Fuel economy vs. speed

We all suspect that going faster decreases your fuel economy, and I did an experiment to verify this!

Experimental setup

Car: 2011 VW Golf 2.0L TDI (common-rail Diesel)
Road: I-5 South, between CA-152 and the Tejon Pass
Other notes: outside air temperature = 60°F = 15°C, tire pressure nominal (38 psi).

I took the measurements from the multi-purpose display in the car dashboard. Each point in the plot is an average over at least 3 miles. Most of the points are from about 10 miles. "Drafting" means following behind a large bluff body (i.e. a truck or a bus) at a distance of 200-300 feet.

I used liters per 100 km for the primary axes (for good reasons), but on the right I have also labeled the equivalent miles per gallon for reference (to ease your transition to the superior L/100km scale).

First-principles model

The blue line in the plot is predicted from published parameters, so it's pretty cool that it matches the experimental results so well!

First I estimated the total drag forces acting on the car as a function of speed. This includes aerodynamic drag (using C_D = 0.32 as specified on VW's website) and rolling resistance (using C_RR = 0.010, which seemed typical for car tires). For a given vehicle speed, I used the tire diameter and the gear ratio (from VW's website) to determine engine speed and torque, then used engine displacement to get BMEP (brake mean effective pressure, a measure of volume-specific engine output). These results are shown in the figure below.

For reference, this Golf's maximum torque is 236 ft*lb and its maximum BMEP is 20 atm, so at 70 mph we are operating at 1/3 load.

Then I looked this up on a BSFC map (I found it on an Internet forum, but the axes are in German so it looks legit) to determine the engine efficiency at that operating point and converted¹ into appropriate units to produce the top figure.

Cars typically operate in a regime where efficiency improves with engine load, and this is no exception: we go from an LHV efficiency² of 33% at 50 mph to 40% at 90 mph. This is why our distance-specific fuel consumption (top figure) only increases 2× from 50 to 90 mph even though the drag force (bottom figure) increased 2.5×.

---

¹Using  ρ_fuel = 0.85 kg/L.
²LHV efficiency is (power output) / (LHV × rate of fuel consumption) where the LHV is a measure of the energy content of the fuel. This is a commonly used efficiency metric and is a decent proxy for thermodynamic efficiency when compared across similar fuel and engine types.