# AskPablo: Well to Wheel Efficiency Part II

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 120 m to reach 60 mph (27 m/s) so the work done by the accelerating vehicle is 452,040 Joules (3767 newtons x 120 m), and since we already know that it takes 8.9 seconds we can find that the power required is 50.8 kW (452.04 kJ / 8.9 s). This roughly half the stated maximum power in the vehicle’s specifications.
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 25 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 240 m with the same amount of energy as the maximum acceleration, which gets us 120 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.

(Click image to enlarge)
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.
To be continued next week…
Pablo Päster
Sustainability Engineer

### 2 responses

1. Nick Aster says:

Brilliant post! I love the part about the Round-a-bouts.

2. Tormod says:

Good aritcle.
If I may, I will contribute with some of my own obsevations.
Why is a hybrid more efficient than a standard drive train?
– Yes, regenerative braking, but that is only one out of many factors.
Other factors:
– No idling when stopped.
– Picks up all sorts of ”free rides” where you momentarily don’t need any power, like slowing down for a red light or slower traffic ahead, or small downhil, but not necessarily so steep that you have to engage the brakes, i.e. if you don’t need the ICE, don’t use it.
– It is also more effifient to run the ICE at 100% of optimal load 50% of the time and store excess energy in batteries than to run the ICE at 50% load fro 100% of the time, because then you will have to feed the parasitic losses like the valve train, oil and water pump etc. only half of the time. And numbers get better in favour of the electric motor the less power you need.
An electric motor is vastly more scalable than an ICE, using only the energy needed on the driveshaft, and can take momentary overloads with great ease (A starter motor is overloaded with several hundred per cent compared to the effect it could sustain continuously). These benefits have to be balanced against having to carry the extra weight of the batteries.
At opimal load, an ICE is at best 25-30% efficient, and all discussions I have seen assumes that this is the case throughout the power range, but I would like to see the efficiency of an ICE graphically as a function of power output. I assume that during low power demand, say 30 hp in slow moving traffic, the efficiency is down to single digits (