. I'm chipping the forehand return sometimes, but on the second serve returns I feel like I'm stepping up in the court and hitting a little bigger than I normally do. That's something you've got to do on the grass."

The struggles of Federer and Rafael Nadal in the first week may give Murray hope that he can go all the way, but the Scot said he did not read too much into their difficulties. "Their opponents played some great tennis, took their chances and played well," Murray said. "Rafa and Roger haven't played badly from what I've seen."