Introduction

I was recently involved in a discussion below the line about the effect of levels of acceleration an electric vehicle range. This was below one of the articles in CleanTechnica. I was arguing that heavy acceleration will reduce range, where another person was saying that it made no difference whatsoever.

The Science

The science is fairly straightforward. Acceleration of a vehicle represents an increase in its kinetic energy. During acceleration, electrical energy from the battery is converted, via the electric motor, into the kinetic energy possessed by the vehicle. The formula for kinetic energy is ½ MV2 where M = mass, and V = velocity. The mass remains the same, but the velocity increases with acceleration, and the kinetic energy increase is by the square of the velocity. So, to reach 8 mph requires four times the energy it takes to reach 4 mph, not just double.

If you want to work it out, 8×8=64, and 4X4= 16, and 4X16=64.

This is why the faster your car is going, the harder it is to stop. However, time does not come into it, so that to increase speed to 60 mph in one second takes the same amount of energy as it would to increase speed to 60 mph in 1 min. It just needs a much more powerful motor to deliver all that energy within such a short length of time.

The Engineering

The science seems to indicate that how quickly a car accelerates should not make any difference to energy consumption. It almost seems too good to be true, that we can drive about in wild abandon, with our foot to the floor, enjoying the exhilaration of an EV’s rapid acceleration, without incurring any penalty. (Except, perhaps, a speeding ticket). In my opinion it is too good to be true, because fast acceleration causes losses in the system. I think this is a good illustration of the difference between science, and engineering.

The losses are as follows-
  1. Faster acceleration leads to higher average speed, which leads to higher air resistance losses.
  2. Rolling resistance also increases with speed.
  3. Higher torque at the shafts increases frictional losses in the reduction gear.
  4. Full acceleration exposes the motor to very high currents, and before the acceleration is achieved, individual motor windings are exposed to those very high currents for longer, which increases thermal losses in the motor.

That is as much as I can think of at the moment.

Measuring the losses

The next question then is by how much would these losses affect energy consumption during high levels of acceleration. I suppose there might well be sophisticated testing devices, and instrumentation, to answer this question precisely, but lacking these, I decided I would do a road test to get some kind of rough answer to the question.

The method I employed was similar to tests I have done before. I drove to a motorway, (free-way), service area on the M1 near where I live, and connected to the fast-charger to bring the battery charge to a precise 80%. It is convenient that my car’s system interrupts the charging when it reaches 80%, so there is no chance of it overshooting. This provides me with a precise starting point that is repeatable on any number of occasions. I chose a destination about 15 miles away, using, ordinary rural roads, with only about a mile, between the service area, and the junction leading off the motorway. I then drove to that destination, and back to the service area on the opposite side of the motorway, so, undertaking a journey of about 30 miles.

I adopted a driving style using maximum acceleration, wherever I could safely do so, but kept to the speed limits, and avoided any heavy braking. I maximised utilisation of regenerative braking, by not using the foot-brake pedal, where possible, and only slightly depressing it when necessary. On most EVs a slight depression of the foot brake, engages additional regenerative braking, rather than the friction brakes, which only operate on further depression. (I learned this from a reader named Frank, through a discussion, following another article. At the time I had made a not unreasonable assumption that all regenerative braking was available on the accelerator pedal.)

On the whole of the 30-mile journey, the only difference in my normal driving style was the heavy acceleration. I also avoided any slipstreaming of vehicles, knowing what a difference that can make. On returning to the service area, I connected to the fast charger again, and photographed the display on the charger, showing the state of charge on my return.

The next day, I repeated the exact same journey, using the exact same procedure, but this time avoided any heavy acceleration, driving smoothly, and gently, at all times. The state of charge on the first day, on my return, was 33%, and the state of charge on this next day, on my return, was 40%, making a difference of 7% in the state of charge, over a 30 mile journey.

Conclusion

This translates to a significant difference, in any longer journey, so that in a 90 mile journey, for example, over 20% of the battery capacity is lost through high levels of acceleration.  In some circumstances, such as long distance motorway, (free-way), cruising, there would not be any accelerating, and decelerating, so these conclusions would not be relevant.  It only applies in city driving, and driving on two lane roads with bends, where there is constant slowing and speeding up.  There is no precise figure really, as it depends on so many variables.

I include pictures in this article showing my car charging up at the service area with the Bridge restaurant in the background. When this was built in May 1966, it was a novel idea to have the restaurant housed on a bridge over the motorway so that people could watch the traffic over their cup of coffee. It is probably less of a novelty now, and people might prefer somewhere more peaceful, and quiet to take their break from motorway driving. I also include pictures of the display on the fast chargers, illustrating the percentage of charge, of the battery, at each stage.

I am aware that this is not a particularly scientific experiment, but I hope it provides a satisfactory answer to the question, about acceleration, and is certainly preferable to the “’tiss so – ’tiss not so”, kind of discussion I was having with my fellow CleanTechnica reader.


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