“Be kind, for everyone you meet is fighting a hard battle” - Often attributed to Plato but likely from Ian McLaren (pseudonym of Reverend John Watson)

Sunday, August 10, 2008

What does a high fuel economy car look like?

To quote Scotty, "you canna change the laws of physics." I'm going to look at what a high fuel economy car would look like, with no assumptions about engine technology breakthroughs. Therefore, there are four fundamental things that we can control: vehicle weight (affects fuel used for acceleration to speed and amount of rolling resistance); tire coefficient of rolling resistance; vehicle frontal area; vehicle shape, reflected in the drag coefficient.

Let's look at cruising. In this case weight only comes in as a factor in rolling resistance, while frontal area and vehicle shape are the factors affecting drag. I've seen an equation that alleges to combine these components - the equation is: Fr=0.5*rho*Cd*A*v^2+Crr*m*g*v where rho is air density, Cd the coefficient of drag, A the frontal area, v is velocity, Crr is coefficient of rolling resistance, m is mass of vehicle, and finally, g is the acceleration of gravity.

I don't buy it. My analysis shows that, at least for first order effects, rolling resistance is not a function of velocity, so let's use Fr=0.5*rho*Cd*A*v^2+Crr*m*g. This is dimensionally correct with both coefficients dimensionless. It is, therefore, plausible and I'm going with it.

So, what can be changed here? We can't change rho or g, and v is whatever the driver chooses to use. I'll list the variables we can change and what would be done:

1. Reduce Cd. This can be done by the manufacturer, there have been vehicles with Cd as low as 0.16, though not many. There are those who modify their vehicles themselves to reduce Cd. To see this in action, visit the Aerodynamics forum at the ecomodder web site. I'd suggest looking for posts by "basjoos" to see the extremes to which this can be taken. A blog post about his vehicle can be found here. If you choose to do this, be careful because aerodynamics can be non-intuitive.

2. Reduce A, frontal area. This means a smaller vehicle in general. For a two-seater, tandem seating might be an option. There are concept vehicles out there that take this route and they will certainly have a low so-called "drag area," the product of Cd and A. Market acceptance is clearly a question.

3. Reduce Crr. This is the amount of force used up by tire rolling resistance. There are low rolling resistance tires out there, and California is contemplating requiring manufacturers to list Crr for tires sold here. The rolling resistance depends in a complicated way on a number of factors, but tires primarily use energy in so-called "hysteresis losses," i.e., flexing portions of the tire without full energy recovery as the tire rotates. Steel wheels on trains have extremely low Crr's since they barely flex at all. For a look at low rolling resistance tires, check here.

4. Reduce m, mass. Obviously, reducing A helps here since, in general, smaller cars weigh less. Lighter materials, less room for storage, smaller fuel tanks, etc. can also be utilized, as can minimally sized engines for the mission at hand. These reductions are synergistic - lighter vehicles need smaller engines, which can utilize lighter drive line components, which can utilize smaller fuel tanks for less fuel weight, etc.

So, a composite, tandem seating car, optimally shaped with little or no trunk and a small fuel tank would appear to be the best prescription. Of course, as is usually the case, the easiest savings coming from driving less and sharing the ride.

As I stated at the outset, this doesn't address possible gains from engine efficiency. In my opinion, dramatic gains aren't likely here. I'll address engine issues in another post.