There are many web sites dedicated to batteries, their chemistry and physics. Here are some links that are very informative:
The Battery University
Battery Chemistry and Calculations
Car and Deep Cycle Battery FAQ
Lee Hart on Battery Maintenance
Batteries and Range
Batteries in a Portable World
Engineering Guidelines for Designing Battery Packs
A battery's capacity is measured in Amp-hours, called "C".
The is the theoretical amount of current a battery delivers when discharged in one hour to the point of 100% depth of discharge.
Not all battery manufacturers determine the capacity by the same method.
Often the companies will discharge it for 3, 5, 5 10 or 20 hours, then calculate the amp-hours based on this value.
For example: If a battery's capacity was measured over 20 hours to be 2 amps, then the capacity rating would be labelled 80 Amp-hours.
However the faster you discharge, the lower the capacity of the battery. If a load of 80 Amps was drawn from this battery, it would probably only last 20-30 minutes.
C-Rate (a.k.a. Hourly Rate)
The C rate is often used to describe battery loads or battery charging. 1C is the capacity rating (Amp-hour) of the battery.
||Hours of Discharge
|1C (1 hour rate)
|C/4 (4 hour rate)
|C/10 (10 hour rate)
|C/20 (20 hour rate)
There are two kinds of energy density for a battery:
|Energy Density Type
|Volumetric Energy Density
||the amount of energy per unit volume
|Gravimetric Energy Density
||the amount of energy per unit weight
Batteries in an Electric Vehicle
To determine the type, size and number of batteries for a given electric vehicle a number of factors must be considered:
- d - Amount of distance expected to be travelled between charges, d
- Ct - Whether flat, rolling or hilly terrain Ct
- Ctf - If in-town stop and go traffic or continous highway speeds Ctf
- Ec - Vehicle efficiency
- Vpack - Pack voltage
From this information we can:
- Determine the number of hours a pack will be used between charges.
- Calculate the pack C rate based on 50% depth of discharge
- Adjust for the type of terrain and type of traffic
Total Energy Used:
Etot = (d * Ec * Ct * Ctf)
Battery C Rate required (to 100% DOD) is:
Since we should only take the batteries to 50% DOD, then the desired C rate is:
For example, say I have a car that has an efficiency of 250Wh/mi. I want to go 50mi between charges on rolling (Ct = 0.9) and some stop and go traffic (Ctf = 0.8). Since I am using a fancy AC system, my pack voltage is 312 Volts.
Etot = (50mi * 250Wh/mi * 0.9 * 0.8) = 9000Wh
C = 9000Wh / 312V = 28.8 amp-hours
Cdesired = 28.8 / 0.5 = 57.6 amp-hours
So for this example, I would like to look for a pack that has a 1C rate of approx 58 amp-hours.
Often, if you are forced to fit a specific pack size (due to weight constraints), you can use this formula to roughly estimate distance