Efficiency comparison - Model S v. Roadster

[bolosky]

Hi Doug,

...my thinking is that at high speeds the power drain would of course increase exponentially in both cases, but the Model S's better aerodynamics would start to narrow the power drain in comparison with the Roadster whose power drain would increase even faster than the Model S.

Larry

Mass makes a difference when you're changing speed or elevation, because both kinetic and gravitational potential energy are linear in speed. At a steady speed on a flat road, it just doesn't matter, so you'd expect that the car with the better CdA would have lower energy use per mile (assuming no differences in the rest of the system like the efficiency of the power train, the tires, etc.) The higher the speed, the more energy/mile is used to overcome drag so the greater advantage the lower CdA car would have. (BTW, drag energy per mile increases quadratically in speed, not exponentially.)

That is, I'd expect that if you were crusising through the flat desert at 80 mph that the S would use less energy for the same distance than the Roadster, possibly by a pretty large margin. Getting to speed and climing hills would be worse, though, and real driving nearly always involves that.

[jerry33]

Mass makes a difference when you're changing speed or elevation, because both kinetic and gravitational potential energy are linear in speed. At a steady speed on a flat road, it just doesn't matter, so you'd expect that the car with the better CdA would have lower energy use per mile (assuming no differences in the rest of the system like the efficiency of the power train, the tires, etc.) The higher the speed, the more energy/mile is used to overcome drag so the greater advantage the lower CdA car would have. (BTW, drag energy per mile increases quadratically in speed, not exponentially.)

That's certainly true. The rule of thumb is that each 500 lbs weight removed on a standard full-sized car (like a Ford 500) provides an increase of one mpg in EPA testing. So you have to remove quite a bit of weight for the difference to be really noticeable (full sized cars in the 1950s were often 6000+ lbs. so the 3000 lbs of today's cars provides a noticeable difference). Motor efficiency, drive train efficiency, tire rolling resistance, and CdA have a larger effect than weight under most conditions. This is why an electric car can have a ton of batteries and still be very efficient.

[Larry Chanin]

Mass makes a difference when you're changing speed or elevation, because both kinetic and gravitational potential energy are linear in speed. At a steady speed on a flat road, it just doesn't matter, so you'd expect that the car with the better CdA would have lower energy use per mile (assuming no differences in the rest of the system like the efficiency of the power train, the tires, etc.) The higher the speed, the more energy/mile is used to overcome drag so the greater advantage the lower CdA car would have. (BTW, drag energy per mile increases quadratically in speed, not exponentially.)

That is, I'd expect that if you were crusising through the flat desert at 80 mph that the S would use less energy for the same distance than the Roadster, possibly by a pretty large margin. Getting to speed and climing hills would be worse, though, and real driving nearly always involves that.

Thanks for the detailed explanation.

Larry

[EVNow]

Mass makes a difference when you're changing speed or elevation, because both kinetic and gravitational potential energy are linear in speed. At a steady speed on a flat road, it just doesn't matter, so you'd expect that the car with the better CdA would have lower energy use per mile (assuming no differences in the rest of the system like the efficiency of the power train, the tires, etc.)

Friction on the tire depends on the mass. So 2 cars with same CdA, but different masses will spend different amount of energy cruising at a steady speed on a flat road.

[daniel]

I'm surprised that the Roadster, which is so low to the ground, has a higher CdA than the much larger Model S. Oh, well, I believe you folks. I'm just surprised.

Now when we talk about efficiency, are we talking about the same driving profile for both cars? Or are we talking about driving each car as each was intended to be driven? A sporty sedan vs a high-performance sports car! I know someone over on Prius Chat who is an early Model S reservation holder and is a high-mpg Prius driver. I expect him to drive his Model S in such a way as to maximize range and efficiency. I like to feel the thrust, and I drive my Roadster pretty hard. Comparing his Model S to my Roadster is a real apples-to-oranges comparison.

[efusco]

I'm surprised that the Roadster, which is so low to the ground, has a higher CdA than the much larger Model S. Oh, well, I believe you folks. I'm just surprised.

Now when we talk about efficiency, are we talking about the same driving profile for both cars? Or are we talking about driving each car as each was intended to be driven? A sporty sedan vs a high-performance sports car! I know someone over on Prius Chat who is an early Model S reservation holder and is a high-mpg Prius driver. I expect him to drive his Model S in such a way as to maximize range and efficiency. I like to feel the thrust, and I drive my Roadster pretty hard. Comparing his Model S to my Roadster is a real apples-to-oranges comparison.

If you're talking about me,Daniel, I have a feeling I'll be driving the Tesla significantly more aggressively than the Prius. With electricity cost so small compared to gas, the range more than enough for me to "play" with, and the available torque I forsee taking the highway more often and probably exceeding the speed limit a bit more as well. May employ some hypermiling techniques from time to time just for fun, but one advantage is using zero gas and not having to think about technique.

[Larry Chanin]

I'm surprised that the Roadster, which is so low to the ground, has a higher CdA than the much larger Model S. Oh, well, I believe you folks. I'm just surprised.

Now when we talk about efficiency, are we talking about the same driving profile for both cars?

Hi Daniel,

To put this in context perhaps it would be useful to see where the discussion started. Initially I was commenting in the Carbon footprint clarification thread stating that Roadsters would produce better results than the Leaf that was used in the subject study. The moderators started this new thread when the discussion veered to discuss efficiency comparisons between the Model S and Roadster.

