To make things more complicated, a lead acid battery has an internal resistance that varies with the state of charge. This means that the voltage measured on the terminals varies with the current being drawn from the battery. Ohm's law states that voltage = current * resistance. And so as the current increases the voltage drop over the internal resistance increases.
So your battery might say it is 12.5v, which might mean that it is about 70% charged with no load on it, or it might be 100% charged, but under a load of maybe 5-6 amps.
So in an ideal world the only way to get a true reading of the state of charge of a battery is to take a reading when it has been sat still for several hours with no charge going in or out ('at rest'). However in the general life of a battery in a motorhome this ideal scenario is very unlikely. The battery is constantly under a load (e.g. the fridge compressor kicking in every 10 minutes or so). Or the solar panels are putting some charge in.
There are two general ways to try and monitor the state of the battery:
- Counting the current going in and out (coulomb counting)
- Monitoring the raw voltage very closely
The Nasa BM-1 is an example of the first approach. It monitors the current very frequently (maybe many times per second) and keeps track of the current drawn over time. If you have a 100Ah battery and the BM-1 monitors that you draw an average of 2 amps over 24 hours then it knows you have drawn 48 amp-hours (Ah) and so have drawn about half of energy out of the battery. In most cases you don't want to go below around 50% repeatedly from a leisure battery otherwise you will shorten it's life.
To make matters even more complicated there is an effect called Peukert's law which states that the greater the current you draw from the battery, the lower its apparent capacity is. This is why proper leisure batteriers give several 'capacities' depending on how much current is drawn from them. This is normally expressed as a fraction of the total capacity. e.g they may say a 'C/20 capacity of 115Ah' This means this if you draw the capacity of the battery (115Ah) over 20 hours (ie. 5.75A) then it will be a 115Ah battery. If, instead, you draw the total capacity over 5 hours, C/5, ie 23 amps, then is will appear more like a 90Ah battery.
So in short, the greater the current you draw from the battery, the smaller the effective battery capacity.
One battery monitor which doesn't use coulomb counting is the SmartGauge. This *just* monitors the battery voltage and from there attempts to mathematically model the battery and estimate the state of charge. To be honest, it sounds like a good idea, but again, as it doesn't monitor the current being drawn I can't see how it can accurately determine the state of charge of a battery under load.
Oh, and if that is not complicated enough, temperature also plays an effect. The ideal temperature for a lead acid battery is 25 degrees C. If the battery is used in temperatures lower than that then the capacity appears smallers. If above that then the capacity appears greater -- but the battery's life will be shortened by higher temps. Think about how your car battery has a harder time starting the car/van when it is cold. This is why.
A battery at 0 degrees C will only 90% of that of one at 25 degrees.
There is a large number of research papers out there that try to formulate ways to estimate the terminal voltage of a lead acid battery under load. I'm hoping to be able to understand some of them and try and use some of the equations in this project.