Well-to-Wheel Efficiency - Part 2
By Pablo Päster
This week we are continuing last week's discussion on vehicle efficiency, from well to wheel. In last week's column I introduced calculations for determining the energy needed to overcome aerodynamic drag and rolling resistance at a constant freeway speed of 65 mph. Using these equations I was able to show that my car is about 18.8% efficient at converting fuel energy into constant forward motion.
But unless you live at the top of a very steep hill you will require additional energy to get up to highway speed. How much energy is used in accelerating your vehicle depends on its mass and how fast you accelerate. My car weighs 1,250 kg and has an acceleration of 3.014 m/s^2 (0-60 in 8.9 seconds). This means that my car requires 3767 newtons (1,250 kg x 3.014 m/s^2) to reach 60 mph under full acceleration. The car requires roughly 240 m to reach 60 mph (27 m/s) so the work done by the accelerating vehicle is 904,080 Joules (3767 newtons x 240 m), and since we already know that it takes 8.9 seconds we can find that the power required is 101.6 kW (904.08 kJ / 8.9 s). This is slightly above the stated maximum power in the vehicle's specifications, which just speaks to the fact that theoretical calculations rarely result in the same values as empirical measurements (although they are close in this case).
If you were to take twice as long to accelerate to 60 mph (18 s) your acceleration would be 1.490 m/s^2 and the force required would be only 1863 newtons, about half of the force required for full acceleration. This force translates to only 50 kW. But by accelerating more slowly means that it takes you twice as long to get up to speed. So does this mean that it doesn't matter how fast you accelerate since it will take the same energy to get up to speed? Well, no. The objective of driving is to get from point A to point B, not to get up to a certain speed in a set amount of time so we should be concerned with the distance traveled per unit of energy. By accelerating half as fast my car will travel 483 m with the same amount of energy as the maximum acceleration, which gets us 240 m (more than 2x as far). From this you can begin to understand why it makes sense to lay off the gas a bit and accelerate like a grandma in her land-yacht.
What this example also shows is that it is much better to maintain a constant speed than it is to slow down and speed up again. This start and stop cycle is why most cars get lower fuel economy in the city than on the highway. The Toyota Prius on the other hand does better in the city because it uses electric motors at slow speeds, recaptures some of its energy with regenerative braking, and its engine is off most of the time.
Roundabouts (AKA rotary or traffic circle) have gained popularity in Europe and more progressive areas of the US like Seattle in recent years. By eliminating a four-way stop intersection and replacing it with a roundabout you allow for the continuous flow of traffic. This not only greatly reduces the unnecessary additional emissions from repeated start-stop cycles but it also reduces vehicle noise and reduces the number of accident opportunities. Using the concepts and equations presented in this and last week's columns I ran a simulation of a 1 mile trip with stop signs and with roundabouts. From the chart below you can see that the trip with roundabouts consumes vastly less energy that the trip with multiple stop and go cycles.
Now what about hills? Well, image sitting at the top of a hill and releasing your brake. Your vehicle would accelerate down the hill until it reaches the bottom or you reach some terminal velocity (when the air resistance and rolling resistance become too great). The reason the vehicle accelerates is due to the force of gravity. Conversely, a vehicle traveling uphill is working to overcome gravity, even if you are traveling at constant velocity. A rocket traveling straight up needs to overcome gravity fully (9.8 m/s^2) but a vehicle on a 45 degree slope only needs to overcome half (4.9 m/s^2). Likewise, varying inclines will impose different magnitudes of gravity's force.
Part III To Be Continued
Pablo Päster is a sustainability engineer who earned is degree from CalPoly and management degree from the Presidio School of Management. He publishes his views at www.AskPablo.org.
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