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After eight matches over seven days of this Olympic women's curling marathon - to be concluded on Thursday - Martin's team, representing Great Britain, will book their place in the semi-finals today if they overcome Germany. They would be in the last four now had they beaten the United States last night, but they lost 6-5 after the extra end.
The match against Germany is Britain's last in the round-robin series and, with five victories and three defeats, it is now virtual sudden-death. However, they would have settled for being in this position before the tournament started. Few were predicting that they would get this far.
Before the Games, Britain's curling hopes had centred mainly on Hammy McMillan's men's team, but, while they were eliminated after losing five of their first six matches, the women have performed above themselves. "It has been very encouraging in a desperate week," Hew Chalmers, the team manager, said.
Yet it is barely a year since Martin required surgery to a knee. Having had to rush back, with her Olympic aspirations in mind, she denied herself the normal rehabilitation. "The knee has not had time to rest," Martin said. "Once I had qualified for the Olympics it was all go. It's fine, though - it's not hurting. I just need to look after it."
Which is what those who know her would have expected her to say. But Mike Hay, the Great Britain coach, said: "Rhona has never used it as an excuse, but we know it hampered her quite a bit. She has had problems since her operation but she has changed her delivery slightly and made the most of it. She had to make some technical adjustments to the position of her foot."
Martin describes herself as "part-time curler, part-time housewife". The curling part is more than just turning up to play. It may appear a game lacking much of a fitness requirement but, at this level, gym training is essential. Competitors must sweep furiously then get the heart-rate down before delivering the stones.
Debbie Knox, 33, a customer services representative, Fiona MacDonald, 27, an account manager, and Janice Rankin, 30, a recruitment administrator, are the other members of the all-Scottish Martin rink.
Rankin is a dedicated trainer, according to her husband, Steve. "Up at six, in the gym for an hour or more, and in work for 8.45," he said.
"A big part of the sport is sweeping and most people do not recognise it for what it is," Warwick Smith, of the Britain men's squad, said. "They think you are just diddling this brush backwards and forwards but it is horrendously tough to sweep flat out for 20 seconds then stop for a minute, and sweep again and again."
Chalmers said: "All of them do at least two to three sessions a week in the gym and, in some cases, four to five. They have a high carbohydrate diet and a have had team policy, since mid-summer, of absolutely no alcohol. They are trying to carry forward the image of curling."
Martin is described by Chalmers as "a good team player, a mature individual, and a level-headed girl". She is leading a team that has been growing in confidence. "These girls are on a roll," Chalmers said. "Their body language is good on the ice, and the opposition know that."
Other than in skating, no British woman has won a Winter Olympic medal and now, with Alex Coomber in skeleton bobsleigh, a double celebration is looming. Yet, like Coomber, who came into her sport through a British Aerospace have-a-go day, Martin's was a chance entry too.
"I was 17 and my brother persuaded me to try," Martin said. "I thought it might be fun."
It was, but not at the first attempt. "I fell, hated it, and I was freezing," she said. "Without my brother's persuasion I probably would not be here doing this now."
A mother of two, Martin's husband and children have stayed behind in Dunlop, Ayrshire, while the Olympics are on. There has been little contact apart from the dozen red roses delivered to her hotel on Valentine's Day. "During the competition you have to forget everything," Martin said. Except how to win. On that Martin's memory is working well.
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