This wasn’t something as simple as mere joy. Carmelita Jeter looked to be hyperventilating on the track in Thessalonika, Greece, back in the summer of 2009. With eyes bulging in disbelief, she gasped and sobbed and screamed, then fell to the track.

She had just won a 100-meter race at a major international grand prix in 10.67 seconds. Though the event lacked the prestige of the 2012 Summer Games in London, where Jeter could become one of the world’s biggest stars, her finishing time plunged her into an unexpected, rarefied realm.

She had become the fastest woman in the world, and the third-fastest in history.

“She was lit up,” said John Smith, her coach and sprint guru. “Her whole aura just changed. I saw something transformed . . . It was remarkable.”

The time, 0.16 of a second faster than her personal best, validated the mentally trying, occasionally humiliating work she had endured under Smith for the previous year. From the first day Jeter arrived to Smith’s Los Angeles-based professional running group late in 2008, Smith used novel, state-of-the-art video technology to bolster a teaching program he had refined for years. He unapologetically tore up her technique.

Smith and a virtual assistant — a digital model of Jeter who could simulate world-record speeds — forced her, in essence, to re-learn how to run at age 29.

But she did not truly comprehend the majesty of the science of sprinting until she crossed the finish line at the jammed stadium in Thessalonika. In that race, Jeter experienced, for the first time in her life, the soaring ease of technical transcendence.

“It took a while,” she said before a recent weekday training session at West Los Angeles College in Culver City. “It didn’t happen overnight. [Before], I was running age group, like a kid. I was just out there running, all over the place, my head bobbing, arms moving from side to side. Now, I look like a professional.”

In that 10.67 seconds, Jeter executed some 50 strides almost perfectly. It was a perfection she could actually feel. The time has been surpassed only by late world-record holder Florence-Griffith Joyner, who ran a 10.49 at the U.S. Olympic trials in 1988, and Marion Jones, who achieved 10.65 in 1998 but later admitted using steroids.

Smith watched the race in Thessalonika on a television monitor from the bowels of the stadium. When he heard the time, he started running. He sprinted through the stadium’s underbelly to get to Jeter, whose raw emotional celebration continued long after the race.

“I didn’t think,” she said. “The gun clicked, and I executed. . . It just came second nature. I looked at the clock and I just fell to the ground. I’m crying and I’m screaming, because . . . I actually did it.”

A week later at a race in Shanghai, Jeter ran even faster, winning in 10.64, a time that made her the second-fleetest woman ever, behind only the legend known as Flo-Jo.

‘This is a job’

At Los Angeles’s Bishop Montgomery High, Jeter displayed blazing natural speed. By the time she was a senior, she had run 11.7 in the 100. At Division II Cal State Dominguez Hills, she became the first athlete from her school to qualify for the Olympic trials, an event that introduced her to the exclusive world of elite sprinting in 2004.

“Being in that setting made me realize, these women are not playing,” said Jeter, who did not make it out of the first round of the 100. “This is a job. I saw a different side of track and field. It pushed me to say, ‘You are capable of doing what these women are doing, but you have to change your mind-set.’”

Jeter continued to train with her college coach after her 2006 graduation. A year later, she qualified for the U.S. team that competed at the world championships in Osaka, and surprisingly won a bronze medal in the 100 as she lowered her personal best to 11.02.

Smith, who barely knew Jeter at the time, recalled watching her in amazement. In a race slowed by a strong headwind, she finished just .01 behind Jamaica’s Veronica Campbell and U.S. teammate Lauryn Williams.

“What she was doing, I’m like, ‘Wow,’ ” Smith said. “In Osaka, when she got third, she was just raw. No technique at all. Head back, arms all over the place. [Yet] she almost won the race. She just leaned the wrong way.”

A year later, after failing to make the 2008 Olympic team, Jeter showed up in Smith’s camp, seeking direction and help. She knew he had previously coached Olympic champion Maurice Greene and other stars.

At her first weight training session, she carried a weight belt and cushion for her neck, intending to use both for support. Smith grabbed the items and threw them across the room in annoyance.

He considered such implements crutches that would prevent the development of proper form. She would train with weights — something she had done little of previously — in precisely the same way she would train on the track: striving for perfect body movements every single time.

“On day one, I was calling my dad like, ‘I don’t think this is going to work,’ ” Jeter recalled. “On the second day, I was like, ‘I don’t want to go to practice.’ On the third day I was like, ‘I don’t think I want to train with him.’ . . . He was really tough on me. Everything was technical, technical, technical.”

In their first weeks together, Smith sensed Jeter’s unease but also her determination. He figured if he couldn’t assuage the former, he would tantalize the latter. At the time, her personal best in the 100 was 10.90. Her mechanics were so unrefined, he felt certain she could gain three-tenths of a second just by sharpening execution.

