The Vector V40R powerboat flipped over and hit a buoy in the Solent in May last year.
The teenage son of the driver spent a month in an induced coma after suffering life-threatening injuries.
He was saved by the "selfless" actions his father after the crash, said the Marine Accident Investigation Branch.
But the report said no written risk assessment had been carried out and the harbour authority had not been informed of the test run.
"None of the crew were wearing seatbelt harnesses or helmets, although this equipment was readily available as its use was mandatory when the boat was participating in organised racing events," it said.
Simon Dredge, aged 17 at the time of the accident on 13 May, was travelling with two others and his father Peter, a champion speedboat racer.
Peter Dredge swerved to miss what he believed was a diver's marker in the water.
The buoys were five-litre plastic containers used as fishing gear markers, which had been laid earlier that day.
They did not comply with the harbour authority's requirements.
"After the accident, when the driver realised his son was probably still inside the cockpit he did not hesitate in diving back under the boat to locate and rescue him.
"But for his swift action it is unlikely that his son would have survived," said the report.
The MAIB said the purpose of the report was not to apportion blame, but for "the prevention of future accidents".

It will add an extra 600 seats a day for commuters into the Welsh capital after being criticised for having too many overcrowded trains.
Arriva Trains Wales, whose Wales and Borders franchise expires in 2018, is adding morning weekday services into Cardiff Central from Barry and Radyr.
Economy minister Ken Skates had said Arriva's profits were "too high."
The Wales and Borders franchise - which is one of the UK's most heavily subsidised, receiving between Â£110m-Â£160m a year - has seen passenger numbers rise from 18 million in 2003 to 30 million.
About 265,000 people use Cardiff Central station weekly and a BBC investigation found overcrowding in Cardiff stations during the morning commute was rising at a faster rate than anywhere else outside London, according to figures from the Department for Transport.
Arriva Trains Wales now plans to add extra capacity and extra trains from 22 May on the following routes
Arriva Trains Wales said the additional trains were "subject to railway approval processes" but the announcement is "one of the most significant improvements to valleys commuters in a decade".
It said to implement the changes, the operator "needed to remove one midday Penarth service and one midday Barry service".
The firm has a zero growth contract - which means it has the same number of trains it had when it began operations in 2003.
It said the additions "would not have been possible" without Network Rail's recent Â£300m signalling upgrade works and new platform eight at Cardiff Central.
"This is one of the most significant improvements to valleys commuters in a decade, since the opening of the Ebbw Vale line," said Arriva Trains Wales customer services director, Lynne Milligan.
"With only a limited number of trains in our fleet and the lack of availability in the UK we have had to work hard to get the most from what we've got."
Network Rail Wales said "more trains are travelling through Cardiff than ever before".
The crew of a powerboat which crashed at 100mph were not using safety equipment during the high-speed test run, a report has said.
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Capacity on the "busiest trains" into Cardiff will double from May, Arriva Trains Wales has said.