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To stop or not to stop

Got to wondering about the following question: regardless of the distance to my destination, if there is a supercharger(s) along the route, overall is it quicker if I go as fast as I want, and recharge when necessary ("wasting" time at the supercharger), or is it better to drive at 55, and trade time spent sitting at the supercharger for distance under way.

My math may be out, but running a number of different scenarios (with/without A/C, different temperatures, etc.) the conclusion I came to is that you should Go For It! and take the high speed option. The SuperChargers charge so fast that any time you lose charging you'll make up with the higher speed. This works for any speed up to about 90 mph

One assumption is that you only charge to the level you need - i.e., if the SC is 30 miles from your destination and you still have 10 miles, you only add another 20. (or if you want to get there with a 20 mile reserve you only charge to 40)

For anything other than an SC - even a HPWC/70A feed - it is better to eek out the miles (unless you need to stop anyway for food, etc.)

Anyone want to run their own calcs and see if you come to the same conclusion?

BTW - my post was prompted by this one: http://www.teslamotors.com/forum/forums/my-trip-la-reallife-range-experi...
[edited for clarity, 2/15]

I won't run the numbers, but your conclusion feels right intuitively. The one time it would not be right is when you can make it all the way home (or to your overnight charging location) by driving a little slower, and thus avoid stopping altogether. A little thought experiment: imagine you are 10 miles from your overnight charging location, and you can reach it by driving 55 mph, but not by driving 56 mph. No matter how fast you charge, you could never complete the charging stop in the few seconds that you would lose by driving at the slower speed.

True - in your scenario the difference is only 12 seconds in arrival time at the two speeds, but about 3-5 miles difference in battery range due to aero drag. You gain/lose 3-5 miles in range for every mph below/above 55 (give or take)

And gain 3-5miles for every minute you are charging...

It's a good question. When I was looking at a 60kwh Tesla, the distance from the Harris Ranch supercharger to my house in los angeles was 199 miles. In the 60kwh version, you can make it going at around 60mph in good conditions (3:19) - or you can say fuck it, go 80mph and zoom to Tejon Ranch supercharger 125 miles away (1:34), charge for a half-hour to put approx 104 miles on (:30) and then zoom at 80 mph to my house 75 miles away (58 mins) for a total trip time of 3:02 (plus the couple minutes of pulling off at Tejon, plugging in, unplugging, getting back on the freeway).

It's kind of a "six of one, half-dozen of the other" situation. Driving 80 is more "fun", and during your 30 minute stop you can stretch your legs, but also risks speeding tickets.

And as you may have seen in another thread, if your charging rate is slower than the superchargers, then driving slower may get you to your destination sooner than driving faster.

Tomorrow I am taking a trip where I will be using mostly 70 amp power sources with twin chargers. Chad Schwitters (in one of his posts) said that, even with that relatively fast charging, driving slower is faster. :) His own preference is to drive faster, and spend more time at the charging locations. However, the same caveat applies with respect to the last charging stop before an overnight stay. I will be charging in Tigard, OR. If I could skip the next planned stop in Eugene, and drive without charging the entire 200 miles from Tigard to Canyonville, where I plan to stay, I could save a couple of hours. I'm going to make that 200 miles only if I drive conservatively. I'll wait and see what my energy consumption is before making that decision.

If someone told me I could drive as fast as I want in my current car, and that I could stop for free gas on the way . . . easy decision. Besides, what's the worst that happens? You hang out at the charger for a few minutes and talk to other MS owners.

Fun rulez!

And it's more fun to eek than to eke.

@nickjhowe

Ok, here are my calculations (rather than using the Seattle-SF trip thread).

I start with the assumption that the "Ideal Range" of the 85 kWh car is 301 miles, and involves a consumption rate of 270 watt-hours/mile. I don't know this for certain, but Rod & Barbara came to that conclusion, and it works pretty well in other calculations.

This yields a usable battery capacity of 81.27 kWh. (301 x 270)

Next, assume a charging rate of 40 rated miles per hour of charge. This is what I got at most of the 70 amp power sources I used on my recent trip. I did get 50 mph on one, so I will look at that assumption as well. 40 rated miles per hour of charge is equivalent to 10.8 kWh per hour of charge (40/301*81.270 kWh).

Now calculate the time required to drive 100 actual miles at 55, 60, and 65 mph, and then to restore the energy used during that drive through charging. To determine the energy consumption at various speeds, I have used the calculator at http://www.teslamotors.com/goelectric#range.

The base case is 55 mph, which produces the "ideal" range of 301 miles. Drive time is 100 miles/55 mph = 1.8 hours. Energy consumed is 27 kWh (270 watt-hours/mile*100 miles/1000), so charge time is 2.4 hours (27 kWh/10.8 kWh/hour). Total time is 1.8+2.4=4.2 hours.

