Battery level seems to fluctuate depending on use

[Panpaper]

I?m pretty sure the battery level went down to half after going full power for a few minutes going up a hill. I switched back to PAS 1 after the hill, and the battery level seemed to go up 2 bars a few minutes later.

Weirdly, going PAS 0 doesn?t seem to cause the readings to go higher.

Does anyone have any insights as to why this happens? Also, how can I get an accurate gauge of the real battery level (for maintaining battery health)

[handlebar]

A battery has what they call internal resistance because its chemical reactions aren't instant. Pulling more amps means more voltage is lost in the battery and less voltage is available at the terminals. When  you stop drawing current, the voltage will rise immediately, then continue to rise as the battery recovers chemically.

The display of the Bolton controller I bought for my Radrunner would show voltage.  The Radpower display I added to my Radmission shows only watts, but I've found a trick. If I'm pedaling with PAS 1, it will show one of three wattage levels. I don't know how it chooses which level to choose, but the middle level is about 50. Read as volts, it will be within a volt of what I would measure with a multimeter if I removed the battery.

[DickB]

The voltage of Li-Ion cells depends upon their State Of Charge (SOC) - how much energy is in them - and how much current is being drawn. Refer to the chart for a Panasonic cell. The SOC can be estimated by measuring the cell (or battery) voltage.

The Rad battery indicators are simple voltmeters, and are meant to be read with no current draw.  This from Rad:

"Check the gauge when the bike is not moving. The LCD display gauge calculates battery life based on the battery power output (instantaneous voltage reading) and can fluctuate while riding if power demand and/or output changes. If you are riding, the battery reading should stabilize at the current battery capacity after about 5 seconds when power assist is off (pedal assist 0 and no throttle applied), the brakes are not activated, and while coasting on the bike."

https://radpowerbikes.zendesk.com/hc/en-us/articles/360006192213

The Rad battery meters are not linear. My chart showing battery voltage vs SOC was made via discharge tests on my Rover 5, and the battery indicator readings determined by substituting a variable power supply for the battery. Note that the bar-type meters can only show a range - for example, 4 bars is anywhere from about 48V to 50.5V, or 50% to 70% SOC.

[Eric7]

It takes some time for the chemistry to balance out as others have said. Hysteresis.  The voltage is measured right at the cathode and anode. But there is maybe 1 mm at least of chemicals (electrolytes) on top of the cathode and anode. You discharge the chemicals right at the cathode and anode and you measure a voltage there.  In reality there is probably a voltage gradient. It takes a bit of time for the chemicals to equilibrate. 

Also, the chemical reactions and side reactions are complicated and not as simple as they explained it - that is why batteries have a range of voltages from fully charged to partially charged to discharged completely beyond rechargeable.

You would probably get a better picture if you can measure the voltage across the whole length width and depth of the chemicals (electrolytes, anode, cathode) and then average or integrate the results. The problem with the current voltage meter is that, due to cost constraints which are reasonable, you are only taking a point source.

If you wait 5 to 10 minutes, don't use the battery, give everything a chance to settle, that would probably give you the best measurement.  But somebody with some experience could probably make an educated guess, integrating in their mind how hard the battery has been working and basing on their experience, and the guess would probably come pretty close.  For example, if I were climbing a hill hard on the throttle for a while, when I get to the top and ride slow, the meter will probably go up one bar.  It probably won't go up 2 bars.  And if I ride hard like that, I can assume I am not going to get the total range (in distance) from that battery. Things work well enough at least for me.