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Battery Physics

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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 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.

C-Rate C-Rate 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 Watt-hours/litre (Wh/l)
Gravimetric Energy Density
the amount of energy per unit weight Watt-hours/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
  • 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:

  1. Determine the number of hours a pack will be used between charges.
  2. Calculate the pack C rate based on 50% depth of discharge
  3. 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:

    C = Etot / Vpack

Since we should only take the batteries to 50% DOD, then the desired C rate is:

    Cdesired = C / .50

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

    d = C / 0.5 * Vpack / Ec

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