So where would this car end up on a list of the coolest – if at all? The arguments will rage long into the night. Me, I’ve never bought into all that wind-in-the-hair nonsense. Give me a piece of metal over my head any time. Who in their right mind would have, say, a Porsche 911 cabriolet over the real thing? Exactly.

So, if convertibles aren’t cool, where does that leave a convertible Rolls-Royce in a world where conspicuous consumption is becoming less and less welcome? The Phantom Drophead Coupe costs well over four crore rupees, occupies a lot of the gorgeous Italian roads I’ve been feeding it along and has the carbon footprint of a Chinese power station, and at times travels just 4.3km in exchange for one litre of fuel. This is not cool.

And yet... Doesn’t the little kid in you cheer at the prospect – real or imagined – of a Rolls-Royce Phantom passing by? A masterpiece, this enormous, baroque yet modern saloon has successfully redefined the concept of luxury motoring. Shorter of chassis and convertible of roof, the Drophead Coupe takes that process a stage further, This is motoring on a truly epic scale.

Here’s how it works. At 100kph, with your foot barely brushing at the throttle pedal, you can stroke this vast land yacht along almost on the whispered suggestion of power alone. It’s a unique sensation. The needle in Rolls’ version of a rev counter, the ‘power reserve’ gauge, hovers around 91. That’s 91 per cent – roughly 412bhp – sitting about twiddling its thumbs at 100kph. Now that is cool.

Mind you, you still need big cojones to get away with the Phantom DHC. Very few of us can manage the full P Diddy, and that’s what it demands. Driving this car is like having port and blue cheese for breakfast, lunch and dinner, Monday to Sunday. The line between feeling like a winner and looking like a loser is an easy one to cross.

For students of socio-economics or bewildered readers, the background is fascinating. Rolls reckons that there are 85,000 'ultra-high net worth' individuals in the world; i.e. people with Rs 150 crore in liquid assets. Their numbers are growing by 10 per cent every year; in the People's Republic of China, that well-known communist regime where the memory of Chairman Mao is fading by the day, it's 20 per cent. The super-luxury car market, where the threshold starts at Rs 70 lakh, is unsurprisingly booming off the back of all this activity. Rolls too: last year it sold 806 cars, up from 300 in 2003. And it has utterly defeated Maybach. Even stupidly rich people, it seems, aren't fooled by a gussied-up S-Class.

Here are a few more facts for you. Phantom owners typically run between five and eight cars (one, apparently, has 145). About 70 per cent own an ocean-going yacht; 40 per cent have jet aircraft. John Lennon had a Rolls-Royce; so, in a profound historical irony, did Lenin. As the gap between the haves and the have-nots becomes a chasm, what you're looking at here is a car so stratospherically special that even a sizeable chunk of the 'haves' can't, in fact, have it.

Has Rolls-Royce been down the pub since the Phantom arrived four years ago? Apparently not. 'Every exterior panel on the Drophead Coupe is new', it claims (get us some dry roasted nuts, would you ...). The team at Good wood has worked 'tirelessly' to turn 2004's 100EX 'experimental' concept car into a reality (... and a bag of pork rinds). A few old boys in a big shed armed with a pair of angle-grinders could have achieved more or less what you see here, but it would never have been so deeply impressive.

It takes almost 19 days to build a complete car. In becoming a DHc' the Phantom's aluminium space frame chassis has been shortened and beefed u~. Its distinctive, triangulated A-pillar is key to the car's roll-over protection, with struts that run all the way to the floor. It has wider sills, and there are additional aluminium extrusions. Two of these add rigidity to the structure above the rear wheel arches. In total, the convertible contains 140m of weld, 20m more than the bigger, longer Phantom saloon. The operation is performed entirely by hand at BMW's 'centre for aluminium competence' over in Germany.

Competence, eh? Imagine what they could do if they really got their shit together.

The Drophead is no prettier than the original Phantom. But that doesn't matter. We're in a land beyond pretty here. In terms of sheer physical presence, the DHC is in a league of its own. It also sits in a parking space of its own, because it's a behemoth: 250mm shorter than the saloon, but longer and railer than its only direct rival, the Bentley Azure. There are smaller planets.

