MONTREAL — High above the Earth, the lives of the Apollo 13 astronauts depended on a series of calculations by Canadian engineers. The slightest miscalculation could have meant death for the three-man crew.

“It carried the seeds of disaster if it went wrong,” says Ben Etkin, who was part of the University of Toronto Institute of Aerospace Studies team who helped rescue the astronauts 40 years ago ...

It was in the separation of the lunar and command modules that the Toronto team played a vital role.

Rockets that usually would have split the two vehicles were inoperable and it was decided to use pressure in the tunnel that connected the two units to perform the manoeuvre.

A ring of explosives located just 10 centimetres from the command module’s hatch would blow away the tunnel connecting the lunar module and the re-entry command module.

“That short tunnel had air in it that was pressurized and when the ring of explosives was set off, the two parts of the returning spacecraft would be pushed apart by the pressure in that tunnel,” Etkin said.

The University of Toronto team was asked to figure out exactly how much pressure was needed to separate the two modules.

“If the pressure was too low, the two parts of the spacecraft would not be pushed apart with sufficient speed,” Etkin noted.

“Above a certain pressure, the shock wave caused by the explosive could damage the entry hatch to the re-entry module.”

Etkin said if the hatch had been damaged it could have meant death for the astronauts during their return.

“During the approach, if the hatch was damaged and they lost air pressure inside the compartment due to leakage through that hatch, it would have been game over,” he said ...