Acknowledging the BikeRadar presenter's caveats, he seems to suggest that the potential 'perfect' chainline offered by such a gearbox is a key 'efficiency' factor. Not sure about that.
A paper reported in the reputable
IHPVA Technical Journal specifically "On the efficiency of bicycle chain drives" by James B. Spicer et al (Johns Hopkins University, Baltimore) and Masahiko Fukuda and Masao Terada (Shimano Inc., Product Engineering Division) (2000) suggests that:
"
chain-line offset and chain lubrication have a
negligible effect on efficiency under laboratory conditions."
It's rather heavy (bit like this possible gearbox, I suspect) so here are is (my) edited DISCUSSION AND CONCLUSIONS extract:
> Primary factors affecting the efficiency include the
sizes of the sprockets in the drive and the tension in the chain.
It was found that larger sprockets provide more efficient transfer of power while smaller sprockets proved
to be less efficient. . . . Typically, a 2–5% loss difference was measured between the 52–11 and the 52–21 sprocket combinations
> . . . the efficiency of the chain drive varied as a function of
chain tension. It was found that the efficiency varied linearly
with the reciprocal of the average chain tension [highest efficiencies occurring at high chain tensions] . . . highest efficiency measured in the study [was] 98.6%, and the lowest, 80.9%, . . .
> It was found that
chain-line offset and chain lubrication have a negligible effect on efficiency under laboratory conditions.
> No significant quantifiable effect of
lubrication could be inferred from these tests.
[Summary] . . . the efficiency of the bicycle chain drive depends intimately on the chain operation as it engages and
departs from the sprockets on the high tension part of the drive."