# Forums

## Optimal speed

## Optimal speed

Submitted by Teslamodels4me on April 25, 2012

Does anyone know the optimal speed to travel 1000 miles? Assume that recharging is done with a supercharger.

Also use the numbers:

45 mph = 378 miles

50 mph = 350 miles

55 mph = 321 miles

60 mph = 295 miles

65 mph = 271 miles

Assume that all road conditions are perfect, no others cars on the road, and that there is a working supercharger available with no awaiting.

These are numbers I got from a computer at the Tesla store.

If you have numbers for high speeds please add those numbers.

The question is at which speed will take the car go 1000 miles in the least amount of time?

EdG| May 1, 2012For comparison, here's the Roadster chart.

I assumed a 53kWh battery which can charge at 21.6 kW (240V * 90 A). I allowed 3 hours per charging stop instead of 45 minutes. And I used the power curve (cubic) derived from the data at https://www.teslamotors.com/display_data.php?data_name=range_table

Reading directly from the simulation numbers, going at 60 mph from a fully charged battery gets down to 7 kWh after driving 3 hours (180 miles) before recharging. No "limp home" mode simulated. Does that ring true?

Teslamodels4me| May 1, 2012@EdG

Thank you, this graph answers many questions, at 450 miles I can reduce the number of charges simply by driving at 50 mph and arrive at the 450 mile mark at the same time that it would take if you were driving at 60 mph. I know that this is not an exact science due to many unforeseen factors but it is a good estimate and an impressive graph. The other thing I noticed was that I would actually arrive earlier at the 450 mile mark sooner traveling at 50 mph than if I were traveling at 70 mph.

Timo| May 2, 2012That's what I got with my calcs. A zig-zag where faster car is sometimes slower, sometimes faster in overall time depending when and how much you need to charge to reach your destination.

Rod and Barbara| May 2, 2012EdG, I think the power consumption charts you have used are not really applicable to the Model S. The chart at http://www.teslamotors.com/goelectric/efficiency represents a generic BEV and I believe cannot be used to forecast Model S performance since it predicts 257 Wh/mile at 65 MPH, which would give a range of 331 miles with an 85 kWh battery.

The Tesla stores have a range estimator (see pictures here: https://plus.google.com/photos/117433471618932049710/albums/572080445134...). The data presented at the beginning of this thread by Teslamodels4me appears to be from this estimator under highway driving conditions with the 85 kWh battery, A/C on and outside temperature of 70 deg. Using this data, 65 MPH yields 288 Wh/mile and 271 miles, a much more reasonable value.

With respect to recharging, based on 3 years experience with my Roadster, when charging during a road trip you only put approximately 80% of the kWh supplied by the power source into the battery. In addition, the battery charge rate drops off significantly above 80% charge as the vehicle limits the amps from the charger. So, if time is a consideration, it is usually best to only charge to 80% of full capacity while in route.

No one has any experience with the Tesla Supercharger, so I think the best idea is to follow the current Tesla estimate at the bottom of the bottom of the Options and Pricing sheet – “replenish 160 miles of travel in about 30 minutes when applied to the 85 kWh vehicle.” I interpret this to mean you can add 45.3 kWh (160 miles/300 miles * 85 kWh) to the battery during a 30 minute supercharge. In order to do this I would assume the battery has to be depleted to at least 22.7 kWh to avoid the potential drop off in charging that occurs at about 80% capacity.

With respect to the Roadster chart, the Roadster has a 55 kWh battery and your recharging scenario is a little aggressive. The fastest charge for a Roadster is with a Roadster High Power Charger (HPC) and then you can charge at 13.4 kW (240V * 70A * 80% efficiency) until the battery reaches 80% capacity.

In both the case of the Model S and the Roadster the most likely charging points for road trips in the immediate future will be NEMA 14-50 (RV parks) and J1772 Level 2 chargers. These will charge at 7.7 kW (240V * 40A * 80% efficiency) and 4.6 kW (240V * 24A * 80% efficiency) respectively. If you run your same graphs with these charge rates, you will find in general that slower speeds produce shorter travel time for long trips.

EdG| May 2, 2012I'd like to do a much more accurate simulation of the Model S, but the link Rod and Barbara posted seems broken. On searching, I found photos of the estimator as shown by Tesla. The only data I have for 70 degrees for the 85kWH battery are:

@65 mph, 271 mi

@45 mph, 378 mi

Two points aren't enough for my curve fitting. Anyone able to point out more data? Once I have that I can incorporate the reality as per Rod and Barbara to come up with a reasonable looking plot.

