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IT IS probably around the mid-point of my second loop-the-loop, several thousand feet above the Nevada desert, when it first occurs to me that I do not have The Right Stuff. Chuck Yeager, the first pilot to break the sound barrier, had this ethereal, gutsy quality in spades and Tom Wolfe’s 1979 book and the subsequent Hollywood film about Yeager’s exploits reveal a fearless all-American hero who pushed his body to the limit, paving the way for the first space missions and Apollo moon landings.

I am not breaking any sound barriers but my body has certainly reached its limit. I am being tossed around the sky by Richard "Tex" Coe, a former US Air Force (USAF) pilot, in an Extra 330LC aerobatic plane and am trying to scream but can’t tell if any noise is coming out of my mouth. The plane pivots and goes into a sharp dive before looping again. I see the ground, then a blinding sun, then the ground again. The intense gravitational force from the loop and subsequent barrel roll makes it feel like there is an elephant sitting on my lap in the cramped cockpit, and the pressure on my eyes seems to be pushing them through the back of my skull.

I am drenched in sweat and don’t know which way is up or down, although I am keenly aware that I am about to be reacquainted with the breakfast sandwich (bacon, egg, cheese on a toasted ciabatta roll) that I unwisely ate an hour before my flight. All I can hear is Tex laughing uproariously. "What do you think of that?" he yells from his seat behind me as we spin around again, my nerves shredded. "Here we go... !"

My morning had started more sedately. I had been invited to sample Las Vegas’s latest offering for visiting thrill-seekers, and drove from my hotel on the Strip to a hangar at Henderson Executive Airport a few miles outside the city. Launched last year, Sky Combat Ace takes customers into the Nevada skies in dual-control planes, giving them a chance to take the controls and to engage in realistic aerial dogfights: a direct hit from a laser-sighted "gun" results in a puff of smoke from the opponent’s plane. The company website promises "absolutely no experience necessary".

At the hangar I meet Tex and his crew and am given a black flight suit to put on. Guest pilots are given a call-sign from a selection of names stuck on a wall. My opponent today, Glenn Davis, owner of a mechanical contracting company in Texas, is "Dead Eye"; Tex assigns me "Roller". So far, so Top Gun.

Next up is an explanation of basic flight manoeuvres, which Tex demonstrates using model planes on the ends of sticks. The planes compete in single combat, he says: his term is "21st-century jousting". He demonstrates how planes circle each other in the air, using phrases such as "lift vectors", "control zone" and "energy management", and showing how to look for an opening to take a shot. "It’s old-school, fighter pilot stuff," he says, from "the glory days of aviation".

When he was in the Air Force, Tex piloted F-16 fighter jets, flying combat missions in Iraq, Afghanistan and Bosnia. But he was part of a military machine that had total command of the skies. "In terms of aerial conflict we haven’t really seen significant combat since Vietnam," he says. One of his roles was to take people along with him for "incentive rides" to give USAF academy students and others a better understanding of flight operations. "It planted a seed," he says. "People should be able to do this without spending 12 years in the military."

When he finished his military career, he secured financial backing and Sky Combat Ace was born, providing visitors to Vegas with an adrenaline-packed alternative to losing your shirt at blackjack. My adrenaline is already pumping and we haven’t even left the ground yet. "This is where you sign your life away," says Tex, chuckling as I study a legal disclaimer that warns of the risks associated with high-speed aerial stunt flying (there are several, but "death" leaps out). And then we are ready. "That’s it," says Tex. "Time to pray to whatever god you believe in."

It is a sweltering summer day in the desert and with the hangar doors open we are hit by a blast of heat. I am struck by how light the Extra 330LC is: Tex drags it out of the hangar, explaining it weighs only 772kg. "Your car weighs more," he says.

Tex guns the engine and we are in the air, ascending sharply before banking and heading towards the nearby Hoover Dam. We fly in close formation with the other two aircraft (the third plane is filming our flight). It is all pleasant and rather relaxing until Tex decides to give me my first taste of G-force, banking the plane into a plummeting rightward turn.

"Ha ha!" he roars through the microphone. "How was that?"

"Great!" I lie, panting heavily and hoping he doesn’t do it again. We begin a more gentle turn over the vast expanse of the dam, which is a magnificent sight from the air, sunlight reflecting from the water, and descend into a rocky canyon, beginning what Tex describes as "dynamic low-level manoeuvring". I prefer to call it "sheer bloody terror" as we zig-zag perilously close to the canyon walls. "Too close?" he yells. "How about this?"

Soon it is my turn to take the controls. The joystick is incredibly sensitive but I eventually get the hang of it, gently easing it back as the nose tilts upwards, clearing the canyon and flying into the desert. Aerial combat is about to begin.

Glenn’s plane is to our right and we start with a couple of practice runs, circling each other. Then Tex lines up the plane and we suddenly have Glenn in our sights: I pull the trigger as his plane drifts across my line of vision and, implausibly, score a direct hit, a plume of smoke shooting from the rear of the aircraft. We circle again, he passes, I fire and, again score a hit. "Great shooting!" Tex yells.

Now we have to evade Glenn but he succeeds in hitting us once before the stunt portion of the flight begins. Tex throws the plane into a series of apparently gravity-defying rolls, flips and turns. We do an aileron roll, when the plane flips on its axis; a torque roll, essentially a spin while the aircraft is on an upwards vertical trajectory, and, probably the most terrifying, a hammer-head, in which the plane soars upwards at 90°, stops dead in the air and flips into a nose-dive, plummeting towards the earth.

At the end of this heart-stopping sequence I make good use of the white paper bag helpfully left in the cockpit for queasy flyers. Tex points the plane in the direction of the airport and gently guides us back to terra firma. I clamber out of the plane, resisting the urge to kiss the ground, and find myself staggering around, legs seemingly turned to jelly. Glenn congratulates my fortuitous sharp-shooting and enthuses about his experience in the air: he flew small Cessnas 20 years ago but says he has never encountered anything like the rush of the rolls and stunts we pulled over the desert. "It got pretty close to being too much a couple of times," he admits. "But it was one of the greatest experiences of my life."

I am just thankful to be back on the ground and doubt I will be rushing back for more hammer-heads any time soon. But for anyone who thinks they might have the right stuff — and the stomach for it — a visit to Sky Combat Ace is essential.

© 2012 The Financial Times Limited