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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?

The slower you go, the more miles you can get out of the battery, they less often you need to recharge and since charging can take at least 30 minutes on a 300 mile pack, then the mph becomes less of a factor between 45 mph and 65 mph. That extra 20 miles per hour cost you 100 miles from your battery. 20 miles vs. over a quarter of your entire battery pack?

For the first two options 45 and 50mph you would have to charge up twice on the road. For the options 55, 60 and 65mph you would have to charge up three times. If you have to charge twice, then you might as well go 55mp or if you have to charge three times then you might as well go 65mph. So the best option is one of those two.

So now lets look at those two options. If you could go 50mph continuously, it would take 20hours. So you just need to add your two charging times to that (about 45min? x2 or 1.5hr) for a total of 21.5hrs. If you could go 65mph continuously, it would take 15h 23min. If you add three charging times to that (about 2h 15min) you get 17hr 37min. So under ideal conditions, the faster speed still gets you there faster. However there may still be a certain point somewhere over 65mph that due to the increased drag and additional recharges it would cause it to take longer to get there.

And it's possible you might be able to use the terrain to go even further on a charge even though the average speed would be the same.

jerry3;
I don't think so. Unless you creep uphill, and speed downhill. ;)

Kinda reminds me of the old story of a spinster driving her Model A at a breakneck 30mph down the main drag. When pulled over, she explained she was almost out of gas so was hurrying to get to the gas pump before she ran out ...
?:/

I can see that when the first Ses are delivered, there's going to have to be a thread for hypermilers! :D

Small correction... where I said '55mp' in the first paragraph, I meant 50mph. 50mph since it was the faster of the 'two recharge' options.

Works well enough in my 2004 Prius:-)

DATE__________ODO____INC_____AVG
--- Trip to NE starts here (warm weather)
08/13/10____111690____625____59.8 (3.9)
08/14/10____112308____618____60.0 (3.9)
08/20/10____112972____663____64.2 (3.7)
08/22/10____113411____438____58.9 (4.0)
08/31/10____113922____510____61.8 (3.8)
--- Trip to NE ends here

--- Trip to NE starts here (cold weather)
01/07/12____128603____481____56.6 (4.2)
-- 13 F here
01/12/12____129042____438____52.7 (4.5)
01/15/12____129420____378____50.3 (4.7)
01/20/12____129094____481____56.2 (4.2)
--- Trip to NE ends here

I’ve thought about this a bit, but I keep coming up with the same problem. I don’t think I’ll be able control myself well enough to go slower even if it gets me there sooner. It’ll just be too much fun to go fast. I think I’ll just have to resign myself to more stops for charging (and highway patrol!).

Write.mikeadams thanks for the info, so far 65 mph is the optimal speed does anyone have numbers for speeds over 65 mph?

I discussed this in the thread "Time for a long distance trip." My conclusion was that for a 1600 mile trip, it made little difference whether you drive at 50, 60, or 70 mph. The total time for the trip was about the same. At 70 you spend less time driving and more time charging. At 50 it's just the opposite. Look at that thread for the details.

Power needed to push the car increaces as the cube of its velocity. I'm not convinced of the free lunch

I discussed this in the thread "Time for a long distance trip." (cerjor)

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

I made some time ago same calculation as cerjor, and was quite surprised how little the speed actually means when you need to use about a hour to recharge fully. The time saved with faster speed is countered by additional time needed to recharge and vise versa.

Square of wind velocity, not cube.

ggr has it correct. Thank you for pointing that out for those who may not be familiar with the formulas. Air drag = 1/2 * p * V^2 * A * Cd......

While we really don't know the exact numbers for the Model S we have some good aproximations. If we use a power form fit for the data given for range and assume we can get 80% of the range in a 45 minute supercharge we can then make some estimates.
MPH-Hours to travel 1000miles-Avg MPH
40-26.50-37.7
45-24.77-40.4
50-22.25-44.9
55-20.43-48.9
60-18.92-52.9
65-18.38-54.4
70-17.29-57.9
75-16.33-61.2
80-17.00-58.8

Now if those superchargers are not available in exactly the spot you need them or if you have to rely on "standard" chargers, this trip is going to take you a whole lot longer .....

