In the news today: Toyota is planning on putting a solar panel on their Prius.
Sounds good, doesn't it? An electric hybrid that's able to be partially powered by the sun.
Well...
How are we sure that its not essentially just a clever sales gimmick?
Here's one take on the "Reality Check" of physics.
A conventional solar panel (Mitsubishi; Sharp) provides 185W of output, and is 65" long x 33" wide: call it roughly 5ft x 3ft. Let's assume no sunroof, so you can install two of them on the roof of a car like a Prius.
Those two panels result in roughly 370W of power under ideal conditions. Let's assume that there's another 10% of roof real estate available and round up the number to a conveniently easy to work with 400W of output.
The article (see link) reports that the A/C system needs up to 5kW of power. Standardizing units, that's 5,000W.
Thus, the panel can provide (400W/5,000W) = 8% of the A/C system's peak demand.
Thus, you can run your A/C "totally on solar" if you only run it at ~8% of its capacity. That doesn't sound like all that much cooling capacity to me.
Okay, let's look at things differently: let's assume that the solar panels can charge the battery pack, even though this isn't mentioned in the article. While we're also at it, let's be an irrational optimist and assume that this storage will be 100% efficient and has no other trade-off factors (such as needing a bigger battery).
So how much power can we store? Classically, solar systems are discussed and designed around the time of day which results in roughly 80% of the total daily collection. This is commonly defined as 10AM-3PM, which is a period of 5 hours. True, there is solar gain before 10AM and after 3PM, but generally it isn't planned for too much, as the sun angle, strength and shading factors are some of the factors for why the panels run at below their ratings and all of these other hours of daylight only collect around ~20%. This is classical Pareto Principle.
So in those 5 hours of good gain, the panels will run at their rating, so this sytem will generate 5hr * 400W =2,000W-Hrs.
Continuing to assume that idealized 100% efficient storage battery, this means that the system can provide 0.4 hours (24 minutes) worth of full A/C per day. For a to/from work commute, that's 12 minutes each way...assuming that you park your car in the sun at work and don't go out to lunch.
Okay, it is better than nothing, but do keep in mind that those panels aren't free. Their retail price is around $2,000.
And more importantly, they aren't weighless. In standard trim, they're just over 35lbs each. Figure that with packaging economies, they can be reduced from 70lbs down to around a 50lb increase in vehicle curb weights. Now ask yourself: an increase of 50lbs in the vehicle's weight hurt the car's fuel economy by how much?
And ditto for that idealized 100% efficient battery. To do 2000 W-hr worth of power storage, you're roughly going to need a battery roughly the size/capacity of a standard automotive Lead-Acid battery. In NiMH, I'd SWAG it at another $500 and 25-30lbs increase in curb weight.
This is just a quick "back of envelope" system analysis, but it looks like at least a 50% salesmanship snake oil for a 'Green' product to me at this point. I'd personally like to see a more comprehensive one done with real values, to specifically include how much the vehicle's cost goes up, weight goes up and MPG goes down (because of that higher weight).
Don't hold your breath.
-hh
Showing posts with label hybrid cars. Show all posts
Showing posts with label hybrid cars. Show all posts
Monday, July 7, 2008
Sunday, December 30, 2007
Thinking about buying hybrid automobile?
Hybrids are all the rage whenever there's a spike in gasoline prices.
But while they might save you some gas, are they really saving you money? Afterall, isn't "saving money" usually the real reason why people want better gas mileage?
So lets see if a hybrid car really does saves us money or not.
There's a lot of things that go into the expense of operating an automobile. Its original cost, insurance, fuel, maintenance, etc. The sum of all of these is around 41 cents per mile, as per IRS tax law provisions (for non-cash donations to charity, etc). But I'm going to simplify things and only look at two of the variables, assuming that the others aren't going to change much.
The two I'm going to look at is the differences in fuel and maintenance expenses.
Fuel seems obvious...miles per gallon. Yup, its that simple, but I'm going to flip it over, to "cents per mile".
But maintenance isn't so straightforward, because Hybrid vehicle technology is more complicated than conventional automotive engines (including diesels). Simplistically, it is a conventional engine, "plus some other stuff" to pay to maintain. Without getting down into the weeds, I'm just going to consider two main components, the electric motor and the battery pack.
Let's get started:
The battery pack: when the Toyota Prius first came out, one of the pieces of information that was also released was the engineering acknowledgment that batteries don't last forever, and that having a bigger battery is going to cost more to replace than that single one that all cars have under the hood. At the time, Toyota estimated that the battery pack would last 100,000 miles, whereupon the cost to replace would be around $3,000. These numbers have probably since been updated, but I'm going to stick with these because they were real numbers and they serve as a good illustration of the cost comparison process: when we amortize this $3000 expense over its 100,000 lifespan, we get ($3,000/100,000) = 3 cents per mile.
The electric motor: its maintenance is hopefully zero, but some will break and need repairs that won't be cheap, plus it will eventually wear out. I don't really want to claim numbers because I've not researched any. However, if its similar to a clutch and/or transmission rebuild, we can probably expect half of a fleet will need such a service done by 100,000 miles and that it will cost at least $1,000. If you do the math, that works out to (1 cent per mile per vehicle)(50% service rate) = 0.5 cent/mile. For sake of keeping this analysis simple, we can assume that this is the lower limit for the sum of a bunch of the new electrical system components , such as the accompanying high voltage harness, etc. Keep in mind that the exact value isn't as important as how it is then used in the cost evaluation process.