So he told her that. During one of their earliest training sessions, he projected she would run a 10.6 — a time she had never even dared to imagine.

When he said it, Smith studied Jeter’s reaction.

She looked at him but didn’t say a word.

“Yeah!” he recalled exclaiming, breaking the silence between them. “You’re crazy like me! You looked at it and entertained it. . . . Let’s shoot for the moon.’ ”

Visualizing technique

For most people, a 100-meter sprint goes by in a blur. But what appears as indecipherable as a foreign alphabet to casual sports fans offers a wealth of information to Smith and Ralph Mann, USA Track and Field’s director of elite sprints and hurdles, who has supplemented Smith’s work in recent years with the sophisticated video analysis.

Mann, who turned his doctoral dissertation on human modeling into the core function of his company CompuSport, played an integral role in helping Jeter comprehend the transformation she was ordered to undergo.

He could create a digital image of Jeter’s body in stick form, and then make the stick figure run a world-record time. He would overlay that image — that of Jeter setting a world record — over Jeter’s body, showing her where she should be every step down the track.

“I was always teaching it,” said Smith, a former quarter-miler at UCLA who developed his approach from a kinesiology course. “But now I have data to sweeten up my information, and she’s the beneficiary of it.”

The visuals from Mann helped; Jeter wanted clear instructions, not a course in advanced physics. To correct her arms, Smith told her to imagine chopping wood while moving down the track. The floppiness in the wrist? Had to go. The weak movement forward and back? Needed purpose and power.

“The forearm, elbow and shoulder — those are three levers,” Smith said. “The key is to have those levers in synch together.”

And all that bouncing and rolling of her head? Smith gets worked up merely trying to explain about how counterproductive it is.

“You got eight pounds sitting on top of everything else,” he said. “You’re bobbing your head, that throws everything off. When you are moving that fast and using that much force, you move your head two degrees over and the stresses run down the body. It makes you sit on the track. You want to stabilize your head, make it work for you.”

Some changes came quickly, but others seemed to defy Jeter’s instincts. She occasionally labored for hours over a small detail, but couldn’t seem to do it. Other times, she got tired of trying.

“Sometimes you’re stubborn,” she said. “Sometimes you don’t want to learn new things. His program is, you’re either going to learn what I teach, or you’re going to leave.

“He would say, ‘Lift your chin, drop your chin, pick up in your hand, tuck in your elbow, lift your knee, arch your back, turn your head,’ ” Jeter said. “I was getting all these commands. I was like, ‘Oh! Okay! All right! All right!’ ”

On a recent weekday morning, Mann and a team of scientists showed up to West Los Angeles College. They pitched a tent, opened some folding tables and set up a pair of computers and video monitors alongside the track.

Then, they recorded Jeter’s start repeatedly, playing it back for her with the image of the world-record-breaking Jeter overlaid on top. After every start, Jeter, Smith, Mann and various others would huddle around the screens, digesting the data on the monitors. The first recording showed a problem with Jeter’s second step out of the blocks.

The model indicated she was striding too far. Mann and Smith explained that a shorter second step would help her generate more power, which would get her to move faster down the track. The larger step was only pushing her higher into the air. Air time is useless time. With just a few attempts, she corrected the overstride.

After studying a host of starts, the analysis moved to a 22-meter segment in the middle of her race. Flaws became more imperceptible.

“Your arms are exactly where they need to be,” Mann said as he stared at a monitor after one of her final sprints. “You are actually beating the model.”

‘A huge transformation’

Since her breakthrough in Thessalonika, Jeter has faced as much skepticism as acclaim. Though Jeter has never flunked a performance-enhancing drug test, her incredible performances and significant time drops have raised eyebrows. She and Smith maintain that anyone who studies her technical advancement and considers the changes she made in the weight room will understand how she runs so fast, that performance-enhancing drugs don’t have to be the answer to the question that Thessalonka and Shanghai generated: Where did that come from?

Calculations from video taken before she joined Smith to last summer demonstrate a decrease in stride length and time in the air, and an increase in stride rate and velocity, according to Mann. The first two clearly indicate technical changes.

“Having seen her performance before she started working with John and now, it’s just a huge transformation,” Mann said. “She’s improved in every area. Back in the days of drugs, there were some athletes where virtually all of their improvement came from strength improvement . . . How they did it was obvious to us.”

Many wonder if she will return to the blinding times of ’09 ever again. Though she won the 100 world title last year in Daegu, South Korea, she hasn’t approached her personal best over the last two seasons. That’s in part because, she said, she’s had mostly bad race-day conditions: cold weather or strong headwinds.

She believes she can hit 10.6 again at some point, but times will not be her first concern in London.

“I’m ready for 2012,” she said. “I’m not looking for a time, because you can win a race in 11-flat . . . It’s always about technique. That’s one thing you’re not able to lose regardless of whether it’s rainy or windy. You have to keep your technique.”