Not to be defending/advocating that uBeam's tech is actually any good, but the inverse square law refers to omnidirectional transmission, while uBeam's claims are related to directional transmission of power.
Have you ever seen an audio frequency transducer (say up to 200 KHz) that delivered an actual beam?
Usually the inverse square law is very much in effect when it comes to audio, this is because the medium (waves in air) behaves as water does with waves do in a pond rather than say the light coming out of a laser or any other focused source of electromagnetic radiation.
Distance from the transmitter will very much be a factor.
I wasn't saying it wa snot a factor, and I totally agree with you, but the inverse square law per its exact definition does not apply here.
I think uBeam is another Theranos, but granted at a much smaller scale. Still can't believe it has raised so much money and so much press without basic questions really being answered.
These people got 53% efficiency at 1 meter, which gives some hope for ultrasonic power transfer: Roes, M.G.L.; Hendrix, M.A.M.; Duarte, J.L., "Contactless energy transfer through air by means of ultrasound," IECON 2011 - 37th Annual Conference on IEEE Industrial Electronics Society , vol., no., pp.1238,1243, 7-10 Nov. 2011
Abstract: An alternative approach to the wireless transfer of energy is proposed, employing acoustic waves in air. Unlike conventional methods, acoustic energy transfer is able to achieve energy transfer at high efficiencies over distances that are large in comparison to the dimensions of the transmitter and the receiver. This paper gives an overview of the principle and explains the different loss mechanisms that come into play. A theoretically limit on the achievable efficiency is calculated. It exceeds that of a comparable inductively coupled system by an order of magnitude. First preliminary measurements indicate that AET is feasible, although the measured efficiency is lower than the predicted theoretical limit.
Ok, I read the paper. You got that completely wrong, the 53% is theoretical performance at 1 meter, the actual peak performance measured was 16% at an extremely small distance and two full orders of magnitude less (so 1%) at a distance of 100 mm.
The maximum output they measured was 37 uW, so 1000 of these would output ~37 mW, with an input power 1000's of times higher.
If anything this paper is a nice example of how theory and practice differ. It also highlights another big loss factor for ultrasound power transmission, the angle of incidence, the power falls of as the co-sine of the angle between the transmitter and the receiver (maximum at 0 degrees, minimum at 90 degrees).
Grr. I can't access that paper but thank you for digging that up. If Animats' calculations above are accurate though then uBeam is at a very small fraction of that 53%.
Is there anything in that paper that could explain the difference?
If you make a free account at deepdyve.com, you can read a free online preview of the paper for 5 minutes. The paper is only six pages long so that might be enough time to find an answer the question. (Or enough time to take six screenshots...).
I don't know any more because that was how I found that and skimmed the paper about three years ago, for a prior discussion of uBeam here on HN.
Yes, I mentioned phased arrays in my earlier comment. Even so that's a lot less focused than what you might believe it does, it's more like a directional wavefront than a focused beam. So you'll still lose lots of power due to the expanding wavefront (conveniently left out of the wikipedia drawings but I can see why they did that).
Back when my dad still worked at Aberdeen University, they had a phased array of maybe 7 or 8 transducers of about 8 cm each, that at a range of 6 inches or so, could deliver a focused beam that would penetrate a phantom / lab animal enough to cook a 2 - 3 cm sphere several cm below the skin.
The research was aimed at basically heating carcinomas above the 44 oC needed to kill the cells.
So you can focus an ultrasound beam, but it seems like a heck of a way to charge a phone.
If you pump enough energy into the source, sure. But your average coffeeshop is not going to replace their ceilingtiles with what would be really inefficient space heaters in order to charge some phones (and cook the inhabitants in the process).
That's the whole point of the exercise here: if the efficiency isn't there the whole thing is dead because you can't be pumping kilowatts into space in order to get a few watts (or milliwatts) back out. The difference between the two will get converted into heat!
So the only way this will work is if the efficiency is really high, much higher than seems to be feasible right now.