Degrade Arc Calculation

Steven Lake

Was sitting here tonight trying to figure out some load values for a battery bank I'm working on and hit onto some rather interesting calculations that I thought I'd share with you. Now these numbers are only "rule of thumb", but they're pretty darned close to OEM specs. Ok, let me explain the math a little.

The standard degrade factor for most batteries I've found is a 40% reduction in amp hours between the 20hr rate and the 1hr rate. That means at the 1hr rate you will have only 60% of your rated capacity available. Now, to figure out all numbers from the 20hr rate down to as low as you want to go (I haven't gone above 20hrs or below 1hr in my math testing, but I'm sure someone can figure out if the numbers hold up there too), you first need to get your 1hr rate. To get that, you need to do this:

AH * 0.6 = 1hr rate. (exp: 35*0.6 = 21ah)

Now, let's say we want to find out the 5 hr rate. Just do 21 (your 1hr rate) divided by 5 (your new 5 hour rate) and then add your 20 hour amp rate. Then, to get your total available amp hours, mutiply that by 5. So your equation looks something like this:

(21/5) + 1.75 = 5.95 amps * 5 = 29.75ah

Now this is probably something you guys already have calculators for, but I found this by accident and thought it'd be neet to share with you guys.

niel

Re: Degrade Arc Calculation

doesn't look right. try it for higher hourly rates like 8hrs or even back to 20hrs. maybe i'm not following how you wanted it calculated?

inetdog

Re: Degrade Arc Calculation

The varying capacity depending on the current draw (as a fraction of capacity) in Lead Acid batteries specifically is called the Peukert Effect, and it is very accurately described by an equation which applies over a wide range of current values. But it depends on a constant called the Peukert exponent, and that number will vary considerably based on the composition of the plates and the construction of the battery.
Numbers you compare for one battery type will not necessarily apply to another battery type. And if you keep the current drain below C/8 (for FLA batteries) the difference among current values in that range will be far less than 40%.

The Peukert effect is important when for some reason you need to have very high intermittent loads on a system. If the current requirement is more than C/8, you should at least look at AGM batteries as an alternative to getting a larger FLA bank.

Steven Lake

Re: Degrade Arc Calculation

Inetdog: I actually am using AGM. I prefer them over any other battery by leaps and bounds. Mostly because they're easy to take care of, and if you charge them right, they last for crazy long amounts of time. I do find your comment about the Peukert Effect to be interesting. As for what Neil is asking on, mostly in relation to your answer, I wasn't really asking a question, but more or less just sharing an interesting mathematical discovery I ran into. Kinda like "Oooo, shiny! Have a look!"

I do admit that a discharge arc or guide would be interesting to have, but as you said it'll vary between batteries, amp hours, components, etc. So you'd probably have to get the OEM drain rate from the battery maker to have an accurate listing of load vs available amp hours. But as I said, my original post was more just a cool observation I made. ^_^

BB.

Re: Degrade Arc Calculation

Smart Gauge has quite a technical section about batteries and Peukert Factor, etc... Including the math and spreadsheets.

-Bill

Steven Lake

Re: Degrade Arc Calculation

Thanks! I'll check it out!

Steven Lake

Re: Degrade Arc Calculation

Wow BB, I've been playing with that spreadsheet they had at the link you gave me, and all I gotta say is, wow. That's been such a HUGE help to answer some questions that it's not even funny. I love how you can plug in numbers or use the existing values to see how much life your battery will have under a given load. That's massively useful. I only wish the spreadsheet allowed you to go below 20ah so I could calculate for the smaller batteries I have, but with a little ingenuity I've figured out a simple way to get around that limitation. Either way, it's been very useful. Thanks. Oddly, it's kinda funny that what started out as a curiosity turned into a solution to a problem I had but didn't think had a solution.

BB.

Re: Degrade Arc Calculation

You are very welcome Steven (and thank Smart Gauge for making their information public--They did the hard work).

I am not quite sure I completely agree with their "enter two battery AH capacities at two different C/xx rates" gives accurate Peukert Factor results. I played with it a little bit and was not convinced it worked correctly (perhaps I was doing something wrong too). The values did not make sense with "known" Peukert constants for a couple of battery types/models and the "typical" ranges of PFs.

-Bill

inetdog

Re: Degrade Arc Calculation

Steven Lake wrote: »

I only wish the spreadsheet allowed you to go below 20ah so I could calculate for the smaller batteries I have, but with a little ingenuity I've figured out a simple way to get around that limitation.

Like multiply the battery AH by 10 and then divide all the results by 10?

Steven Lake

Re: Degrade Arc Calculation

Inetdog, yeah, that's what I did. For my 7ah (out of pure curiosity) I multiplied by 3 (to get 21), got my value and then divided by 3. As best I can tell, it's accurate enough for what I need.

BB, yeah, I figure the spreadsheet is only a "general" estimate of values. But what I'm most interested in is the runtimes at a given load. If I can get a rough number in that area, I then round down to get the more likely runtime which is plenty enough for what I'm after since I only need ballpark on most of my stuff.

inetdog

Re: Degrade Arc Calculation

Steven Lake wrote: »

Inetdog, yeah, that's what I did. For my 7ah (out of pure curiosity) I multiplied by 3 (to get 21), got my value and then divided by 3. As best I can tell, it's accurate enough for what I need.

It is not just accurate enough, it is mathematically exact. (Which is not critical given that the spreadsheet is only loosely applicable to any individual battery unless you have the real measurements for it as input.)

Steven Lake

Re: Degrade Arc Calculation

lol. I meant the sheet itself is accurate enough for what I need, not the math to get the amp hours for batteries less than 20ah. :P