August 2004
Battery Links
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
Battery Glossary
Engineering Guidelines for Designing Battery Packs
Battery Capacity
A battery's capacity is measured in Amphours, 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 amphours 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 Amphours.
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 2030 minutes.
CRate (a.k.a. Hourly Rate)
The C rate is often used to describe battery loads or battery charging. 1C is the capacity rating (Amphour) of the battery.
CRate 
CRate 
Hours of Discharge 
1C (1 hour rate)

1C 
1 hour 
C/4 (4 hour rate)

0.25C 
4 hours 
C/10 (10 hour rate)

0.1C 
10 hours 
C/20 (20 hour rate)

0.05C 
20 hours 
Energy Density
There are two kinds of energy density for a battery:
Energy Density Type 
Definition 
Units 
Volumetric Energy Density

the amount of energy per unit volume 
Watthours/litre (Wh/l) 
Gravimetric Energy Density

the amount of energy per unit weight 
Watthours/kilogram (Wh/kg) 
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
 C_{t}  Whether flat, rolling or hilly terrain Ct
 C_{tf}  If intown stop and go traffic or continous highway speeds Ctf
 E_{c}  Vehicle efficiency
 V_{pack}  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:
E_{tot} = (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.
E_{tot} = (50mi * 250Wh/mi * 0.9 * 0.8) = 9000Wh
C = 9000Wh / 312V = 28.8 amphours
C_{desired} = 28.8 / 0.5 = 57.6 amphours
So for this example, I would like to look for a pack that has a 1C rate of approx 58 amphours.
Often, if you are forced to fit a specific pack size (due to weight constraints), you can use this formula to roughly estimate distance
d = C / 0.5 * V_{pack} / E_{c}

