## Mobile Antennas, Air Resistance, and Fuel Economy

I've now had a screwdriver antenna mounted on my roof for a week, and I noticed that I got less miles on a tankfull of gas than I normally do. It's real noticeable, because normally, a tank lasts 4 days of commuting (both ways), so I need to fill at one end of the trip (roughly 410 miles). This time, the tank empty warning came up halfway home, with about 375 miles on the tank instead of the usual 400 plus. Hmmm.. is it the air conditioner (it's been somewhat hot recently) or the increased air drag, or, is my right foot a bit heavier this week? More testing is required.

In any event, this brings up an interesting "systems tradeoff". The screwdriver antenna is fairly large (!), but it has good efficiency. However, one could use a physically smaller antenna and make up for the poorer radiation efficiency and losses in the matching network with a power amplifier and/or receive pre-amp. Amps are expensive though.

First, assume that I am getting about 5-10% worse gas mileage (23 instead of 25 mi/gal). Over the 25,000 miles I drive in a year, it will take about 80-90 gallons more, which, at \$2/gallon, is about \$160-\$180/yr. Over 3 years, that's about \$500, which is a start towards that 12V powered linear.

### Some other alternatives

Since most of my driving is on the freeway, where aerodynamic drag dominates, I could reduce the HP requirement by driving slightly slower. HP goes as the cube of velocity, but it's not quite that simple, because at a lower speed, one needs to drive more time to get to the destination. Fuel consumption (in a pounds/hr sense) is probably linear with power output, and the overall fuel to get there is proportional to the square of the speed. So:

fueltotal = fuelrate * ttrip
tnew = told * vold/vnew
fuelratenew = fuelrateold * (vnew/vold)^3
fuelnew = fuelold * vold/vnew * (vnew/vold)^3 = fuelold * (vnew/vold)^2

All this works out to the new speed should be about 96% of the old speed. Hmm.. slow down a few mi/hr, and I can make up the difference. Of course, traffic might have been light, and I actually drove faster, on average, than usual. One might also want to take into account the difference in temperature, since the drag is proportional to density.. a 10C change in average temperature is about 3% drag change.

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### What is the drag of that antenna, anyway?

Let's assume it is a circular rod, 10 feet long and 3" in diameter (the whip, even though smaller, has a very high drag cross section). The cross sectional area is around 2.5 square feet, and a cylinder has a Cd of somewhere between .5 and 1.0, so let's take 1 for now. Let's assume 80 mi/hr (117 ft/sec) for now, as well.

Drag (pounds) = Vmph^2 * Area(ft^2) * Cd/391 = 80*80*2.5/391 = about 41 pounds(!)
HP = V(ftsec) * drag/ 550 = 117 * 41/550 = 8.7 HP

Typical gasoline engines have a brake fuel specific of 1/2 lb fuel/horsepower hour, so that 8.7 corresponds to 4.4 pounds/hr extra fuel to push the antenna through the air at 80 mi/hr. If you normally get 25 mi/gal at 80 mi/hr, you're normally burning about 19.2 pounds/hr. That 4.4 pounds is an increase of 25%, or a mileage hit of 20% (i.e. 25 mi/gal down to 20 mi/gal).

Clearly, I'm not getting that big a hit: I don't drive 80 mi/hr (average), the Cd probably isn't 1, and the cross sectional area probably isn't 2.5 sq ft. However, it IS in the right ball park!

radio/mobilempg.htm - 2 September 2002 - Jim Lux - W6RMK