@John: I think rider input is making the difference there John, since the pedalbike facts are, as far as I know:
1) lighter (so not necessarily, but usually, smaller) wheels require less energy to accelerate, so lighter wheeled bikes accelerate better:
The adage is "a pound on the wheels equals two on the frame" meaning it takes twice the energy per unit weight to accelerate mass on a wheel than on the frame (including rider! - so reducing total wheel weight by say a full 2lb/~1kg would only give the same benefit as the rider losing 4lb/~2kg!) Very much a "performance" issue then, for when you're at your minimum weight already!
2) also lighter mass of bike & rider is easier to accelerate - as said above, follow the adage.
3) larger diameter wheels have less rolling resistance than smaller wheels: the main source of drag at lower speeds; high drag tyres (non-slicks e.g. knobbly MTB tyres or many tyres with too much unnecessary "ripply tread" or of a poor compound for rolling on road) will also seriously impede the top speed & efficiency at that speed). Also less bearing friction so more efficient.
Other efficiency losses from drivetrain, bearings etc. only make a big difference between bikes, I think, if the components are poor quality/design or poorly maintained. (all things being equal, the above factors are the main ones affecting efficiency, and rider weight & fitness probably the biggest! Still we're cycling to help stay/get fit & healthy, eh?!
)
Appropriate gearing always is important of course, but I've only outlined some of the main variables between bikes affecting efficiency.
EDIT: So far as I can tell, the main gains in the Q bike were from adding appropriate gearing to pedal-assist the motor, and significantly reducing the rolling resistance (and puncture risk!) with the tyre change - highlighting the relatively larger benefit of lower rolling resistance tyres on 20", though similar tyres on larger wheel sizes would also give large benefits. Both changes do work together to increase both "rollability & pedalability" of the Q: taking even a relatively small load off the motor can significantly increase efficiency and range - some hub motor bikes give up to 50% extra range with just a little pedalling
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Stuart.