Everyday engineering: MBD & MPG (Part-3 F=MA)

Sometimes simple is good enough.  Let’s start by reviewing what goes into fuel consumption for a car; e.g., what are the forces acting on it?

  • Acceleration: getting the car from 0 to 55 (and above) requires force
  • Aerodynamic drag: the faster you go the higher it is
  • Gravity: uphill or down, it has a way of changing your speed

Using these three forces acting on the vehicle, we can (when we add in losses) calculate the energy needed to get from point A to point B. (And if you are curious about how the data for A to B is collected check out this previous post)

Simple models

Our simple model uses the Lat / Lon / Elevation and Speed data we downloaded as part of the last blog post for our points A to B. 

Counting your losses

In a frictionless, lossless world, my car with regenerative braking(1) could reach 100% efficiency.  However, your car-not (2) able to do this in the real world. Our first pass of “driving the route” will make the following assumptions:

  • We hit every stoplight(3)
  • We drive at the speed limit(4)
  • There is no traffic(5)
  • Standard profile acceleration and deceleration between speed zones(6)
  • 20% energy recapture on braking.

The first route: To the Tech Center!

My first working commute was from Farmington Hills Michigan to GM’s Warren(7) Tech Center.  If we break it down by distance and stops we get the following table.(8)

0.265 15
Farmington Hills to Warren Tech Center

Between each point, there is a deceleration to stop(9) followed by an acceleration to the target speed.  If we put this information into the Simulink model we get the following energy usage profile.  There is an interesting modeling point between points 1, 2 and 3; it is a short stretch of the road section of road where the car does not have time to get up to speed before you have to slow down.  I’ve included the Stateflow chart that I created to solve this look ahead in the footnotes.(10)

Full Trip
Regen Effects

Because this trip was mainly highway there was very little chance for regenerative breaking;(11) in contrast, my ADI (Applied Dynamics International) commute had many more start-stop moments with more regenerative braking events.

ADI Route

City Commute

Reviewing the data from these two routes reinforces some basic knowledge:

  • Total distance is only one factor in energy usage
  • Energy usage goes up with rate of travel
  • Start-stop events (with acceleration) have a large impact on energy use (e.g. steady speed is better)
  • Yellow is an odd default choice for plotting color.

In next week’s post we will add in a “human” driver model to improve the accel and decel behavior of these models.


  1. For a short introduction to the efficiency of regenerative braking I recommend this link.  In short, there are two limitations to capturing energy from regenerative braking. First, a portion of the brake force is applied through conventional brake pads. Second, the torque/speed of the wheels at braking cannot be tuned for optimal energy capture.  As a first pass approximation, we will assume that 20% of the energy is re-captured during brake implementation.
  2. To instructors of Thermodynamics courses, please feel free to use this joke under a GPL Open Source License.
  3. It only ever seems this way when you are driving.
  4. Generally this is true with the exception of 25 MPH zones which always seem way slower than anyone drives.
  5. Ok, so that never happens, but one could dream.
  6. The first pass approximation of this is 10 mph/sec on acceleration, and 20 mph/sec on deceleration.
  7. GM Technical Center is a large complex with tunnels connecting all the buildings; I often thought that I was working in a “rabbit’s warren.”
  8. For the first pass, we are assuming a “flat” drive.  In southeast Michigan, this is generally true.
  9. The stops require a “look ahead” model, e.g., we have to know when to start stopping.
  10. I implemented this as a Stateflow chart with the intention that additional logic will be added to account for the driver behavior model in subsequent updates.  For now, it is a simple accel / deccel / hold calculation.
  1. And because this was in 1995 there was zero chance for regenerative braking.  GM had the EV1 then but I did not own one.

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