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Model S Range Estimates Based on What Speed?

Anyone care to offer an opinion on what speed the range for the various battery options is based on? I couldn't find anything on the T website about this.

In case you are wondering why I ask, range decreases at an exponential rate with reference to speed. An easy to remember example of this is: if you drive at 50mph you use almost exactly half the power (and therefore fuel) that you do driving at 70mph. I am talking about true 50mph and 70mph here, not what your speedo says as there are notoriously unreliable at higher speeds - and on a level road with no wind.

If you want to test this theory, use a GPS based speedo at least and one with a good signal. Or have a look here... ...and you can play with the numbers to your hearts content.

Incidentally, this exponential decrease in range is almost entirely dependent on the frontal area of the vehicle - the area you would get if you took a front (or rear) elevation drawing of the vehicle and measured the total area of the vehicle including wheels and wing mirrors but excluding the space below the vehicle, between the wheels. The formula is... Drag force = 0.5 X density of air X speed squared (the exponential bit) X coefficient of drag (Cd) X frontal area.

One way the Model S minimises the Cd is to have a very smooth belly pan. 99% of vehicles have a very rough one and this induces a good 10% increase in drag ie reduces the miles per gallon performance by 10%.

Regards, MW

Probably combined EPA rating.

And 50 vs 70 doesn't increase your fuel consumption by 100%. There is also rolling resistance which is the bigger the heavier the car is, and that is pretty constant at any speed. Type S rolling resistance is probably the major loss up to 50-60 mph, so even that you do lose exponentially more due air drag, you still don't get quite that big increase of energy consumption with that speed increase.

I read this model type (S) will be produced at the NUMMI Assembly Plant in San Hose, CA. I worked at this facility as a Senior Engineering Consultant when it was owned by GM and Toyota.

I worked in the Auto and Truck industries for many years, plant launches, amongst other. I am very impressed with Tesla, and their design and management team, as my skill is in plant launches. I worked for all Big-3 in Michigan, traveled throughout US and Canada for plant launches. Worked for Hughes Aircraft assigned as Plant launch Engineer and Manager.

Who do I contact for a position with this company? Finally someone is producing a quality vehicle in the US again. I want to help Tesla with high volume production.

I understand quality and engineering, this product will have a high demand world wide, and I can help to meet that demand. Some auto makers in past would lose orders due to plant launch problems, I would fly in to analyze and assist.

As a mathematician and pilot I have to point out that the drag goes up quadratically, not exponentially. That's what the "squared" means.


Your contact point is

AFAIK the speeds are according to the usual EPA mixed driving formulas. There was a detailed analysis on some of the old blogs, but I don't know if that's still available.

One thing to note is that the usual ratio of highway/city driving is reversed. Cruising on a highway is where an ICE car gets best mileage, but the EV does much better in slow city traffic, especially considering the regeneration bonus in stop-start traffic (slowing down without brakes, the usual way with an EV, repowers the batteries).

Nit-picker! In less formal terms, drag goes up as the square of the speed -- which is a form of exponential increase.

Greg,ggr, you are right and Brian H, you are dead wrong and its not nit-picking.
Do the math,
If speed goes up in ratio 1, 2, 3, 4, 5,
then a linear relationship goes as1, 2, 3, 4, 5,
and a square or quadratic goes 1, 4, 9, 16, 25,
But an exponential can go 1, 10, 100, 1000, 10,000
Square is not a form of exponential, but both are very different non-linear functions.
It seems popular to describe all non-linear functions as exponential, to create fear in the mathematically challenged

Paul, your impatience is exceeded only by your igno.. lack of knowledge. Exponential growth can have ANY base for the exponent, not just 10. Squaring each step is base 2, natural log growth is base e, order of magnitude is base 10, etc. It appears you only can comprehend one of those at time.

To repeat, an exponential function is "A function in which an independent variable appears as an exponent." YCLIU

Paul, because of 'limitation of comprehension' problems, I guess I'd better be explicit about what I was referring to with "impatience": the triple post. I wouldn't want to exacerbate your egregious discombobulation!

The triple post may be related to the fact that Paul did not notice the blue banner that tells us it has to be approved by a moderator ... ?

The independent variable is the speed. It is "speed squared". It is not anything to the power of speed. So it isn't exponential. But anyway, enough dead horse flogging. Fortunately I can drive my car at 80 and get almost as far as driving it at 70.


