Expressed as an engineering problem, the challenge is to consistently develop maximum downward force at a specific point on a cantilevered beam.
The complicating factor: The downward push is powered by gravity and channelled into the ball of a human foot, and the beam in question is a rough glass-fibre diving board whose finicky properties mean you have to hit the right spot – or within a centimetre or two of it.
Done right, you are flung up to the proper elevation to then spin 4 1/2 times before smoothly entering the water some 10 feet below the board.
And if you don't hit it flush?
Let's just say no one cares to think much about that.
It can also be a struggle to describe what it feels like when you're doing it.
"The spinning happens much faster than a 3 1/2 , the speed is incredible," Canadian diver Alexandre Despatie, a two-time Olympic silver medalist, said when asked how it feels.
"It's a very technical dive, as well as demanding."
The mechanics of the dive – which have been broken down into minute constituent parts by Diving Canada's experts – require tremendous arm strength to maintain the tuck.
"You have to keep it really tight, and you need to be patient on the board," Despatie said.
If the 27-year-old is to win a third medal in his fourth Games this summer in London, he will have to perfect dive 190C, the forward 4 1/2 somersault, or what everyone in the sport simply calls "the quad."
"It's almost a necessity to have it now if you expect to win," said Despatie, who was one of the early adopters of quad dives when he competed on the 10-metre tower.
The manoeuvre requires brute power, impeccable balance and an astronaut's sense of spatial awareness.
Edmonton-based diving eminence Herb Flewwelling, a former national team coach who is Canada's leading expert on the biomechanics of the sport, said years of science have gone into developing the skills and techniques the quad requires.
They are, broadly: Generating maximum power on the "hurdle," where the diver jumps onto the board to create thrust, maintaining appropriate balance and body position through takeoff, exploding through the revolutions, and straightening in time to enter the water.
That means using trampolines and special harnesses to learn how to optimize tumbling. There is also sophisticated video equipment to analyze footwork on the board, spinning in the air, and, crucially, the final splash as a diver breaks the water.
(The national diving team has been working to develop new high-speed camera technology to analyze entries – the problem is overcoming bubbles to get a clear shot.)
The emphasis on biomechanics – led by pioneers such as Flewwelling, who still acts as a technical adviser to the national team – has also been accompanied by ever-more sophisticated training regimes.
Like many top divers, Despatie takes ballet to help improve his balance and body awareness.
Precision matters a great deal, and so does strength, which is why divers tend to look as if they were sculpted from marble.
Missing the takeoff sweet spot by as little as two or three centimetres can result in a loss of acceleration that throws the timing out of whack; being off axis balance-wise can have disastrous consequences.
Despatie only recently returned to training after hitting his head on the diving board while practising an inward 3 1/2 (where the diver has his back to the water and jumps in toward the board).
Diving at the international level is hard, and the quad is just about the hardest thing a big-meet diver will have to do – although the forward 2 1/2 with three twists is close.
(Some Chinese competitors do that one in addition to the quad.)
Despatie's edge is his ability to do all the dives at a high level; the Canadian's quad may not be as good as Chinese diver He Chong's, but the three-time world champion is able to perform a wide variety of dives well enough to keep close on points.
"It's a little like a golf tournament: They can all make the spectacular shots, it's about who puts it together among the group of six or seven top guys and carries it throughout the round," said Mitch Geller, technical director of Diving Canada. "The great equalizer is that someone always has an Achilles heel, it's a question of how weak is their weakest link? Alex is strong throughout his list, he's truly a jack-of-all-trades."
Because points for each dive are tied to the degree of difficulty – and diving is about wringing every possible point out of every dive – consistency is key. And it's hard to get the quad down consistently.
"Objectively, it's probably 40-per-cent harder than a 3 1/2 , only certain people can do it, like Alex," Geller said. "There's a lot of complexity in getting the perfect tumble … the other problem is what the divers see is a blur."
But the training regimen Despatie and other top divers use – a combination of arduous repetition on the board, and aerial tumbling work – has yielded an interesting byproduct.
In a study he conducted on past Olympic winners, Flewwelling discovered their brains had an almost freakish ability to estimate even the smallest slivers of time.
"Within a 100th of a second, roughly," he said.
In a sport where visual cues are fleeting – and in a quad, moving almost too fast to see – an acute sense of where you are in a rotation that takes about one-third of a second is a precious tool to have.
And the careful breaking down of each dive's components has enabled people such as Flewwelling to come up with new hurdle techniques – one of his 12-year-old protégés has found a way to increase her power by nearly 20 per cent.
He estimates it won't be long before it's copied by other nations, like all Olympic pursuits, there is a good deal of imitation.
And in the arms race of sorts within diving, sometimes even the bad ideas and flaws end up getting lifted.
"In the 1970s, some Chinese coaches got hold of films of a pretty successful U.S. diver, who had a bad habit of looking at his feet when he dove. That's not something you typically want to do, but pretty soon all the Chinese divers were looking at their feet," he said.
"Later, some U.S. coaches saw that the Chinese were doing that and brought it back to their athletes. So sometimes trying to improve your knowledge actually sets you back."
This is the eighth part in a 10-part series on the science behind athletes' preparation for the London 2012 Summer Games. Next week: Track and Field