Calculating A/H rating on lead acid batteries


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Recently, I was asked to help a customer with a battery circuit in which he wanted to put 10 12V batteries in series to increase the A/H rating by ten times. I knew that this was not the correct method to do what he wanted to do.

In short, batteries in series increase the source voltage to the circuit, while batteries in parallel increase available current. If you look at the circuit diagrams below, it may help.

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In the drawings above you can see that in a series circuit, if the load looks at the batteries it is seeing two cells or two voltage sources, and the current has to flow from one cell to the other on the way to the load. In the Parallel circuit the load is seeing one cell with twice the plate width so the voltage is the same as a single cell but the current can flow from either or both cells directly to the load. With two independent sources of current you are effectively doubling the current capacity.

However, working on this project made me realize that A/H cold cranking amps and a few other terms were not items I’d previously been well familiar with, so I needed to do some research. I decided to pick a couple 12 VDC lead acid batteries as test parts and start digging.

I found one that says 20 A/h so does that mean it can run at 1 amp for 20 hours or 20amps for 1 hour?
The way I understand this it should be 1A for 20 hours at 25°C / 77°F

As a standard 12V lead acid deep cycle batteries are tested at a 20Hr rate unless noted. Always check the manufacturer’s data sheet to be certain of testing conditions - specifications mean nothing without knowing what conditions the specifications are good for.

Starting batteries are tested at a 10hr rate, with the same caveat
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So on a particular battery, to discharge the battery in 20 hours the tested current was 1.2 Amps. I looked at a second 12v battery and found they had a 20A/h rating at the 20 hour rate and tested current was 1 Amp. They also had a notation of forward voltage 1.75V per cell which is the voltage per cell when discharged.

I went back to the original battery datasheet and it said cut off voltage 10.5V. so based on the 12V battery being 6 2v cells I took the 10.5 / 6 to get 1.75V to be sure we were comparing apples to apples so to speak. I also saw a note that the posted rates were an average of three charge discharge cycles and not the minimums. This is an explanation of why the 1.2 amp where we would expect to see 1A for 20 hours to get a 20/Ah rating. This muddies the water a bit but it’s also a good example of why you always want to look at the datasheet.

So I have a battery that is rated for 20 A/H, or 1 amp for 20 hrs and I need 2 amps. In the data sheet it is showing 1.9A amps will drain the battery in 10hrs how can this be? We could Just blame Wilhelm Peukert but the truth is he is credited for explaining the situation and providing formula’s to help us out. As the rate of discharge increases, the battery’s available capacity decreases, approximately according to Peukert’s law.

In other words the faster you drain a lead acid battery the less total current you have to work with over the charge life of the battery. In my example above, the 20 amp hour battery above can produce 1 amp for 20 hours or 20 amp/hours but at 1.9 it is dead at 10 hours or 19 amp/hours, and according to Peukert’s law the 2 amp rate that I wanted will make this worse yet.

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Where H is the rated discharge time (in hours)
C is the rated capacity at that discharge rate (in ampere hours)
I is the actual discharge current (in amperes)
k is the Peukert constant (unitless)
t is the actual time to discharge the battery (in hours)

The formula for figuring out k is as follows:

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So with that the original rating is 20Ah at the 1 amp for 20 hour rate.
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And the 2nd set of numbers was 1.9 amps at the 10 hour time which is 19 Ah
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k = 1.079914285

To summarize the math. If I plan to use this battery at 2amps I will get less than ten hours before I have to charge it.

To verify the math: 20/(1.9x1.079914285)=19 Ah so divided by 1.9A is 10 hours to discharge which matches the datasheet specification. Doing the same for my 2 amp draw I find I can go 9.46 hours. (if I am at 25 degree Celsius battery is new etc…)

Very Important note If you intend to mix battery chemistries like a Nickel Cadmium and a Nickel metal Hydride You will need to do additional research. If you intend to mix voltages or current ratings you will need to do more research it is not covered here, (Especially if you intend to recharge your battery bank as a single unit). In this report we are looking at multiples of the same battery.

SOME BATTERY DEFINITIONS

A battery bank is the joining of two or more batteries together for a single application
A series connection sums the voltage of the two batteries, but it keeps the same amperage rating (also known as Amp Hours).
Parallel connections will increase your available current rating, but the voltage will stay the same.
COLD CRANKING AMPS (CCA): US definition
The maximum amperes that can be continuously removed from a battery for 30 seconds at zero degrees F before the voltage drops too low to use. Generally this term is used only for engine starting batteries.
CRANKING AMPS (CA): US definition The same as CCA, but at 32 degrees F (0 C) temperature.
LIFE CYCLE One cycle of a battery from full charge to full discharge and back to full charge again. The total number of cycles a battery can perform is its Cycle Life. Most battery manufacturers will not discus the Cycle Life of their product.
AMP HOURS (A/H) There are different definitions based on the type of battery. When a battery is giving an AH (Amp Hour) rating it should be accompanied by the number of hours that rate is taken at. Make sure you are comparing similar rates when looking for your applications needs.

  • For deep cycle batteries the standard rating is 20 hours.
  • Starting batteries are typically rated at a 10Hr rate.

Very Important note If you intend to mix battery chemistries like a Nickel Cadmium and a Nickel metal Hydride You will need to do additional research. If you intend to mix voltages or current ratings you will need to do more research it is not covered here, (Especially if you intend to recharge your battery bank). In this report we are looking at multiples of the same battery only.