Rod and Barbara| May 2, 2012EdG, Look at the data provided by Teslamodels4me at the beginning of this thread. He has ranges for 45, 50, 55, 60, and 65 MPH.

EdG| May 3, 2012I've modified my Roadster simulation to Rod and Barbara's suggestions (first plot below). Now charging using numbers given (May 2 post above) for NEMA 14-50 at 240V * 40A * 80%. Charging period is 4.5 hours to get near 80% charge from the low of under 8% at the charging stop. Of course, if your destination is within reach after charging for less time, you would unplug earlier.

Note that driving at 40 mph gets over 250 miles on the initial full charge, while driving at 80 mph doesn't get that far until leaving the second RV park (off the graph).

As for the Model S simulation, I apologize for not having realized the original post used real Tesla numbers. Unfortunately, those numbers are almost linear and to the nearest integer, so my Model S simulation based on curve fitting those numbers may be a little off for speeds outside that range. Also, I have no idea how Tesla derived those numbers. Did they assume one might "limp" in to finish the range? Are they overly conservative guesses? There may be other factors lumped in to them. I've put in two 5% losses during charging (95% * 95% * 90kW) for different elements' losses as per Timo, but I don't know if that's too optimistic, pessimistic or just right. Small differences here don't change the plot very much. During these 3/4 hour charging stops, the battery doesn't get above 80% of full capacity, but is very close to it.

Using the Tesla Estimator's numbers, here's what I got:

It seems clear that driving the Model S for distance, at highway speeds, is much more feasible than such a road trip would be in the Roadster.

kublai| May 3, 2012Not sure if anyone has mentioned this, but would it be possible to program the model S to travel to a destination or some distance within a period of time. It would calculate the optimal speed to reach the destination in shortest amount of time taking into consideration charging locations and durations. It then plots the results on the map screen.

Teslamodels4me| May 3, 2012Kublai, that would make a great app.

Rod and Barbara| May 3, 2012EdG, Thanks for the new graphs. What the graphs tell me is that having superchargers available for charging is a game-changer for BEVs with respect to road trips. The Model S graph would likely look similar to the Roadster's if it had to use NEMA 14-50 charging stations.

Brian H| May 4, 2012There are lots of interesting "race results" from that if you pick a particular mileage or range. E.g., at 250 miles, it goes 70-80-50-60-40. At 350 miles and over, it's 80-70-60-50-40--except that at 360-440, it's 70(by a nose)-80-60-50-40. 40 and 50 never win, but 60 is "place" by a nose at 250-290.

;)

Brian H| May 4, 2012P.S.

The 350+ and 200- results are about the same (in descending order of speed) except that exactly at 200 80 collapses at the finish line and needs urgent rehydration to even walk to the barn.

Brian H| May 4, 2012Spike Jones, where are you now when we need you?

http://tinyurl.com/Feedlebomb

The names, btw, are police jargon for various offenses they usually deal with!

EdG| May 4, 2012@Rod and Barbara: I ran a few versions of the simulator using the Model S numbers with the NEMA charge speeds. Those simulations with the more reasonable number of charging stops do indeed strongly resemble the Roadster graphs I posted. So it does seem correct to conclude that much faster charging is the answer to the inevitable square law losses faster driving incurs.

EdG| May 14, 2012Given the new data at http://www.teslamotors.com/blog/model-s-efficiency-and-range, I've updated the previous Model S estimates. Just in case high power chargers are installed every kilometer on the autobahn, I've shown speeds up to 130 mph.

Brian H| May 15, 2012Heh. At 130, about 2/5 of the time is spent 'rapid charging'. At 90, about 1/4. And the 130mph gets you about 30 extra miles over 12 hrs, which is a net of 2.5mph benefit for your 40 mph higher highway speed.

Brian H| May 15, 2012At about 9 hrs, the 90 and 130 lines intersect, which means you could do the 90 up till then, and then switch over to 130 for the last 3 hrs, and get your increment up to a margin of 10 mph benefit for that last stretch.

EdG| May 15, 2012Because the energy used per mile is monotonically increasing as you increase speed above 25 mph, lower speeds get you further for each kilowatt-hour in your battery.

On the other hand, higher speeds generally get you there faster.

As Rod and Barbara said, the point of this exercise is to be aware that, for longer trips than you can make on one charge, one must be aware of the charging duration and its impact on your travel plans. The graphs I've posted show that the Model S can actually get you there faster by driving faster (up to about 80mph), but only as long as you have very fast charging available. Much slower charging likely means going slower will get you to your destination faster.

