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## Model S Range Estimates Based on What Speed?

## 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... http://www.evconvert.com/tools/evcalc/ ...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

Timo| August 26, 2010Probably 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.

DanAderhold| August 26, 2010I 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.

ggr| August 26, 2010As a mathematician and pilot I have to point out that the drag goes up quadratically, not exponentially. That's what the "squared" means.

Greg.

Brian H| August 27, 2010Dan;

Your contact point is http://www.teslamotors.com/careers

Brian H| August 27, 2010Martin;

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).

Brian H| August 27, 2010ggr;

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

Paul19| August 27, 2010Greg,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

Brian H| August 29, 2010Paul, 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

Brian H| August 29, 2010P.S.;

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!

Georg| August 29, 2010The 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 ... ?

ggr| August 29, 2010The 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.

Greg.

Paul19| August 30, 2010OOPS! 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"?

eldrichfire| September 1, 2010How 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.

dsm363| September 1, 2010check the Tesla blog archives. This should answer at least part of your question

http://www.teslamotors.com/blog/roadster-efficiency-and-range

Timo| September 1, 2010@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).

nlukin| September 3, 2010From the post on wiki:

http://en.wikipedia.org/wiki/Tesla_Model_S#cite_note-Ramsey2009-25

Performance

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 http://green.autoblog.com/2009/03/26/tesla-model-s-50-000-ev-sedan-seats...

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.

nlukin| September 3, 2010Also to add. See wiki for examples of drag coefficient on other cars: http://en.wikipedia.org/wiki/Automobile_drag_coefficient

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 :)

TslaFan| September 6, 2010Lot 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.

ChristianG| September 7, 2010Is 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.

FutureX| September 7, 2010Unless 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.

FutureX

wjjw73| September 12, 2010I 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)...

Timo| September 12, 2010@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.

TabascoBob| September 12, 2010Hi 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.

wjjw73| September 13, 2010@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... :-/

Timo| September 13, 2010@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).

bcn0209| October 30, 2010lets 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!

Roblab| October 30, 2010Let'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.

James13| November 5, 2010Remember: 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.

SteveU| November 6, 2010James13, 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.

ECam| November 13, 2010Just 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.

Mark Petersen| November 14, 2010yes we all know that speed affects range, so I think it would be nice to be able to limit the power usage

if there is X kWH on the battery and you need to travel Y miles, limit the top speed to Z

Whistle| November 14, 2010the faster batteries can be charged quickly, without causing damage to the cells, the better. In a few years or by the end of the decade, there shouldn't be a reason why driving across country in an EV is any more difficult than doing it in any other vehicle.

I know a good amount of people who do regularly drive more than 300 miles in a single day(especially alot of people who live near new york that drive up to boston for a day, and vice versa), and when you consider that not all cars will be ordered with that 300mile pack, even short trips can become complicated.

For EV's to truly become mass market, they will need to overcome that gap, as long as it exists, it can be used as a reason to NOT buy them. Most people may only drive that distance very infrequently, but at the same time, most people buy insurance beyond what is legally required to use it very infrequently or never.

Since Tesla has shown the drive train technology is mature enough for mass marketing, it looks like its mostly an issue of batteries for those occasional long distance trips.

Brian H| November 14, 2010Whistle;

consider the % of the market that has those 300 mi./day requirements. It's so small you'd have a hard time measuring it accurately. Not a concern for a company opening up the market to the most buyers possible. And later, the battery boys will solve the problem on their own.

I.e., this is not a serious concern for Tesla for the foreseeable (practical) future.

Whistle| November 15, 2010Thats basically what I was getting at, but when those long hauls do come up, potential buyers will feel alot more comfortable when they know they won't have to sit around for a long time to recharge. I imagine it wouldn't be as much of a problem for hte Model S as it doesn't seemed to have really deterred any real number of people based on the pre-order numbers, but with bluestar, that could possibly be a bigger problem. I imagine electric cars will be used more in urban or dense suburban areas as opposed to rural areas based on infrastructure though.

Timo| November 15, 2010Considering that preorder is now going somewhere close to 4000, and Tesla doesn't even have prototype ready yet, that number is rather high. I expect it to raise *fast* after they get the real Model S drivable prototype ready and production running.

I'm pretty sure the % of people driving over 300 miles regularly and own only one car is quite a bit higher in Europe than in US. Not a niche market. My sisters husband will be doing trip like that every weekend, maybe even more frequently. Though most of the Europe is quite a bit more densely populated than Finland, so maybe my point of view is a bit biased. Then again, owning car here costs a lot more than in US, so single car families are way more common.

Even if 99.9% of annual driving is done less than 300 miles (which I believe is overestimate) that doesn't mean that 99.9% of car owners don't need that range. It only takes 1/3 of the potential drivers doing that trip once a year to get that figure. 33% is not a small number.

BYT| November 16, 2010I myself tend to rent a car when I am driving for very long distances since I can get one for about $30 a day with unlimited miles and save the wear and tear on my other cars.

Douglas3| November 16, 2010Does this even matter? I drive a Roadster daily, and I don't think about the range. It's simply not a factor; I have a "full tank" every morning, and I have rarely used half of it.

For road trips it is more of a factor, but as long as you have a place to stop for lunch and charge up, a 400 mile trip is trivially easy.

Currently I'm keeping my SUV just for winter driving (we get serious snow here, salt, sand, etc., and I want to keep my Roadster pretty). When the Model S arrives I will sell the SUV and go fully electric. If I need to go on a 2000 mile road trip where it's not convenient to charge, I'll just rent an ICE car. It's cheaper and less trouble than having a rarely-used car depreciating in my garage.

