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Every so often one encounters a myth about electric vehicles that's so odd it makes you scratch your head. When it happens just once, it's easy to dismiss, but when it keeps popping up, it becomes time to address it.
In recent weeks, I've seen multiple people assert that, “Sure, you can take EVs on road trips on major highways now, but I like to take the backroads, and there are few to no chargers on backroads. EVs can’t do backroads trips!”  Now, this obviously confused me – not simply because of the fact that it's not true that chargers exist only on major highways, but also for the obvious reason that even if you choose not to drive on a highway, surely you're going to be frequently crossing highways – quite often, near a charger.  Yet simply pointing these facts out is generally met with heavy skepticism.
In order to further expound on this, I decided to conduct an experiment. I wrote a Python script to create 50 random road trips (images at the bottom of this article) which were then simulated by A Better Route Planner, an excellent tool that takes into account a wide variety of factors to create a simulation of a drive in any of a variety of EVs, as well as to help plan routes and stops. Most critically, ABRP has an “Avoid highways” option, making it a perfect fit for this task.
Some notes about the various test factors follow (+ = beneficial to the EVs, – = adverse to the EVs, * neutral to the EVs):
  • (+) The vehicle chosen was a Model 3 LR RWD Aero, an excellent road-tripping EV.
  • (-) Upgrades to 145kW, in progress, were not considered for the (currently 120kW) V2 Superchargers, and the V3 rollout is only scheduled to begin en masse later this summer/fall.
  • (-) ABRP uses relatively conservative assumptions about energy consumption
  • (-) ABRP is extremely aggressive about keeping you off of highways when you tell it to avoid them; it'll prefer to let you almost run out of electricity or slow way, way down than spend even a moment driving on a highway.
  • (*) The routes were picked randomly within a simple bounding box across the continental United States. Some routes had to be discarded due to being impossible (such as being out to sea).
  • (-) While people frequently visit or pass through remote areas, road trips are most often done in areas where more people live (as can be seen in road traffic figures), which also tend to have a higher density of chargers. The software is however quite likely to pick trips out in the middle of bloody nowhere.
  • (*) Vehicles were chosen with a variety of ages (degradation modeled on that of the Model S, although it should be if anything lower for the 3), payload weights, road conditions, and winds (both headwinds and tailwinds).
  • (*) ABRP was instructed to not let the charge level drop below 10%.
  • (*) Stock ABRP values were used for everything not specified above, including 3 minutes of overhead (similar to gas station overhead) for every stop.  This time is subtracted from the length of a stay, since it's not time you actually spend at a given location.
  • (-) While in the real world, people road trip most during times of year when there's good weather, and often delay trips when there's bad weather, no attempt was made to emulate this; the vehicles are simulated in sometimes extremely hostile conditions.
  • (-) Tires become more efficient as they wear down. No attempt was made to account for this.
  • (+) For third-party chargers, the CHAdeMO adapter may not yield as high speeds as native CCS support; a CCS adapter is coming but not yet available (European Model 3s support CCS natively). This may yield higher speeds at US third-party stations than would actually be achieved.  Regardless, usage of third-party stations was relatively rare, and omitting or slowing them did not make a significant difference to the results.
  • (-) Some trips were long enough that they would almost certainly be done with an overnight stay.  This was not modeled. An overnight stay with charging equates to the removal of a long charging stop and part of a subsequent stop (as one charges to full overnight, unlike during a midday stop)
A spreadsheet of the data can be found here. Some graphs summing up the results can be seen below.  First, the distribution of trip lengths and trip times is as follows:

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As can be seen, most are “all-day single-day trips”, along with some partial day and two-day trips.
As for the cost per mile of these trips, not including charging before you leave or after you arrive (a 30mpg gasoline car at $3.00/gal is listed in red):

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The “exceptionally expensive” cases, while sometimes in part involving driving in particularly bad conditions (such as nearly 50mph headwinds or far-below-freezing temperatures), are most commonly due to the use of third party charging stations – particularly Volkswagen's “Electrify America” network, which costs much more than Tesla's Supercharger network.
The number of stops on the trip and the average time between stops can be seen below:

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 Recall that for long “overnight” trips where one charges full at their rest stop, a long charging stop and part of its subsequent stop should be subtracted.

