While I should have been doing homework, I was reading this article on the more technical details of Brad Berman's 531 mile roadtrip:

http://www.plugincars.com/inside-scoop-tesla-super-smart-supercharger-network-124676.htm.

The article inspired a question in me. If I was a Tesla engineer, and had the option to put a supercharging station wherever I wanted, how would I get a model S across the country as fast as possible. Also, how long would it take and how much should I charge up the battery at each stop?

It's not as easy a question to answer as you might think. Range is dramatically reduced as the vehicle travels faster. Traveling faster means more stops, more stops means more time spent charging. Other variables include when charging the battery, how much does the rate of charge decrease. If charging it to full takes 1.5 hours, and charging to half full only takes 30 minutes, perhaps one should stop more frequently.

Funny though, after all this thought it turns out, **I can't answer the question accurately.** My initial data is showing that charging from about 10-65% is the best option. One really must know accurately the function for the rate of charge to determine the most efficient charging habits. Regardless I work through below what data is needed and how to apply it. If you'd like the spreadsheet feel free to email me at:

While I tried to derive a very neat equation I was struggling. So I went to excel and used the shot gun method; get a bunch of data points and see what happens.

My algorithm was this:

Time = {(TripDistance / Speed) + (TripDistance/(vRange(Speed)*SOChargePoint) * chargeTime(Charge))}

The first term gives you driving time and the second, the number of stops to be made multiplied by the time of the stop. vRange(Speed) is the vehicles range as a function of speed and chargeTime(Charge) the time to charge the vehicle as a function of charge. (SOChargePoint is the point where you charge the system up to each time). For both functions I substituted various actual values as I don't know what the mathematical vRange approximation, nor the equation for the rate of charge for the supercharger.

After looking at the article, the charge rate seemed to be 38% faster for the lower charged state of the battery (pixel based estimation). (1.44%/minute average for second two charges versus 1.05%/minute for first charge).

Using this data I assume the following:

about 34 minutes for 50% state of charge

about 85 minutes for 90% state of charge.

I take a guess of about 55 minutes for 75%.

The spreadsheet shows that no matter what SOC you charge to, you should drive 80mph all the time.

**The time to go 3000miles is 55 hours with a 50% SOCp, 55.5 hours for 75% SOCp and 61 hours @ 0.9 SOCp. **

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Why not put the spreadsheet on google drive & make it public?

https://docs.google.com/open?id=0B-BFJJz2YX0LY2JWQnJncnpTWkE There you are. I should have just done that originally. Note that cell G3 says full state of charge, it should say 0.9 SOCp.

This is pretty interesting, but I have to say that for me the thought of driving across country is pretty unattractive anyway. Trying to do it "the fastest way possible" makes it sound like an absolute nightmare. But as a navel gazing exercise in burning time until one's Model S arrives, well, it has been thoroughly hashed out several times before though. This thread has a chart, and the second post is one of Volker.Berlin's invaluable pointers to other threads on the topic.

http://www.teslamotors.com/forum/forums/range-vs-speed-graph

MandL, Realize those posts were done prior to the supercharger information so charge times became a huge factor in trip time. Now with the supercharger those graphs have to be redone. As a Roadser owner I had done several spreadsheets to determine what my best rate of travel time would be when going on long trips and found the same trouble with creating a good chart as aschulz90 has found. I have not tried redoing them with the supercharger info yet.

The biggest issue with trying to create this info is it is not a straight line graph but rather a discontinous function (i.e charging time varies with amount of charge needed). We need a good mathematician to formulate an equation which works well for this as a spreadsheet will never be able to do this perfectly without a formula.

Volker.Berlin's Thread on the topic:

http://www.teslamotors.com/forum/forums/time-long-distance-trip.

I like his/her energy based method alot. But I don't think it accounts for the change in rate of charge as the battery pack's SOC increases. Interestingly both calculations don't seem to be trip distance dependent. there seems to be an optimal travel strategy.

All 3 columns appear to have the same data. Maybe a variable is missed for 70% and 90% columns.

This is very interesting. Thanks for posting and starting this discussion.

Seems to me that there should be a program that would derive an equation from a set of points on a graph. This may exist somewhere - does it exist in Excel? If it does, you can easily formulate a complete formula for what you want based on the graphs published by Tesla and any emperical data taken during a Super Charge (or averaged over a number of Super Charges).

This is why it was so important and desirable to have a low coefficient of drag. lower the CD, flatter the curve.

It is going to be a lot more complicated.

The watts used by the motor are going to increase going up in elevation and you won't get as much back going down.

Traffic is going to drop your speed off the perfect range.

Some people use A/C no matter what the temperature is outside.

Rain or snow will decrease your range.

You have to figure it at the posted speed limit not what the people will actually drive for legal reasons.

The engineer has to take all that into consideration not just the best speed according to a formula. You will have to calculate the slowest less efficient distance to the supercharger otherwise you are leaving people stranded on the road on rainy days. Once that is done the driver has to calculate the most efficient speed depending on conditions and distance needed to travel.

http://www.jurassictest.ch/GR/

Add Vehicle: Tesla S.

This takes elevation change into account.

I have made the cross country round trip twice (ICE style). Once from DC to San Francisco (5 days). And once from Florida to San Diego (4 days). Here's what I learned.

If I ever decided to do it again, I will take my time and enjoy the journey. If I have the benefit of superchargers, I would only use them once per day (mid day). I would limit my daily drive to a max of 400 miles, leaving plenty of time for overnight charging at 30A or 50A. I will plan to stay in some nice hotels where there is plenty to see and do. I would have a great breakfast and a great dinner everyday. I will not eat behind the wheel. If the trip takes 7 days (so what), then I will have enjoyed the journey much more than my previous trips - when I was driving 12 hours a day with bloodshot eyes.

Dave,

Spoken like a guy about to enter the ranks of the retired. ;-)

Larry

@David M.: Amen brother!

This article (cross-posted from another thread) gives some valuable hints for your planning:

http://www.plugincars.com/inside-scoop-tesla-super-smart-supercharger-ne...