Anyway, to answer your question I was discussing efficiency as quantified by the watt-hr/mi characteristics of the respective vehicles. The subject U.C.S. study used 340 watt-hr/mi for the Leaf. From Tesla's published watt-hr/mile vs. speed graph for the Roadster I was able to estimate that at 55 mph the Roadster would draw about 230 watt-hr/mile.

A similar chart for the Model S would be helpful in addressing our comparisons because it would incorporate all of the factors, weight, rolling resistance, aerodynamics, etc., in one aggregate efficiency number at various speeds.

Perhaps one of the more knowledgeable forum members can confirm this, but I would imagine that when measuring or calculating efficiency of vehicles, pains are taken to reduce differences induced due to driving style, inclined driving conditions, wind, etc.

Larry

[daniel]

If you're talking about me,Daniel, I have a feeling I'll be driving the Tesla significantly more aggressively than the Prius. With electricity cost so small compared to gas, the range more than enough for me to "play" with, and the available torque I forsee taking the highway more often and probably exceeding the speed limit a bit more as well. May employ some hypermiling techniques from time to time just for fun, but one advantage is using zero gas and not having to think about technique.

Coming over to the dark side, eh, Evan?

Hi Daniel,

To put this in context perhaps it would be useful to see where the discussion started. Initially I was commenting in the Carbon footprint clarification thread stating that Roadsters would produce better results than the Leaf that was used in the subject study. The moderators started this new thread when discussion veered to discuss efficiency comparisons between the Model S and Roadster.

Anyway, to answer your question I was discussing efficiency as quantified by the watt-hr/mi characteristics of the respective vehicles. The subject U.C.S. study used 340 watt-hr/mi for the Leaf. From Tesla's published watt-hr/mile vs. speed graph for the Roadster I was able to estimate that at 55 mph the Roadster would draw about 230 watt-hr/mile.

A similar chart for the Model S would be helpful in addressing our comparisons because it would incorporate all of the factors, weight, rolling resistance, aerodynamics, etc., in one aggregate efficiency number at various speeds.

Larry

Thanks. Larry.

Is that figure for the Roadster Wh from the battery, or from the wall? From the wall, I think I burn a lot more Wh, but then I've never measured at 55 mph. On the freeway I drive the limit (70 mph outside of town here) and in town I accelerate hard up to the speed limit for the road I'm on unless there's a car in front of me. My point was that this is a high-performance sports car, and even though it can be driven 55 for range, it was built to do so much more.

I never drive the Prius 70 mph. For one thing, it doesn't feel safe. The Roadster feels really solid. And for another, like Evan, I'm more concerned about fuel when I'm burning foreign gasoline than when I'm burning locally-made water-derived electrons. (Washington state = water power.) And the Prius is a car that says "I'm efficient," whereas the Roadster is a car that says "I'm a hot-rod."

[rabar10]

Thanks Larry for the link-back to the original thread. Agree that it helps with context here.

A similar chart for the Model S would be helpful in addressing our comparisons because it would incorporate all of the factors, weight, rolling resistance, aerodynamics, etc., in one aggregate efficiency number at various speeds.

I've created a rough-guess Model S chart in Excel, by using the Roadster data (TM's Excel data files for the Roadster are available from JB's blog post on Roadster Efficiency and Range), and applying multipliers for each of these different metrics to translate from Roadster to Model S. (Chart referenced on this site earlier: Model S (Performance edition) 1/4 mile time)

I used the following Model S multipliers from Roadster data-points:

• Aerodynamic losses, 0.98. This came largely from trying to get the end results to line up with the spec-ed ranges of the 60- and 85-kWh Model S at 55 mph, after the factors below were estimated. Note that this result infers an ever-so-slightly lower CdA for the Model S.
• Drivetrain losses, 1.02. Same drivetrain layout (single induction motor with digital inverter/controller, rear axle differential, etc.) so no reason to assume any big differences here.
• Tire losses, 1.57. Estimated from weight difference only, Roadster at 2690 lbs and Model S estimate of 4225 lbs.
• Ancillary, 1.6. That big touch-screen has to take more energy to run. But big-picture, it's a small and roughly constant power draw regardless of speed, so doesn't have a measurable impact on range @>20mph.

Criticisms of the above welcome.

[Larry Chanin]

Thanks. Larry.

Is that figure for the Roadster Wh from the battery, or from the wall? From the wall, I think I burn a lot more Wh, but then I've never measured at 55 mph. On the freeway I drive the limit (70 mph outside of town here) and in town I accelerate hard up to the speed limit for the road I'm on unless there's a car in front of me. My point was that this is a high-performance sports car, and even though it can be driven 55 for range, it was built to do so much more.

I never drive the Prius 70 mph. For one thing, it doesn't feel safe. The Roadster feels really solid. And for another, like Evan, I'm more concerned about fuel when I'm burning foreign gasoline than when I'm burning locally-made water-derived electrons. (Washington state = water power.) And the Prius is a car that says "I'm efficient," whereas the Roadster is a car that says "I'm a hot-rod."

Hi Daniel,

I'm not sure I follow you. Again this efficiency is in the context of a study in which I imagine that pains are taken to try to eliminate differences induced by driving style, terain, wind, etc.

Larry