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See the [WikiPedia article] for details. But in a nutshell, Peukerts effect means that you are using more of the energy from your battery pack than your ammeter alone can tell you. And the effect is higher when the ratio between the size of the battery pack (in amp-hours) and the amp-draw in use is low. So for example Peukerts effect will be hardly noticeable when drawing 100amps off a 10,000AH battery pack. But drawing 100 amps off of a 200AH battery pack will show a significant impact.

Because the effect increases as that ratio increases (i.e. at higher amp draw ratio), you can't just take an average of your amp draw and calculate Peukerts impact from that. Luckily there are meters out (such as Link10 and SmartGauge) which allow you to enter the Peukert value for your battery and it will then monitor in real-time the actual amp drain from your pack. 

So remember - the larger the bank in proportion to your average draw, the more usable amps you can draw from the bank. This is significant!!

 For example: My cruising amp-draw is 50amps - that gets me about 4.2kts in calm water. If I use a 230AH bank (8, 115AH batteries), and use a 50% DOD (depth of discharge) goal, I will get only 70AH usable from the pack (5.8nm). But if I increase the size of my bank by 50% (add 4 more batteries), I get 120AH usable (10nm) - a 70% increase in range.

The Peukert value can vary quite a lot among batteries from different manufacturers or even specific models. There are basically two strategies in selecting batteries - optimizing for usable energy density (seek out lower Peukerts values) or optimizing for price (batteries with higher Peukerts tend to be lower priced)

[Theory] Based on my reading, the other thing to cosider about Peukert is that there apparently is a recovery period - the effect is based on sustained draw. So if you give your batteries a rest, they will recover somewhat. So "pulsing" your throttle (throttle down every, 20 minutes or so) should allow you to recover some of the energy normally lost to Peukert.

Lithium Ion batteries have almost no measurable Peukert effect - so you can in theory use a smaller pack (in AH) than you would for lead-acid or other technologies where this is a factor -- significantly affecting the overall price of the string. To put that in perspective, I would only need a 240AH Lithium pack to get the same usable energy as my 345AH lead-acid pack.

The Peukert value for a battery can be calculated from it's AH rating , the rating time, and the reserve capacity values.