MOST OF US DO NOT BOTHER to consider all the factors that affect the fuel performance of an automobile-that is, how many miles it gets to a gallon of gasoline. If we can measure the ways in which this energy is used, then we can consider how to improve the efficiency of our own car. Designers use similar information in striving to boost the fuel economy of future vehicles. Specifically, we need to examine the frictional forces that must be overcome in driving.

On level ground at constant speed, the engine of an automobile works against three kinds of friction: rolling resistance of the tires, friction within the engine, and air drag. These frictional sources largely determine a vehicle's energy use. Yet the coefficients representing these fuel-wasting forces are rarely published. With care, you can measure the friction and calculate the consequences for fuel economy. Most of the proposed measurements will work only on a manual transmission automobile. Also needed are some space in a parking area, a scale, a stopwatch, and a little-used, level and straight road way, half a mile or more in length. We did our experiments with a 1989 Honda Civic sedan.

The first variable to measure is the coefficient of rolling resistance of the tires (represented by CR). The force needed to overcome this resistance is proportional to the car's weight and is roughly independent of its speed. To measure the resistance, place your vehicle in neutral on a smooth, level parking area with the engine off. Pull it horizontally with a rope looped through the windows and attached to a spring scale. A level affixed to the rope may help. Alternatively, push your car from behind with a bathroom scale (protect the vehicle with a heavy cloth). You should find a force roughly between 20 and 40 pounds. Our reading came in at about 25 pounds.

Unfortunately, this measurement is crude. If either the parking surface or the scale is angled by 0.1 degree from the horizontal, it will change the measurement by five pounds for a typical 1,300-kilogram (3,000-pound) vehicle. It is also difficult to move the car at a steady speed, which is necessary to avoid inertial effects. A good idea is to have two people divide the tasks. One pulls, and the other reads the scale. To correct for grade, repeat the experiment in the reverse direction and average the results. To obtain the coefficient of rolling resistance, divide the measured force by the vehicle's weight, which is listed in the owner's manual. With properly inflated original equipment tires, the coefficient should roughly equal 1 percent.

Aside from the effect of inflation pressure, several factors can confound the measurement of rolling resistance. One is bearing friction, which fortunately tends to be much smaller than tire resistance. Another is brake drag, which arises from the slight contact between the pads and rotors on the disk brakes. This contact may contribute one to two pounds of drag, amounting to about 5 percent of the rolling resistance. The coarseness of the road surface also affects rolling resistance; smooth, paved surfaces provide the greatest accuracy.

Now measure the engine drag. The procedure is the same as that for rolling resistance, except that the transmission is in top gear. The scale reading provides the combined force of rolling resistance and engine drag. With our Honda Civic, we measured roughly 100 pounds, which means that engine drag is about three times greater than tire drag. (In typical driving, engine drag is somewhat less because depressing the accelerator opens the throttle slightly more than simple coasting does.) But the measurement is rough because the force is uneven as the cylinders go through their strokes.

Deriving the coefficient that characterizes this friction is a bit complicated We must compare our measurements with the work performed by a "standard engine." By definition, a standard engine generates 100 joules of work to rotate the crankshaft once when the throttle is almost closed-that is, when the accelerator is up, in its rest position.

The actual frictional work is then given as the product of 100 joules and the coefficient of engine friction, CE (a term coined for this column). To derive this coefficient, you need to know the volume swept through by the pistons (called engine displacement). This value, given in liters, is listed in the manual.

You also need the number of revolutions the engine's crankshaft turns for every meter that the vehicle travels in top gear. We represent this number by n. One way to find n is to read off the revolutions per minute from the tachometer (if you have one) while driving in top gear. Divide this number by the vehicle speed in miles per hour, then further divide by 60 and by 0.447 meter per second (equal to one mile per hour). (A more involved method, ideal for people who enjoy number crunching, is to look up the overall gear ratio from the manual and use the tire circumference to calculate the distance the car moves and the number of crankshaft revolutions.) As a rough check on your results, note that vehicles are designed so that n varies from about 1 with large-displacement V-8 engines to almost 2 for small engines.

In our experiment, we multiplied the measured net force of 75 pounds by 4.45, in order to convert pounds to newtons (the metric unit of force). For this car, n = 1.68 revolutions per meter, and the engine displacement is 1.5 liters. Thus, C_E = 75 x 4.45/(100 x 1.68 x 1.5) = 1.3. The frictional work is therefore 130 joules per liter per revolution.

The last frictional force with which we must contend is air drag. To find it, we need to get the car on the road. The technique measures the time it takes for a vehicle to drop 10 miles per hour from an initial speed. You need to go back and forth on the same stretch of road and average the times to correct approximately for any sloping in the road and for any wind.