At 60 mph, the calculator gives a range of 277 miles. The energy consumption rate is 81,270/277=293.39 watt-hours/mile. Consumption in 100 miles= 29.339 kWh. Charge time= 29.339/10.8=2.7 hours. Drive time is 100/60=1.7 hours. Total time is 1.7+2.7=4.4 hours.

At 65 mph, the calculator gives a range of 255 miles. The energy consumption rate is 81,270/255=318.7 watt-hours/mile. Consumption in 100 miles=31.87 kWh. Charge time=31.87/10.8=2.95 hours. Drive time =100/65=1.54 hours. Total time is 1.54+2.95=4.49 hours.

If the charger could add 50 miles per hour of charge, it would be the equivalent of 13.5 kWh per hour of charge (50/301*81.27=13.5). In that case, charging time to recover the energy consumed at 55 mph would be 27/13.5=2 hours, and total time would be 1.8+2=3.8 hours.

At 60 mph, charge time would be 29.339/13.5=2.17 hours, and total time would be 1.7+2.17=3.87 hours.

At 65 mph, charge time would be 31.87/13.5=2.37 hours, and total time would be 1.54+2.36=3.9 hours.

So, even charging at 50 miles per hour of charge, it is very slightly faster to drive slow.

I do think that the crossover point would be a charger considerably less powerful than a supercharger, as the differences are very small.

Oops. I just made a big mistake. I used ideal miles to compute consumption amounts, but rated miles to compute charge time (e.g., 40 miles per hour of charge). This would not change the conclusion for charging at a rate of 40 mph (since the conclusion is the same using a charging rate 25% higher). However, it could well change the conclusion at the faster 50 mph rate. I'll go back to the drawing board, but not tonight. :)

I ran the numbers again, but converted the charge rate properly, i.e., 50 rated miles per hour of charge/265 rated miles*82.27 kWh=15.3 kWh per hour of charge (not 13.5). When I used this in the computation, I got the following:

55 mph: 3.56 hours total time
60 mph: 3.61 hours total time
65 mph: 3.62 hours total time

So the conclusion stays the same: faster is slower, but not by much.

Faster is more fun but by much. :-)

I'd argue the opposite point. By avoiding interstate highways, you tend to stay on lower speed roads that tend to have more winding and hills (i.e. fun!). You drive slower, but in many cases it is a more direct route to the destination, and the scenery is way more interesting than the interstate route.

I am not sure if this is true everywhere, but I've been loving the lower speed "hypermiling" routes that I've been using since I got the S. My job involves occasional 170 mile round trips (in northestern cold weather) and I have a 60 kWh battery, so I was a bit concerned, but even using a lousy 110 outlet at the meetings where I get only ~1 rated m/hour of charging, but don't lose range to cold) I am getting there and back with 46 rated miles left, so well above the 200 rated miles.

My "range anxiety" is greatly relieved at this point, as this car addresses my driving needs perfectly! I might behave differently if there was a SuperCharger on this route, but surface roads are fun in their own way.

@Leofingal - surface roads aren't usually shorter, at least the ones I am familiar with -- in fact, by winding around hills and valleys, they are more "fractal" than the direct route chosen by interstates. As an example, the surface route from Atlanta to Huntsville, despite looking much more direct on the map, is actually about 30mi longer and takes 1.5 hours longer.

Hopefully this will display correctly. Been playing with some numbers. Below is based off Ideal range, and the distance/speed graph from the TM performance and efficiency blog post.

KW is the power drawn from the battery to maintain that speed.
Min/KWh is how many minutes it takes to burn through a KWh, ditto seconds
Duration is how long it will take to flatten the battery, in Hours or minutes.

So, under ideal conditions (72°, calm, flat, driver only, no accessories, 19" wheels) at 130mph you are sucking nearly 140KW, burn through a KWh every 28 sec and will flatten the battery in 36 min. Get to it people!

Speed Ideal Wh/        Min/  Sec/   Duration
 mph  Range mile  KW   KWh   Kwh   Hours  Min
  10   390  214   2.1  6.00  360   39.0  2342
  15   442  189   2.8  4.00  240   29.5  1767
  20   456  184   3.7  3.00  180   22.8  1368
  25   451  185   4.6  2.40  144   18.0  1083
  30   435  193   5.8  2.00  120   14.5   869
  35   413  203   7.1  1.71  103   11.8   707
  40   389  215   8.6  1.50   90    9.7   583
  45   364  230  10.4  1.33   80    8.1   485
  50   337  248  12.4  1.20   72    6.7   404
  55   310  270  14.9  1.09   65    5.6   338
  60   285  294  17.6  1.00   60    4.8   285
  65   263  318  20.7  0.92   55    4.1   243
  70   241  348  24.3  0.86   51    3.4   206
  75   221  378  28.4  0.80   48    2.9   177
  80   202  413  33.1  0.75   45    2.5   152
  85   184  455  38.7  0.71   42    2.2   130
  90   167  501  45.1  0.67   40    1.9   111
  95   152  552  52.5  0.63   38    1.6    96
 100   137  610  61.0  0.60   36    1.4    82
 105   124  673  70.7  0.57   34    1.2    71
 110   113  744  81.8  0.55   33    1.0    61
 115   102  820  94.3  0.52   31    0.9    53
 120    93  903 108.3  0.50   30    0.8    46
 125    85  988 123.5  0.48   29    0.7    41
 130    78 1075 139.7  0.46   28    0.6    36

