What Peukert Meant
Peukert’s Law, describing battery capacity, became misunderstood following a seriously-flawed US article in the mid-1980s. While not often referred to since, here’s what Peukert really meant. It relates primarily to lead-acid batteries – (not lithium).
Pic: associated with https://www.youtube.com/watch?v=rWr7hdmuLUU
In 1894, Peukert explained a battery’s capacity is simply expressible. Peukert defined it as ‘ability to support a constant current over time’. His example involved a 100 amp-hour battery. Peukert maintained that if it sustained a 5 amp draw for 20 hours (at still usable voltage), it could be rated at 100 amp-hours.
Around 1984, a US company argued publicly that this was wrong. It argued that if subject to a 50 amp load, its stored energy is depleted by more than 50 amp hours. It subsequently referred to this as Peukert loss. This claim was accepted by many. It’s on Wikipedia to this day. It resulted in ‘Peukert loss’ being commonly used. The argument, however, is massively flawed. It mistakes energy for power (and vice versa) throughout.
Energy and power defined
Energy is the capacity for doing work. Its base unit is expressible in amps. Integrating current flow (amps) over time is expressed in amp-hours.
Power is the rate at which work is done. Its base unit is the watt. It is work done, or expended, at one joule per second. Power is thus totally different from energy. It relates to the rate at which energy is used.
Stacking 200 one kg cans on a two metre high shelf (one or two at a time) needs a calculable amount of energy. It does not, however, need much power (a child can do it). A weight lifter heaving up 200 kg by two metres in a second or two uses the same amount of energy, but needs a lot more power.
Most the time, using (the term) ‘power’ when energy is meant does not matter. But if misused technically, whatever follows makes no sense.
Here is an extract from the flawed US article. (The entire argument is still on Wikipedia. (Google Peukert’s Law)
‘Mr Peukert first devised a formula that showed numerically how discharging at high rates actually removes more power . . . than a simple calculation would show it to do. For instance discharging at 10 amps does not remove twice as much power as discharging at 5 amps. It removes slightly more. . . discharging at higher rates removes more amp hours.’
Peukert did not say this. The writer not only confuses power for energy throughout the article, but in the associated maths-related articles thereafter.
What Peukert really meant
Particularly with lead-acid batteries, when energy is drawn, the battery voltage falls. As an example, were a battery able to sustain 5 amps for 20 hours (before falling below 10.6 volts) it can be rated at 100 amp-hours. When a heavier load (say 50 amps) is connected across that battery, its voltage falls more rapidly. After (say) 60 minutes, it is likely below 10.6 volts.
The battery is consequently unable to sustain that discharge rate. But its energy has been depleted by 50 amp hours. No more – nor less.
A lead-acid battery reacts very slowly. Once that 50 amp load is removed it slowly recovers. Off-load voltage will be 12.2-12.3 volts. It may still be able to supply 50 amps, but this time for only 30 minutes. Delivered available capacity is now 75%. The 25% remaining is still available, but now at five or so amps.
So, what Peukert really meant is that rate of discharge does not affect overall capacity. That which it affects is only its usable capacity when loaded above its rated current. In other words its rated capacity (energy) is still available, but only at its intended (rated) current. Some see that as ‘available capacity’.
Peukert ‘loss’ defies physics
Energy cannot be totally ‘lost’ as such. It is only changeable into another form. So where and how, with batteries, does that ‘lost’ energy (that the flawed argument calls ‘power’ ) go? Even heavily discharging batteries don’t jump up and down or, sing operatic arias. The only minor ‘loss’ is about 1% – as heat.
What Peukert really meant – as an exponent
When energy, in any form, is changed into another form, some of that energy’s ‘quantity’ becomes unavailable to do work. It may, for example, become heat. That ‘loss’ process is known as entropy.
Peukert suggests the amount of battery energy available (at different discharge rates) is expressible as an exponent. An (impossible) 1.0 indicates that the discharge rate makes no difference. Most batteries have an exponent of 1.1 to 1.4. (Most LiFePO4’s are likely to be <1.05).
Is what Peukert really meant provable?
What Peukert really meant is readily proven. It has been shown practically many times. There is a very minor entropic heat loss (<2%) but too small to reliably measure except in a temperature controlled laboratory.
Checking what Peukert really meant is easy. Nevertheless people on forums dispute it endlessly. You can readily test it yourself. The following video demonstrates it, but at some length.
Does what Peukert really meant matter?
Knowing what it’s really about can save you a lot of money!
A 200 amp hour battery under a 50 amp load sustains that load about 2.3 times longer than can an (otherwise identical) 100 amp hour battery. It is effectively 230 amp hour (in terms of available energy). In typical RV service a 400 amp such battery performs much as a LiFePO4.
Big AGM batteries are truly effective for RV use. If their weight is not critical they are good, cheap and simple if operated from 100% to 60% state of charge. Furthermore: an occasional deeper discharge does next to no harm.
Lithium-iron batteries and what Peukert really meant
Lithium-iron batteries sustain their voltage under very high loads. It is that which enables an 18 amp hour LiFePO4 to jump start a 4WD engine many times. They are likewise chargable at much higher rates, but need expertise to do. See: Jump Starters Really Do Work
I thank Julian and IanB (their forum names) for invaluable comments. Also Tony Lee for advising on his long RV experience with a 400 amp hour AGM battery bank.
If you find this article of interest you will find Caravan & Motorhome Electrics even more so. (It’s also by many auto electricians). Consider also Caravan & Motorhome Book and Camper Trailer Book. Solar That Really Works is for RVs. Solar Success is for home and property systems.
Please add this Link if you this article assists understanding on forums.