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.