So somewhere around 70 to 75 is the predicted minimum time. This is a good thing because as JohnEC pointed out, we'll be traveling that fast anyway! ;-)

My guess is that if you exclude supercharging (say you didn't get an S that supports supercharging), you may find yourself taking the slower, windier (not like breeze, but curvy) trips through the non expressways to get places. This might be pretty refreshing actually. This will extend your usable range, and enable you to find new and interesting places to drive. You could plan your trips around interesting stops/restaurants off the beaten path, and discover a whole new world around your normal routes. I think this might be fun.

BruceR;
Here's your table using the <pre> tag:

```MPH  Hours to travel  Avg MPH
1000miles
40      26.50          37.7
45      24.77          40.4
50      22.25          44.9
55      20.43          48.9
60      18.92          52.9
65      18.38          54.4
70      17.29          57.9
75      16.33          61.2
80      17.00          58.8
```

"Pre"serves your spaces; don't use tabs, tho'.

Here's my graph (if posted correctly) of distance vs. time for some continuous driving.
Assumptions: 85kWh battery, starts fully charged; simulation granularity is 15 minutes; when battery gets low, there's a fast charger right there; you spend 3/4 hour charging at 90kW.

I did a best fit on the curve shown at http://www.teslamotors.com/goelectric/efficiency and am using the formula: kW used = (.0254 R*R + .7 R + 103) where R is the rate of speed in MPH.

To get there the fastest, go faster. Unless you're in the cross-over areas.

That's what I get for guesstimating it rather then actually crunching numbers. I also figured for much longer charge times.

@ EdG, I assume that the plateau on each line (avg speed) is the charging period. Would you actually be able to go a little over 300 miles at 70mph before charging? Have I misread the graph?

EdG,

Very interesting graph, but I'm a little confused. The original poster showed that at 55 mph the Model S has a range of 321 miles. (I assume that is with aero wheels.) Your graph seems to show a range of over 300 miles without a charge at 70 mph. The Roadster, upon which your data is based, can't achieve that sort of range either at that speed.

Am I misinterpreting what the graph is displaying?

Thanks.

Larry

Good catch. I'm going to reprogram the simulation to stop for recharging at some reasonable number other than 0. I'll have it stop when getting below 10 kWh and re-post.

If anyone else sees an issue here, please let me know - I'd rather fix them all at once!

Stop whenever below 10kWh

I'm missing something, because if I'm reading the chart correctly, you're saying that you can go about 350 miles at 60 mph before the first charge. That would be nice, but it's higher than the 300 miles at 55 mph (or even 320 with aero wheels).

Also, AFAIK 30-45 min of charging on the supercharger gains around 50% (i.e., ca. 40 kWh) on the 300-mile-battery. Charging to full 100% takes considerably longer than just twice that.

My charging rate is likely off. I assumed the full wattage is added, without loss, to the battery. So the charging rate is probably too fast. I picked 45 minutes of charging because Elon said it would charge to about 80% in that much time. My simulation shows close to that, so either there is little loss (??) or the wattage of the high speed charging unit is rated by results, not the source (????). I don't know. I just used the numbers I have. On the optimistic side, it's also possible that the car will really perform to this range, but the various numerical claims made have been very conservative.

Any tweaks to these assumptions that sound closer to reality can be added.

After said tweaks, I can do the same for a high speed 60kWh battery and lower speed charging for all sizes, if desired.

In many ways it sort of doesn't matter because a 500-700 mile trip basically takes the entire day. The main difference is that you start earlier if it's going to take 14 hours. And having a forced stop for an hour every 250-300 miles is probably something that will really improve highway safety.

I thought using the supercharger more than once per day would unnecessarily degrade the battery. I read somewhere that TM recommends not using it more than that.

Drag increases as the square of velocity, but the higher velocity requires the work to be done faster so the power increases as the cube of velocity. So, both statements are correct depending on the question you are asking.

From http://en.wikipedia.org/wiki/Drag_(physics)#Power

Note that the power needed to push an object through a fluid increases as the cube of the velocity. A car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7.5 kW) to overcome air drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW). With a doubling of speed the drag (force) quadruples per the formula. Exerting four times the force over a fixed distance produces four times as much work. At twice the speed the work (resulting in displacement over a fixed distance) is done twice as fast. Since power is the rate of doing work, four times the work done in half the time requires eight times the power.

So, power does increase with the cube of velocity.

But, I think we are measuring charge consumed per mile rather than per time period. So I think the charge consumed per mile goes up with the square of the velocity and only when you look at the time it took do you see the cubed value for the power requirement (in other words, the engine has to have cubically higher power to achieve that speed against the wind, but its consumption per mile is only quadratically higher). Or, is my math off?