[Rhodes22-list] Peukert's Equation

[Joseph Hadzima]

Eschew Obfuscation!

from one of my favorite bumper snickers!


--- elle <watermusic38 at yahoo.com> wrote:

> B.,
> If you can't clarify, obfuscate.
> 
> Go sail.
> 
> elle
> 
> --- Bill Effros <bill at effros.com> wrote:
> 
> > L.
> > 
> > (A small woman with a short fuse?)
> > 
> > Here is an explanation of Peukert's Equation that I
> > have not simplified.
> > 
> > If the mathematical symbols do not come through, go
> > to this site:
> > 
> > http://www.smartgauge.co.uk/peukert.html
> > 
> > Bill Effros
> > 
> > *A proper explanation of Peukert's Equation
> > (Peukert's Law)*
> > 
> > Mr Peukert first devised a formula that showed
> > numerically how 
> > discharging at higher rates actually removes more
> > power from the battery 
> > than a simple calculation would show it to do. For
> > instance discharging 
> > at 10 amps does not remove twice as much power as
> > discharging at 5 amps. 
> > It removes slightly more. Therefore a 100 amp hour
> > battery (at the 20hr 
> > rating) could provide 5 amps for 20 hours, but it
> > could not provide 10 
> > amps for 10 hours. The available time would actually
> > be slightly less.
> > 
> > Mr Peukert wrote down a formula for describing how
> > much less time would 
> > be available. Please note that in the first
> > paragraph I say "Mr Peukert 
> > first devised a formula for....". This is because he
> > is generally 
> > regarded as being the man who first discovered the
> > phenomenon. This is 
> > incorrect. The effect had been known for many years
> > beforehand and was 
> > first noted by a certain Mr Schroder several years
> > before Peukert 
> > devised his formula. Mr Peukert simply quantified it
> > in a way that had 
> > never been done before. However the effect is now
> > known as Peukert's 
> > effect, the formula for calculating it is known as
> > Peukert's equation, 
> > and the important number, unique to each battery
> > type, that is put into 
> > the equation in order to perform the calculation, is
> > known as Peukert's 
> > exponent. Note that Peukert's exponent changes as
> > the battery ages.
> > 
> > Please note that there are two ways of looking at
> > this effect. We could 
> > say that discharging at higher currents reduces the
> > total available 
> > power that can be got out of a battery. So a 100 amp
> > hour battery might 
> > become say an 80 amp hour battery at higher
> > discharge rates. This is 
> > technically the correct way of looking at it.
> > 
> > However it is easier to assume that the total
> > available power in the 
> > battery remains identical whatever the discharge
> > rate. But that 
> > discharging at higher rates removes more amp hours.
> > This is the method 
> > of explanation used throughout this website and on
> > the Peukert 
> > calculator spreadsheet.
> > 
> > Note that whichever method is used, the figures and
> > effect remain 
> > identical in both cases. It's just that we consider
> > the second method to 
> > be easier to understand and "get your head round".
> > 
> > Peukert's equation can be found all over place. On
> > the internet, in 
> > battery data sheets and documents, in battery sales
> > literature, in 
> > battery monitoring equipment manuals etc. It is
> > usually written as I^n T 
> > = C
> > 
> > Where:
> > 
> > I = the discharge current in amps
> > T = the time in hours
> > C = the capacity of the battery in amp hours
> > n = Peukert's exponent for that particular battery
> > type
> > 
> > The idea is that the time (T) that a certain battery
> > can run a certain 
> > load for can be calculated by rearranging the
> > equation to read T = C/I^n
> > 
> > Please note that this equation, seen all over the
> > place, is wrong. 
> > Actually, I'd better rephrase that. The equation is
> > not wrong. But the 
> > way people attempt to apply it to the battery
> > capacity is wrong.
> > 
> > This equation cannot be used on batteries that are
> > specified at (say) 
> > the 20 hour rate, or the 10 hour rate or any other
> > "hour" rate. It will 
> > not work. For an explanation of why and what
> > equation you need to use 
> > read the rest of this article.
> > 
> > Alternatively go here
> > <http://www.smartgauge.co.uk/peukert3.html> to 
> > find a suitable solution without understanding why.
> > 
> > Even a cursory attempt at using it will show that it
> > simply cannot be 
> > correct.
> > 
> > So let's try using this equation and see what we
> > get.
> > 
> > The first problem we come across is that the battery
> > capacity does not 
> > state any type of rating. Is this the 100 hour rate?
> > the 50 hour rate, 
> > the 20 hour rate? or some other rate?
> > 
> > Most people assume it to be the 20 hour rate so we
> > shall do the same here.
> > 
> > Take a battery rated as being 100 Ahr (at the 20
> > hour rate - the most 
> > usual specification) with a Peukert's exponent of
> > 1.3 (a typical figure 
> > for a deep cycle wet cell).
> > 
> > The rating on this battery means it can provide 100
> > amp hours in total 
> > at the 20 hour discharge rate. That is what the
> > rating means. This 
> > battery, when new, can provide 5 amps for 20 hours.
> > 
> > However, if we plug these numbers into the usual
> > Peukert's equation (the 
> > one that we see all over the place) we get:-
> > 
> > T = C/I^n
> > T = 100/5^1.3
> > T = 100/8.1
> > T = 12.3 hours - yet we *know*, from the
> > specification, that it can 
> > provide this current for 20 hours!
> > 
> > Just plugging the battery's actual known capacity
> > onto the equation 
> > gives us the wrong result.
> > 
> > Ok, let's do a quick check on this. Let's do exactly
> > the same 
> > calculation but this time we will use 2 of the same
> > battery i.e. 200 amp 
> > hours, and the load will be exactly twice as much
> > i.e. 10 amps instead 
> > of 5 amps. Common sense (and experience and
> > calculations) tells us that 
> > the run time will be exactly the same as a single
> > battery at 5 amps load.
> > 
> > T = C/I^n
> > T = 200/10^1.3
> > T = 200/19.9
> > T = 10.0 hours - But we all *know* that it should be
> > the same as the 
> > above example
> > 
> > Let's just double check on this to make sure we
> > haven't missed something.
> > 
> > The first result above suggests that this battery
> > can actually only 
> > provide 5 amps for 12.3 hours. That makes it a 5 X
> > 12.3 amp hour battery 
> > at this discharge rate. That means this equation
> 
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