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Optimal speed

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

There 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.

;)

P.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.

Spike 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!

@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.

Given 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.

Heh. 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.

At 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.

Because 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.

Any chance you can post this on Google Spreadsheets, and make it available to people?

how much miles can I drive with fullspeed? (130MpH/Autobahn)

@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.

At 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?

From 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.

I'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!".

@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_8ZOZ1ZMdGgxWk8xd09sblgxa0RRc0FDSk1Ea3c#gid=0

I’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.

What 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)

I 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:

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...

Math is simple, metallurgy is not. TM had 2 gears on early Roadsters, and the motor's torque broke them.

@ 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...

Just 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.

@ uedinet

Around 97 miles (150km)...

Cheers...

rex1825,

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%.