Gas Mileage Rant

I saw this article on DIGG and couldn't help but respond. Original blog is here: http://www.jeffwoelker.com/2007/05/24/30-mpg-is-laughable-us-auto-makers-are-joking-right/

I apologize but I screwed up my calculations pretty badly initially because I was at work when I did it. Starting fresh here we go:

By my rough calculations the max fuel economy of a car would be about 160 MPG with no acceleration, braking, or wind resistance. Math as follows:

http://www.nafa.org/Content/NavigationMenu/Resource_Center/Alternative_Fuels/Energy_Equivalents/Energy_Equivalents.htm

states that a gallon of gas contains 114,100 BTU’s of energy.

Expressed in joules this is about 120 million joules.

http://www.google.com/search?q=114000+BTU+in+joules&start=0&ie=utf-8&oe=utf-8&client=firefox-a&rls=org.mozilla:en-US:official

1 joule = 1 newton* 1 meter

According to Wikipedia the rolling resistance only from the tires for a 1000 kg (2200 lb) car is 300 Newtons.

one mile is about 1600 meters so one mile consumes 480,000 joules. This will become important later to compare apples to apples for wind resistance.

If you only take into account the rolling resistance you get

120,000,000/300 or 400,000 which is 400 km or about 250 miles

If you add in wind resistance which is about 10 hp according to wikipedia at 50 mph (80 kph)

http://en.wikipedia.org/wiki/Drag_(physics)#Power

This is where I was wrong before. I calculated the joules to travel 50 miles and applied that as the total resistance for the whole gallon not the joules to travel one mile. So the corrected math follows:

1 horse power = 745 watts = 745 joules/s


10 hp = 7450 joules per second. To travel one mile at 50 mph takes 72 seconds. Thus for wind resistance it consumes 536400 joules per mile at 50 mph.

if we add joules per mile for rolling resistance of 480,000 to wind resistance of 536,400 I get 1,016,400 joules per mile. Thus without doing the exact math my new estimate for a "maximum" fuel efficiency is about 120 miles per gallon.

I stand by this still:
Keep in mind that these numbers represent 100% efficiency of the engine and no energy lost to acceleration or braking. Even by lowering the wind resistance by half you are only looking at a theoretical maximum of 160 mpg or so. To post that we should be able to acheive 300 or 500 MPG is absolutely ludicrous. Before people jump all over me about using electric cars or other nonsense keep in mind that all I did was use the energy value of the fuel so if that energy comes from a battery, nuclear generator, or gas engine is irrelevant.

I agree that these assumptions do assume that lost of things are fixed. However, the weight of the car can only go so low and the rolling friction of the wheels needs to remain constant by weight to allow for safe acceleration and decceleration. If the rolling resistance were reduced the amount of energy that could be applied to the wheels before they lost traction would go down. If you have ever spun your tires this is because the force applied by the engine to the wheels is greater than the force applied to the tires by the road. the mechanics are identical on braking as well so a car with low rollign resistnace couldn't stop very well.

Certainly the cars could be made lighter but again my assumption is on the low side when you consider that a Yaris, which is pretty much the smallest car you can buy weighs 2290 lbs without any gas or passengers.

http://www.toyota.com/yaris/specs.html

To refine my argument for drag being relatively constant I looked up the drag coefficient for the Accord and the Camry:

7.39 - 1994 Honda Accord EX
7.57 - 1992 Toyota Camry

Compare this to the EV1 which I will assume is the theoretical limit and you get:

3.95 - 1996 GM EV1

http://en.wikipedia.org/wiki/Drag_coefficient#Typical_values_and_examples

While not exactly half it is close enough for me to stand behind my theoretical maximum for a 1000 kg car being about 160 MPG with no accelration or braking only traveling constantly at 50 MPH.

Once you add in acceleration, braking, AC, Radio and other features that Americans demand this theoretical maximum will drop in a hurry. THis also assumes that 100 percent of the energy produced in the engine is converted to usable energy which is strictly impossible.

As a side note on Solar panels they are basically irrelevant on a car. This is stolen from the Digg comments:

This draws on info from:
http://mb-soft.com/public2/energyso.html &
http://www.nafa.org/Content/NavigationMenu/Resource_Center/Alternative_Fuels/Energy_Equivalents/Energy_Equivalents.htm

If we get 130 BTU's of energy per sq. foot from solar, and
we put 6 sq. feet of solar panels on a car and
those panels are 50% efficient (don't squabble on that number, it's just for this example)
we get 390 BTU's of energy into the battery for every hour of sunlight.
12 hours of sunlight per day (as an average) gives us
4,680 BTU's of energy into the batteries.

A gallon of gas has 114,100 BTU's of energy
4,680 / 114,100 = 4% of a gallon of gas

So, if our hypothetical car gets 50 mpg, it will go about 2 miles on the sunlight it absorbs in a day.

That number is actually a little depressing.

Again this goes to actual energy usage not how efficiently that energy is used or where it comes from.

Electric cars are another place where people claim that there is a reduction in gas usage whichis correct. However, it is not a decrease in energy usage. The electricity for the car to charge must come from somewhere. According to the DOE "In 2005, more than half (51%) of the country's 3.9 trillion kilowatthours of electricity used coal as its source of energy." Therefore all of these greenies that are using electric cars are actually using more coal than any other source to power thier cars.


As an economics major I firmly believe that the changes will have to come from the market. As long as the government is supporting artificially low prices for gas by not taxing it higher (not a misprint I mean another dollar or more per gallon) then people will not demand these innovations from the auto industry. They will continue choosing to live far from their work or drive ridiculously big cars. The biggest reason congress can not raise CAFE standards is that consumers refuse to buy smaller cars.

Despite record high gas prices driving is UP this year and truck sales have barely slown down. Imagine if the whole world worked like this. The more expensive gas becomes the more we buy and use. Imagine if you went to a store to find that the price of soda had increased so you decided to buy more than you would have if it cost less. THat is patently absurd. Yet every day American's announce loudly and clearly that gas is inexpensive and adjust their habits accordingly. Until a rise in prices leads to a change in behaviour nothing will change.

Furthermore, despite this run up in price a Prius is still not economically viable based on current gas prices. Take a driver that drives 12000 miles per year or 1000 miles per month. Gas bill for a camry hybrid 966(300 gallons * 3.22 avg price per gallon) is vs a camry is 1136 (353 gallon * 3.22 avg price per gallon). This difference in gas bill is $170/year assuming no interest it would take 45 years to justify the $7730 extra in sticker price based on fuel economy alone. Gas would have to average $10/gallon for the repayment time to be only 5 years for a product which must be replaced every three years. I am not saying that you should not buy a hybrid but you should know that you are buying it for status no economics.

http://www.toyota.com/camry/specs.html

Ultimastely the reason we don't have more efficient cars is that consumers aren't willing to accept them yet and never will until the economics of the situation change. If you truly want to see fuel economy increase then you should cheer every time the price of crude or your price at the pump increases because it brings closer the day that we will see real change in the energy consumption habits.

In conclusion if you are unhappy with gas prices vote with the only vote that can't be taken away, your pocketbook. Buy a smaller car, move closer to work, or carpool. You can not continue to complain that Exxon made $10 billion dollars last year as you crank the AC in your house and drive your SUV 80 mph to the rally. You are not being victimized by the oil company, you are hurting yourself.

I for one will continue to drive while it is still affordable.