Question on Peukert's Formula

[lordraiden]

Hi all, I've been lurking for a long time and finally decided to get in on the discussions. I've already searched the forums and there's references to Peukert's formula (which I stumbled onto several months ago researching off grid solar systems) and I came across a rather interesting question. In one of the statements I ran across I noticed that it said "[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]in Peukert's formula[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular] [/FONT]C is the theoretical capacity (in amp-hours) and is equal to [FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]the [/FONT]actual capacity at one amp."

Now forg[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]ive me for my [/FONT][/FONT]naivety[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular] in [FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]this, [FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]but what I[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]'ve read in other places [FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]they show the amp hour rate at[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular] increments like C5 ([FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]capacity at the 5 hour r[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]ate[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]) and C20 (the 20 hour rate) yet for Alkalines and other D adn lower batteries it's rated at C1, or [FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]h[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]ow many amps (or in this application mil[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]liamps)[/FONT] [FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]total over one hour.[/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT][/FONT] So am I s[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]omehow missing the obvious answer here[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]? Because if C is [/FONT][/FONT]cap[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]acity at 1 amp, where does the f[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]igures like C20 come from? Or am I totally over th[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]inking this? [/FONT][/FONT][/FONT][/FONT]:confused:[FONT=Arial,Helvetica,Geneva,Swiss,SunSans-Regular]
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[Kitchen Panda]

Hi all, I've been lurking for a long time and finally decided to get in on the discussions. I've already searched the forums and there's references to Peukert's formula (which I stumbled onto several months ago researching off grid solar systems) and I came across a rather interesting question. In one of the statements I ran across I noticed that it said "in Peukert's formulaC is the theoretical capacity (in amp-hours) and is equal to the actual capacity at one amp."

Now forgive me for my naivety in this, but what I've read in other places they show the amp hour rate at increments like C5 (capacity at the 5 hour rate) and C20 (the 20 hour rate) yet for Alkalines and other D adn lower batteries it's rated at C1, or how many amps (or in this application milliamps) total over one hour. So am I somehow missing the obvious answer here? Because if C is capacity at 1 amp, where does the figures like C20 come from? Or am I totally over thinking this? :confused:

The more I read about batteries, the less I understand about them.

As I understand it, Peukert's law is supposed to model a whole bunch of the electrochemical processes in a discharging battery. It really applies to lead-acid batteries which have rather porous electrodes. The problem is that it is expressed at a constant 1 ampere discharge, which is not the way battereis are tested, as you note. A battery discharged at a high rate uses mostly the electrode material near the surface, which is the most "accessible" for ions to move in and out of the electrolyte.

At slower rates, there's time for the electrolyte (and ions) to diffuse deeper into the electrode, so more of the electrode material can take part in the discharge reaction.

It's of great practical value in, for example, WWII submarines - even if you've run the batteries down with a short burst of high power, you can reconnect for lower discharge rate and get a very valuable extra operating time at lower current. I'm sure more than one WWII skipper brought his boat home due to this factor.

On the other hand, the one time I sat down with a lead-acid battery manufacturer's data sheet and tried to fit their 15 minute, 1 hour, 2 hour, etc. discharge capacities to a Peukert curve, I couldn't make it fit.

This is in addition to "internal resistance" which is the metallic resistance of all the electrodes, connectors, terminals, etc. plus some allowance for the every-varying resistance of the electrolyte itself.

Other chemistries than lead-acid batteries don't seem to have such a neat equation, so estimating their state of charge is much harder. Discharging an alkaline battery at a 1 hour rate is a pretty fast discharge; they really are more efficient (give more of their theoretical capacity) at 10 or 20 hour discharge rates. Internal resistance, again, plus the limited rate at which ions can move around inside the cell, are what I understand to be the reason for the difference.

Bill
( of course Wikipedia has an article...Wikipedia has articles about everything...but you'd probably be better off looking at the cited references instead of the article itself.)

 

[Justin Case]

Hi all, I've been lurking for a long time and finally decided to get in on the discussions. I've already searched the forums and there's references to Peukert's formula (which I stumbled onto several months ago researching off grid solar systems) and I came across a rather interesting question. In one of the statements I ran across I noticed that it said "in Peukert's formulaC is the theoretical capacity (in amp-hours) and is equal to the actual capacity at one amp."

Now forgive me for my naivety in this, but what I've read in other places they show the amp hour rate at increments like C5 (capacity at the 5 hour rate) and C20 (the 20 hour rate) yet for Alkalines and other D adn lower batteries it's rated at C1, or how many amps (or in this application milliamps) total over one hour. So am I somehow missing the obvious answer here? Because if C is capacity at 1 amp, where does the figures like C20 come from? Or am I totally over thinking this? :confused:

Your nomenclature is incorrect. The 20 hr rate is C/20, i.e., 1/20 of the C rate. That should make sense since C is the rate to discharge the cell or battery in one hour. If it takes 20 hrs to discharge the cell or battery, then that rate must be smaller than C, and in fact must be 1/20 of C by definition, or C/20. Similarly, the term for your 5 hour rate is also incorrect. It is C/5, not C5.

 

[lordraiden]

Thanks guys. I guess I wasn't wrong being confused after all. And despite all the research I've done it's still proven to be quite the learning curve understanding how electricity and chemistry and all that work together. I'm a mechanics kinda guy, so I'm used to working with constants that have very neat and tidy power curves and all that. So to have things sorta all over the board with batteries has really proven confusing. T_T But the explaination that Kitchen Panda gave does go a long ways towards helping me understand it. :)