Energy management for solar car racing is critical. For our upcoming endurance test at PACCAR Technical Center, we want to travel as far as possible in roughly 7 and a half hours. To travel as efficiently as possible, we must make precise decisions on how fast to drive the car.

The power needed to overcome rolling resistance increases proportionally to the velocity of the car. The power needed to overcome drag increases to the velocity cubed of the car. This means that the car is less efficient at higher speeds. In order to maximize the distance we travel, we must use just the right amount of power such that we end the day at close to 0% usable battery capacity. However, if we drain the battery too far, it may become unusable in the future due to chemical damage. So the number is closer to 10%.

To find the most efficient velocity to travel at, we first needed to collect data on how much power our car consumed at various speeds. This was done during a full test day at PACCAR, where we drove the car for several hours to obtain a wide variety of data. During the testing session, we used our telemetry system combined with a program called Grafana to view the data live as we went around the track. Using the collected data, we plotted a speed versus power consumption graph, removing outliers, and obtained a line of best fit that showed us how much power we would consume at a certain speed.

Mathematical models for the performance (power vs. speed) of our previous car, Jimmy, and current car, Sockeye. There is an improvement.

We also wanted to understand the total amount of power available to us so that we could figure out what the optimum speed would be during the endurance test. Solar panels produce the most energy when the sun is at its highest, so if we wanted to find out how much total energy would be produced by our solar panels, we first had to collect data during solar noon. We did this and found that when the sun was at its highest on a clear day, our solar panels peaked at around 685 watts. If you track the sun’s motion over several days, you can find that the motion of the sun is similar to that of a sine wave. So, using this information and our collected data, we created an equation using sin that would best represent the amount of power our solar panels would get each hour, as shown below.

Estimated solar array input. X axis is time (hours after midnight). Y axis is power (W). The estimated peak solar input is 685 watts at 1:15pm (PST).

We plan to drive from 9:15 a.m. to 4:45 p.m. and expect to be receiving energy from the sun during those times. Since we had obtained an equation to calculate power over time, we only had to find the area under the curve between 9.15 and 16.75 to find the total amount of energy the solar panels would provide to us over the day, which is approximately 4651 watt-hours. Combining that with the 90% of the battery we have available, we obtain a total amount of available energy of 8476 watt-hours. We want to stretch this amount over a period of 7.5 hours, so if we divide the total amount of power available by the hours we will drive, we get a total of 1130 watt-hours consumed per hour (watts). If we put both the speed vs. power equation and the watts consumed per hour equation on the same graph, the point at which the two intersect is the speed at which we want to be driving throughout the endurance test.

The intersection on this graph indicates that the optimal speed for us to drive the car is approximately 69 km/h.

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