The batteries used in the MeloYelo e-bikes are made up of groups of several Lithium Ion cells, with the groups connected in series to produce the desired voltage.  The range of voltage between fully charged and fully discharged is much greater with these cells than many other battery types: typically 4.2V per cell when fully charged, 3V per cell fully discharged. They are rated for voltage half way through their range: usually 3.6V. In the case of the “36V” batteries, there are 10 groups of cells in series, so fully charged voltage will be approx 42V and the fully discharged voltage will be approx 30V.

The “energy remaining to voltage” graph is not a simple linear curve, and is dependent on battery temperature and rate of discharge. So on a hot day, with the battery discharging quickly (say on Level 5 assist) the curve will be different to a cool day with light load.

It is therefore basically impossible for a simple “battery gauge” to accurately relate voltage to remaining energy accurately in all circumstances, and they can at best be a general indicator.

Here’s a graph showing the different discharge characteristics at different discharge rates of a particular cell (not necessarily the exact cells used in the MeloYelo batteries, but the characteristic will be similar). As you can see the voltage / energy curves differ significantly.

The “C” shown is the rate of discharge, not temperature: it is the ratio of discharge current to the capacity of the battery. For example of you were drawing a current of 2.5A from a battery rated at 2.5Ah, that would be a “1C” discharge rate. If you were drawing a current of 10A, that would be 10/2.5 = 4C discharge, and a current of 1A would be 1 /2.5 = 0.4C discharge rate.

So you can see from this graph that this particular cell would fall to 3.6V at 80% discharge (20% energy remaining) when discharged at a 1C rate (blue line), but would not fall to that voltage until around 93% discharged (only 7% remaining) if discharged slowly, at 0.2C rate (green line).

To repeat: because of this characteristic of Lithium Ion cells, it is impossible for a simple voltmeter or voltage based “battery indicator” display to be completely and repeatably accurate in all circumstances, regardless of the quality of the equipment or how carefully it has been programmed.

They should be regarded as a general indicator only.