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Notice that the average time between stops is surprisingly long – similar to, if not longer than, most people generally take between stops during trips in gasoline cars (one can of course take more frequent stops if they choose). Stopping is thus not an imposition, but a requirement of your need to refresh your bladder, your legs, your stomach and your mind.  Part of the reason for the long time between stops is that backroads generally have lower average speeds than major highways; this not only means that it takes longer to travel a given distance, but additionally, EVs become more efficient at lower speeds.

As for the length of the charging stops during the various trips and the percentage of the trip spent charging:

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Figures for unupgraded V2 chargers — the whole network of which will soon be getting 21% more powerful via software update. The new standard (V3) chargers are 108% more powerful than V2 (at low SoCs). The right side of the graph is for the most part higher than the left because of a combination of road trips during horrid weather conditions and/or a strict adherence to a policy of “zero highway driving”, even where this means using slow 3rd party chargers or charging to needlessly high SoCs.

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Two gasoline vehicles have been included, on presumed 1200-mile trips.  Red (left) is doing a cannonball run and only stops long enough to fill their 15-gallon tank on their 30mpg car (3 minutes overhead + 2 minutes fill time per stop), eating only snacks that they have within the car and peeing into a bottle. Orange (right) alternates between taking a 5-10 minute stretch/bathroom/fillup stop and a 30 minute meal stop every 2 1/2 hours on the road.

To see how much of a difference the upcoming V3 standard makes, here's a 2017 Model 3 charging on a V3 charger:

2% – 10 miles – 0 mins (126 kW)
5% – 16 miles – 1 min (250 kW)
20% – 62 miles – 4 mins (250 kW)
21% – 65 miles – 4.5 mins (Taper from peak starts – 248 kW)
30% – 92 miles – 6 mins (218 kW)
40% – 123 miles – 8.5 mins (179 kW)
50% – 153 miles – 11 mins (142 kW)
60% – 184 miles – 14.5 mins (108 kW)
70% – 213 miles – 19 mins (87 kW)
80% – 245 miles – 24.5 mins (56 kW)
90% – 275 miles – 34 mins (36 kW)
This would be expected to cut typical charge times in the simulated trips to 50-70% of what’s listed. 
Let's examine our results. First, let us look at the two worst cases. Because unfortunately for us, the program decided to do two routes from eastern North Dakota to eastern Montana – which just happens to be the only place in the continental US with a large hole in the Supercharger network. As a result, the software is forced to make awkward detours to the south, increasing trip times. Additionally, ABRP's strict adherence to “no highway” policies becomes far worse here, causing it to require significant slowdowns and/or lower arrival charge levels (red segments). Waypoint hints even had to be given to ABRP to help it find said routes.
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Attempting to go from rural North Dakota to middle-of-nowhere Montana, this route fell into the only major Supercharger gap left in the United States (North Dakota to eastern Montana). In its attempts to stay off the interstate (e.g. avoiding the Supercharger in Billings and the one southwest of Pierre), it‘s twice forced to reduce speed to 44mph and to arrive at a lower-than-desired state of charge.

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A good-weather trip from eastern North Dakota to eastern Montana. Also falling into the “North Dakota Gap”, the path had to be routed on a circuitous route that significantly lengthened the total trip time.
These two cases – applicable only to the “North Dakota Hole” – should indeed be considered failures for the task at hand, and if anybody plans to frequent the backroads of North Dakota and Montana in the present day, this becomes a legitimate argument against doing so in a BEV.  That said, charging network growth rates are tremendous – the number of Superchargers has roughly doubled in the past two years, while the Electrify America network didn't even exist two years ago – and this hole will likely be plugged soon enough.
There are a couple cases elsewhere where ABRP's strict adherence to a “no highways, even for a moment” policy led to “red line” slowdown situations:

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From the mountains east of Phoenix to east of Monterrey, Mexico in a 7-year-old vehicle. ABRP‘s insistence on keeping on mountainous backroads and away from charger-rich I-10 requires a slowdown from ~55mph to ~44mph on that leg.

