I’ve always wondered what is the most efficient way to drive somewhere far. Since I drive from SF-LA quite a bit, the I-5 drives became prime opportunities for me to study the best way to do this long drive. In this optimization exercise, factors in our fitness function are driver comfort, energy consumption, cost, and overall drive time.

**TLDR:** Find a decently fast vehicle in the fast lane, and put your car in radar cruise control. Pass only when needed. If you care to see why read along.

## The Long Story

I was quite bored during a few up and downs on the I-5, so I decided to take some data on different driving behaviors. It’s well known that platooning can help reduce drag. In fact, cyclists platoon all the time to save energy. In a lot of races, you’ll see an interesting behavior where racers will actually try to avoid being the first in a platoon. (The cycling term for this technique is called drafting)

So how much does it actually help to platoon someone when you’re driving an aerodynamically sound sedan?

During the drive, I sneak up behind various type of vehicles at various speeds and gathered the energy efficiency reading from my Model 3’s energy monitor.

I also experimented with driving the car in cruise control at various constant speeds as the control sets. Here is the raw data at a glance

Speed(mph) | Cruise Distance | Object in Front | Power(Wh/Mile) |

85 | 2 Auto Pilot Units | Sedan | 275 |

87 | 2 Auto Pilot Units | Van | 300 |

75 | 2 Auto Pilot Units | Box | 260 |

82 | 2 Auto Pilot Units | Pickup | 300 |

80 | 2 Auto Pilot Units | SUV | 260 |

85 | Infinite | Cruise Control | 310 |

80 | Infinite | Cruise Control | 275 |

80 | 2 Auto Pilot Units | Box | 270 |

85 | 2 Auto Pilot Units | Box | 260 |

87 | Infinite | Cruise Control | 345 |

78 | 2 Auto Pilot Units | Van | 270 |

88 | Infinite | Cruise Control | 370 |

Let’s take a jab at digesting this data in a meaningful way. First off, let’s attempt to understand the car’s speed -> power usage relationship. We know at high speed, the car’s primary source of energy consumption is a drag. Let’s model the cruise control data points to an ideal model

According to the drag equation

Where: D is Drag force experienced by the vehicle in Newton. Cd is the drag coefficient, which is 0.23 for Model 3. ρ is the density of air, which is 1.225 kg/m^3. V is the velocity of the car in m/s. A is the incident area of the car subject to drag, for Model 3 is 2.52m^2, the rough cross-section area looking from the front of the car.

We also know that the battery’s chemical energy -> car’s kinetic energy is not perfectly efficient. We designate η as the gross efficiency from what you read on the energy monitor to the actual energy contributed to moving the car. η is the only unknown here, hence we’ll attempt to estimate η using the real-world data collected. Given our η is just an estimate and the real η is probably not a naive constant but rather a complex variable, we must limit the range of speed where a η can be estimated. The dataset works in our favor since the speed range is limited to 75-90 mph.

The Power Efficiency number can be calculated through some pretty basic math

After curve fitting, we yield η=70%. Totally reasonable considering electrical transmission loss, inverter switching loss, magnetization loss, bearing friction loss, tire loss, etc…

Now that we know the internal efficiency of the car at this speed range, we can go ahead and digest the data to generate something useful. We know that driving in the turbulent wake reduced drag, in math, this is reflected in a reduction in the drag coefficient Cd. So we will solve for Cd given all other parameters fro the collected data.

Speed(mph) | Cruise Distance | Object in Front | Power(Wh/Mile) | Cd |

85 | 2 | Box | 260 | 0.1827176877 |

85 | 2 | Sedan | 295 | 0.2073142995 |

87 | 2 | Van | 300 | 0.2012462718 |

80 | 2 | SUV | 260 | 0.2062711396 |

80 | 2 | Box | 270 | 0.214204645 |

78 | 2 | Van | 270 | 0.22533033 |

82 | 2 | Pickup | 290 | 0.2189855141 |

87 | Inf | Cruise Control | 345 | 0.2314332125 |

75 | 2 | Box | 260 | 0.2346907188 |

88 | Inf | Cruise Control | 370 | 0.2425947923 |

85 | Inf | Cruise Control | 310 | 0.2178557045 |

80 | Inf | Cruise Control | 275 | 0.2181713977 |

After average aggregating the table by type, we end up with this.

Now it’s become clear to us that platooning behind another vehicle generally reduces the drag coefficient by ~10%, which means the same battery will get you 10% further if you platoon.

The 10% saving may not seem like much, but let’s add up the other factors in an EV trip. As mentioned earlier, trip time, cost, and stress factory are all subjects for consideration.

## The Case of the LA<->SJ Drive

#### Time and Cost

Consider two types of driver behavior. Driver A finds a spot in the fast lane and cruise-follow behind another car, he/she averages 80 mph for the drive. Drive B drives as fast as possible, passing cars at every opportunity, Driver B averages 85 mph for the drive.

Assumptions: They both drive Tesla Model 3 LR with a 75kWh battery; Distance from SJ to LA is 340 Miles; Drivers only drain the battery from 80%-20%(below 20% is sketchy, charging above 80% gets really slow due to the reduced voltage overhead), it takes 30 minutes of ramp-to-ramp time on a 120kW supercharger to charge from 20%-80%. Cost of electricity if $0.15/kWh. We assume the drive is overall flat for the sake of doing math.

Style | Platoon | Pass people |

Cd | 0.21 | 0.23 |

Speed(mph) | 80 | 85 |

Mileage(Wh/mi) | 264.70 | 327.28 |

Effective Range(mi) | 283.33 | 229.16 |

20%-80% Range(mi) | 170.00 | 137.49 |

Stops Needed | 1 | 2 |

Drive Time(hr) | 4.25 | 4 |

Charge Time(hr) | 0.5 | 1 |

Trip Time(hr) | 4.75 | 5 |

Energy Used(kWh) | 89.99 | 111.27 |

Cost($) | $13.50 | $16.69 |

WHAT HAPPENED HERE?

Driving super fast and pass at every opportunity actually backfired. The lack of platooning and high speed ended up costing 23% more energy per mile, which added a whole other stop to the trip to charge. It not only cots more time, but also money for the extra energy burned.

#### The Takeaway

Needless to say, I don’t encourage driving like an jerk and speed past people at every opportunity you have. Besides the obvious time and money penalties, driving faster and passing a lot means you are not only at elevated risk of accidents but also at elevated risks of getting a ticket. Driving fast on a stretch of cop’s favorite I-5 is a real mental stressor since you have to stay highly alert and look out polícias who will not hesitate to fine you $$$$. At the end of the day, Driver A will get to the destination excused, slower, have paid more money. Meanwhile, Driver B found a nice platoon to join, kicked back with Autopilot on, snacked on some chips and finished a whole new audiobook. Besides some minor back pain, Driver B arrives rejuvenated, enlightend, faster, safer, and cheaper.