CAP'DECOUVERTE, France -- Lance Armstrong lives to be challenged, and at this year's Tour de France, he is up against the biggest challenges he has faced in the past five.

It will be a brutal fight all the way to the finish line in Paris, and Lance is committed to giving every last ounce of his energy to win his fifth yellow jersey.

Jan Ullrich is perhaps the most talented cyclist in the world, and he announced his return to the top of professional cycling with a resounding win in Friday's 12th stage individual time trial.

Lance, U.S. Postal Service team director Johan Bruyneel, and I knew Ullrich's potential for the time trial, and once we saw the results of stage 12, the strategy for the Pyrenees became perfectly clear.

In order for Lance to win this year's Tour, he needs to attack Ullrich in the Pyrenees and build more of a lead than the German can take back in the stage 19 time trial. Lance has an advantage over Ullrich on steep ascents, and he is going to have to exploit that every chance he gets.

Power-to-weight ratio is one of the measures used to compare Tour de France contenders, and Armstrong has an advantage over Ullrich in that he has a higher ratio. To determine the ratio, we take a rider's maximum sustainable power and divide it by his weight in kilograms, giving us a value in watts per kilogram.

Power-to-weight ratio matters most in the mountains, where riders have to use their power to overcome the effects of gravity. If two riders produce the same wattage, the lighter man will climb faster. On flat ground, gravity and body weight don't matter as much, and the man who can produce the highest wattage has the advantage.

Having a high ratio gives Lance the ability to accelerate faster than his rivals on climbs. The steeper the pitch, the more this advantage is accentuated. Ullrich produces a lot of power and can maintain a very high climbing pace, but he is a big man and struggles to accelerate in response to attacks. Lance needs to exploit his power-to-weight ratio advantage and attack Ullrich in the Pyrenees.

There are precedents to support Lance's strategy. In 2000, he and Ullrich finished within 40 seconds of each other in the individual time trial, and then Armstrong took more than three minutes from the German on the summit finish to Hautacam. In 2001, the men were separated by one minute in a 31-kilometer individual time trial, and Lance accelerated away from Ullrich on Alp d'Huez to gain two minutes in about six kilometers of climbing. And earlier in this Tour, Lance again left Ullrich behind on the opening steep slopes of Alp d'Huez and finished 1:24 ahead of him.

The Spanish climbers in the Tour de France may help Armstrong accomplish his goals. The Pyrenees are on the border between Spain and France, and the Spanish fans come out in droves to support their heroes. It's not that Spanish climbers want Armstrong to win, but rather that they want to attack for stage wins and to move up the overall standings for themselves.

Euskaltel-Euskadi's Iban Mayo and ibanesto.com's Francisco Mancebo are now more than four minutes behind Armstrong, and more important, more than three minutes behind Alexandre Vinokourov in third place overall. While Ullrich and Armstrong are fighting for the top two places on the Tour de France podium, the Spaniards need to attack in the mountains for a chance at finishing third in Paris. Their efforts may inadvertently help Lance by increasing the pressure on Ullrich in the Pyrenees.

Ullrich appears to be stronger than in previous Tours, and Lance may take smaller chunks of time on each mountain stage than he has before, but the important thing is to build on the 34-second lead he preserved in the stage 12 time trial. Not only does this mean leaving Ullrich behind in the mountains, but it also means going for stage victories to try to get the 20-second time bonus awarded to the stage winner. The best-case scenario for Lance would be to leave the Pyrenees leading Ullrich by two minutes or more.

Lance Armstrong has always said the victories he values most are the ones earned through the hardest struggles. That's why the yellow jersey will never compare to his victory over cancer, the challenge he is most proud to have overcome.

The Tour de France is inconsequential compared to beating cancer, but Lance lives to make the most of his second chance at life. He set his sights on a fifth Tour de France victory, he knows he has to rise to the challenges facing him, and he won't back down without a fight.

Chris Carmichael has been Lance Armstrong's coach since 1990 and has guided him to four consecutive Tour de France titles. He is writing a twice-weekly column for The Associated Press during the Tour de France.