It's easy to spot our hire car when we arrive at Frankfurt airport. It's the one causing a commotion, at the centre of a small circle of curious onlookers. But then, calling the Carver a car is like calling champagne table wine. It's not really a car at all. It's a machine beamed down from the future.
It has two back wheels, like a car, but the front wheel of a motorbike. The driving seat looks like the cockpit of a fighter plane, and right now the front half is tilted at a 45-degree angle, a neat trick that's the key to its appeal, which enables it to "carve" around corners. And the technical stuff: a convertible with a 660cc turbocharged engine, it does 0-60 in eight seconds with a top speed of around 115mph.
It's such an exclusive machine that there are only 200 in the world, with about 30 here in Germany. And for three days only, this one's mine. But first I've got to learn to drive it . . .
Carsten Becker is my guide and, with fellow Carver expert Felix Zuckschwerdt, he gives me a quick drill in how to handle the tilting mechanism. Basically, you drive it exactly like a normal car, except you accelerate into corners, as you would on a motorbike. Crucially, you have to get used to your world tilting from side to side like a fairground ride.
Brief over, I'm ready to hit the road, or the autobahn, to be exact. "It's easier to get used to it on straight roads," Carsten assures me. I'm not sure if he notices how white my knuckles are, gripped around the racing-style steering wheel.
But once on the highway, I'm surprised by how quickly I take to the Carver. Germany is a nation of car lovers, and the autobahn on a weekend is like a meeting of car ads . . . but all eyes are on me: people hang out of windows laughing, wave and point, and give me the thumbs up at the lights. Unbidden, Kraftwerk's Autobahn pops into my head. I'm a machine! Look at me go. I catch sight of the speedometer, 160km/h (around 100mph). Slow by German standards, but as a Sunday driver, I'm horrified.
We soon leave the autobahn and head towards the Black Forest. I've been given a detailed map, with suggested stopping-off points, to that night's destination outside Freiberg. Idyllic villages slide past, wooden chalets decked out with flowers, country churches and carved shop fronts already decorated with Halloween pumpkins. Deeply wooded hills rise up on either side, and every so often the fresh tang of pine fills the air as we pass logging mills.
Freiberg is a historic university town with lively bars and restaurants, and a beautiful, ornate cathedral. We arrive at the Hotel Schloss Reinach with the sun still shining for a cool Weiss beer in the garden before tucking in to venison with beetroot and apple.
The following day we continue into the heart of the Black Forest, and I can understand why Carsten calls the roads here perfect "Carver roads". They loop gracefully up and down the mountains and I find myself eagerly hoping for the next set of dramatic curves so I can push the tilt to its limit. It's like skiing on a bike. Each town we stop at draws new admirers. As we eat schnitzel in the old market square at Freudenstadt, a child comes up to ask if I can make it fly. By the time we reach Hotel Heiligstein, among the vineyards near Baden-Baden, I'm completely used to the curiosity. It turns driving into a really sociable way of travelling.
Before we head back to Frankfurt we stop for lunch at Hirschhorn Schloss, one of the many old castles in this region. It sits on top of a steep hill with spectacular views over the Neckar river. A terrace restaurant serves traditional dishes such as sausage and cabbage, and Flammkuchen, a type of German pizza. As I eat, a disturbing thought crosses my mind: to my horror, I find myself agreeing with Jeremy Clarkson. As he concluded on Top Gear recently, the Carver is possibly the most fun you can have in a car.
• i2c Tourmanagement (00 49 61 75 79 88 62, i2c-tourmanagement.de) runs bespoke Carver tours. A two-person, three-day package costs from €2,399, including fuel, four-star accommodation with dinner and breakfast, transfers and itinerary. Hotel Schloss Reinach, Freiburg (+49 76 64 40 70, schlossreinach.de), has doubles from €109. Hotel Heiligenstein, Baden-Baden (+49 72 23 96 140, hotel-heiligenstein.de), has doubles from €110. British Airways (0844 493 0787, ba.com) flies from Heathrow and London City to Frankfurt from £109 rtn inc taxes. For more information on Carver cars, visit carverconcept.com