The drive train efficiency is no where near 99%!
Sorry, I didn't mean to suggest that it was, it was an example to show that whatever the relationship, even if it's squared, the effect may still be practically irrelevant. The point as originally stated ("
If you accelerate at twice the power your losses are 4 times higher.") is, I think, misleading. The losses are higher for a very short time, and how large is that loss compared to others when considering the much, much larger energy consumption to go a significant distance.
That's the main point. In normal use the acceleration phase is a tiny fraction of what the car spends its time doing. Sure, if you look at the average energy per unit distance over a very small time, it will matter, but over a minute? Five minutes?
The other thing which seems unclear is the reason why losses are not proportional to speed all the way to zero. There are a number of effects being summed, such that there turns out to be an optimal speed which is well above zero (roughly 25 mph / 40 km/h). Suppose you are accelerating up to that most efficient speed. If you accelerate faster then you spend less time in the less efficient speed zone, so that's an effect in
favour of accelerating faster. A small (probably very small) effect, but again, it just doesn't seem clear that the arguments made so far amount to more than waving a wand and saying "this effect is significant and the others aren't".
I'd like to see experimental proof. The experimental evidence I've seen suggests that degree of acceleration is not as large an effect as many other factors. I can reach "ideal" average energy usage per unit distance (something around 160 - 170 Wh/km =~ 256- 270 Wh/mile) driving in town while accelerating quite significantly. That's in the spring when temperatures are such that I can leave the climate control off. With temperatures 10 to 15 degrees C cooler (18 to 27 F) I see more like 180 to 200 Wh/km (288 to 320 Wh/mi) over the same route. Climate control, or other temperature effects, seem to be a consumer of energy in a different league to whether one accelerates quickly for 3 seconds, once every minute or two. And at highway speeds the difference can easily be 50% between a slow speed and a fast one (say 90 km/h to 120 km/h); I would argue that this effect totally completely swamps any acceleration effects. i.e. the critical piece of information is that if maximizing range is important,
slow down. And if you can handle turning off climate control but leave the windows up, do that too. Also of critical importance: avoid using the brakes. I think that if there's an effect due to acceleration, it is tiny compared to these.
Is it possible to get instrumentation accurate enough to measure total energy consumption to the second, and do repeated trials of something like
0-50 km/h at maximum acceleration, hold 50 km/h to a distance of, say, 500 m
vs
0-50 km/h at 1/2 full power, hold 50 km/h to the same distance
vs
0-50 km/h at 1/4 full power, hold 50 km/h to the same distance
? i.e. remove the effect of regenerative braking from the experiment. I would genuinely like to know the answer, with different top speeds and with different distances.
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Lots of stop and go, even though it is only about 7 miles each way (takes about 1/2 hour or more each way). Back in the SF Bay area, we normally use about 350 whr/mile, but here in LA with the much more aggressive driving and lots and lots of stop and stop and go, we are often above 500 whr/mile and always above 400.
7 miles in 1/2 an hour is 14 miles per hour. That's a much less efficient speed than average city speeds of 20-25 miles per hour. (Just search for the range vs average speed graph). I'm not saying that that is the only effect, just that it can explain at least some of the difference. The other factor is that the longer it takes, the longer other parasitic loads have an effect. Climate control springs to mind. If you leave the climate control off and it takes longer to get from A to B then the car will definitely consume more energy for climate control.
Most importantly, though: do you use the car's brakes at all? Every time you use the brakes, the car is converting all kinetic energy into heat in, and wearing of, the brakes. I suspect that that's the biggest culprit.