[pdonis]

For a proper evaluation, the tested alternatives should be (a) stop-and-go driving with an average velocity of V, versus (b) driving at a constant velocity of V. In that comparison, a constant velocity is much more efficient.

I completely agree, if you are trying to run a scientific experiment. But if you're driving on real-world roads, you're faced with a different set of choices. As I said, you can't expect to drive 400 miles at a steady speed of 25 mph in the real world.

Adding a given amount of energy E to a moving object requires the same expenditure of energy regardless of how quickly or slowly it's done

I wasn't saying that accelerating/decelerating more gently saves energy. I was saying that it probably prevented the regen system on the car from activating at all, meaning that none of the vehicle's kinetic energy was recaptured. Since he could not avoid stopping and starting again (since you can't drive 400 miles at a steady 25 mph on real-world roads), if it had been possible to reclaim some energy through regen during deceleration, it would have increased his range compared to stopping and starting again with zero regen. That's all I was saying, and it's completely consistent with what you're saying.

It's not clear at this point whether Broder was actually told by someone at Tesla that stop-and-go driving was more efficient or not, but if so, that person needs an education.

Not necessarily, because Broder's choice was not between stop and go driving at an average speed of 25 mph, or driving at a steady 25 mph. It was between stop and go driving in Manhattan (you are not, I trust, claiming that it's possible to drive through Manhattan at a steady 25 mph without stopping), at an average speed of 25 mph or so, and driving on freeways at an average speed of, say, 60 mph. Given that choice, it's entirely possible that the stop and go driving would give more range; the exact tradeoff would depend on details like the vehicle's drag coefficient, rolling friction, efficiency of regen, etc.

[lutusp]

> I completely agree, if you are trying to run a scientific experiment. But if you're driving on real-world roads, you're faced with a different set of choices. As I said, you can't expect to drive 400 miles at a steady speed of 25 mph in the real world.

A red herring. Whatever speed seems appropriate, steady speed is more efficient than stop-and go driving. My only point is that the advice to intentionally engage in stop-and-go driving is mistaken.

[pdonis]

Whatever speed seems appropriate, steady speed is more efficient than stop-and go driving.

A red herring, because the real-world choice is usually between stop and go driving at a low average speed, and steady-state driving at a high average speed. It's irrelevant to point out that a choice that was not actually available (steady-state driving at a low average speed) would be more efficient.

My only point is that the advice to intentionally engage in stop-and-go driving is mistaken.

Not necessarily, if the actual choice is as I said above. Did you read the last part of my previous post?

[lutusp]

> A red herring, because the real-world choice is usually between stop and go driving at a low average speed, and steady-state driving at a high average speed.

That's false, breathtakingly ignorant, and you have completely abandoned the original topic, which is to establish whether the advice given to Broder by Tesla (to engage in stop-and-go driving) would help or hinder battery duration and vehicle range. In point of fact, it would hinder battery duration.

> Not necessarily, if the actual choice is as I said above.

Try to focus on something other than your wish to be "right" in spite of the facts. Stop-and-go driving decreases the range of an electric vehicle, and it was incorrect advice to give to a nontechnical journalist.

Pretend to be a scientist, as hard as you may find that. Consider variables one at a time. The driver wants to maximize distance, so he is not going to travel above a moderate speed (this is proven by the fact that Broder knew this and traveled at a moderate speed after he realized his predicament). What is in question is solely whether stop-and-go driving aids or hinders maximum range. It hinders it -- this is physics 101.

[pdonis]

That's false

You're kidding, right? The choice Broder had was between driving on a freeway and driving through Manhattan. It was not in any way a choice between stop and go driving and steady-state driving at the same average speed.

Stop-and-go driving decreases the range of an electric vehicle

Compared to steady-state driving at the same average speed, yes. Compared to steady-state driving at a significantly higher average speed, not necessarily.

this is physics 101.

Okay, let's do some physics. The energy required to move a car through a distance D is F * D, where F is the force needed to push the car. For travel at a steady speed, F is given by the following equation:

F = c0 + c1 * v + c2 * v^2

where c0, c1, and c2 are constants that are determined by vehicle and environmental characteristics. (Briefly, c0 is the coefficient of friction between the tires and the road times the weight of the car; c1 is a (usually very small) constant related to the internal friction of rotating parts in the car; c2 is 1/2 rho Cd A, where rho is the air density, Cd is the car's drag coefficient, and A is the car's cross-sectional area. The key is that all of these things can be taken to be constant for the duration of the trip.)

For stop and go driving, F is given by the above formula times a constant e, where e is determined by the efficiency of regen; if e = 1 then regen is 100% efficient and all of the the vehicle's kinetic energy is reclaimed on each decel. If e > 1 then regen only captures a portion of the vehicle's kinetic energy, the portion being 1/e.