I think the more interesting question, at least until Superchargers are built out, is if you were planning on stopping for a meal anyway (let's say an hour), what does that do to the equation? Ie, if you get an hour of charging "for free", does it suggest an optimal speed to minimize overall travel time?

So I played around with some figures. Assuming:
You start with a full battery
You finish with an empty battery
You drive 1000 miles
You fit food/bathroom stops around the charging requirements of the car, then you get:
Trip Time Vs Charge Rate
Vertical axis is total travel time in hours; horizontal axis is speed

So, if you can only use NEMA 14-50, your best bet is to drive at 55mph
If you have twin inverters and J1772 at 70A, 65 is your ideal speed
WIth SuperChargers? Pedal to the metal.
If you can only use 110V? Borrow an ICE car.

These calcs were based on ideal range. Assuming you will do 20% worse than ideal consumption, then if you are planning on a 40A charger drop your speed to 50; other speeds remain the same.

@jat - if you give me a different distance I can plug it in and see what falls out. I can add in an 'override' for a long rest stop, regardless of charging time.

Cool graph Nick!

at least on the 5 (interstate 5) in California, driving 55 or 60 is NOT safe. the speed limit is 70, so you should drive at least 70 mph and use the superchargers.
@archibaldcrane from Harris Ranch to Arcadia is 205 miles, and I would definitely stop at Tejon Ranch to top off. You are going to climb over the Grapevine and that's going to eat some miles,

oh btw, I said Arcadia because I have done this trip a couple of times now. and by charging to only 200 rated miles at Harris Ranch, I arrived at Tejon Ranch with only 38 miles (averaging 71.6 mph for the 116 miles distance), so lets say I charged fully at Harris Ranch, then I may end up with 98 miles range, and you have to go 83 miles on that, going up to more than 4000 feet, not for me. I do change my driving habits by stopping at the superchargers, I used to just stop for 10 minutes, gas up and go nonstop the whole way, using the superchargers, we added only 1.5 hours (including stopping for dinner at Harris Ranch) to the travel time, much more relaxing and no need to worry about running out of range.

Nickjhowe:

I was just doing a sanity check on the chart above and have a question. You state at 60mph, you have a range of 285miles and are consuming energy at a rate of about 294WH/mile, which all sounds correct from the Tesla data we've all read. But at 60mph, you are traveling about 1mile/minute. Thus, you should only be consuming about 0.294KWH/minute, not 1.0KWH/minute as your chart states. In fact you would have to consuming nearly 1000WH/mile at 60mph to burn at 1.0KWH/minute. Please check your math for columns Min/KWH and Sec/KWH. Otherwise, nice chart.

@mthanos - thanks. Yup Error on my part. This one should be correct.

Speed Ideal Wh/        Min/  Sec/   Duration
 mph  Range mile  KW   KWh   Kwh   Hours  Min
  10   390  214   2.1 28.0  1679   39.0  2342
  15   442  189   2.8 21.1  1267   29.5  1767
  20   456  184   3.7 16.3   981   22.8  1368
  25   451  185   4.6 12.9   776   18.0  1083
  30   435  193   5.8 10.4   623   14.5   869
  35   413  203   7.1  8.5   507   11.8   707
  40   389  215   8.6  7.0   418    9.7   583
  45   364  230  10.4  5.8   348    8.1   485
  50   337  248  12.4  4.8   290    6.7   404
  55   310  270  14.9  4.0   242    5.6   338
  60   285  294  17.6  3.4   204    4.8   285
  65   263  318  20.7  2.9   174    4.1   243
  70   241  348  24.3  2.5   148    3.4   206
  75   221  378  28.4  2.1   127    2.9   177
  80   202  413  33.1  1.8   109    2.5   152
  85   184  455  38.7  1.5    93    2.2   130
  90   167  501  45.1  1.3    80    1.9   111
  95   152  552  52.5  1.1    69    1.6    96
 100   137  610  61.0  1.0    59    1.4    82
 105   124  673  70.7  0.8    51    1.2    71
 110   113  744  81.8  0.7    44    1.0    61
 115   102  820  94.3  0.6    38    0.9    53
 120    93  903 108.3  0.6    33    0.8    46
 125    85  988 123.5  0.5    29    0.7    41
 130    78 1075 139.7  0.4    26    0.6    36

Nice work, Nick.

Now to get someone to drive 130 mph for 37 minutes to test it ...


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