After the September 11^th attacks, a newfound sense of patriotism swept across this country faster than reports of the latest anthrax scare. From wearing jeweled flag pins to displaying Old Glory on storefront windows, people are expressing their patriotism in myriad ways.

In October, Florida's legislature even rushed through a quickie patriotism law. The bill requires school districts to establish patriotic programs, mandating that the Pledge of Allegiance be recited each day at every public school. Students must also stand and place their hand over their heart during its recitation.

I'm all for patriotism, but is there a point at which things can go too far?

Suppose, for example, that Florida's House now passes a law requiring that a flag be flown from all vehicles. Given the number of flags flapping on the roads here in Massachusetts, a law probably isn't necessary, but bear with me.

A nice touch of patriotism, perhaps-but at what price? Mounting anything to a vehicle's antenna will result in added drag and lower fuel consumption. To determine the exact impact, I sought out Fred Browand, a professor of Aerospace & Mechanical Engineering at the University of Southern California who specializes in vehicle aerodynamics.

Browand calculates that the increase in drag produced by a 10 by 15 inch flag mounted on an SUV traveling at 60 mph is 1-2%, depending on the weight of the flag material. At highway speeds, a 2% drag increase will increase fuel consumption by approximately 1%. (For complete calculations, see below.)

Assuming a fuel economy of 20 mph, that works out to only about one extra gallon of gas for every 2,000 miles driven-or about 5 gallons per year. As Browand points out, that's no big deal. No small potatoes, though, when you consider that some 11.4 million vehicles are currently registered in Florida.

Florida would do better to pass a law requiring flags to be posted inside vehicles. Better yet, leave it to each of us to decide how we want to express our patriotism.

The price for patriotism

Drag of a Flag

Assume the size of a typical small flag is, say 10" by 15". Mount the flag in the airstream above the car window or on the antenna, and-with help from the classic, go-to book for drag estimates by Hoerner (now out of print)-you may estimate that a typical light truck, minivan or SUV would experience a drag increase of 1%-2% depending upon the weight of the flag material. (This estimate includes the drag of the flag support, and takes account of a 20% increase in speed locally in the vicinity of the flag.) Two flags would have twice this drag penalty.

S.F. Hoerner, Fluid dynamic drag: practical information on aerodynamic drag and hydrodynamic resistance, [Midland Park, NJ], (1965).

Fuel Consumption

Since fuel is consumed to overcome drag, the added drag will result in additional fuel consumption. The fuel consumption can be estimated from the work of Sovran, who demonstrated that the percentage increase in fuel consumption is proportional to the percentage increase in drag. The constant relating the two-call it C-depends upon how the vehicle is driven. Using these ideas, Zabat et al., made estimates of the constant for a typical minivan or SUV vehicle operated on city streets with mostly slow driving, C=0.15, and operated at highway speeds of 55-60 MPH, giving C=0.5.

At highway speed, a drag increase of 2%, will result in a fuel expenditure increase of about 1%. If the minivan, or SUV or truck has a fuel economy of 20 miles per gallon, then every 2000 miles driven results in an additional gallon of gasoline expended. Peanuts you say, and I would agree! But if 20 million cars and trucks drive 2000 miles every two months, the price tag is a measurable 20 million gallons of gasoline, or-at a price of $1.50 per gallon-$15,000,000 per month.

G. Sovran, "Tractive-energy-based formulae for the impact of aerodynamics on fuel economy over the EPA driving schedules", SAE paper No. 830304 (1983).

M. Zabat, N. Stabile, S. Frascaroli, F. Browand, "The aerodynamic performance of platoons", PATH Research Paper No. UCB-ITS-PRR-95-35, (1995), (http://www.dcdata.com/path/path.htm)