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Why does accelerating fast use more energy than accelerating slowly?
- Thread starter ratsbew
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- Driving Dynamics Model S
Coasting lowers your average speed over the stopping distance, so less energy is expended over that distance than if you maintain your speed up to the stopping point. If you wait to use regen until you're at the stopping point, you use twice the energy getting there than just coasting. You still have all of the initial kinetic energy, so if regen was 100% you would use the same amount of energy as coasting, the original kinetic energy. You do get there faster, though.
On the other hand if you regen down to 1/2 speed initially, as opposed to a linear ramp down, maintain that speed to the stopping point and then regen to a stop, you use only 1/2 as much energy to cover the stopping distance. The rest goes back into the battery at whatever the efficiency of regen is. This is a consequence of power going up as the speed cubed. At 1/2 speed the power required is 1/8. Kinetic energy is being dissipated much more rapidly at the initial speed. By immediately bringing the speed down to 1/2, 3/4 of the energy is captured and the car continues on at the much lower power level. 1/2 of the original energy is used to maintain this power level to the stopping point so 1/4 of the 3/4 is still available. 1/4 of the kinetic energy is still in the car and can be captured by regen. Half goes to getting the car to the end and half gets recaptured by regen. The regen half is subject to the regen efficiency, though.
Half speed is the average of the linear ramp, so you cover the stopping distance in the same amount of time.
The more energy you recover at the start, the lower your average speed and the greater your energy savings.
But people might get pissed if you're going 1 mph over the 1000 foot stopping distance.
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Ah, I recall from Intro to Physics:
There was a young lady named Bright,
who travelled much faster than light,
she set out one day,
in a relative way,
and arrived the previous night.
I suppose that requires Maximum Plaid.
This is consistent with ICE findings from BMW testing done some years back when they were evaluating optimal fuel efficiency in acceleration in connection with meeting fuel economy standards. I do not have the data they released anymore but i clearly recall the results: accelerating at about 2/3 throttle produced the best fuel efficiency. At the time teh test was made with both then-current production diesel and gasoline models, which astonishingly (to me, anyway) showed the identical 2/3 throttle for best acceleration efficiency. They also demonstrated another ICE point made here that the most efficient thermodynamic cruise is maximum torque. The latter point totally ignores aerodynamics, which are more important than are thermodynamics above, IIRC, 80 kph.
I never saw any BEV comparable data, but based on posts here and elsewhere, I suspect that battery temperature rise and absolute level is more of a factor than the actual acceleration rate in acceleration efficiency. However, overall BEV efficiency has all the passive losses, transmission/conversion losses as larger factors than pure acceleration rate.
Lacking any specific data, and not being an EE I have no technical qualification for my last point, the underlined part. Am I missing the point, or are BEV's inherently less sensitive to acceleration rate than are any ICE?
Say you need to drive 1 mile. You zing to 60 with no wheelspin in 5 seconds. It will take you about 62.5 second to cover a mile, so your average speed is a hair under 60mph.
Now you take 20 seconds to get to 60. It will take you about 70 seconds to cover a mile, so your average speed is lower.
Method 2 has less aero losses, takes longer, but does store the same kinetic energy.
The time losses are more expensive to you than the power losses. With an EV, just let 'er rip.
BTW - This does not apply to ICE vehicles due to power enrichment and high RPM pumping and frictional losses.
Now you take 20 seconds to get to 60. It will take you about 70 seconds to cover a mile, so your average speed is lower.
Method 2 has less aero losses, takes longer, but does store the same kinetic energy.
The time losses are more expensive to you than the power losses. With an EV, just let 'er rip.
BTW - This does not apply to ICE vehicles due to power enrichment and high RPM pumping and frictional losses.
Chickenlittle
Banned
gavine
Petrol Head turned EV Enthusiast
I have seen EV reviews and people saying that driving hard will lower range, but in my experience, driving hard (accelerating quickly) has very minimal affect on range (assuming limited use of friction brakes). To me, what really affects range is cruising speed. My i3 is very sensitive to this. It has a 22kWh battery and I can zip around as much as I want with the range hit not noticeable. As soon as I get out on the highway, I can immediately notice the range drop if I go fast and a range bump if I take back roads and go slow. The i3 range meter is very dynamic in that it will fluctuate the remaining range up and down while driving.
It depends on what percentage the periods of hard acceleration are of the total trip. If you're a lead foot and the lights are timed badly on a short trip, it can make a difference.
Do you have a lead foot in the volt? The losses go up with the acceleration squared, so you really have to abuse the accelerator to see the big difference. In general the acceleration period is so short that it make little difference to a typical trip.
But the OP's question wasn't how much, but why.
