[Rhodes22-list] Peukert's Equation

[elle]

Bumper Snicker??

LOL

elle

--- Joseph Hadzima <josef508 at yahoo.com> wrote:

> 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
> > 
> === message truncated ===
> 
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