Even Neil Armstrong would admit it’s a pretty big leap: to bale out of a balloon more than 20 miles above the surface of Earth, on the very edge of space, and let gravity take its course for a hair-raising seven minutes.

But this is what two men are racing to do, the only question being which one will jump first. In one corner is Michel Fournier, a 64-year-old former French paratrooper who has sold his furniture to finance the venture and says he has dedicated his life to making the jump. In the other is Steve Truglia, a former SAS soldier and stuntman from east London who believes the attempt is “the last great stunt left to do; the biggest adventure in the world”.

Whoever manages to make the jump first and survive it will break a world record that has stood for nearly 50 years. They will instantly take their place in the history books for completing the highest freefall as well as becoming the first person to break the sound barrier unaided.

Already the war of words between the two jumpers is hotting up. Fournier claims he is on course to complete the jump as early as this summer, which means he will beat Truglia to the record by a full year. He shrugs off concerns about his age and health, saying: “I am optimistic.”

However, Truglia, 47, says his plans won’t be altered by Fournier’s advanced schedule. “He has been saying he will make the jump for years, and so far he hasn’t,” he says. “There has been a lot of talk and no action; so far he hasn’t even been close. I am younger, fitter, more experienced and I am a doer – I can talk a great talk but I like to walk the walk.”

It takes a certain type of person to want to leap from the edge of space and plummet to the ground at more than 700mph, but Truglia – who made his name doing stunts in the Bond movies – believes he has what it takes. “I have been sat on a cherry picker, set on fire and then I’ve done a high fall for the cameras while not being able to see the bags underneath,” he says. “Being able to operate under that kind of pressure and do the right thing very quickly is a massive advantage when attempting something like this.”

It will take more than nerve to make the attempt a success: the technical hurdles are massive. At 120,000ft (22.7 miles to be exact) the temperature is about -100C and the air pressure is around 0.002 bar – almost a vacuum. To survive that, Truglia will be wearing a custom-made pressurised spacesuit from the same Russian company that produced Yuri Gagarin’s suit (“how cool is that?”), and he will be carrying his own oxygen.

The suit will be plugged into the life-support system onboard the balloon’s gondola for the ascent, which will keep the pressure constant. It will be unplugged when the time comes to jump, and Truglia will switch to a manual system that he will carry with him in a briefcase-sized box for the descent.

But first he has to get there. The journey into the upper stratosphere will take about 4½ hours with the gondola open to the elements, swinging beneath a huge, helium-filled balloon. Because the balloon’s gas expands as the atmosphere thins, the canvas must also be capable of expanding. “From zero to 120,000ft the balloon will expand 500 times,” says Truglia. “So on the ground it will look like a very long sausage, but up at 120,000ft it will be pumpkin shaped.”

The balloon, which is being custom-made by Andy Elson, the man behind the Breitling Orbiter 2 world circumnavigation attempt by balloon, will be 200ft high, and when fully inflated, 600ft across. “That means you have a huge surface area that isn’t filled as it is rising with a tiny bit of helium in the top, so the slightest breath of wind will put enormous pressure on it.”

If he gets his timing wrong there will be more than a breath of wind when he hits 80,000ft and the jet stream, a narrow air current. “There are two two-week windows when there is a gap in the jet stream, and I have to get through that gap or it’s ‘game over’,” he says.

“If I fail, the strength of the wind will rip the canvas and the capsule will come plunging down to earth. That’s fine because I have a parachute, but it will mean I got nearly there but not quite there.”

Once he is through the jet stream gap, the adventure begins in earnest. Truglia is following in the slipstream of arguably the most famous parachute jump ever. It was made by Joseph Kittinger, a US air force officer, who in the late 1950s was charged with taking part in a series of military tests designed to assess how effective a parachute would be for pilots forced to eject from the new jet aircraft that could travel at high altitudes. He made three jumps from ever increasing altitudes, the final one being in 1960, from 102,800ft (19.5 miles). He fell for 4min and 36sec, reaching a maximum speed of 714mph – according to US air force records – before opening his parachute at 18,000ft.

In the process he set the record for the highest balloon ascent, highest and longest parachute jump, and fastest unaided speed through the atmosphere by a man. Nobody has come near the records until now.

“I don’t know what to expect for the simple reason that no one really knows,” says Truglia. “I think the biggest threat will be making sure the suit doesn’t get damaged. If it does – say, maybe because it catches on the parachute harness – at any point after about 70,000ft, I am dead. Science tells us that in a near vacuum like that at 120,000ft, if your suit fails, your blood boils. I don’t know if that would actually happen, but you would probably have some sort of embolism and die very quickly.”

He will also need to make sure his oxygen supply is adequate and functioning: in 1964, during an attempt to beat Kittinger’s record, an amateur skydiver ran out of oxygen on the descent and suffocated before reaching the ground. Not that Truglia is dwelling on such possibilities now. “There will be enough time for that on the way up, watching the world get smaller and the sky turn black. But I can’t wait to be there, with the stars at eye level. There is no sound, no wind, the sun is blinding, and you can clearly see the curvature of Earth.”

The descent will be more hurried. Whereas most skydivers reach a terminal velocity of 120mph in about 12sec, Truglia will hit around 750mph in the same amount of time because of the thinness of the air, and will break the sound barrier. As he falls, air resistance will grow and he will slow back down to 120mph after about 30,000ft.

“The big thing is going to be resisting going into a spin,” he says. “Because there is no air to freefall in, whatever motion you start is very hard to correct. It’s very easy to start rotating and that can quickly end up at ridiculous rpm.”

To counteract the threat he will deploy a small stabilising parachute to keep his body facing Earth the moment he leaps from the gondola. Once in the dive, things are largely out of his hands. “I won’t have much to do, so I will be concentrating very hard and monitoring safety systems, checking I’m not breathing erratically, and watching my altitude.”

Because of the risk of losing consciousness during the drop, a parachute will automatically deploy at around 10,000ft unless he has already pulled the ripcord.

“Other than that, the main dangers are going to be getting hit by a passing airliner – which shouldn’t happen because they will know I am there – or twisting an ankle on landing,” Truglia says.

Before any of this, however, he needs to be sure that Fournier hasn’t already broken the record with his planned jump of 130,000ft (24.6 miles) in the early summer. Both men intend to launch from the same airstrip in Canada.

“If he is delayed by a year we could find ourselves next to each other,” says Truglia. “I wish him the best of luck, but I just don’t think he is able to do it – not with the equipment he has, and the strategy.”

In May Truglia will attempt to set the European record with a jump from 52,000ft as part of his training. He says it is a “statement of intent” as well as a ploy to raise sponsorship funds.

But for the big jump he already has one important backer. “I e-mailed Kittinger, telling him