The Tarmac has turned sticky in the heat. Sweat stings my eyes and yet I’m shivering. My stomach lurches, my head spins, my teeth chatter. Following a train of thought becomes impossible, as if each idea were too tired to pass the baton to the next. So my mind empties, until I’m aware of nothing but the need to maintain the slow rhythm of the pedals, to keep grinding uphill until I reach the next hairpin.

Be warned: cycling is addictive, and this is where it will lead you – perhaps not to this exact road, the infamous climb up to the ski resort of Alpe d’Huez, but probably here to the French Alps and certainly to this twilight world of exhaustion. Like the thousands of others taking up the sport (London has seen its number of cyclists double in the past seven years and New York saw a 29 per cent rise last year), I had begun with a modest commute. Then I bought a speedometer one idle lunch hour, and my fate was sealed: it was a natural progression to go from racing the other commuters between red lights, to buying a racing bike, training at weekends, flirting with Lycra and obsessively watching the Tour de France.

Football, tennis and rugby had always left me cold but here was an event so brutal that there was no need for subtle appreciation of sporting technique. The annual three-week, 2,000-plus mile race around France, which this weekend reaches the Alps and the hardest stages so far, has the air of gladiatorial combat. For the entertainment of spectators, the riders push themselves to the edge of endurance and sometimes beyond. Take the famous occasion in 1987 when the Irish rider Stephen Roche reached the finish line in La Plagne only to collapse, unable to move for half an hour and communicating with doctors only by blinking. He was eventually taken off by ambulance but the next day had to get up and ride another 116 miles. Britain’s most celebrated rider remains Tom Simpson, who in 1967 collapsed and died by the roadside on another sun-baked French mountain. Two others have died flying off mountain roads during high-speed descents, and in the first four days of this year’s race, five riders have suffered broken bones.

Cyclists seem to relish the morbid and the masochistic. The recently opened Rapha Cycling Clubs in New York and London proclaim their dedication to the “glory and suffering” of the sport. Lance Armstrong, seven-time Tour winner, was once asked what pleasure he took in riding for such long periods. “I don’t understand the question,” he replied, then later, in his autobiography confided: “I didn’t do it for pleasure, I did it for pain.”

Which is perhaps why every summer, more and more cyclists head to the Alps to put themselves through hell. Many do so by taking part in organised, one-day timed challenges. Last weekend, for example, 5,200 riders took part in La Marmotte, a 109-mile ride from Bourg d’Oisans to Alpe d’Huez. Next weekend 9,500 more will ride L’Etape, the route of which changes each year, to correspond to one of the toughest stages in that year’s Tour de France.

Others do week-long organised tours, using the services of a professional company to transport kit from hotel to hotel, provide mechanical support, and sometimes even trail behind the riders with a van in case the climbing gets too much.

I’d opted for the simpler alternative, so-called “credit-card touring”. Basically, this means taking just a small saddlebag, with room for one change of clothes and a toothbrush. Anything else you need, you stick on your credit card, and each night you hand your cycling clothes to the hotel laundry.

Travelling light, a friend and I were free to plot our own route, a four-day loop that included seven of the most famous Tour climbs. Riding them would be the equivalent of a cricket fan getting to play at Lord’s or the Oval. And using the overnight sleeper train to travel from Paris to the start, Bourg St Maurice, meant we could leave London on Thursday night and be back on Tuesday morning. It would be a sporting epic, squeezed into a mini-break.

From Bourg St Maurice, we pedalled up to Val d’Isère. After three and a half hours we reached the top, the 2,770m-high Col d’Iseran, where we turned in speechless circles, taking in the view. Then it was onwards, a glorious 35mph whizz down the far side of the mountain and into the Maurienne valley, before climbing again up to the resort of Valloire and our first hotel.

There followed one of cycling’s few wholly enjoyable aspects – the nightly carnival of guilt-free carbo-loading. In La Maison d’Angeline, a pretty restaurant in an old stone house, we indulged in dried sausages and hams, croziflettes (a local kind of pasta buried in melted cheese), then steaks and fruit tarts. After seven hours in the saddle, the heavy mountain food suddenly made sense.

The following days took us over the cols of Galibier, Croix de Fer and Madeleine and brought some low points – the terrifying moments when, flying downhill, we suddenly plunged into pitch-black and heavily pot-holed road tunnels; the night we arrived exhausted and crying out for a hot bath, to find the hotel had given away the room; and the time a bee flew unnoticed down my jersey, its stings making me think I was having a heart attack.

But they also brought fabulous views, glimpses of eagles, pretty hamlets and picnics in the long grass beside the road. And they brought us to the 21 hairpins of Alpe d’Huez.

It’s a road drenched in Tour history. At the bottom, we pass a plaque showing the record time for the 14km climb from the valley floor to the ski resort, 1,150m higher (37 minutes, by Marco Pantani in 1997). Each corner is numbered, allowing us to count down the amount of suffering left. Painted across the Tarmac are messages of support to the professionals – “Allez Sastre!” – while the gutters are littered with energy gel wrappers.

At each hairpin, there is momentary relief as the road levels off slightly, before the next upward ramp reveals itself. It would be easy to panic, especially as we are soon overtaken by a woman jogging, but we stay calm and simply submit to the next 90 minutes of pain. Cyclists love to talk in philosophical terms about such moments – of the opportunity to “find yourself” on the road. Perhaps this is true, but as I near the summit I understand that for me, this is simply the perfect escape: you are so utterly absorbed in the challenge that all daily worries simply vanish. And the beer at the top is pretty good, too.

Rail Europe (www.raileurope.com) offers return tickets from Paris to Bourg St Maurice from £66 (£109 from London). The Tour de France finishes in Paris on July 25

Tom Robbins is the FT’s travel editor

Challenges for serious cyclists

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