THE crew of a Loch Lomond cabin cruiser sailed past an inflatable speedboat thinking that the girl on board was waving at them in greeting. In fact, the distraught teenager was trying to flag them down to help her drowning father and sister.

The tragedy is described in a report into the deaths earlier this year of Angus Buchanan, 45, from Glasgow, and his 13year-old daughter Holly, who were pitched into the loch's icy waters when their craft lurched abruptly to one side.

A preliminary report into the tragedy on March 13 found that the boat's steering system was faulty, and that the family - Mr Buchanan, Holly, and her sister Chloe, 15 - had not been wearing life-jackets.

Yesterday's full report by the Marine Accident Investigation Branch (MAIB) described Chloe's attempts to save the other two, signalling in vain for help from the cruiser, then steering the rigid inflatable boat (RIB) back to the accident scene and jumping in after them.

When she reached Holly, she placed her hands under her arms and attempted to keep her head above the surface, then tried without success to lift her on to the RIB.

"However, despite courageous attempts to rescue her sister, the effects of cold water forced [Chloe] to reboard the RIB, after which she lost sight of both her younger sister and her father, " the report says. In spite of extensive searching by rescue teams and helicopters, the two were never found.

The report said: "A passing cruiser had seen the RIB at a distance and saw the elder daughter raise an arm. However, the people on the cruiser mistook this gesture as a greeting, and not one of alarm, and they continued, oblivious to the emergency, passing between the RIB and the two in the water."

After her vain rescue attempt, Chloe steered towards two fishermen in a boat, who raised the alarm by mobile phone.

Mr Buchanan, an experienced ocean-going yachtsman but with limited experience on RIBs, had taken his daughters for a day trip for the first time that season, the boat having been laid-up for the winter.

On the way to the Balloch slipway, where they launched the boat, the realised they had forgotten their life-jackets, but decided to press on with the trip. They travelled for about 20 minutes to the island of Inchlonaig, where they picnicked. The accident happened in Milarrochy Bay, not long after they had set off for home.

The report concluded that the accident was caused by the loss of hydraulic oil from the boat steering system. Leakage of oil, and the entry of air and water into the system, rendered the steering unstable, causing it to veer violently to port.

A water temperature of around 3C would have caused cold shock, rapidly reducing their ability to stay afloat, the MAIB said. In addition, the "kill cord" that would have cut out the engine when Mr Buchanan was thrown into the water was not attached to him.

As a result the boat kept going, travelling some distance from the scene as Chloe struggled to her feet and made her way forward to take the helm.

If the kill cord had been in operation, the boat would have come to a halt, possibly close enough to the accident scene toallow the two to swim for safety, the report says.

The organisation has already warned that the tragedy could have been avoided had the family been wearing lifejackets. They could have kept Mr Buchanan and Holly alive for some time, even if they were unconscious.

Among the MAIB's conclusions is a recommendation that anyone using power boats should first attend a practical course by the Royal Yachting Association.

Since the accident, the Loch Lomond & Trossachs National Park Authority has reviewed its bylaws concerning life-jackets. They are likely to be made compulsory by boat users by next summer, the MAIB said.