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A cold winter trip from west of Wichita, KS to east of Bloomington, IL. A slowdown is required in order to avoid interstate driving (e.g. avoiding the multiple chargers in Wichita, Salina, and Topeka); under less frigid conditions, it would not have been required. 

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A cold winter trip from northwestern Oklahoma deep into the Colorado Rockies. Due to the very low temperatures and avoidance of interstates, a slowdown is needed for one leg. Most of the charging cost is due to one of the charging stops being a VW „Electrify America“ charger.

Additionally, there were two cases where ABRP reported a nominal “slowdown”, yet the speed they reported was basically the same speed that Google reports as normal for said route. Consequently, these – while “redlined” – should probably not be considered slowdowns.

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A winter drive from north-central Oregon to north of Kings Canyon in California, in an old vehicle. ABRP reports a slowdown, yet the speed that they report is faster than what Google reports as the expected speed for that road.

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A mid-summer drive in a moderately-old vehicle from southwest Wyoming to the deserts of northern Mexico. A „slowdown“ is reported from Albuquerque, NM to El Paso, TX, but it‘s only 2mph slower than what Google reports for that route. 
In all of these cases, allowing highway travel for just part of the trip (sometimes just a dozen miles or so) makes the red-line go away.
While one may expect that trying to avoid all highways would lead to frequent detours and backtracking to get to charging stations, this turned out not to be the case – indeed, in only three situations did this happen, 6-10 miles each time. One was one of the North Dakota trips, while the other two were:

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A winter drive from the northern California coast to northwest of Denver with a passenger or two and a moderate tailwind. A brief side detour is made at Price, UT.

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A winter drive into a fierce headwind from central Washington to southeastern Oregon. The very high wind-driven consumption combines with two stops at expensive VW „Electrify America“ chargers to yield a very high power bill. 

This honestly should not be unfamiliar to people driving gasoline cars in remote areas.

In every single other case – regardless of how awful the driving conditions were or where the trip was – there was neither red-lining slowdowns nor any backtracking detours at all.  All remaining valid cases follow (read: prepare to scroll down! Summary follows)

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A spring/fall day in good weather from Lake Michigan to northwest of Denver with a fully-loaded car.  

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An early-summer drive from the Mississippi Delta to Cleveland with a significant headwind. Over 70% of the electricity bill is at VW‘s „Electrify America“ stations, for less than 40% of the mileage. 

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Southeast Missouri to coastal South Carolina in a heavy spring/fall rainstorm with a passenger or two.

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A spring drive from inland northern California to near Santa Barbara in a heavy rainstorm.

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A spring-fall trip from eastern Oklahoma to the Texas panhandle in a 1-year-old vehicle. A strong tailwind makes the trip a breeze without any charging.

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A summer trip from Morehead City to northeast Richmond with a passenger; no charging needed.

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A winter trip from Lafayette to north of Abilene.

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A late-winter trip from Baton Rouge to the Texas Panhandle in a fairly old vehicle.

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Winter drive from Sudbury, Canada to south of Madison, WI in a 7-year old vehicle with a passenger or two and a moderate tailwind. A short ferry ride is involved (price not included).

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A spring/fall drive from Evansville, IN to Shreveport, LA with a passenger in an old vehicle. Charging would be much cheaper except that a VW „Electrify America“ charger was used in lieu of a Tesla Supercharger in order to stay off the interstate.

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An early spring/late fall drive from northeastern Iowa to northwestern Arkansas with a passenger or two, rainy weather, and light to moderate headwinds.

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A late winter drive from eastern Washington to Yuma, AZ in a full, old car, through rainy weather, with a moderate to strong tailwind.

