# Different Formulas

Solar Expert Posts: 131 ✭✭✭✭✭
1. Could anyone give me the different formulas for figuring charging times with XX ah batteries, xx panel wattages, safe charging rates, and what is the optimal discharge for a battery before recharging to keep battery life as long as possible.

2. Without going and looking at all the specs on most of the charge controllers out there I was wondering to they have the option to charge car batteries?

Thanks

## Comments

• Solar Expert Posts: 1,164 ✭✭
Re: Different Formulas

Car batteries are no different than deep cycle batteries except for the plates, for the most part. Same charging voltages.

There are not really any hard an fast formulas. Some batteries have a max charge rate. It is basically how many amp-hours the battery needs to fill up divided by how many amps the panels put out. That gives you hours to charge, or at least close.
• Solar Expert Posts: 131 ✭✭✭✭✭
Re: Different Formulas

Alright great. How about figuring charing XX ah battery, knowing the wattage from the panel?

I am going to start writing all this stuff down. I hear bits and pieces of different formulas or how to figure stuff out and i would like to compile them for future reference.
• Solar Expert Posts: 131 ✭✭✭✭✭
Re: Different Formulas

Also I guess it depends on the percentage the battery was discharged. So for a XXah battery that has had 20% drawn from it and having a XXwattage panel, how do I figure that out? Just need a rough idea how to do this, sorry for the ignorance.
• Super Moderators, Administrators Posts: 30,737 admin
Re: Different Formulas

A lot of calculations are just variations of the basic electrical formulas... Or, here is another website. And here is another.

Anyway, to answer your question about power, work, and Amp*Hours...

Basic volts, amperes, ohms relationship:

V=I*R (voltage=current*resistance)
I=V/R
R=V/I

Power (watts--this is a "rate", sort of like Miles per Hour):

P= V*I = V^2 / R = I^2 * R

Work (Watt*Hours--sort of how far did you go--not scientific unit, but used for house/commercial wiring):

W=P*Time=P*Hours (P may substitute with any Power equality)

And for house/commercial billing, we use kiloWatt*Hour

1 kWHr = 1,000 Watt*Hours

Lastly, Amp*Hours... Not a real useful for most work as you have to know the volts that the Amp*Hours relates to. However, when working with DC / Battery systems, it makes many calculations simpler:

Amp*Hours = just Amperes * Hours (time)
Amp*Hours = Watt*Hours / Volts
Watt*Hours = Amp*Hours*Volts

So, a 20 Amp*Hour battery (using 20 Hour Rating), will delivery 1 amp for 20 hour (1a*20h=20AH).

However, it is not true that a 20AH battery will deliver 20 amps for 1 hour--As the battery has internal resistance and chemical limitations... So the 1 Hour Rate will be something like 13 AH.

And conversely, the 100 Hour Rate may be 25 Amp*Hours.

Normally, we aim at the 20 hour rate for discharging (something like 8 hour per night for 3 nights without sun). The charging rule of thumb is around 5%-13% of the 20 AH rate--any less, the flooded cell lead acid may not mix the electrolyte properly during equalization. Any more than 13%, you may overheat the battery (or, at least, it may be a waste of over sizing the charger/solar panels).

Another rule of thumb, we try not to discharge the battery below 50% to ensure longer life. To much deep cycling will reduce battery life.

Last rule of thumb for tonight--try not to let a battery sit below 75% state of charge for any length of time (more than a handful of hours). If the battery is allowed to set below 75% state of charge for days, weeks, months--the sulfates will harden and the battery will never fully recover its original capacity (Battery FAQ).

So, for a first level approximation... You have a 100 AH battery (20 hour rate), 50% max discharge (recommended). It will give you:

100 AH / 20 Hours = 5 amps for 20 hours
100 AH (at 20 Hour rate) * 50% max discharge = 50 AH usable
50 AH (usable) / 5 amps = 10 hours to 50% discharge.

To charge, recommend charger rated at roughly 5%-13% of battery capacity:

100 AH * 5% = 5 amps (minimum)
100 AH * 13% = 13 amps (maximum)

If you discharged your battery by 50% or 50 AH (note, a flooded cell lead acid battery is roughly 80% efficient):

50AH / 5 amps * 1/80% eff = 12.5 hours (minimum charge time)
50AH / 13 amps * 1/80% eff = 4.8 hours (minimum)

Note, that flooded cell lead acid batteries recharge pretty quickly up to 80-95% of capacity--the last part usually takes longer (at reduce current).

I have made lots of simplifications here--and some of them are probably pretty close to being too simplified--so take this a a basic framework to hang the details as you continue to read.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Solar Expert Posts: 1,164 ✭✭
Re: Different Formulas

It's basic math. There are no elaborate formulas.

If you have a 100 AH battery, and it is 20% discharged (80% DOD), then you need to replace 20 AH.

If the panel puts out 4 amps, then it will take about 5 hours, + any losses.
• Solar Expert Posts: 131 ✭✭✭✭✭
Re: Different Formulas

Thanks you guys for just the basic stuff, thats pretty much what I was looking for!
• Solar Expert Posts: 131 ✭✭✭✭✭
Re: Different Formulas
BB. wrote: »
A lot of calculations are just variations of the basic electrical formulas... Or, here is another website. And here is another.

Anyway, to answer your question about power, work, and Amp*Hours...

Basic volts, amperes, ohms relationship:

V=I*R (voltage=current*resistance)
I=V/R
R=V/I

Power (watts--this is a "rate", sort of like Miles per Hour):

P= V*I = V^2 / R = I^2 * R

Work (Watt*Hours--sort of how far did you go--not scientific unit, but used for house/commercial wiring):

W=P*Time=P*Hours (P may substitute with any Power equality)

And for house/commercial billing, we use kiloWatt*Hour

1 kWHr = 1,000 Watt*Hours

Lastly, Amp*Hours... Not a real useful for most work as you have to know the volts that the Amp*Hours relates to. However, when working with DC / Ba
• Super Moderators, Administrators Posts: 30,737 admin
Re: Different Formulas

I guess I should clarify--A flooded cell lead Acid Battery is ~80% energy efficient... But, excluding equalization is very close to 100% efficient when working with current (50 AH out, requires about 50 AH to recharge).

Where they are 80% efficient is when voltage is taken into account (and probably including equalization). The battery discharges around 12.5 volts and recharges around 14.2-15 volts--the difference; P=I*V ... V is lower during discharge (lower watts) vs V being higher during recharging (higher watts).

Another reason people like to work with Amp*Hours with batteries--less "conversion factors"... However, because many electronic devices are really constant power devices (for example, a 120 VAC inverter, as the battery voltage goes down, the current pulled by the inverter goes up to keep its output regulated), the power efficiency factor does need to be taken into account.

-Bill
Near San Francisco California: 3.5kWatt Grid Tied Solar power system+small backup genset
• Solar Expert Posts: 8,875 ✭✭✭✭✭
Re: Different Formulas

The batteries "State Of Charge" is also a BIG factor in charging it. The first 80% of capacity can be recharged fairly fast, at high current rates. As the battery aproaches full charge, the charge rate must slow, as the battery is less efficient storing the power away.
It's possible the last 20% of charging can take longer then the first 30% of capacity. (don't discharge below 50%)
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