The interesting planning will come when you're about 1.5 full trips away from your destination, around 400 miles for the 85kWh battery as shown. In that case, you should plan well on how to use your speed and plot out charging locations to suit.

adn| May 15, 2012Any chance you can post this on Google Spreadsheets, and make it available to people?

uedinet| May 15, 2012how much miles can I drive with fullspeed? (130MpH/Autobahn)

EdG| May 15, 2012@uedinet: 113kWh per hour of driving at 130 mph. So you can go from, say, 85 kWh on the battery to 5 kWh in about 42 minutes - about 90 miles - if the car will allow you to go at that speed till the battery is that low.

@ADN: The spreadsheet is incomprehensible to any but me as is, and I don't really see much value for its use other than what I've already done, so I'm not really interested in spending a lot of time cleaning it up. On the other hand, the numbers provided by Tesla at http://www.teslamotors.com/blog/model-s-efficiency-and-range stop at 80mph. My curve fit yields the following for energy usage per mile at various speeds:

MPH wH/mile

40 204

50 234

60 275

70 327

80 390

90 464

100 549

110 645

120 751

130 869

You should be able to figure what you need from those numbers. Example: you have 50 kWh in your battery. Your destination is 40 miles away. If you travel at 70 mph, your battery would lose (327 wH/mile)*(40 miles) wH - or 13 kWh on such a trip, so you'd have 50-13 = 37 kWh left.

Teslamodels4me| May 15, 2012At what point does the battery go into " limp mode " or safety mode and limit the speed to preserve the battery or does it let the driver drain the battery to 0%? Anyone see information on this?

Teoatawki| May 15, 2012From Road & Track review of the roadster- "there are an additional 20 or so miles of reserve available in limp-home mode."

I expect it will be similar for the S.

From the Tesla blog responding to the bricking issue- "Of course you can drive a Model S to 0 percent charge, but even in that circumstance, if you plug it in within 30 days, the battery will recover normally."

The car will do everything it can to prevent damage to the battery pack.

ggr| May 16, 2012I'm not sure what the algorithm will be in the Model S, or even what it is exactly in the roadster. But here is roughly what happens in the roadster.

In standard mode, the battery display goes yellow with about 30 "expected" miles remaining (that is based on your current driving). At about 20 miles it goes red. Soon after that it gives a warning display, and reduces power just like in range mode. At any time you can switch to range mode, and the bottom 10% battery capacity becomes available (another 15-20 miles if you nurse it). Once the battery becomes low, about 20 miles of range mode left, it can no longer estimate the range very well, so it just says "0 -- plug in now!".

adn| May 18, 2012@EdG, and others: I took the time and encoded this spreadsheet as a public Google Spreadsheet. Its sort of fun because you can play around with how long it takes to charge, and the battery consumption assumptions and see the impact on range. It's also interesting to look at ways you could maximize your range/minimize your time for a given trip you need to take. Enjoy: https://docs.google.com/spreadsheet/ccc?key=0AnTR_8ZOZ1ZMdGgxWk8xd09sblg...

Rod and Barbara| May 21, 2012I’ve put together a spreadsheet to facilitate trip planning in a Tesla Model S or Roadster. The spreadsheet presents data for the Roadster and the three Model S battery sizes for speeds from 40 MPH to 80 MPH. The input parameters are trip range, elevation changes, and vehicle climate control status. The spreadsheet then presents the driving time, number of charging stops required, percent of battery charge needed in route, and the battery charge remaining upon arrival at the destination for each vehicle/speed combination. The spreadsheet also presents the charging time and total travel time for each vehicle/speed combination for several different chargers – the Supercharger, the Model S High Power Wall Connector, the Roadster High Power Connector, NEMA 14-50, J1772 Level 2, and a US standard 120V wall outlet.

The spreadsheet assumes the trip starts in fully charged Range mode, the car is recharged if the charge state reaches 10% charge remaining, the car only charges to maximum of 80% charge during enroute charges, and the car arrives at the destination with at least 10% charge remaining. Enroute charges do not fill the battery above 80% because the charge rate drops off above 80% in the Roadster and the spreadsheet assumes this behavior will be similar in the Model S.

The spreadsheet also includes a set of instructions at the top of the spreadsheet and extensive notes on data sources and assumptions at the bottom of the spreadsheet.

