Andy Murray's US Open campaign gathered pace in the early hours of Tuesday morning when he comprehensively disarmed Milos Raonic, the self-styled Missile from Montenegro, but it was launched with three days of downtime with just himself for company.

The 25-year-old from Dunblane tends to be surrounded by an entourage of coaches, well wishers and hangers on, so there was something liberating in a self-sufficient stroll around New York City. "When I got here I took three days off and just spent some time on my own," said the Scot, who took just two hours to see off the No.15 seed by a 6-4, 6-4, 6-2 score. "I hadn't had any time on my own since the Olympics and I felt I needed to spend some time away from the guys because it can get a bit sterile sometimes.

"I just watched some of the football on television and got breakfast, lunch and dinner," he added. "I didn't have a pint of Guinness or anything like that but I did have a massage in the hotel spa. I got a massage from a big lady with large hands so it was nice to relax and be on my own. When I'm at home I'm always with Kim or friends so this was the first in a while I had a couple of days by myself, walking around doing my own thing. It was nice."

The Scot is continuing to focus on himself on his route through this tournament. He was back to his Olympic best against the big serving Canadian on Arthur Ashe, managing to negotiate his way into the quarter finals for the eighth successive Grand Slam without being subjected to a single break point. He was delighted to get his work done promptly, avoiding getting snarled up in the rain showers which have struck the Eastern Seabord of the US in the last 24 hours, and keeping pace with world No.1 Roger Federer, who moved into the last eight for the 34th successive major with a walkover against Mardy Fish.

A bullish Murray said he couldn't care less how the other supposed contenders for this title were faring. "To be honest I wasn't interested in Roger getting a walk-over or [Tomas] Berdych getting through quickly," the Scot said. "It was just important for me to get through what was an unbelievably tricky match and had the potential to be a lot tougher than it was. I was glad to get through and even more satisfied when we walked off to see the rain. It was perfect timing."

Next up for the Scot is Marin Cilic, against whom he suffered a wounding loss here in 2009. The world No. 4 has won all six of his other meetings with the Croat – including a rain-affected, and deceptively simple, victory at Wimbledon earlier this year – but that defeat in 2009 forced the Scot into some serious introspection. "I have improved a lot since then," he said. "But while I didn't make a big deal about it at the time I couldn't hit a topspin backhand for about eight weeks after that.

"I shouldn't have played in the Davis Cup the week after, although I got no thanks for doing so from certain people in the team. I don't so much remember the loss as the certain other things afterwards. But I have a lot of respect for him and I have to try and figure out a different way of playing against him."

The prophets of doom were out in force ahead of his meeting with Raonic, but Murray has learned to trust in his own instinct and ability. The results he has recorded in recent seasons haven't happened by accident and they have fostered the self reliance of a champion. "The important thing is to remember what you have achieved in the game," he said. "If you never look at that and just think how tough Raonic is then you might not play your best. I need to try and remember that I have won some big tournaments, I have won the Olympics and been in the final at three of the four slams. I've been at the top of the game for a long time now so I need to remember that when I get into these situations deep in the big events."

There has been some silverware for Team Murray already this week. Ivan Lendl, his coach, not only provides the blueprint for becoming a multiple Grand Slam winner after losing your first four major finals, but Monday's night match allowed him to participate in the club championship at his local golf club in Connecticut. "He won 9 & 7 in the final so he was fairly happy with himself when he came in before the match," said Murray. "But I think that is his golfing done for the next few days so hopefully his eyes will be on the quarter finals now."

The world No.4 is also proving adept at steering clear of the hazards.