BMW i3 is a city car suitable for city driving, but if you ever take it for a long stretch it might be interesting to understand how to drive to arrive to your destination as quickly as possible. High speed increases consumption, reduces range and requires more charging stops, but low speed adds much to driving time. What is the best?
In the post “Range for Speed” we saw how increased speed reduces range. It turned out that the range is almost linear to the speed. You can drive about twice as long in modest 50 km/h (30 mph) compared to 120 km/h (75 mph).
In the post “Rapid Charger Effect” we understood that the power from a rapid charger peaks after about 10 minutes, and then decreases quickly. After half an hour, the power (in kW) is down to a quarter of the maximum.
Let us combine the lessons to understand how fast we should drive and how long time we should charge if we want to reach our destination as quickly as possible. There will be some simplifications and assumptions in order to put together an optimization and I want to emphasize that conditions such as temperature, road topography, rapid chargers, etc. will affect the outcome.
An assumption that we have to make is how long time, in addition to the actual charging time, it takes to charge the car. We assume that it takes 5 minutes to leave the highway, initiate charging and then make it back to the highway again. It is tight and allows no hassle or calls to customer service to understand why a charger is not working as it should.
Let us further assume that we are going out on a real long trip and have 1000 km (about 600 miles) to our destination. We begin our journey fully charged and can use all of the 18.8 kWh (battery is 22 kWh, but BMW has limited the amount that could be used to extend battery life).
It is not optimal to stay too long by a rapid charger because the power decreases quickly. However, subsequent distances depend on how long time we stopped to reload. With the assumptions made, it turns out that it is best to charge 10 – 20 minutes each time (excluding the five minutes to and from the highway). The total time does not change significantly in this range, and it is more about preference how many stops you want to make. At 100 km/h (62 mph) and 20 minutes charging stops there will be 40 minutes driving time on each charge resulting in a total of 13 stops (5.4 hours off the highway). If you instead choose to just charge only 10 minutes, you can only drive 25 minutes after each stop, which requires 21 stops, but with roughly the same total time off the highway. I would prefer 20 minutes charging, and slightly fewer stops.
Speed affects the overall time a lot and it is easy to believe that it is optimal to be light on the accelerator to increase range and have fewer stops. Making the calculation I no long believe this is correct. A lower speed means that much longer driving time and it is better to keep high speed and charge more frequently. It is found that the optimum speed is around 110 km/h (68 mph).
An important assumption in the optimization is of course that there is always a rapid charger at hand. We know we are not there (yet). So speed and charge time must be adjusted so that the range is sufficient for the next charging station, but at a speed of 110 km/h (68 mph) and charging time of 20 minutes the distance is 58 km between the loading stations and this is actually realistic in many locations.
With the optimum speed of 110 km/h (68 mph) and optimal charge time of 20 minutes it would take a total of 15 hours to drive the 1000 km, of which more than 6 hours off the highway to charge. BMW i3 is king in the city but not a car to take for long mountain drives. Important to add is that the whole optimization is based on the BMW i3 pure electric vehicle (BEV). With the Range Extender (REX) the result is probably different.
- BMW i3 is a terrific city car but not designed for long road trips resulting in many charging stops
- Total time is lowest with a high speed and frequent charging stops. Optimal speed is higher than 100 km/h (60 mph)
- As power drops significantly the longer the stop at a rapid charger, it is optimal to limit each stop to 20 minutes
- Sometimes, the charge time may need be increased and the speed reduced to make it to the next rapid charger