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Efficiency = Total Cost of Ownership

[28 September 2006]

Two assertions that I have repeatedly seen made about electric bicycle engines were that 1) they were more-economical than a gasoline engine, and that 2) they were kinder to the environment.

To detirmine that we would need to be able to find out the actual pollution produced by the manufacture and the operation of each, for their useful lifetimes. Unfortunately there isn't any easy way to do that directly.

About the best estimate we can use is to assume that the cost of an item is a measure of the resources that went into making it--and if we assume that the use of resources in any item typically represents the amount of pollution that manufacturing that item caused, then the price of any item is a measure of the pollution that was produced when the item was manufactured. This way one can compare the operating costs of two contrasting vehicles, and make an estimate of their relative ecological impacts.

This comparison is between bicycle engine kits and their operating costs. The cost of the bicycles is not included, and the purchase price of the engines is not factored in as well (as it is presumable that if you operated either bicycle engine for a long enough time, it would save money, compared to using a automobile would).

The Bionx system is an electric-motor kit for bicycles that is considered to be one of the better-quality brands, and it usually has four battery choices available. Some electric motor setups can apply full power but the Bionx uses a "metered assist" design, where the motor is set to a certain percentage of rider effort, with 200% being the highest level of assist. It will not apply any power unless the rider does, so it is not possible to test the motor's power alone.

For the gasoline engine I didn't use any specific example. There are 2-cycle and 4-cycle engine kits available, but I only specify a 4-cycle as they use lubricating oil more efficiently. The "200 MPG" claim is typical for these engines in this use, and is present on multiple websites selling them. Owners replying online stated that it is a reasonable estimate.

In the screenshot above, the green-background box represents the cost totals for operating the Bionx electric setup.

Column B lists the four battery types, column C lists the approximate miles of assist available from each battery when used at the 200% assist level. Column D is the number of recharge cycles that each battery is generally-expected to last(see note #1). Column E is the replacement cost of the batteries as listed at one online seller. Column F is an estimate of the total miles that the battery would be able to "cover", this being the estimated miles per-charge multiplied by the total number of discharge cycles per battery, and then multiplied by 66% to account for the "assist level". Column G represents the cost of recharging the battery for the total expected discharge cycles, the cost of each recharge being estimated at around five cents(see note #2). Column H (in violet) represents the operating cost-per-mile for each of the four batteries: that is, the battery + expected recharging costs of each divided by their expected/rated mileage.

The blue-background box represents the operating costs of an example of a representative gasoline engine. Column F notes the typical MPG estimate, column G notes the typical fuel costs (as of this writing [9/24/2006]) and the final column H (in dark-blue print) notes the estimated cost-per-mile. There are other regular costs of operating a 4-cycle engine that are not included here (such as oil changes) but these aren't noted here because I was not certain about the recommended intervals of them. Adding the cost of oil changes would certainly raise the operating cost, but we'll get back to that matter further below.

The argument could also be made that the price of fuel is quite volatile, and it goes up and down, and as fuel becomes more scarce it will most-certainly rise in price in the future. It is rather obvious that comparing the electric operating costs vs. the gasoline-engine costs that the gasoline is currently much less expensive--but how much would fuel prices need to rise to make the electric option more economical? That is the totals in the green box in column I, shown in red. For each of the four battery types, these are the prices to which gasoline would have to rise (per-gallon) to match the operating cost of the electric motor system. ...-And it could even be noted that these figures are too low--the price of gasoline also essentially represents energy costs, and so it is entirely presumable that if the price of fuel-energy goes up, then the prices of any manufactured goods will rise as well, as they generally require fuel energy at some point in their manufacture.

What about those "omitted costs" of the gasoline engine? Take a look at the screenshot below.

The figures in column A represent the typical full-charge mileage capacities of the same four different batteries. Column B has 365 days for each, as we will figure the cost savings for using the four different battery options for a regular year, and assuming that we will discharge the electrics' batteries once per day. Column C is the total miles divided by .66 (making the allowance for the 200% "assist level" afforded by the Bionx example system). Column D is the costs-per-mile of the electric systems, and column E is the cost of using each system to its rated capacity every day for a year. Column F is the cost of fuelling the gasoline engine for the same rated miles. Column G is the cost savings of the gasoline engine over the electric, for a one year period, and over the amount of miles that the electric would be able to operate at one battery discharge per day.

I noted before that I could not inlcude all the costs of the gasoline engine, because I wasn't sure of what they were, when they occurred or how to estimate them--but it becomes obvious here that the cost savings of the gasoline engine is so large that anything as minor as oil changes (probably the most-regular maintenance that would need to be performed) doesn't come close to making up the cost difference. In cell F4 for instance--$45.17 of gasoline at $2.50 per gallon comes to a bit over 18 gallons, and motor oil is [currently] priced at around $3/quart. $290 will buy you about 96+ quarts of oil. A 4-cycle engine that burns 18 gallons of fuel isn't going to need 96 quarts of oil to do it (the cost of oil changes for running ~10,000 miles is about two dollars, see note #3).

I don't know what the life span of either of the engines is.
I have no idea in practical terms what the lifespan of the electric motors is, but under normal use it is far longer than the life span of an individual battery.

There are numerous people who have gotten 15,000 miles out of the gasoline engines and fewer still who have used them even longer than that, but the price of the gasoline engines alone is only about $250-$300. Even if the gasoline engine only lasted one year, replacing it once per year would just about be even with the cost of keeping the electric system in batteries.

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Does that mean you shouldn't buy an electric? That's not my decision, I'm not in charge of how other people spend their money.
There are some instances where internal-combustion engines aren't useful at all, and others still where either could work but electrics have valuable advantages--but "economical operation" and "saving the environment" probably aren't one of them.
At this point, two facts become clear:

1. Either of these choices probably does a lot less damage to the environment than buying and operating a car or a motorcycle over the same time period would.

2. Either of these choices will damage the environment, but using the gasoline engine will likely damage it less than the electric would.

This study originated out of an incident online where it was claimed that an electric always polluted less than a gasoline-engine would; the persons who claimed it seemed mostly concerned with smog and not a lot with much any other type. It's long been a (somewhat tired) argument against electrics that they merely "displace" the pollution, and the usual argument was that an electric was displacing its pollution to the power-generation plant. That much is true, but not for the typical reason claimed: most of the pollution that occurs with an electric vehicle is what happens not where the charging electricity comes from, but where the batteries are made and disposed of (or recycled).

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Notes

#1--the NiMH batteries are rated for "400-500" discharge cycles, so I split the difference and used 450 for the figure

#2--the "$.05 per charge" is a low estimate for what U.S. users of electrics claim is their recharging costs. Most people claime around $.07, but this would vary with region and battery size, so I just used a low estimate.

#3--the oil changes I know the cost of now, as the engine manual gives them. The engine needs 100ml of oil, and needs to be changed out after the first 20 hours of operation, and from then on every 50 hours. Mileage-wise, the first oil change needs to be at 600 miles and then every 1,500 miles after that. A quart of oil contains ~950 ml and costs around $2.20, so oil changes for this engine only cost a bit over twenty-two cents each. To run 9,300 miles the cost would still only amount to less than two dollars of oil. The air filter is a reuseable sponge type, so there's essentially no maintenance cost (cleaning and re-oiling it is all it will need for a few hundred hours at least). The spark plug life I haven't found in the manual yet, but most people don't bother to replace them until the engine has trouble running and they check the spark plug and see that it needs replacing.

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