As an example of the kind of data the spreadsheet produces here are the optimum results for a 500-mile trip, without elevation changes, with vehicle climate control off for two vehicles and three chargers:

85 kWh Model S 40 kWh Model S

Supercharger

Speed (MPH) 80 n/a

# Charges 2 n/a

Travel Time (hrs) 7.8 n/a

NEMA 14-50

Speed (MPH) 55 55

# Charges 1 3

Travel Time (hrs) 15.7 19.3

J1772

Speed (MPH) 45 45

# Charges 1 3

Travel Time (hrs) 17.6 23.4

The spreadsheet can be found at http://www.box.com/shared/deb4ec8cc468632eb9b7. You will need to download a copy of the spreadsheet in order to enter data and see results. Questions or comments can be made on this thread or via email to Rod at tesla25@verizon.net.

Brian H| May 22, 2012Nice! I downloaded into LibreOffice and it opened immediately.

Supergreekster| May 23, 2012What is interesting is when u calculate for lower charging rates, all of sudden the faster speeds turn out slower because of the proportionally higher charging times. Optimal speed becomes about 70. With "high speed charger" (62mi range per hour)

rex1825| January 13, 2014I don't know guys about you, but why do I have a feeling that Model S should come with gearbox!?!?

Looking toward those graphs, and according to this two graphs:

http://www.autoguide.com/auto-news/wp-content/uploads//2012/05/graph1.png

http://www.autoguide.com/auto-news/wp-content/uploads//2012/05/graph2.png

I'd say that Tesla Model S electric motor has optimal consumption vs range at speeds around 15-30mph (25-50km/h) which corresponds to 1800-3600rpm.

Now, we know that most powerful Model S does at 16k rpm exact 135mph, so if you do the maths you'll get the numbers.

...not saying that those guys from Tesla didn't count on all, but looking toward simple math, I'd say that this same electric motor connected to real transmission, if, let's say on that tranny running on 2700rpm, would car go 80mph (130km/h) and counting that on that same rpm in Model S car can go around 20h without stop, now let's take aerodynamics at higher speed and reduce this number by 50% (I'm sure it would be less then 50% around 30% or so), this means it would run for 10h @ 80mph, which means it'll do 800+ miles without problem on single load.

Donno bout you guys, but math is really simple and I know it is not so simple, but how hard can it be?

Cheers...

Brian H| January 14, 2014Math is simple, metallurgy is not. TM had 2 gears on early Roadsters, and the motor's torque broke them.

rex1825| January 14, 2014@ Brian H,

didn't know that, I tough that all Tesla cars had only fixed gear.

Well, one thing I'd like to know, if economy would be better with gears?

Cheers...

stevealex1| January 14, 2014Just a note about the weather. A one way 117 mile journey which was successfully accomplished, round trip, in the summer, could not be done without a charge for the return trip in November (in the northeast). Used 152 miles of range to travel 117 miles with heater running at mostly 65 mph.

rex1825| January 15, 2014@ uedinet

Around 97 miles (150km)...

Cheers...

jkn| January 21, 2014rex1825,

No it would not. I don't have efficiency map for Tesla. So look at this: www.acpropulsion.com/datasheet/ac150gen2.pdf

1: Efficiency does not change much on horizontal direction (constant power & changing RPM). So gears would be useless.

2: Efficiency drops at very low power. Again gears would be useless. For this obvious solution is to add small motor in front.

3: Max power (= max torque) at low RPM has poor efficiency. Gears would help. Tesla has removed this problem with powerful motor. Max torque is not needed at low speed.

I did a fit into Wh/mile curve in end of www.teslamotors.com/forum/forums/whmile-equation thread. Result was so good that curve could be computer generated.

Without simulation and starting with rather optimistic numbers from EdGs post + range with 85 kWh. Average speed assuming battery has same charge (between 0 and 50%) at start and end of trip. Also assuming charging is done between 0 and 50% of SOC.

MPH Wh/mi R mi v1 v2 v3

40 204 417 38 36 36

50 234 363 46 44 43

60 275 309 53 50 48

70 327 260 58 53 50

80 390 218 64 59 55

90 464 183 68 60 56

100 549 155 70 61 55

110 645 132 71 60 54

120 751 113 70 58 52

130 869 98 69 56 49

average speed = range / (driving time + charging time)

v1, v2, v3 = average speed (MPH), with different assumptions:

v1, with 50% charge in 20 minutes (= 127.5 kW charging P).

v2, with 50% charge in 30 minutes (= 85 kW charging P).

v3, = v2 with ranges reduced to 80%.

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