And before I go on, it is true that we don't see these costs on a day-to-day basis: they show up when the car eventually gets service or repair, or by when we sell or trade-in the car before the repair is needed: more wear is invariably be reflected in a lower resale price, just like how you'll get a higher price after you've just made repairs, new tires, etc.
Okay, so the simple summary of the above essentially is that a hybrid costs more to keep maintained, and based on just these two factors, our estimate of this these expenses are (3 + 0.5) cents per mile driven.
And what this means is ~46 MPG (Prius) isn't the whole story: its 46MPG with a 3.5 cent/mile handicap that needs to be better, and we need to figure out the math to see if that's the case or not.
Assume: Regular Gasoline at $3.00/gal
46 MPG is thus: $3.00 / 46 miles = 6.5 cents per mile (direct fuel cost).
6.5 cents/mile + 3.5 cents/mile hybrid higher costs = 10 cents/mile (incremental hybrid cost)
Converting 10 cents/mile back into MPG: ($3.00/0.10) = 30 MPG
Thus, a Prius that's actually getting 46 MPG is the same as a normal car that's getting 30 MPG after we factor in the hybrid's higher incremental maintenance costs.
And since there's diesels that can do better than 30 MPG (even after we handicap their fuel cost), the simple bottom line is that a hybrid doesn't have the lowest cost per mile.
But while they might save you some gas, are they really saving you money? Afterall, isn't "saving money" usually the real reason why people want better gas mileage?
So lets see if a hybrid car really does saves us money or not.
There's a lot of things that go into the expense of operating an automobile. Its original cost, insurance, fuel, maintenance, etc. The sum of all of these is around 41 cents per mile, as per IRS tax law provisions (for non-cash donations to charity, etc). But I'm going to simplify things and only look at two of the variables, assuming that the others aren't going to change much.
The two I'm going to look at is the differences in fuel and maintenance expenses.
Fuel seems obvious...miles per gallon. Yup, its that simple, but I'm going to flip it over, to "cents per mile".
But maintenance isn't so straightforward, because Hybrid vehicle technology is more complicated than conventional automotive engines (including diesels). Simplistically, it is a conventional engine, "plus some other stuff" to pay to maintain. Without getting down into the weeds, I'm just going to consider two main components, the electric motor and the battery pack.
Let's get started:
The battery pack: when the Toyota Prius first came out, one of the pieces of information that was also released was the engineering acknowledgment that batteries don't last forever, and that having a bigger battery is going to cost more to replace than that single one that all cars have under the hood. At the time, Toyota estimated that the battery pack would last 100,000 miles, whereupon the cost to replace would be around $3,000. These numbers have probably since been updated, but I'm going to stick with these because they were real numbers and they serve as a good illustration of the cost comparison process: when we amortize this $3000 expense over its 100,000 lifespan, we get ($3,000/100,000) = 3 cents per mile.
The electric motor: its maintenance is hopefully zero, but some will break and need repairs that won't be cheap, plus it will eventually wear out. I don't really want to claim numbers because I've not researched any. However, if its similar to a clutch and/or transmission rebuild, we can probably expect half of a fleet will need such a service done by 100,000 miles and that it will cost at least $1,000. If you do the math, that works out to (1 cent per mile per vehicle)(50% service rate) = 0.5 cent/mile. For sake of keeping this analysis simple, we can assume that this is the lower limit for the sum of a bunch of the new electrical system components , such as the accompanying high voltage harness, etc. Keep in mind that the exact value isn't as important as how it is then used in the cost evaluation process.
And before I go on, it is true that we don't see these costs on a day-to-day basis: they show up when the car eventually gets service or repair, or by when we sell or trade-in the car before the repair is needed: more wear is invariably be reflected in a lower resale price, just like how you'll get a higher price after you've just made repairs, new tires, etc.
Okay, so the simple summary of the above essentially is that a hybrid costs more to keep maintained, and based on just these two factors, our estimate of this these expenses are (3 + 0.5) cents per mile driven.
And what this means is ~46 MPG (Prius) isn't the whole story: its 46MPG with a 3.5 cent/mile handicap that needs to be better, and we need to figure out the math to see if that's the case or not.
Assume: Regular Gasoline at $3.00/gal
46 MPG is thus: $3.00 / 46 miles = 6.5 cents per mile (direct fuel cost).
6.5 cents/mile + 3.5 cents/mile hybrid higher costs = 10 cents/mile (incremental hybrid cost)
Converting 10 cents/mile back into MPG: ($3.00/0.10) = 30 MPG
Thus, a Prius that's actually getting 46 MPG is the same as a normal car that's getting 30 MPG after we factor in the hybrid's higher incremental maintenance costs.
And since there's diesels that can do better than 30 MPG (even after we handicap their fuel cost), the simple bottom line is that a hybrid doesn't have the lowest cost per mile.
Do feel free to update & refine my numbers to make them more accurate. However, you can't violate the general process of accounting for all operating expenses, and in particular the simple fact that a more complicated machine inevitably costs more to maintain.
-hh
-hh
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