I had an interesting experience yesterday and I'm hoping someone can help me make sense of it. My IPS 121+ went out with me for my first serious uphill ride and I collected some numbers I can't quite explain.
My wheel has a nominal 350 Wh (Watt hour) energy capacity. I'm a pretty big guy (~100kg) and I went up a 75 meter (vertical) hill at a pretty slow pace, maybe around 6-8 km/h, total road distance about 1.5 km; parts of the hill are pretty steep. Initial battery state as reported by the IPS app was around 70%. By the time I got to the top of the hill, the app was reporting 35%.
Assuming that the percentage reported by the app refers to the energy left in the battery and not something else, my wheel used about 35% of 350 Wh = 122 Wh of energy bringing me up the hill. The actual physical (gravitational potential) energy of moving 115 kg (me + wheel) up 75m is ~85 kilojoules, or about 24 Wh. Going up a pretty steep incline, with really strong power draws from the batteries, plus all the balancing and everything else using energy on the wheel, it seemed reasonable to see a 20% efficiency. To recap:
24 Wh: minimum energy required to move me up the hill.
35%: battery capacity change
122 Wh: 35% of 350 Wh, the nominal battery capacity, the estimated actual energy used to move me up the hill.
20% energy efficiency: seems low, but what do I know?
Then what happened next surprised me.
I rode my wheel back down the hill, expecting to get back some amount of the lost energy through regenerative braking. From somewhere I got a 50% efficiency number on regenerative braking, so I expected to get back a little bit of energy. And indeed at the bottom of the hill, my battery was back up to 52% charge. So I got back 17% of my battery, which makes sense -- I used 35% going up, and got back 17% -- about half -- going down.
Except that would imply that my battery accumulated 60 Wh or energy going down a hill that only has 24 Wh of potential energy. Either IPS has managed a 250% efficiency in regenerative braking (someone call the Nobel committee!), or my math or physics is wrong. To recap:
24 Wh: maximum possible energy gained by rolling downhill
17%: battery capacity change (a gain this time)
60 Wh: 17% of 350 Wh, the estimated actual energy recovered by going downhill.
250% energy efficiency: huh?
Anyone have any insight? Are the battery ratings optimistic? Is the charge meter in the app wrong or non-linear or something else? Perhaps the actual nature of battery chemistry means my battery underreported charge after a big power draw?
If I assume that my wheel does recover 50% of downhill energy, and thus 24Wh / 2 = 12 Wh represents 17% of my battery, then its true (usable?) energy capacity would be only 70 Wh, a far cry from 350 Wh. (If this is common among EUs, someone must have noticed by now, right?)
Thoughts? Explanations? Ideas? Errors?