Well put Eric. I didn't mean to imply my LiFePO4 cells are not affected by Peukert, just much less than lead. As to the capacity rating given by Winston of 100 a-hr, I have found that in real life my 100 a-hr cells deliver 117 a-hr with all cells still above 3.0 volts. Others on the Cruiser's Forum report this same 17% more than stated a-hr on their 400, 700, and 1,000 a-hr banks. I have 346 cycles of 80% DOD and they still give 117 a-hr remaining above 3.0 volts per cell.
Bob
From: "ewdysar@yahoo.com" <ewdysar@yahoo.com>
To: electricboats@yahoogroups.com
Sent: Thursday, March 13, 2014 11:36 AM
Subject: Re: [Electric Boats] Electric Kayak
Hi Bob,
Thanks for the reply. These specifics help a lot. Just one clarification. LiFePO4 batteries are affected by Peukert's Effect, albeit to a much lessor amount than other battery types. It sounds like your 4mph cruise is pulling about 120W (10A) give or take. As such you're operating at 0.1C of the 100Ah capacity. At such low rates, Peukert's has little measurable effect. However, I typically cruise at 0.3-0.5C and Peukert starts to eat into the overall range range of my 8kWh (160Ah@50V) LiFePO4 battery pack.
As a quick primer to newer folks in the group, most of us are aware that batteries have a lower capacity at high loads than at low loads. A 100Ah battery may deliver 100Ah at a 5A load (20h*5A), but the same battery will only deliver 70Ah at a 20A load (3.54h*20A) and only 56Ah at a 50A load (1.12h* 50A). This is easily observable but hard for the layman to predict. In 1897, the German scientist W. Peukert quantified these losses with a formula that describes Peukert's Law. Due to internal resistance of a battery, large currents going into or coming out of the battery will heat up the battery (also easily observable). Batteries with lower internal resistance have lower losses to this effect. Peukert's formula uses the Peukert Exponent (PE) to quantify and predict those losses.
Each battery type has its own specific PE, however, each battery chemistry has a range of likely PE values. Here are a few average PEs for the battery types that are typically used in our boats.
Flooded Lead Acid (FLA) - PE = 1.25
Absorbed Gas Mat (AGM) - PE = 1.10
Lithium (LiFePO4) - PE = 1.03
The example calculations of the 100Ah battery that I used earlier were done for a FLA battery using a PE of 1.25.
So what does this mean? An excerpt of a post that I made in Sept 2012 is included below. If you want more technical info about Peukert's Effect, click on the link to message 21237. Also the cost estimates are a couple of years old now, but they are still fairly representative of readily available deals. If you find a better deal for any of these battery types, good for you. Let's not turn this thread into battery bargain hunter conversation.
And here is a bit of group etiquette. One will notice that battery capacity is listed in Wh and current load is listed in W. There are a lot of different system voltages represented in this group. Quoting only Ah or A doesn't really say much about your boat and means that others can't relate to the info that you are trying to provide. Working in watts puts us on a level playing field. If you don't want to do that, at least include your system voltage along with your amp-based info.
>
> ---------------------------------------------
> This is what I posted on April 20 2012 in post #21398
>
> Perhaps you mean something like this post that I made back in Jan 2012
(post#20750) and reposted in this month (post #21237). I directly compared the
weight and cost of the same usable capacity of different battery types.
Peukert's has already been factored in. You can read the whole post here
http://groups.yahoo.com/group/electricboats/message/21237
>
> You said "Additional concerns are that the estimated Puekert coefficients
might be 1.0 for Lithium, 1.1 for AGM, and 1.3 for Flooded. Estimated safe
discharge levels might be 80% for Lithium, 60% for AGM, and 50% for Flooded."
>
> In case you want to check my math, for my calcs I used a PE of 1.03 for Li (no
battery is 1.0), 1.1 for AGM and 1.25 for FLA. And you can see that I used
discharge levels of 80%, 70% and 60% respectively.
>
> -- Excerpt from post #21237 -----------------------------------
> Let's do the math for a battery pack that has a usable 2.5 hour range at 2500W
(6.25kWh used).
>
> FLA 14.25kWh to 60% DoD at 2500W = 2.5 hours = 633 lbs, cost about $1500
> AGM 10.5kWh to 70% DoD at 2500W = 2.5 hours = 520 lbs, cost about $2500
> LiFePO4 8.25kWh to 80% DoD at 2500W = 2.5 hours = 200 lbs, cost about $3500
>
> So now the lithiums are 2.3 times the cost of the T-105 FLAs but they are less
than 1/3 the weight for the same range at this load. So for most boaters, I
recommend AGMs as a good balance of price to range.
> ------------------------------------
> Another point to consider is that the math is dependent on the load. Because
of Peukert's Effect, higher load/capacity ratios favor Lithium, but lower
load/capacity ratios make AGM and flooded look better. Aiming for the same
amount of energy consumed, here's a similar chart at 4000W for 1.5 hours (6kWh
used)
>
> FLA 15.1kWh to 60% DoD at 4000W = 1.5 hours = 670 lbs, cost about $1600
> AGM 10.5kWh to 70% DoD at 4000W = 1.5 hours = 520 lbs, cost about $2550
> LiFePO4 8kWh to 80% DoD at 4000W = 1.5 hours = 200 lbs, cost about $3400
>
> Here's the another chart at 1500W for 4 hours (6kWh used)
>
> FLA 12.5kWh to 60% DoD at 1500W = 4 hours = 550 lbs, cost about $1350
> AGM 9.6kWh to 70% DoD at 1500W = 4 hours = 475 lbs, cost about $2350
> LiFePO4 7.8kWh to 80% DoD at 1500W = 4 hours = 195 lbs, cost about $3300
>
> Looking at 6kWh usable at both 4000W and 1500W, we can see that FLA cost 40%
of Li at 1500W and 47% of Li at 4000W, entirely because of Peukert's Effect. You
can see where this is trending.
>
> I hope that this helps.
>
> Fair winds,
> Eric
> Marina del Rey, CA
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