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A spring/fall drive with a passenger or two from Toronto to northwest of Grand Forks, in a 10-year-old vehicle. Two ferry rides are involved, incl. one across Lake Michigan (ferry prices not included).

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A Groundhog‘s Day drive from Puxatawney, PA to southern Georgia, in an old car with a passenger, in cold but otherwise good weather. Half the charging cost comes from the one VW „Electrify America“ stop.

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A good-weather drive from Chesapeake Bay to Brunswick, GA. Charging is expensive because both stops are at VW‘s „Electrify America“ chargers.

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A spring/fall drive from east of Lubbock, TX to near Brownsville, with a moderate headwind.

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A winter drive from northwest of Austin, TX to the Mississippi Delta southeast of New Orleans, with a light to moderate tailwind, rain, and a full vehicle. The Mississippi is crossed via ferry at one point (cost not included).

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A spring/fall trip from western Ohio to east of Sudbury, Ontario, on a rainy day and in an old vehicle. A short ferry ride is involved (cost not included).

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A cold midwinter drive from southern Missouri to north of Minneapolis, with a light to moderate headwind in an old vehicle. The temperatures (averaging -10°F) lead to the high consumption and thus more frequent stops.

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An early spring/late fall trip from east of Detroit to east of Wichita, KS with a moderate tailwind and a fairly old vehicle. The price does not reflect the low consumption due to two Electrify America stops.

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A trip from south-central Iowa to western Kansas on a good winter‘s day.

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A spring/fall trip from Matomoros, Mexico to the Louisiana Delta, with a heavy headwind. A single stop at a VW „Electrify America“ charger makes up most of the trip cost.

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A winter trip from South Dakota to northeast Minnesota. In order to avoid interstates, a fairly long stop is made at a slower charger at the University of Minnesota – Morris.

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A spring/fall trip from New Hampshire to the North Carolina coast, with a light to moderate headwind and a moderately old vehicle.

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A spring/fall trip from northern Mexico to central New Mexico with a fairly heavily loaded, fairly old vehicle.

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A spring/fall trip from the Santa Barabara coast to northwest of San Francisco, with a moderately strong tailwind and an old vehicle. The fact that the trip was actually instructed to travel across the Pacific ocean apparently didn’t bother ABRP  ;).

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A winter trip from upstate Maine to west of Ottawa, in a heavy snowstorm.

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An abnormally cold midwinter trip from Jacksonville, FL to the western Appalachians in a 10-year-old vehicle.

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A nice-weather drive from west of Portland, OR to northwest of Boise, ID, with a light to moderate tailwind and a fairly heavily loaded vehicle.

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A spring/fall drive with a mild to moderate tailwind from Cape Canaveral to the Mississippi Delta, in a fairly old vehicle.

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A rainy summer drive from east of Savannah to north of Little Rock with a fairly heavily loaded vehicle.

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A cold winter drive from southwest of Albuquerque to northeastern Utah with a mild tailwind.

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A mild winter drive (from Beaver Island in Lake Michigan, via ferry) to north of Minneapolis.
What can we take away from this?  In summary:
  • Excepting the “North Dakota Hole“, which will surely be closed very early in the lifespan of any EV purchased today, a “good road tripping EV” can easily manage backwoods trips between arbitrary points in the continental United States – regardless of the road and weather conditions, payload, and even accounting for battery degradation in older vehicles.  In rare cases one might need to take a leg or two on a highway, but these are edge cases, and far from the general rule.
  • It's almost impossible to drive for long distances without crossing a major highway unless you're driving in circles.
  • EVs frequently travel further on backroads than they do on highways, with less frequent stops required.
  • Electrify America really needs to lower their prices. The stark difference between Supercharger and Electrify America pricing really stood out in this comparison.
  • Extreme-cold temperatures, and particularly gale-force headwinds, will ruin your energy consumption – but even that had little impact on the overall ability of EVs to make comfortable road trips on backwoods roads with today's infrastructure – let alone tomorrow's.