'Now might be a good time to clench your buttocks or your fists," Captain Steve Allright announces over the plane's PA as the most frightened flight to ever take off from Dublin Airport taxis down the runway.

"Clench. And release. And clench. And release. We're at 70 miles per hour. This is perfectly normal. All perfectly normal," the British Airways pilot says, his voice as soft and smooth as honey.

The plane’s pace picks up. “One hundred miles per hour. Perfectly normal. I want more smiling. Smiling and breathing. Everything is normal. One hundred and seventy miles per hour. Everything is normal.”

All around me are ashen-faced folk. Some are hyperventilating, others crying. No one is happy. Everything is a long way from normal. The plane leaves the ground.

Whoosh.

The sharp intake of breath from the 60 people who have paid €299 to take the BA Flying With Confidence course almost drowns out the engine’s drone. The captain with the most comforting name in flying keeps talking, reminding everyone that everything will be alright.

Allright has a first class degree in aeronautics and has piloted Boeing 747s since 1990. To date almost 50,000 people have completed his course in Heathrow, Gatwick, Glasgow, Edinburgh, New York, Dubai and Johannesburg with 98 per cent passing with flying colours.

The day starts with the good captain talking us through the noises we might hear before and during a flight. He explains the plane’s internal bings and bongs and the outside thuds. He goes into detail about an aircraft’s structure and how it can fly.

He tells us there's just one wing on a jet, running through the plane's torso so it can't physically break off in turbulence. A Boeing 777's wing produces 260 tonnes of lift while a Jumbo Jet can glide for 50km without engines, he says.

Everything is designed to put nervous flyers at their ease and help them deal with “ a proper psychological disorder”.

He says, broadly speaking, those with the fear fall into to two camps: people frightened of planes crashing and people terrified of having a panic attack or doing something embarrassing onboard.

“The definition of a phobia is that it is an irrational fear so we attack it on two fronts,” he says. “We give people a knowledge-based tool kit and there’s the psychological side. We teach people techniques to break into their fear and to take control of the mind and body, to be able to think more clearly.”

One in four people sitting on any plane has at least some degree of fear with one in 10 suffering badly. The fear affects all ages, though women are slightly more prone to it than men.

Ronald Reagan grew fearful after a rough flight in California in 1937 and for nearly 30 years he criss-crossed the US by train. As a politician he had no choice but to deal with his fear. Once a fellow passenger congratulated him on beating the phobia, to which he replied: "Overcome it? Hell! I'm holding this plane up in the air by sheer willpower."

Abba’s Agnetha Fältskog had a reputation for being reclusive but was just terrified of flying as she explained in a series of interviews two years ago. She said a bad fear turned unmanageable after a private jet she was on encountered bad weather in the US in 1979. “The pilot failed to land at the first attempt but then we landed at the second try . . . this event was a turning point,” she said.

When non-flying Dutchman Dennis Bergkamp joined Arsenal from Inter Milan in 1995, he had it written into his contract that he would never have to fly for football. His fear developed after multiple flights on small "boneshaker jets".

The scale of his fear was revealed in his autobiography. “It got so bad I would look up at the sky during away games to see what the weather was like. Were there any clouds coming? Sometimes I was preoccupied by the flight home while I was playing football. It was hell.”

The footballer, the politician and the singer were afraid because they’d flown through a perceived or actual incident. But these incidents are normal and safe, says Allright.

He cites the “go-around”, that moment experienced by the Abba singer. “It happens. It’s a normal part of flying. The go-around is always done for safety reasons.”

He says turbulence is caused by air currents and is a “trigger event” which switches on anxiety . While “it is uncomfortable, it is not dangerous”. He says this a lot over the course of the day.

“I always introduce it with one word: nature. What do babies do in turbulence? They sleep. Once you can convince a person that the plane is never in any structural danger – and that is one of the few 100 per cent guarantees I can give – the fear eases.”

Allright says 10 of the 60 people here today might have the “magic wand moment” and will disembark saying “they’re completely cured. The rest will be taking their first steps in learning how to manage their anxieties better.”

