On 20/09/2017 10:09, T i m wrote:
On Wed, 20 Sep 2017 08:36:50 +0100, Martin Brown
wrote:

On 19/09/2017 19:02, T i m wrote:
Reference 'C' gives:
Current, Time to fully discharge:
21A, 1h (i.e. C/1)
11.9A, 2h (i.e. C/2)
5.40A, 5h (i.e. C/5)
3.10A, 10h (i.e. C/10)
1.60A, 20h (i.e. C/20)
0.36A, 100h (i.e. C/100)

The trick is to work out what varies most smoothly with load.

If you work out the battery capacity in Ah and then fit that against
current I you get a reasonable quadratic approximation of capacity

Capacity (Ah) = 35.3 - 1.56*I + 0.04*I^2

It is always going to be a bit rough and ready since individual
batteries will vary from the abuse they have suffered in service.

A linear model would underestimate the low current lifetime

Capacity (Ah) = 33.2 - 0.66I

Datasheet batteries always seem to last longer than real world ones!

You should be able to reproduce these models by putting the numbers into
Excel and plotting I*t against I.


Hi Martin and thanks for the feedback. I can follow some of it. ;-)

More thinking out loud on it all .... Considering a graph of various
discharge rates shows that the effective capacity does vary as a
function of the discharge rate, I think it would still be worthwhile
trying to accommodate it to some degree if possible (accepting all the
caveats you mention etc). I agree though that whilst a linear function
would be better than nothing at all, it may not reflect the situation
was well as it *might*, if we could find that mathematical solution,
even though it's only ever going to be an approximation at best. I was
never looking for a laboratory solution here. ;-)

On that though, I can (re)evaluate the batteries capacity over time
and modify the numbers accordingly and could even automatically
compensate for temperature (if the typical temperature range
difference we are likely to go boating would be significant etc).

So it's just a matter of (initially especially) seeing if we can make
use / sense of the published data for my specific battery(ies) and if
that isn't sufficient, if we can use the stats from something similar
to at least start the ball rolling?

It's just knowing that there can be such a marked difference in
capacity as a function of the current drawn ... and my potential
maximum current (30A) *is* significant to this, even with 3 batteries
in parallel (~90Ah) there is a very good chance that some massaging of
the readings to predict a particular depth of discharge threshold
would be worthwhile.

A quick and dirty value for the discharge threshold is when the terminal
voltage drops below some arbitrary limit ISTR 10.5 or something. You
never want to take an individual cell below some critical value which is
temperature dependent or permanent damage will result. The weakest cell
in a stack of them always gives up the ghost first.

To a good approximation the terminal voltage ends up as

V = V0 - Ir

Where I is the current you are drawing and r is the internal resistance
of the battery (which itself is a weak function of temperature and I).

In practice the difference may help to protect the battery if you just
use a fixed voltage cutoff value since if you are discharging it quickly
it will inevitably be hotter and potentially gassing slightly.

If I retained the original resistor based 'speed control', even I,
once I guesstimated what the capacity would be for the currents
typically seen at the 5 set speeds, could possibly write some code
that applied the variable.

Not sure I understand what you are trying to do but a MOSFET based PWM
speed controller will give you something like 90% efficiency. This will
give you a lot more battery life if you use low power most of the time.

Whereas a resistor will be wasting a lot of power dissipated as heat.
Using a better more efficient speed controller is a far better option
than managing the decline of the poor battery.

--
Regards,
Martin Brown