I beat the crap outta the kids Volts. I even run them at the AutoX events like the Vettes. It's a riot to flat foot a car and not have to worry about attracting helicopters.
EDIT - Although I do feather the accelerator on the Blue one on launch. It will spin the tires even with the babysitters on just like the Caddys and Vettes.
gavine
Petrol Head turned EV Enthusiast
Not really related to this thread but a nice drag race between i3 REX and Gen2 Volt. i3 BEV would have been a different story (1 second faster than REX):
That is only if the i3 BEV could actually make it to the dragstrip, race, then make it back home in Texas. That is a serious consideration.
Some things to note. You see the power to weight by looking at the trap speeds. The BMW wins the power to weight war.
The ETs are tied into the 60 foot times. The Chevy only gets a good launch the first pass. Driver error on the next two. You need to pedal a 2016+ Volt for best results.
The Chevy gains 16mph between the 330 and finish. The i3 gains 14. This means the Volt might catch the i3 no matter what.
The Chevy always gets it's nose out front at roughly 30mph. This is why the Volt feels good in urban traffic.
gavine
Petrol Head turned EV Enthusiast
Mine is a BEV and even that is a little sluggish right off the line. The car definitely limits torque from the start. I'm not sure if it's due to wheel spin or just to preserve the drive train. Once you get to about 10MPH, it starts to pull harder. Coming from a Model S, I have to say I'm disappointed in the off-the-line of the i3.....lots of other things as well compared to Tesla, but still a great little car.
Some concrete examples. A 5000 lb S including driver at 40 MPH with a frontal area of 2.5 square meters and a cd of .24:
Air Resistance = 2.94 hp
Rolling Resistance = 6.97 hp
At 80 MPH:
Air Resistance = 23.49 hp
Rolling Resistance = 13.87 hp
But you missed my point. What you said is true and if you go slower you'll use less energy. That's not what I was saying.
What I was saying is to use as little braking...even regen braking as possible will be the most efficient for whatever average speed you're going. In you're example, it would have been even more efficient to have never sped up to speed x and then slow down to 1/2 x. You would have been better off accelerating up to speed 1/2 x without exceeding it.
Some more examples:
If you cruise at 70 MPH on a perfectly flat road, you'll use less energy than if you regen to 65 and then accelerate back to 70 and rinse and repeat. You can try this experiment yourself by cycling between 65 and 70. Even though your average speed is a little lower than 70, you're wh / mile will skyrocket.
This is why I beat cruise control on terrain that has slightly up and down hills because the system will regen brake in order to hold constant speed rather than allowing regen braking even if it means I edge up a few mph above the cruise setpoint. But at some point the difference in resistance exceeds the savings of not regen braking.
The opposite example of this is going down the backside of say the Grapvine. If I let the car coast without allowing regen braking, it will easily hit 90 MPH or eve 95 at some grades to match air resistance. In this case, it's less efficient than using regen braking to hold the speed. Since I'm going to get to bottom of the hill eventually, in this scenario, the most efficient way to do it is to regen brake to keep the car to it's slowest speed possible.
The next scenario is something I do several times a week in my commute. There's a climb and descent I take during my commute. On decent side going home, if I let the car coast, it will hit 85 MPH. I'll use regen to keep it to 70. Now if I keep it to 70 until the bottom of the hill and then apply power to keep it at 70 as I get to the bottom and level out, my wh/mile is higher for that stretch than if I allow the car to coast up to 78 right before hitting the bottom and then coast back to 70 MPH after I hit the bottom. In this scenario, the extra energy taken by air resistance and rolling resistance is less than the energy it took to cover the same distance after I hit the bottom of the hill at 70 vs 78 and coasting back down to 70.
In you're example of 1/2, you're right because there's different in energy lost at twice the speed exceeds, by a lot, the inefficiency of regen braking.
BTW, I got my best wh / mile ever in my P85D last night coming home to Merced from San Jose of 265 wh / mile holding at 65 and never allowing regen. It's tough because if you're going to decrease you're speed you have to never show orange by modulating the pedel to neutral. At the bottom of decents, let your speed rise a little more than your setpoint and then coast back down to your setpoint before pulling energy from the battery again.
That's why I gave the example that uses more energy at the same average speed. There are hypermiling techniques that don't cost time.
I think you missed my point. You should use regen. If you're going some speed and decide to coast to a stop, you'll coast a certain distance in a certain amount of time. If at the point in time when you decided to coast, you instead regen down to the average of the coasting speed and maintain that speed, you'll come to the stopping point at the same place at the same time as if you had coasted. But because of the lower speed and cubic decrease in power you will use less energy than if you had coasted. You can then regen the remaining kinetic energy down to zero speed. So you are wasting energy if you just coast to a stop.
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