So if we compare stop and go driving at an average speed v1 to steady-state driving at an average speed v2, we have

E1 = F1 * D = e (c0 + c1 * v1 + c2 * v1^2) * D

E2 = F2 * D = (c0 + c1 * v2 + c2 * v2^2) * D

If we take v2 = 2 * v1, which is a conservative estimate for Broder's situation (25 mph average speed in the city vs. 50 mph average speed on the freeway), we have

E2 = (c0 + 2 * c1 * v1 + 4 * c2 * v1^2) * D

Now subtract to get the net energy difference:

E2 - E1 = [(1 - e) * c0 + (2 - e) * c1 * v1 + (4 - e) * c2 * v1^2] * D

Regen typically recaptures about 80 percent of a vehicle's kinetic energy, meaning e is about 1.25. So we have

E2 - E1 = [-0.25 * c0 + 0.75 * c1 + v1 + 2.75 * c2 * v1^2] * D

This is going to be positive for any vehicle except a heavy one with a low drag coefficient; practically no vehicles have that. So stop and go driving at 25 mph is going to save energy compared to steady state driving at 50 mph. This is the sort of calculation that I suspect was in the minds of the Tesla people when they told Broder that the stop and go segment in Manhattan was going to give him better range than driving on the freeway.

[lutusp]

> Compared to steady-state driving at the same average speed, yes. Compared to steady-state driving at a significantly higher average speed, not necessarily.

Look -- stop trying to change the subject. Obviously if Broder wanted to maximize range and with the choice to either engage in stop-and-go driving or drive at a constant speed with the same average speed, physics says drive at a constant speed. Your claim that one can only drive fast or engage in stop-and-go driving is false. If the point is to maximize the car's range, the driver can drive at any speed he cares to. And Broder did just that -- he drove as slowly as necessary to prevent pointless losses of energy.

Do you really think that the police will arrest you if you drive too slow on the freeway? Tell that to a long-haul trucker.

> Regen typically recaptures about 80 percent of a vehicle's kinetic energy

Absolutely false. Source: http://auto.howstuffworks.com/auto-parts/brakes/brake-types/...

Quote: "The miraculous thing about regenerative braking is that it may be able to capture as much as half of that wasted energy and put it back to work."

Source: http://theeestory.ning.com/forum/topics/regenerative-braking...

Quote: "Tesla Motors claims an 87% efficiency for powering the electric motor with the energy in the batteries, and the same efficiency in returning motor power to the batteries via regenerative braking. TM also claims an average 80% mechanical efficiency (this goes down as friction increases at very low speeds), including tire loss. So if I have it right, round trip efficiency from taking electricity out of the battery pack to putting it back in, after regen recovery, would theoretically be .87 x .8 x .8 x .87 = 48.4%. But the Roadster uses regenerative braking only on the rear wheels, so if you actually use the brake pedal (instead of coasting with the regenerative braking on) , then the recovery will be far less. The front disc brakes will absorb most (over half) of the kinetic energy when using the brake pedal, because braking action throws more weight to the front of a car."

Your preliminary assumptions are spectacularly wrong. According to the above, the energy recovered in the Model S is about 20% of that required to get the car to its present speed.

> So if we compare stop and go driving at an average speed v1 to steady-state driving at an average speed v2 ...

Learn about science, and don't post again until you do. Science isolates one variable, the topic of study, and keeps everything else the same to the degree that's practical.

Regenerative braking is much less efficient than driving at a steady pace.

[pdonis]

stop trying to change the subject

I'm not. The subject is whether or not the Tesla people gave Broder good advice. Obviously that depends on what information he gave them and what they based their advice on. You are basically saying that Broder asked them: "I can drive at 25 mph steady state, or do stop and go driving at an average speed of 25 mph; which will give me better range?" If that were indeed the question he had asked Tesla, you are entirely correct that "stop and go" would have been the wrong answer.

But I believe the question Broder actually asked Tesla was more like: "I can drive at 50 mph on the freeway steady state, or do stop and go driving at an average speed of 25 mph; which will give me better range?" If that was the question he asked Tesla, "stop and go" could have been a correct answer. That's my point.

According to the above, the energy recovered in the Model S is about 20% of that required to get the car to its present speed.

The quote you gave referred to the Roadster; as far as I know the Model S uses regen on all four wheels [Edit: probably not--see below]. That would make it 48.4%, not 20%, assuming there are no other differences between the Roadster and the Model S.

If the correct number is 48.4%, that makes e about 2; so my equation would look like this:

E2 - E1 = [- c0 + 2 * c2 * v1^2] * D

I agree this is less likely to be positive; I would have to see detailed numbers for the Tesla Model S to get a better estimate of c0 and c2. The Tesla people who gave Broder the advice presumably had such detailed data, so they would have been able to make a more accurate calculation of estimated range for each alternative.

Science isolates one variable, the topic of study, and keeps everything else the same to the degree that's practical.

Exactly: to the degree that's practical. Broder was not running a controlled scientific experiment; he was running a real-world test of a vehicle.

[Edit: Looking at the Model S specs on the Tesla web site, they do say it's a rear wheel drive vehicle, and there's no mention of separate regen motors for the front wheels. If so, and if the 20% figure for energy recovery is correct, that would make it extremely unlikely that a calculation like the one I've done would give a positive number. If the Tesla people were basing their response on such a calculation, their numbers for regen energy recovery must be significantly higher than 20%, or they were estimating a significantly higher freeway speed than 50 mph, or (most likely) a combination of the two.]