Updated: Jul 19
In 1970, Garand Goubau described the performance of wireless power transfer as a function of the area of the transmitter (At), receiver (Ar) the wavelength of the radio frequency (lamda) and the separation distance (D). This equation (known as Tau) yields a value that can then be used to determine how much transmitted energy arrives on the receiver. Looking at the above, you can see values above about 2.8 Tau get you 100% power arriving at the receiver. This has been confirmed analytically and experimentally, with phased arrays also conforming to this predicted performance. We believe you can actually exceed the above performance as well, and intend to demonstrate that in the next few months.
Guess what? A space based solar power system moving energy to the ground can achieve Tau above 2.8. At our maximum 40,000 km separation distance between ground station and satellite array, we only need a 2 km receiver to achieve that 100% - far lower than other designs as we intend to operate at 3cm wavelength. This allows far less land use than prior proposals, in fact almost five times less than a utility-scale solar farm for the same power level.
So what else is wireless power transfer good for? Many have suggested we try to replace high tension wires that dot the landscape. Others have worked on ways to recharge robots and other low power consumers while they are moving. So far, low power density of the beam prevents powering aircraft. We would argue that the development and deployment of wireless power transfer actually is best suited for Space Solar Power. The reason is this chart below.
You can see that the received power is logarithmic with aperture size as taught by Goubau. This means that for surface-to-surface power you need 8m at either end to just get a kilometer with decent efficiency, and 32m for 16km (which is about as far as you can get on the ground without being on a platform up in the air). These apertures are big, and hard to build to withstand weather. However, in space those issues don't exist and on the ground you can spread out as the aperture is facing the sky.
We would argue that Space Solar Power is a perfect fit for wireless power transfer.