Beauty is in the eye of the beholder, and recommend wearing sunglasses before beholding the DHC. Every one of its lamps, as with the saloon, somehow seems too small, lost in its vastness. It looks better - like so many nineteenth century buildings - lit up at night. Still, it manages its proportions pretty well and is a fabulously imposing thing, even if it falls short of outright elegance. The mammoth Rolls-Royce grille is at a jauntier angle now, and the car's body powers back from it in an epic, widescreen way.

But there's no getting round that mammothness. The DHC's H-point is comparable to an SUV's, and feels it. It also weighs 2,620kg. If it wasn't made from aluminium, you'd have to seek a special license to drive the Phantom.

There are some excellent touches though. The lid under which the roof stows is finished in a 30-piece teak wood that supports the car’s nautical inspiration. The bonnet can be had in stainless steel (the team admits to looking at a DeLorean, which rather undermines the quote from Henry Royce in the press kit about taking the best that exists and ,making it better) even though its proximity to the DHC’s super-heated aluminium front wings is potentially troublesome (aluminium on steel corrodes quickly). And the rear-opening doors are extremely elegant and surprisingly practical.

Then there’s the cabin. Again, there’s nothing like it. A Lexus LS460 comfortably outpoints it on gadgetry, but doesn’t comfortably outpoint it on comfort. Or appearance. The seats are superb, the fit and finish is exceptional, the design and layout of the instruments timeless. The materials are designed to be hard-wearing too. The floor mats are made of sisal, a super-strong Mexican natural fibre.

If we’re being fussy, the polished wood on the dashboard jars a little with thee teak that runs across the door tops. The cash-rich time-poor RR customer will also have even less patience with the i-Drive than a time-rich cash-poor one – there’s no menu/escape button so you could be trapped forever – although the Lexicon Logic 7 stereo is the best I’ve heard outside a professional recording studio. This is a standard fit, unlike the stainless steel bonnet and teak roof ‘deck’ (you choose how much extra income you want to blow). So, what exactly do you get for four-crore-plus?

One hell of an experience. Imagine a spectrum of motoring sensation. Or a pie chart. If the Ariel Atom is at one end, the Phantom DHC is right at the other. But they meet near the top, like two politicians with opposing ideologies, and what they have in common is unbelievable character and focus.

As per the SUV comparison, you climb up into the Drophead Coupe. The seats slide forward to allow passengers into the rear compartment; the runners, exposed and covered in plastic in most cars, the finished in chrome. Somewhere up ahead in the distance is the Spirit of Ecstasy; she’ll be the first to get it if you screw up a parking manoeuvre (with your insurer not far behind).

Yet commanding all this metal is a strangely delicate process. A slender column-mounted stalk puts you in charge of the six-speed transmission: up for reverse, down for drive, push in for park. Easy. The handbrake is electric, triggered by pushing a small button beside the start/stop one. The Phantom has a 453bhp 6.75-litre V12 engine, but you won’t hear it at tick over. No car is quieter.

You can barely hear it at 100 or 110kph either. Roof down, this is a nice speed to travel at, even if you do feel vaguely like an opiated player in an F Scott Fitzgerald novel. Turn-in? Steering feedback? Forget all that. You drive this thing with one finger, caressing it through a corner. Forward progress is silky, the ride as pillowy as you’d imagine without disconnecting you completely form the real world. The Drophead’s dampers have been re-calibrated, but it’s still cushion-of-air stuff. Even on 21-inch alloy wheels, the Phantom wears big tyres (taller on the front incidentally). And it shows.

The Rolls is a barge, right? Wrong. Somehow, despite its mass and planetary dimensions, it really handles. It’s stuff, and stiff cars usually go where you point them, even big ones. Its steering geometry is the same as the saloon’s, although a shorter wheelbase is said to promote agility. And it is agile. The Rolls rolls obviously, and in long, constant radius corners – like roundabouts for example – can adopt highly amusing angles. If three’s anyone in the back, they’ll probably start hitting you in the head at this point. How do you avoid this? Of course: by slowing down.

Which brings me to the bit I most love about this car. You simply don’t need to drive it until its door handles are scraping on the ground to feel like you are really driving. There is no envelope to push here. Simply being in it is the point o it, irrespective of what speed you are doing or how many corners the road ahead has.

Which means that what we have here, with global public opinion swinging towards the state of paranoia that it has been, is the perfect vehicle over now. Forget the Toyota Prius or Ford Mondeo. If I’m going to be stuck in a traffic jam on blazing hot day, please, Lord, make sure it’s in a Rolls-Royce Phantom Drophead Coupe.

Let them eat cake...