OOPS! sorry about triple thread, yes, I didn't notice... etc!
but, if we want to nit-pick one last time,try: If speed goes up in ratio 1, 2, 3, 4, 5, 6, 7, 8
then a linear ratio goes 1, 2, 3, 4, 5, 6, 7, 8
and a square or quadratic goes 1, 4, 9, 16, 25, 36, 49, 64
But an exponential base 2 goes 1, 2, 4, 8, 16, 32, 64, 128
Sorry Brian, but whatever base you use, the result is always the same, you just can't force a quadratic to be a form of exponential! Being insulting is no help if the math is wrong. Enough! The real question: When can I get my "S"?

How about someone just answer the question instead of debating the proper use of mathematical terms? I would like to know what speed they are basing their charge time on and how that miles per charge varies with speed. I really don't need to know the mathematics behind it.

check the Tesla blog archives. This should answer at least part of your question

@eldrichfire; to add dsm363 comment Type S will be a bit heavier so you need to add a bit in rolling resistance, but it is also quite a bit more aerodynamic than Roadster so air drag should stay approx same (better Cd, but more A so CdA is about same, I'm guessing).

From the post on wiki:

Acceleration of the 4,000 pounds (1,800 kg) vehicle is anticipated to be 0–60 mph (97 km/h) in 5.6 seconds aided by a drag coefficient of 0.28.

Also: from

The 300-mile range is possible (vs the Roadster's 244-mile range) because the S has 8,000 battery cells vs. 6,000 in the Roadster, the batteries have been improved in mass and volumetric performance, and there is more advanced cell chemistry in each cell, and the S has a cd of about .27 vs. the Roadster's drag coefficient of .35.

Also to add. See wiki for examples of drag coefficient on other cars:

Nice to note that at 0.27, Model S would be only 0.02 worse than Prius with a drag cf of 0.25 (what an ungly car!). Kuddos to The Other Guys movie for making fun of Prius :)

Lot of tech talk above but ultimately for the regular driver its the range they are going to get with regular driving. Tesla should understand that they are doing a major shift here.

Majority of the public thinks electric is too new, its unreliable, it will require constant charging, they are scared there is no gas engine as a backup and lots more...

The range question that's being discussed here is CRITICAL. Users are going to have a phobia buying this car if they feel they have to charge it everyday or won't get enough range out of a charge.

This is Critical.

Is it? An electric car is a sacrifice in Range Simple as it is. with the 180mile pack I probalby get 97% of all my car travels done. With 240mile pack 99.5% and for the rest I'd need something like a 1000mile pack or even more...

So in the near future there will allways be trip you'll not be able to do with an electric car. You can't just drive 20 houres to your holiday destination and be happy. With the EV it will be a 5 days roadtrip there.

The question is, are you doing such trips or not? Am I ready to take alternative transportations instead of my own car? So it's more a question in advance for what things you use that car. and +/- 20 miles will not make any difference in that decision.

Teslas cars are superb products in my opinion. And I really really want them. But they don't come without sacrifices. So depending on my driving habits in 2 years I might even keep my current car for those trips, but who knows.

Unless you drive 200 miles a day, every day, there really isn't a range issue. I drive 20 miles a day to and from work which means I could ultimately go a week and half without charging. Realistically I would charge every night so would always be topped off. The vast vast majority of people do not share this "I need to drive 300+ miles right now!" mentality and is a generally promoted idea by paid naysayers or those who can't stand change.

When cell phones first came out people didn't want to become reliant on them for fear the battery would run out and leave them stranded. (My Dad to this day turns his cell phone off when he's done making a call!) This never was a problem and had nothing to do with battery longevity or capacity. The same is true for Tesla's EV's. I can't say the same for the "married-to-the-oil-companies" EV manufacturers as their cars will probably only get 40 miles per charge thus 'proving' that EV's don't work and gas is the only way to go.


I am driving mainly very short distances (city) and every 2nd week I have to drive 250 Miles and 90% highway with a min. speed of 80 mph. So my question is if this "long" trip cn be done with that speed? How can I be sure that it is possible? If this is not possible the Model S is the wrong coice for me (I already preordered it)...

@wjjw73, using data from Roadster you get only about 180 mile range with 300 mile battery with speed 80 mph. To get that 250 mile out of 300 mile battery you need to drive 65 mph or less.

That's for Roadster. Type S is a bit more aerodynamic so it might not suffer so much about higher speeds.

Anyway you probably need a charging point in your trip. Same as me, except that I need over 400 mile range at 65-55 mph range.

BTW. which road is 250 mile long with 80+mph legal speeds? Only places where I know that could be possible are some Germany autobahns.

