My first sight of Emma Raducanu at this US Open came on one of those typical late summer New York days: oppressively hot, and uncomfortably humid.

Raducanu had secured some excellent wins since reaching the fourth round of Wimbledon in July, mostly notably in her run to the final of the WTA Challenger event in Chicago the previous week.

But having only arrived in New York on the Monday, and due to play three qualifying matches in three days from the Wednesday, there was some concern among the coaching team that fatigue may be an issue.

A flight home had been booked for the following weekend, but that would prove an unnecessary precaution, as the longest trip of Raducanu's life had plenty of miles left to run.

The first qualifier in history to reach a Grand Slam final takes the view you should try and live like a local when on the road. She tries to do her own shopping, and likes to make her own breakfast. A lox bagel (of salmon and cream cheese) would be her first choice, and on the odd trip around Manhattan, frozen yoghurt in Times Square does not go amiss.

Raducanu is here with coach Andrew Richardson, LTA physio Will Herbert and her IMG agent Chris Helliar. Iain Bates, the LTA's head of women's tennis, is also in New York and because Richardson is left-handed, has been the nominated right-handed server in practice.

He has not seen so much of her in the evenings, though.

"It's not been a huge amount. She's very much kept herself to herself," he says.

"I had dinner with Andrew a couple of times, and her agent a couple of times, but not with Emma - she's just been doing whatever she's been doing in her hotel room and keeping herself to herself."

Support has also been provided by Tim Henman, who is working for television in New York, and Andy Murray, who has been watching avidly from the UK. Raducanu also spoke backstage to Virginia Wade after her fourth round victory.

Little did she know then that she would soon become the first British woman to reach a Grand Slam final since Wade at Wimbledon in 1977.

The list of media demands has grown as the fortnight has progressed. We have been granted among our first, in-person (masked) radio interviews since the pandemic began, and there has been interest from the New York Times, Fox Asia, the Japanese broadcaster Wowow, and even Der Spiegel magazine from Germany.

As well, naturally, as ESPN - the host broadcasters in the United States. Raducanu has been engaging and charming throughout, and won a new fan on her regular visits to the ESPN set.

"She has the same grace that she has on court," host Chris McKendry told me.

"She's very calm, she's very collected. She's composed, very well spoken. I love her story of going to traditional school and having her friends outside tennis who have kept her very grounded.

"She seems to be very interested in other topics. The other day we were talking about her studies and she has a very good brain for numbers. She told me on her bucket list is a visit to Wall Street.

"I don't want to get her hopes up but often if you win this tournament they have you ring the opening bell for the exchange. It's not often an 18-year-old champion tennis player wants to sit down and talk about Wall Street."

All Raducanu's challenges have been met head on. She fell asleep at 9pm on the night the torrential rain and tornado warning brought so much flooding and destruction to the region.

The following morning, she was due to play her second round match against Zhang Shuai at 11am local time. The journey in from Manhattan took a full 90 minutes. Raducanu missed her initial practice session, but seemed totally unperturbed.

Playing in the Arthur Ashe Stadium is also not to be taken lightly. There are seats for 24,000 people, 360 LED lights shining down from the roof during the night session, and 10 metre high digital billboards which spell out the names of the players in large, bold, flashing lettering.

And then there is the time away from home. The trip is now in its seventh week, a stark contrast to the 15 months spent at home studying and training during the pandemic.

But that is perhaps where Emma Raducanu has more in common with any other teenager.

'Are you missing your parents, and missing home?' I asked her once, in reference to the weeks spent in San Jose, Pennsylvania, Chicago and now New York.

"Isn't it every 18-year-old's dream?" was her nicely timed reply.