This part of the experiment requires two people. One gives full attention to driving, while the other handles the stopwatch and records the results. Find a straight, smooth, level road with little traffic at the time. Be careful not to interfere with other vehicles and do not make these measurements at night.

To determine air drag, measure the coast-down time with the clutch pedal down in two speed ranges. For example, you might use 50 to 40 mph and then 40 to 30 mph. Just be sure they are safe for the road conditions. The two ranges should be different enough for a good measurement. In our experiment, we found coast-down times of 17.7 seconds and 24.0 seconds for the respective ranges (that is, at average speeds of 45 and 35 mph). Unless you are an expert you will find considerable variability in the times, even in the same direction. You need to read the speedometer straight on and be highly systematic in using the stopwatch. Practice until you feel you have achieved some reliability.

Using the equations in the box on the left, we found that the difference of air-drag forces at these two speeds was 74 newtons, or 16.6 pounds, for an automobile mass of 1,110 kilograms, which includes the passengers. (The difference measurement eliminates the resistance offered by the tires.) From this value, you can infer the air drag at other speeds. To find the value at, say, 70 mph, multiply the air-drag force just calculated by 70²/(45² - 35²). For the example discussed, the air drag at 70 mph is 102 pounds.

What we want to calculate is the efficiency with which your car cuts through air. It is the product of the frontal area of the vehicle, A, in square meters, and the air-drag coefficient, CD, a dimensionless number describing how streamlined the vehicle is. The box gives the necessary equation. For the Honda Civic sedan, we found the product C_DA to be 0.77 square meter.

To find the drag coefficient itself, you need to determine the frontal area. One way is to make a scale drawing of the vehicle's silhouette as seen from well in front. Include the tires but not the empty space between them. As a check, multiply the width by the height by 0.833, the typical factor for current cars. With the Honda Civic, the frontal area is 1.89 square meters, so the measured C_D is 0.41. The actual drag coefficient is probably less; estimates in the literature list it at about 0.35.

With coast-down observations and the equations in the box, you can double-check the values derived for rolling resistance and engine friction in the parking-lot measurements. To find the rolling resistance coefficient, substitute one of the coast-down measurements already made into the proper equation in the box. Our Honda Civic produced a coefficient of 0.0086-close to what we found in the parking lot. Note that rolling resistance depends on tire pressure The coefficient is roughly proportional to the square root of the gauge pressure. For example, if you lower the pressure 20 percent, you should find that the force increases about 10 percent.

Next, measure engine drag during coast-down. Leaving the vehicle in high gear, time the coast-down. Although it muddles the interpretation slightly, leave the engine running during the measurement. That way you will not lock the steering after you turn the engine off and can drive at the end of the coast-down without slowing down further and perhaps interfering with traffic. In our measurements with the Civic, the 50- to 40-mph coast-down time was 9.1 seconds. Using an expression in the box, you can figure that the engine drag is 265 newtons, or 60 pounds. You can check that the corresponding coefficient is equal to 1.0, a reasonable result and probably more accurate than the 1.3 value we found earlier.

The frictional coefficients calculated here can be used to estimate fuel economy without further measurement. Assume that the indicated efficiency of the engine (the efficiency before accounting for frictional losses) is 38 percent, a value typically listed in the literature. This number expresses the ratio of the total work by gases on the piston surface (during the high-pressure strokes) to the combustion energy of the fuel. The fuel economy is then determined according to the equations in the box.

We calculated the fuel economy at two speeds, as shown in the table in Figure 1. The speeds roughly correspond to the overall average speeds for the official urban and highway driving cycles. The fuel economies agree fairly well with Environmental Protection Agency estimates for this car: 34 and 46 miles per gallon for the urban and highway cycles, respectively. If we consider the energy losses in the brakes during city driving, which decreases the fuel economy by about 10 percent, we obtain even better agreement.

Our results may be misleadingly good. Not only were there experimental errors, but the driving cycles involve various speeds, which complicates the air-and engine-drag calculation. Nevertheless, these methods should enable you to determine where most of the energy is going during a drive.

The analysis presented here offers some hints for improving your fuel economy. Because the total amount of friction an engine must overcome depends on the number of revolutions of the crankshaft, shifting up early to reach a cruising velocity and cruising in high gear will lessen engine friction Removing roof racks will improve efficiency by decreasing air drag. Keeping tires correctly inflated will reduce rolling resistance.

You can explore several other variables that could affect fuel efficiency. Try coasting down with the windows open or with the air conditioning on to see how much of a difference that makes. You could also check to see if the ambient temperature plays a role. A cold engine should be less efficient than a warm one. With some imagination, you can squeeze a few extra miles out of a gallon of gas.

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