HAVANA — Endurance swimmer Penny Palfrey pushed through the calm waters of the Florida Straits Saturday, enduring jellyfish stings but otherwise encountering perfect conditions as she passed the halfway mark in her attempt to become the first woman to swim unassisted from Cuba to Florida.

The 49-year-old grandmother was still going strong 70 miles from her starting point at a marina in the Cuban capital, said Scott Woodburn, who is part of Palfrey’s landing team in the Florida Keys.

Woodburn said Palfrey was smiling and barking orders at team members accompanying her on kayaks and a catamaran as she kept up a torrid pace in a battle that tested the limits of human endurance and the will of the high seas.

She is “alert and swimming physically strong,” Woodburn said, adding that the bathwater-warm waters remained calm. “It couldn’t be better for her.”

Palfrey is no stranger to jellyfish stings, which forced her to abort two past swims in Hawaii.

A 20-year veteran of distance swimming, Palfrey’s personal best came last year when she completed 67 miles between Little Cayman and Grand Cayman islands.

The British-born Australian swimmer set off from Havana early Friday, slathering herself in sunblock and lubricant to prevent chafing. A member of Palfrey’s crew was tweeting to fans, while a webpage updated her location every 10 minutes or so based on data from a GPS device worn by the swimmer.

The site briefly went down overnight when it had to be reset, but was working again early Saturday.

As she presses into a second day, Palfrey will have to fight through physical and mental fatigue while fending off dehydration, hypothermia and dangerous marine life.

At her current rate, it would take her a bit more than 56 hours to complete the swim, slightly above her initial estimates. She would get to Florida this afternoon.

If Palfrey succeeds, she’ll go into the record books as the first woman to swim the Straits without the aid of a shark cage. Instead, she’s relying on equipment that surrounds her with an electrical field to deter the predators. Her support team consisted of more than a dozen navigators, handlers and medical personnel who were escorting her on the 44-foot catamaran Sealuver.

Australian Susie Maroney made the crossing in 1997 at age 22, but with a shark cage. American Diana Nyad made two unsuccessful cageless attempts last year on either side of her 62nd birthday, but had to call them off due to a debilitating asthma attack and painful Portuguese man o’ war stings. She plans to try again this summer.

Palfrey began the swim in a regular sporting swimsuit, but said Friday that she planned to put on a porous, non-buoyant Lycra bodysuit that provides cover down to the wrists and ankles whenever jellyfish may be a threat. That’s particularly the case at night.