Speed to drive for best Fuel Economy

Posted by pikesan on Oct 17, 2008 in How-To & Tech | 2 comments

I was cruising the web looking for something and I found this discussion. What speed should you drive to get your best fuel economy?

interestingly enough, the discussion was from a story from the site Truth about Cars. That site kicks out a shocking amount of car related content. From the story folks at truthaboutcars.com were trying to help everyone understand a formula that actually came from Howstuffworks.com, another great site to kill several hours… try taking the Alligator quiz or see if a platypus could poison you. The How Stuff works guys did alot better job, but didn’t really give any background.

After the story, several folks chimed in with their “truth”. In reality, they said alot that was dead wrong and then some close, but not right.

The equation they were using to answer the question was:

Road Load Power = aV + bV^2 + cV^3

where a, b and c are constants and V is the symbol for velocity or let’s just say SPEED. There was some mention of where this equation came from, but unfortunately, it wasn’t quite right. I also want to say what “Road Load” means. Road Load is when you’re cruising… not going faster or slower (not accelerating) so your power output is balanced to the power required to keep your car moving at that speed.

Where does the Power come from and what are a, b and c?

Back up a sec and first consider “Road Load”. Load is a force. Road Load is the force on your car when you’re not going faster or slower. It’s your resistance or “drag force”. How are force and power related? Hang on a minute…

It’s easy to find your Road Load driving force or resistance by what’s called a coast down test. That’s a test that’s alot like it sounds. You drive to about 80mph (no need to go faster, but why is really hard to explain… suffice to say 80’s enough) then put the car in neutral and measure how much time is needed to “coast down” to about 10mph. The time data, measured in pairs, like 80-70 and 70-60 can be used to find your coast down information – for that one particular car.

After coast down, you’ll know the driving force (not power, not yet) you need to keep your car moving. The equation is a 2nd order polynomial that looks like: a + bV + cV^2.

• a= rolling drag, it’s a constant that comes mostly from the tires deforming and vehicle weight (notice it doesn’t care how fast you’re driving)
• b= mechanical friction, pumps and other things (depends on speed, usually very small compared to the others)
• c= wind drag, depends on frontal area (think about shining a flash light into the front of your car, the shadow it casts is the frontal area.)

A term more people might have heard of is Cd. Cd is related to the “c” of this equation by:

Wind resistance or wind drag = c V^2 = 1/2 x air density x A x Cd x V^2

A is the front area. The Cd you hear about has more to do with the SHAPE of a car. A low Cd means a vehicle with the same frontal area (think about a passenger van vs. a bullet train) makes less wind resistance because the vehicle’s shape is better (more aerodynamic).

Let’s move on to the question about power.

Power = force x velocity. (in our case Road Load x velocity)

Enjoy the math… (a + bV + cV^2) x V = aV + bV^2 + cV^3.

You can find the a, b & c from the EPA website for new cars and they’re the same constants found from coast down testing. (I’ve heard, I tried to give you a link, but couldn’t find it) Coastdown data is used to find the EPA fuel economy. But, don’t think it’s coastdown’s fault that nobody every gets their EPA sticker advertised fuel economy. It’s not!

Are you thoroughly confused yet? You might as well be cause this still doesn’t even consider the efficiency of the motor, Brake specific Fuel Consumption or BSFC or the power per fuel used.

To really answer this question, you need more data. And unfortunately, the data comes from experiment or a bunch more calculations with alot of assumptions. Unless you’re building the car, you probably won’t know this stuff.

There’s a bunch more I could say about this. Does anyone care? Or would you rather “Drop the hammer!!” and have fun! Last time I checked, “Bonnie”, my 4 cylinder 27 Roadster gets 21mpg. Works for me!