Hi folks, I'm interested in the range discussion because I have three regular trips where I'll be traveling early morning/late evening on NJ/NY/PA interstates where the routine cruising speed is 75+ ("legal" being interpreted locally as "keep up or get run over.") My three destinations are, respectively, 99, 120, and 145 miles each way. I try to stay over, but frequently do these trips in one day and at this time I'm not certain of being able to recharge with permission. Therefore, the range issue is important. Also, because I put close to 20k per year on my car now, leasing is not an option, and I worry about the effective life of the battery.

All that said, I love the way the car looks and I want to drive the Tesla because of their committment to EVs. I'm almost ready to place my order but I need to satisfy a few nagging doubts.

@timo, I'm working and living in Czech Republic and have to drive to Austria. In both countries the speed of 80mph is still under the limit of max. speed on highways. ;-) So it's legal here...
So I'm afraid I need the double time to go there than with "normal" car... :-/

@wjjw73, I'm not sure about capabilities of Type S onboard charger, but if it accepts ordinary 400V 3phase voltage then you might have your "charger" at some service station in that trip without any special EV chargers. With that power it doesn't take very long to get those needed extra miles to get to your destination. I'd say it is worth exploring if there are any charging possibilities in that trip. 250 miles 180 mile range = 70 miles extra. 70 miles is roughly 21 kWh. 400V@32A = 12.8kW => 1.5 hours.

Not that bad. You would get to your destination in 3 hours without charging with 80mph, 4.5 with it. With 65 mph you would get there in 3.8 hours, so straight run would be a bit faster, but not much.

Of course if you can get a real 50kW charger there then that stop would be less than half an hour (and type S is said to have 45min charging from empty to 80% full, which means a lot more than 50kW charger is possible for it).

lets say the Model S is super slippery like a .03 drag coefficient. Lets say the battery is a 120volt unit (for argument). Lets (based on engineering) say the car needs around 10-15 HP to maintain 70MPH which is about what a Honda Insight needs. 1HP=740 watts so, 15 HP=11100 watts or 11.1 KW!!$Q#*Q^# thats a lot of juice flowing. Now lets convert that to amps! 11100watts/120volts=92.5 amps! WOW! Now, lets keep this up for 300 miles shall we? at 70MPH you have to drive for 4.28 hours to reach 300 miles... So drawing 92.5 amps/hour to drive 70 miles per hour would take a 92.5 amp-hour battery....multiply by 4.2 times and you get a 388 amp-hour battery. Thats with no stereo, headlights, or losses to friction, heat, or anything else. Since you probably need another 1500 watts for brake lights, headlamps, and other accessories and factoring in a 96% efficient drivetrain, you are looking at a 450amp-hour battery pack! THAT'S HUGE! Its enough power to weld with!

Let's assume that Tesla says they will have a 300 mile range car. Let's assume that Tesla says the c/d will be around .27. Lets assume that most modern EVs have 300+ volt power to the motor.
Let's assume that these variables point to a battery pack of roughly 95 kWh.
I was having trouble following your math, but I really don't think you need to do it. Tesla Engineers have figured it all out, and thankfully, I don't need to. In a few months, you can call them and get all this data.

Remember: You leave the house everyday with a full tank, awakening knowing your Tesla Model S has just finished off-peak charging,5.5 cents/KWH where I live. For a Roadster, at I believe 52KWH per charge, that's less than $3 (three dollars) for 240 miles. "240 miles per gallon", if you will. And no tail pipe. And you never stand at a gas station in the rain. In fact, you never stand at a gas station. And to re-state: you leave the house everyday with a full tank. The point: these facts,along with a range higher already than we imagined just years ago will surely quell the Fears of The Masses. cD of 0.27. May we all dress in that kind of Drag.

James13, while this doesn't change your calculations very much the wall-to-wheel power use is different (uses more power) than the battery-to-wheel. Or to put it another way, to put 52KWh of power into a battery takes more than 52KWh of power from the wall. My roadster requires roughly 250 Wh/mile battery-to-wheel and about 330 Wh/mile wall-to-wheel. I suspect the ratio will be similar for the model S even if the numbers are different.

Just like a gas or diesel powered car, the faster you go, the sooner you have to get gas (charge up). We all know that driving at 75mph will give you less range than driving at 55mph. Also, fast acceleration, as opposed to more gradual acceleration to speed will also have an affect on how far you can go. Fuel usage in a gas or diesel car, or battery power usage in an electric car will each be similarly affected depending on the power usage of one's individual driving style. Air resistance, rolling resistance and drive efficiency are all factors in the emperical formula used in calculating the power needed to run the car, and thus the anticipated range of the design. For an owner, however, learning how the range of your electric car is affected by your style of driving is the most important thing to consider.

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