# Converting Fossil Fuel Energy to Battery Energy: Understanding Your Electric Car

By Tom Bartley • Mar 9th, 2009 • Category: Battery Technology for Hybrid and Electric Cars

A word about **battery** “**power**” and “**energy**“: **Batteries store energy and supply power**. It’s that simple.

But in casual conversation both words are tossed around to mean just about the same thing. Here is a primer to help keep your powers and energies straight. Warning: you’ll exercise your brain in this post, so read on at your own risk.

## Electrical Power and Energy

First let’s look at units of measurement and how to convert from one unit to another.

In physics, power is strength; and energy is how long the power keeps going or, simply, energy equals power times time. Power and energy are both units useful to describing the performance and capability of batteries. Power is expressed in watts (W) or kilowatts (kW, or 1,000 W) and energy is expressed watt-hours (Wh) or kilowatt-hours (kWh, or 1,000 Wh).

To help explain power and energy in context, here’s an illustration. The San Diego Gas & Electric company (SDG&E) provides power to my home in San Diego and on my electric bill I am usually charged between $.13 and $.15/kWh of energy used. For comparison, typical amounts charged for electric energy in the U.S. range from about $.02 to $.20 per kWh with a surcharge if the power exceeds a threshold level. The national average is reportedly about $.08/kWh. The City of San Francisco pays about $.024/kWh because they own the hydroelectric dam. And Disneyland pays the City of Anaheim about $.04/kWh in the middle of the night when power demands are low.

So that’s how we quantify electrical power and energy. To compare energy from batteries with other sources of energy (natural gas or gasoline, for example), we need to know how to express energy in these fuels.

## Energy in Fuels

Fuel combustion chemists like to use energy units of calories (cal) and British Thermal Units (Btus). Natural gas (CH4) is sold by the Btu and liquid fuels are sold by the gallon (or liter) with a specification of Btus per gallon. Again SDG&E provides my gas in San Diego and on my gas bill the average charge is about $.88/therm, where a therm is equal to 100,000 Btus, which is a little less than the energy content of a gallon of gasoline (about 114,100 Btus). To relate natural gas and electricity, 1 kWh = 3,414 Btus or 0.034 therms and 1 therm = 29.3 kWh.

Are you confused yet? Then forget what you just read above. Here’s a summary:

- 1 therm = 100,000 Btus
- 1 gallon of gasoline = 114,100 Btus
- 1 kWh = 3,414 Btus or 0.034 therms
- 1 therm = 29.3 KWh

Feeling smart yet? Then here’s a question: which is cheaper for me to use, my gas (natural gas) or my electricity? As you might expect, the answer is: My gas is cheaper (at $.03/kWh), because most of my electricity is generated by burning that same natural gas to convert to electricity and there are always energy losses in the process.

## Energy of a Moving Car

Car designers like to talk about power and gallons of gasoline rather than energy. They like to use units of horsepower (Hp) where 1 Hp = 746 W. The basic energy content of gasoline is 114,100 Btus or 33.4 kWh before conversion to mechanical energy (by burning in an engine). Because of engine efficiency losses and other factors, less than 1/3 of the fuel energy is actually available as mechanical energy at the engine output with the rest being lost as heat energy.

The energy of a moving car can be calculated using the formula below. The letter x is used as the multiplication sign.

Energy = (Weight/64) x (Speed)²

where Weight is the weight of the car and Speed is its speed at a given time.

As you can probably guess, we’re really looking at a supply and demand situation. On the supply side we have energy provided by the fuel (gasoline energy through the engine or battery energy through the electric drive motor). On the demand side we have the car with a certain mass/weight required to go at a certain speed. As mentioned above, there is always efficiency or loss of energy involved when converting from the energy supply to what the car demands.

So knowing the energy of the moving car and how long it took to get to that speed, and the energy of the battery or gasoline engine expended to get there, we can start to understand the energy efficiencies of the car’s propulsion and the acceptable performance provided by the available power level.

To keep this analysis simple and easy to understand, I have ignored various other elements that need to be considered such as discussion on the weight and speed as related to the units of power (kW or Hp) and energy (KWh or Hph). However, to play in the intelligent bantering about of power and energy in transportation and vehicle efficiency issues requires a ready reference book of conversion factors between units and a reliable associate to check the calculations. (Even the most experienced professional can occasionally be caught forgetting that a pound force = 32 x pound mass.) I sometimes use the Internet and reliable websites for a quick source of reference conversions.

## Using Batteries to Power the Cars

I hope you now have good background basics on gasoline and battery power and energy, and their relationship as applied to all kinds of vehicles, including cars. With the proper relationship and conversion factors in place, we can begin analyzing and comparing gasoline and battery electricity in plug-in and hybrid vehicles.

The next step is an exciting one. We’ll discuss how batteries, as the primary energy source, are put in cars and look at characteristics that determine range, operating cost, and battery replacement.

**Tom Bartley** is an industry veteran with 30 years of experience in general business, marketing, project and product management, and engineering research and development. Mr. Bartley provided executive management support including technical and business oversight to heavy-duty hybrid-electric prototype projects as they evolved into production. He developed cost models for energy storage and fuel savings, and power models for ultracapacitor packs. Mr. Bartley is well known throughout the industry of heavy-duty hybrid-electric buses and trucks, having delivered many papers and presentations since 2003. Mr. Bartley maintains a blog at TomBartleyIdeas.com. Follow twitter.com/TLBartley.

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Google coughed up your page and it’s OK as an overview of the different kinds of energy. But your formula “Energy = (Weight/64) x (Speed)²” is useless and wrong without units! Why divide by 64?! I know E = ½mv² , I was hoping to find a nifty JavaScript calculator that tells me a 3000 pound Prius moving at 30 mph has X kW·h of kinetic energy. Wikipedia’s Kinetic energy article and Google’s awesome “3000 lb in kg”, “30 mph in m/s” instant conversions suggest that X is 0.03 kW·h.

You’re right about the units. E=½mv2 But F=ma, where a=g if F=weight. Substituting, E=½(F/g)v2 . If I use the units of lbs for F; 32 ft/sec2 for g, the acceleration of gravity; and feet/sec for v, the speed; the result is E=(weight/64) x (Speed)2 in units of ft-lbs(force) of energy. 2,655,200 ft-lb(f) = 1 kWh

Using your Prius numbers of 3000 lbs and 30 mph (44 ft/sec)

E = (3000/64) x (44)2 = 90,750 ft-lb(f) = 0.03418 kWh = 34.18 Wh

Coincidentally, the 30 mph energy is nearly equal to the 30 ft elevation gravity energy of 90,000 ft-lb(f) = 0.03390 kWh = 33.90 Wh

The 30 feet elevation and 30 mph energy equivalence works for a vehicle of any weight. So if freeway on ramps all headed downhill you would get a free 30 mph. Conversely, if you were going 30 mph heading up a freeway exit ramp you would stop at the top without using your brakes.

At 60 mph the distance is 4 x 30 = 120 feet because of the velocity squared factor.