After Allright comes clinical psychologist Dr Stephen Petrie. He admits he has suffered from a chronic fear of flying and talks about the superstitions he used to get himself to board. He always wore stripy boxer shorts.

“Underwear was the key to flight safety,” he tells a laughing room. He carried a crucifix – although he was an atheist – and had a lucky penny. He always had to touch the outside of the plane before boarding and had to sit in seat number 23.

His superstitions or “safety behaviours” sound exhausting. He tells us they served a couple of purposes. “They offer short-term reassurances but they also reassert that flying is something dangerous, something inherently dangerous. It is not.”

He describes the fear of flying as the “Rolls-Royce of phobias”, one which is “pretty cool, complex, diverse. It involves the fear of heights, claustrophobia, the fear of fear, that meta worry when you are not sure what you are worried about so you worry about the worry.

“But it is also a most treatable phobia and one which is easy to fix. We can demonstrate how safe flying is and we can retrain the brain to accept flying. It might be a bit stressful but if you have the tools and techniques you can handle the stress. I don’t want to trivialise it, it can be debilitating and it can be devastating.”

Very briefly he refers to the Germanwings tragedy which happened days earlier. That crash – and others – can lead to confirmation bias but don't perceptibly change the safety stats. The chances of dying in a plane crash are still one in 11 million climbing to one in 19 million if you're flying on planes starting and finishing in the developed world.

“It is the safest thing you’re going to do today,” he says, his voice full of reassurance. “Get that into your head. It is the safest place you can get ill. We have defibrillators and trained paramedics up there and the response time is seconds.”

Imelda Matchett developed a fear of flying at the age of 13 on a flight in Mexico which flew through a thunderstorm. "Progressively it got worse until a couple of years ago when I was due to fly to Portugal with my mother and friend."

On the morning of the flight she got out of bed and told herself she couldn’t get board the plane. “I was very disappointed in myself. I decided at that point that I needed to get help. I’ve done a course before but I wanted to do this because it has a flight at the end.

“ I’m not nervous really. I think that’s because everyone is in the same boat. I think people who don’t have the fear don’t really understand it.”

She falls silent and Petrie opens the floor to questions. A woman says she feels “dread when the plane is landing. There is this surge of fear.” He tells her to “surf the surge, ride it out, you will get the better of it”.

Another woman asks if the end result will be “more about coping with your fear than getting over it. Will it ever end?” She sounds very sad. He tells her some people “will nail it today; for some people it will be the start of the process”.

We head to the airport’s departure gate. Before we leave the hotel where the course is taking place, four people hand back their boarding cards. They’re not ready. Another person jumps ship at the gate.

Aoife Kennedy sticks with it. Her fear meant she missed her own honeymoon. "We were meant to go to Dubai but I'd a meltdown in the airport. After that I stopped flying altogether. I feel like I've lost my confidence. I don't like that I can't get off the island. It boxes you in and it is just really embarrassing," she says.

I take my seat at the back. It’s hard not to feel tense. Passengers are rubbing each other’s backs and whispering words of encouragement. A man opposite me is in bits. He wants a different seat. A safer seat. He’s shaking.

Cliodhna Duggan from Raheny is a senior first officer on a Boeing 777 but today she's acting as cabin crew as is fellow BA pilot and sister Aoife. Cliodhna sits beside the shaking man and reassures him. "Maybe I'll give this seat a try, maybe I'll be able to switch later but for now I'll give it go. Maybe I'll be okay here," he says.

After the flight – complete with a wobbly landing – there’s applause. Matchett is relieved. And more confident.

“It makes senses. All the bumps and sounds are explained. I am going to Athens in August. I think I will be able to do it.”

Kennedy is upbeat. She and her husband plan to fly to London this summer. She thinks, right now, she will be up for it. She knows the world is waiting for her. See Tom Kelly on taking the controls of an Airbus in a flight simulator at Turkish Airlines’ training centre in Istanbul, page 34