Talk:Peukert's law

Dimensional stuff

I've never used this law ( I'm a theorist) but there must be a constant overlooked there because it doesn't make sense if you do a dimensional analysis unless k=1. Maybe the units of C_p is not always A.h?? —Preceding unsigned comment added by 190.42.194.235 (talk) 19:27, 8 July 2008 (UTC)

I agree that theoretically, the dimensions don't seem to work out in the C_p = I^k t equation.

Clearly this is an empirical law, rather than one derived from theory.

The other equation, as well as the "modified" equations in the Chris Gibson references, appear to at least have the correct dimensions.

--68.0.124.33 (talk) 17:33, 13 July 2008 (UTC)

Whether or not is is a phenomenological equation doesn't matter. In this equation one must change I to I/I₀, i.e. the fraction of the current over a reference current, so that it is a dimensionless number. And then one must multiply by a reference current,

using dimensions:

C_p = (I/I₀)^k * I_a *t

or with dimensionless variables C`=C<sub>p</sub>/C<sub>0</sub>, I`=I/I₀ and t`=t/t₀,

C` = (I`)^k t`,

This is not only strictly true, it also means that people wanting to use this equation can find the correct reference values here, without having to find them for yourselves.

Eirikov (talk) 08:27, 2 October 2009 (UTC)

You are quite right. I made the dimensionally accurate formula the primary one, with an apology for the usual but incorrect formula. CLandau (talk) 04:22, 21 October 2010 (UTC)

I think a graph is needed here to help explain the effect.2.219.126.222 (talk) 17:25, 13 August 2011 (UTC)

Who was Peukert?

Hmmm... as a reader I'd be interested in knowing the origen of the name. Who was Peukert? 82.93.133.130 12:49, 29 November 2006 (UTC)

I added a reference to the original Peukert article and a contemporary paper about it LHOON 13:44, 29 November 2006 (UTC)

other battery equations

This article says this equation applies to "lead-acid battery". What about other kinds of batteries -- alkaline, NiMH, Lithium, etc.? What equation applies to them?

Also, this equation implies constant-current -- which is reasonable for continuously-running devices that use a linear voltage regulator. Is it reasonable to integrate this equation for non-constant-current loads? In particular:

• devices that use switching voltage regulators to pull constant *power* (rather than constant *current*) out of the battery, so as the battery voltage slowly ramps down, the battery current pulled out slowly ramps up.
• devices that periodically use a burst of high current to do something useful, then hibernate between those times at some lower current.

Or is there some other equation that would be more appropriate for estimating the run-time of these battery-powered devices? --68.0.124.33 (talk) 17:53, 13 July 2008 (UTC)

Yes it is perfectly acceptable to integrate the equation for non constant loads. Many battery monitors do just that. —Preceding unsigned comment added by 86.147.122.184 (talk) 10:19, 7 August 2008 (UTC)

Not according to the Doerffel reference. CLandau (talk) 04:22, 21 October 2010 (UTC)

See my comment below. Eric Kvaalen (talk) 09:04, 31 December 2010 (UTC)

Peukert's "Law" obviously not true

In September 2009 I added a paragraph pointing out that this "law" cannot be true at very small discharge rates because it would mean that the total charge, I×t, would become infinite. This is obviously impossible since there is only a finite amount of reactants (lead, lead oxide, and sulfuric acid) in the battery. Within a few days someone anonymously deleted that saying, "Removed paragraph. Incorrect. At zero discharge rate the time available WOULD be infinite were it not for self discharge." Well yes, but I said the total charge, not the time!

I also added a "clarification needed" note asking how valid this "law" is, and this was also deleted by an anonymous person who wrote, "Removed question. The equation is referenced, accepted and valid." It may be referenced and accepted by many people, but it's still obviously false for low values of I! So it's not "valid". It's only "valid" over a certain range, and even there I see no theoretical reason for it to be valid, so it's probably just a convenient approximation.

Applying this to the question above about whether Peukert's law can be integrated when I is not constant, the answer is obviously no if the discharge rate strays into the low region where the "law" is invalid. Also, it's not obvious how to integrate it. One could perhaps say that at any given time the battery is using up its initial "capacity" at a rate of 1 divided by the "t" variable of the law. In other words, we declare that there is a variable, call it x, which starts off at 1 when the battery is fully charged, and decreases according to:

${dx \over dt}=-{\left({\frac {I(t)H}{C}}\right)^{k}}/H$

where I am now using t to mean the elapsed time. When x reaches zero, the battery is dead. This might work fairly well so long as one doesn't spend much time at low values of I where the "law" is invalid. On the other hand, at very low values of I it doesn't matter much because then my differential equation says that x will go down very slowly, which is true even if the rate is off by a large factor. In other words, integrating might work fairly well so long as most of the discharging (the decrease of x) takes place at reasonably high rates.

Eric Kvaalen (talk) 09:04, 31 December 2010 (UTC)

You're absolutely correct. Integrating a discharge rate corrected for Peukert's exponent throughout a discharge only works if the discharge rate remains constant. It fails if the discharge rate varies, even if it remains quite high. Starting with a high discharge rate, then reducing the rate will result in a pessimistic time remaining calculation and vice versa.

The contributor who argued that many battery monitors "do just that" is quite correct, they do. But that doesn't mean it works very well. —Preceding unsigned comment added by 2.102.22.198 (talk) 14:03, 4 March 2011 (UTC)

Explanation

The section headed "Explanation" should be removed in its entirety. It contains two references, both of which are unreliable. The rest of the section is original research and therefore also unnacceptable. It is also mostly wrong. As are the two referenced items. — Preceding unsigned comment added by 2A00:23C4:8A82:FF00:4586:ED3E:7E7:5692 (talk) 10:05, 3 July 2021 (UTC)