Range vs Battery (AmpHour / WattHour) capacity in bike reviews.
There is a very important aspect of simple physics which I feel is not given enough attention and that is simply the large and significant Potential Energy (qv.) involved in lifting any ("average", not overweight) rider of, say, 80kg up through a change in ground height. This
has to come from somewhere and if not the battery, then from the rider's pedal efforts.
Therfore I think an important point not sufficiently emphasised or noted is the rider weight and the total hill climb height tackled on rides. This can outweigh all other energy draws on the battery and these numbers perhaps should be stipulated and made clear on all reviews, even if the elevations tackled are a very very rough estimate.
For example:
To raise an 80kg individual plus 25kg bike weight up to the top of a half dozen 100ft hills (182.88m height change) will require
[105 x g x 182.88] = [105 x 9.8 x 182.88] = 188,184 Joules.
(g is the grav. constant near the earth's surface = 9.8 m/sec/sec).
A typical 300Wh battery has the energy equivalent of 1080 KiloJoules.
Therefore even assuming 100% efficiency in energy conversion through the motor, using a hub motor with a throttle (no pedal effort input), you would use up over 17% (188.14/1080 = 0.174) of the energy in your battery. And if the rider is, say 125kg, then this would use up 25% of your battery. Or put another way your battery (under ideal circumstances and inputting energy on its own) would be one quarter depleted just getting you up one 500ft hill plus one 100ft hill. And this is considering only the energy needed for change in vertical height before the adding in of other frictional energy losses and less than 100% energy conversion by the motor. One can also see why the weight of the rider makes such an enormous difference in the calculations, including consideration of number of stop-starts (building up kinetic energy of the bike+rider and then losing it). Without substantial energy input from the rider, the bike+rider would never manage any slopes for any distance. The 'average' fit looking 5'10" man would weigh around 80kg; just going up to 125kg in the rider probably mandates a 50% or even doubling of the battery capacity if it is a hilly area -- or the rider should get him/herself fit more quickly to get a reasonable range!
Some might wonder what happens to all that Potential Energy acquired when you get to the top of the hill. Well, unfortunately it is all lost in heat (wheel braking) and air resistance drag when you go down the other side. You
might be able to utilise a little bit of the acquired Kinetic Energy to carry you a short distance up the consecutive hill or along the flat at the bottom, but to all intents and purposes 99% is lost when you go down a hill. Still, the wind in your hair temporarily whipping past is a bonus!.
Some physics info below (if it pastes alright..) I hope others also find I have done the arithmetic right in my first post to this forum....!
Regards
WR