Vawlkus| November 18, 2010Douglas3: You know that the Roadster's largely carbon fibre right? That stuff doesn't rust you know :)

Douglas3| November 18, 2010LOL! Of course I know it's carbon fibre body and aluminum frame. Rust isn't the any part of the reason for parking it during the worst of the winter.

They pour gobs of sand on the roads here, which includes nasty little stone nuggets that put holes in your paint when kicked up by the car in front of you. I doubt the paint armor will stop that.

The roads are also covered in salt, which gets all over everything, and it's especially hard on the carpets. (It inevitably gets all over the inside of the car, carried on your boots.)

That salt and sand will end up plastered all over the ledge underneath the door, and will probably get all over your clothes.

Hand washing. At -20 degrees C. No thanks. I'd freeze my butt, and the driveway would turn into a skating rink.

Once the snow banks start building up, you have trouble seeing around corners in an SUV. It'll be much worse in a Roadster.

I've heard that the Roadster is quite good in snow. But we get snowstorms that accumulate significantly higher than the bottom of the Roadster. Trust me, if the snow gets so high the bottom of the car is sitting on it, it's not gonna move. On big snowstorms they do the side streets last, which means the last 1/2 km of my trip home is sometimes on a nice deep unplowed street. That means there's a pretty good chance I won't be able to get it home.

I think that's all the reasons...

I will take it out on nice days during the winter, but I doubt I'll be driving it anything like daily. Like I am now.

jkirkebo| November 20, 2010"I myself tend to rent a car when I am driving for very long distances since I can get one for about $30 a day with unlimited miles and save the wear and tear on my other cars."

You canæt rent a car at that rate in Europe. In Norway, it'll cost you at least $220/day if you want to put many miles on it, and that's not for a large car like the Model S, more like a Ford Focus 1.6L.

ml1211| November 21, 2010One factor I have not seen addressed is traffic. If I sit in traffic averaging 15 mph for 30% of my 60 mile commute how does that affect my range? Is 300 mile range still 300 miles? I live in New England, traffic around Boston is a very real concern, especially in the winter when temperatures tend to average below freezing. Does anyone know if Tesla has tested their batteries in cold climates?

qwk| November 21, 2010The slower you go the more range you have. A roadster can get over 300 miles traveling less than 35 mph. Teslas battery packs are temp controlled so no worries there. You will use a little more power in extreme temperatures, but not enough to worry about.

Timo| November 21, 2010In fact with that speed (15-25mph) Roadster theoretical range is over 400 miles. It is just the optimal speed for maximum range.

I'd say look at blog http://www.teslamotors.com/blog/roadster-efficiency-and-range, but that seems to behave weirdly, almost always the charts that belong in that blog do not show up. There are several of those, Wh/mile / speed, losses / speed, miles / speed at least. Tried to reload it several times and at max I got two of those.

Timo| November 21, 2010Got it to finally show that range vs speed chart after zillion reloads (but not the other two at the same time), and with 25mph range is a bit less than 400 miles. Optimal range is between 15 and 20 mph.

Whistle| November 23, 2010"One factor I have not seen addressed is traffic. If I sit in traffic averaging 15 mph for 30% of my 60 mile commute how does that affect my range? Is 300 mile range still 300 miles? I live in New England, traffic around Boston is a very real concern, especially in the winter when temperatures tend to average below freezing. Does anyone know if Tesla has tested their batteries in cold climates? "

Theres something about the combination of use and the battery giving off some heat in use and the built in battery temp control that should keep it working fine, I haven't seen any specific cold weather reviews, but to my understanding it works fine in those conditions

Timo| November 23, 2010Roadster battery is fine even over -20C cold. Just not for near empty left outside for storage at that temperature. Somewhere in older blogs there is a video where they test Roadster winter handling in Sweden. Pretty cool video.

There is actually some optimal temperature where battery cooling/heating system needs least power to keep them at the right temperature and I bet it is pretty close to zero Celsius (which is the freezing point, in case people using Fahrenheit don't know it).

bhp| November 23, 2010Range = speed X runtime hours

Speed = 5, 10, 20, 35 etc etc……(miles /km)….whatever….

Run time hours = Kwh (battery pack) / Kw (power required)

Kwh (battery pack) = 42Kwh(5000-cells), 65Kwh(8000 cells), 85Kwh(8000 cells)

Kw (power required) = (Air resistance + rolling resistance) X speed / % efficiency

Air resistance = Fair = 1/2 Cd A p v2

Rolling resistance = μ (r+ brake and steering) x GWV x g

_________________________________________________________________

NOTE: the range will vary according to the acceleration also.....

because more the acceleration more (pulse) power is required.

Thus more C-rate from the 18650 cell........so the over-all "Ah"

decreases........

Timo| November 24, 2010Kw (power required) = (Air resistance + rolling resistance) X speed / % efficiency

Those are main losses, bun ancillary losses are not small either, AC on/off, lights, radio etc. draw enough power that it is significant, but small, fraction of the losses in slow speeds.

You have one excess "speed" in that calculation (both rolling and air resistance formulas already include it).

bhp| November 24, 2010@ time: my friend i don't have a excess "speed" in the formula..!

because my aero: i have used v square not v cube,

and there is no v in my rolling resistance....

which i later added it...........

Brian H| November 24, 2010The slower you go, the more mileage you get. I'd expect that time spent at 15mph to extend your range. The specifics would be hard to figger. Note also that stop-start traffic is actually good for EV range, since the regen recovers much of your kinetic energy.

Sounds to me like you should see an extra 25-50 miles on that max, just a WAG.

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