Much greater surface area, so that part makes sense at least for flame-based cooking. I doubt it offers any benefit for non-flame-based cooking (elements, ceramic, etc. It might actually be a detriment because it would dissipate more energy. It goes both ways).
It looks like the inside of the pan has the same fins, which makes sense otherwise they'd have uneven thicknesses. That would be a serious cleaning issue.
> "It looks like the inside of the pan has the same fins, which makes sense otherwise they'd have uneven thicknesses. That would be a serious cleaning issue."
It would also make it nearly impossible to cook anything that needed to be stirred to prevent burning. Stirring a regular pot with a rubber spatula is pretty easy, but getting into all of those nooks? That looks like a royal pain.
It's probably alright for things that won't burn though, like soups.
So, methods that don't rely on the convection of air to the pan. I would guess an induction cook top would be a better example than a ceramic element.
At a quick glance, if these efficiency percentages being thrown around are actually comparable(maybe not), than induction still beats fancy convection pots even with heatsink bottoms like these:
http://www.appliancemagazine.com/editorial.php?article=2257&...
> It looks like the inside of the pan has the same fins
I couldn't find out if it does. I found others, like the pots in the link above that have a flat inside.
My guess is that using a pressure cooker with an induction cooktop fed by on-site solar would be the most efficiency possible, but I have not done the math and would love to be corrected.
>It looks like the inside of the pan has the same fins, which makes sense otherwise they'd have uneven thicknesses. That would be a serious cleaning issue.
Doesn't look like that at all to me; in fact I think if the inside was finned it would be an immediate no-go for most, for the very reason you've stated.
Given that the company goes to enormous lengths to never show or talk about the inside of the pan, I have to assume this is the Achilles heal. If the fins aren't replicated on the inside, then some areas will be mm from the flame, other areas cms (which, as an aside, means an enormous amount of material per pan) -- aluminum is a decent heat conductor, but that would still be a very bad recipe for cookware.
In addition they would be ridiculously expensive to manufacture if the fins were only on the outside. Normally cookware is made on a lathe (http://youtu.be/8uuFWzkRcAg?t=1m12s) or a press from sheet metal. So, if you have areas that are thicker than others you'd need to use an entirely different method of manufacturing them... like casting or welding on the "fins" after the rest of the pot/pan was shaped.
That reminds me of the guy who tried to protect his fingers from the pedestal grinder by using the sleeve of his hoodie instead of walking 20 feet to the tool room to get some gloves. His sleeve got caught at torn completely off. Fortunately he wasn't hurt and banned from the metal shop.
Might be wrong, but I suspect they don't show the inside because it looks like a normal saucepan and it's the futuristic exterior that likely gets them sales. Just can't see how a saucepan with those fins inside would be at all useful, whether they're far more efficient or not. Couldn't stir a sauce or easily cook pasta, etc?
It does mean they're covering maybe 60-70% of the UK's market (where this pan is sold) - gas use is very prevalent in the UK due to historically having being cheaper than electricity.
I don't see where it looks like there are fins on the inside, and I disagree with your insistence below that it must for heat-transfer reasons - the fins are (relatively) thin, so I'd estimate no point on the inside of the circumference would be several centimetres from the [hot air]. Besides, part of the point of the fins is that they capture heat from the air. Without any math required, if the fin is a reasonable conductor, this means the air is hotter than the fin, which is hotter than the inside of the pan. Where fins join the pan there's a large surface area capturing heat from the air going to a smaller area of pan, compared to gaps between fins where the area in contact with the air is approximately equal to the area of inside pan.
edit:
[Disclosure] Dr Povey was one of my tutors, and the bearded fellow with glasses in the video was a peer at college (six engineers in my year).
It looks like the inside of the pan has the same fins, which makes sense otherwise they'd have uneven thicknesses. That would be a serious cleaning issue.