After attaching the sensor to the car and calibrating it, students drive to a local gravel company to weigh the car and its contents. While driving along, they see graphs of position and velocity versus time.

Figure 5 is a good pedagogical place to begin to understand torque, acceleration, and gear ratios in a qualitative way. In this particular example the car began from rest, and the driver floored it and shifted through the gears in the natural way. When the throttle is wide open, most car engines deliver a constant torque over a broad range of engine speeds. The gearing of the transmission and final drive make the engine spin faster than the wheels and also make the torque on the wheels larger than the torque of the engine. Both effects are simply the factor of the overall gear ratio. So the constant engine torque becomes a higher but constant torque on the wheels. This torque on the wheels contacting the road causes a constant force to accelerate the car (ignoring drag for the moment). On the graph one can see linear sections within each gear, suggesting a constant acceleration. In the higher gears, the gear ratio is smaller so the torque on the wheels is lower, yielding a lower acceleration.

Figure 5.

For the actual data collection, we cover a much wider range of engine speeds than one gets by the normal shifting pattern of Fig. 5. With the car moving slowly in a particular gear (clutch engaged), the gas pedal is floored and data are collected while the engine winds up to the red line or until the speed limit is reached. Then the car is slowed back down again. Now, crawling along in a different gear, the car is floored again. In this manner, data is collected in all the gears but with overlapping speeds as shown in Fig. 6. In fact it is the highest gears that give the best data at low engine speeds and the lowest gears show the high end.

Figure 6.

Air drag and rolling friction are measured by a coasting run. For this we put the car in neutral and coast from a speed of about 50 mph to a stop. Since the coasting trial is especially sensitive to the wind, we use a handheld anemometer to measure the wind speed.

We carry out all the tests on a one-mile straight stretch of road on prairie land that we estimated to be flat to about 0.5 m. Most of the acceleration runs required only a portion of a mile, but the air-drag tests often require somewhat more than a mile and so must be pieced together from two overlapping runs, as shown in Fig. 7.

Figure 7.

In order to convert the measurement of car speed into engine rotational speed, we need the overall gear ratios. These are surprisingly hard to find for many cars and are not always consistent even within a model year. Instead of trying to look them up, we now measure them by using an engine-speed probe. This was constructed by "disconnecting" the clamp-on probe from a timing light and connecting it to a second circuit virtually identical to the circuit for the magnetic probe. The only change was the addition of a low pass filter to clean up the input. When this probe is clamped onto a spark-plug wire, it gives a signal each time that cylinder fires. Car engines are all four cycle and so a complete cycle involves four strokes (intake, compression, power, and exhaust) or two crankshaft revolutions. Thus the probe signal rate is one-half of the engine speed since each cylinder fires once every two rotations. We were hoping to use this probe together with the wheel probe. Unfortunately the Logger Pro software cannot handle two such inputs simultaneously (unlike most probes, which measure a quantity when prompted, these are sending a time signal). Instead we have a switch to change which probe is being monitored. So we have the students drive at a constant speed and switch back and forth between probes. The ratio of the two signals is exactly one-half of the overall gear ratio. This has to be done for each gear.

In the analysis of the coasting data, we experimentally determine the drag versus speed. This is commonly expressed in terms of a dimensionless drag coefficient that is occasionally quoted by manufacturers who are particularly proud of their aerodynamic design. To put our drag coefficients into standard form for comparison, the students need to measure the cross-sectional area of the car. We find this by taking a head-on picture of the car from a distance and measuring the picture with a compensating polar planimeter (a delightfully simple mechanical device for measuring irregular areas on maps).