Obviously both charts start with a filled tank/battery and ignore fuel/energy production. It only makes sense to belabor charging loss if you take the gas equivalents like fuel used in transportation to the gas station into account, and gasoline evaporative losses, and storage tank losses and so on.
I find the presentation confusing too, but with my limited understanding I think the total energy that's available to be used isn't 100% but 122%; the 100% is the share that is electricity.
In the bottom left corner, the image says "Percentage total may exceed 100% because regenerative braking recaptures energy and reuses it."
Also, it says: "Energy to wheels: 65% to 69% + 22% (recovered) = 87% to 91%"
Switch to the "City" tab, and the result is "94% to 100%".
It's not impossible to produce more useful work than the electricity being used - see for example heat pumps, which derive most of the heat from cooling down water (or air) which is "free", so they can generate 3-4W of heat out of 1W of electricity.
Of course, but the energy input of the battery consists of the electricity that was charged at the power socket plus the kinetic energy that is captured by regenerative braking.
First, you accelerate - this converts electricity from the battery into kinetic energy. Then, you brake - this converts kinetic energy to electricity and stores it in the battery. You can then convert it back into kinetic energy the next time you accelerate. Effectively you get to spend 22 out of 100Wh that you put in at the power socket twice. You can get 122Wh from the output of the battery before it's empty because it has a second input.
I find the confusing thing about this argument is that the kinetic energy that is eventually recuperated due to braking is counted as productive work. So this 87-91% ratio is how much kinetic energy was produced in total ("Energy to Wheels") - whether it eventually turned out to be useless due to braking or not - divided by the electricity charged at the power socket.
In contrast, an ICE car can't recuperate at all for lack of technology to synthesize gasoline, so the kinetic energy is converted to waste heat energy.
What would violate the principles of physics is if the captured energy were larger than the electricity that was originally put in (assuming no other inputs like a downward slope) - that would be a perpetual motion machine. At 100% recuperation, the car could never move.
> but the energy input of the battery consists of the electricity that was charged at the power socket plus the kinetic energy that is captured by regenerative braking.
The kinetic energy also came from the battery. There is no "extra" energy coming from nowhere.
> You can get 122Wh from the output of the battery before it's empty because it has a second input.
No, no, no. You cannot extract 122Wh from a battery that only has 100Wh in it. That "second input" also came from the battery. If your notion worked, you'd be a shoo-in for a Nobel Prize.
