When is it time to replace the battery?

^^^ this. Before I more or less retired it, I had a Luna 17.5ah 52v pack with almost 4000 cycles on it. That came from twice-daily charging (commute and charge at home and office) where I religiously charged to 80%, did not discharge below about 40% and performed monthly 100% balance charges. It was also using Samsung 25R cells which laugh at heavy loads, and since it was a single battery in a 2-battery 2wd bike, it didn't get beat on that hard. The pack is still alive and well. So, if you treat a pack right the 800 cycles you hear about are meaningless. You can get less than 400 too if you treat the pack wrong, or its made by chimps.

Insofar as being able to determine battery wear: Your battery will still charge to its full capacity as it did on Day 1. However, when it starts to wear down you will see that voltage 'flash off' until it drops to a lower level, and that is you actual voltage capacity. I can do a better job of explaining this with an example:

I have a battery that is a 52v battery. aka a '14S' pack. A 14S pack's actual peak voltage is 58.8v (just like a 48v battery is really 54.6v when full). So on this worn battery, I can charge it to 100%: 58.8v. Almost before I get down my driveway (which is about 20 feet) my voltage drops to 56.5v. From 56.5v on down, the pack slowly discharges as I'd expect it to.

To be able to spot this sort of thing, you have to have your screen display set to show you voltage and not percentage or worse.. a battery graphic with bars.

This is the most popular page on my site by a long shot:

What do you consider a full charge? As you've mentioned you don't take it below 40%? So you are only using 40% battery capacity at a time. As you've said you only charge to 80%.
 
I've miscalculated distance on my ebike twice, and took the battery till it turned off. I assume the BMS tuned it off. Since there is a safety feature on the BMS, how detrimental is this to the battery?
 
I've miscalculated distance on my ebike twice, and took the battery till it turned off. I assume the BMS tuned it off. Since there is a safety feature on the BMS, how detrimental is this to the battery?
Depending on your BMS.. they typically shutdown somewhere between 20 to 30% of actual battery capacity so though I try to avoid it... I wouldn't have a heart attack over it.
And those numbers can actually be higher if done under load due to voltage sag.
 
What do you consider a full charge? As you've mentioned you don't take it below 40%? So you are only using 40% battery capacity at a time. As you've said you only charge to 80%.
Full charge is whatever it is on a pack for a given voltage. But in terms of the pack usage you have things pretty much nailed.

I commuted on that bike so I knew how long my trip was. I charged at my work garage, so no concerns about running out on the way home. And same story for the next day's ride back since I also have a home charger.

When you use a bike for regular daily transportation across known distances, you can dial things in pretty well. And of course if I had to I could skip a charge at home or work... maybe shorten my route on the flip side. Or lets say I have a bank deposit to make (@PedalUma 's ears just perked up) I will charge at a higher amp rate for the morning before and afternoon after I get back from said bank, to make up for the extra midday trip. At home that night I'll be a little lower on the remaining SOC, but I can do the same variation in charging current to adjust for that.
 
The lifespan of ebike batteries can last at least 5 years and they could easily withstand 1,000 charge cycles to charge your batteries quickly. You also notice these signs such as slow charging, loss of mileage, and any damages,... that your battery needs to be changed.
 
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