What is the most efficient travel speed?

[aikisteve]

For us Europeans there is always a big question when we go on road trips and have to crosse Germany. Do we have fun on the Autobahn and drive fast, but charge more? Or is it less time consuming to drive slower and charge less? This week I took it to the test and compared driving 120 kph to 150-ish kph (wanted to do 160kph, but traffic was too heavy to allow for that)

Even though driving faster is consuming more, you don't need to charge that much longer due to lower SOC with high kW rate. Of course, the equation doesn't really add up anymore when you intend to drive 200kph for a longer time. At some point, consumption becomes too high and charging times too long.

 

[The Duke]

I believe the theoretical lowest total travel time is when your kwh for travel = kwh for charging. Good luck going that fast.

 

[csanders90D]

That formula is wrong, because it doesn't take into account the air resistance losses increasing with the square of your speed and the charge tapering as your battery gets full. The formula should be: derivative (driving kWh / time saved by speeding up) = charging kW at end of charge session. That math is messy, so here's a few numbers I came up with:

10kW: 46mph
20kW: 59mph
30kW: 67mph
40kW: 74mph
50kW: 80mph
60kW: 85mph

Remember that the charging kW is at the END of your charge session. The charging mph on the car's display is average of the whole session, and is useless for this.

 

[The Duke]

Thanks for being more thorough.

Mine DOES take into account the speed/wind resistance and even elevation changes. They all go into KWH for travel which is why I used the general term. Same for KWH charging. Charging rates vary by place, temperature and battery charge. When you repeat trips experience will teach you your KW use and charging rates. Evening out the two gives you the lowest travel time. For me on Hwy 5 to it's about 100 MPH, which I do not do. I am charging from 10 to 80%. This agrees with an extrapolation of your figures for an average of 75KW charging.

 

[csanders90D]

You missed my point about using the ending charge rate, which will be much less than 75kW. When you charge "extra" to drive faster, that "extra" energy is the slowest part to be added at the top of the battery.

As an example, when you accelerate from 99 to 100 mph, that saves you 36 seconds over 100 miles, but costs you an extra 0.95 kWh. For that to be worth while, you'd need to charge that 0.95 kWh in 36 seconds or less. 0.95 kWh / 36 seconds = 97.4 kW.

 

[scottm]

That formula is wrong, because it doesn't take into account the air resistance losses increasing with the square of your speed and the charge tapering as your battery gets full. The formula should be: derivative (driving kWh / time saved by speeding up) = charging kW at end of charge session. That math is messy, so here's a few numbers I came up with:

10kW: 46mph
20kW: 59mph
30kW: 67mph
40kW: 74mph
50kW: 80mph
60kW: 85mph

Remember that the charging kW is at the END of your charge session. The charging mph on the car's display is average of the whole session, and is useless for this.

Could you interpret this table a bit .. I'm a bit mystified, but interested.

 

[scottm]

I thought the most efficient travel speed on model S is around 27 mph.

Measure of efficiency being distance traveled for a given charge. Assume level ground, sea level, 20C, blah blah blah.

And in a more real world, keep the speed below 50 mph because that's where wind resistance starts to become a factor. Which is something you can practically eliminate as a factor simply by driving slower. Hence the dash warnings, "slow down to reach your destination".

Tesla should have completed the warning sentence, "slow down to reach your destination later, rather than never".

Oh, and a fresh coat of car wax makes your car slipperier. And pump up your tires +5psi over the normal when you're going for these efficiency test runs.

 

[csanders90D]

That table is a relationship between charging speed and driving speed, in order to get the lowest total travel time (charging + driving). So, if you only have 10kW L2 chargers available, you should drive 46mph between chargers in order to have the lowest total time. This is assuming you have enough juice to reach your next charge stop and are just deciding between "drive faster and charge more" vs "drive slow and charge less."

In practice, there are far more variables that aren't included in this formula (wind speed, elevation, bladder emptying time, etc.) so you can't plan a trip to this level of precision.

 

[cwerdna]

Model S Efficiency and Range
Roadster Efficiency and Range | Blog | Tesla Motors

 

[The Duke]

You missed my point about using the ending charge rate,

Nope, did not miss that. Did you miss my charge from 10% - 80% note?
You are correct, of course, but that is factored into the average "KWh for charging".

 

[Buster1]

@blincoln I think had a chart based on thousands of real world miles in ABRP. Most efficient for a MS was about 45 mph.

 

[blincoln]

@blincoln I think had a chart based on thousands of real world miles in ABRP. Most efficient for a MS was about 45 mph.

Yes, this post may be of interest: A Better Routeplanner (there is more info later in the thread).

 

[csanders90D]

Nope, did not miss that. Did you miss my charge from 10% - 80% note?
You are correct, of course, but that is factored into the average "KWh for charging".

Let's imagine a race, with two identical cars with 75kWh batteries. Both start at Charger A with 10% charge, and want to end up at Charger B 100 miles away with 10% charge. I plan to drive at 90 mph and will charge just enough to make that possible. You plan to drive at 100 mph and charge just enough to make that possible.

We both plug in and start charging. For this race, it doesn't matter how fast the low end of the battery charges, because our identical cars are both getting the same rate, whether that's 120kW or 10kW. Let's say both batteries hit 72% charge at 12:00 noon, and I unplug and start driving at that time.

Driving at 90 mph uses 464 Wh/mi for a total of 46.4 kWh or 62% of my battery, leaving 10% as I arrive at Charger B. Drive time is 66 min 40 sec, making my arrival 1:06:40.

Driving at 100 mph uses 535 Wh/mi for a total of 53.5 kWh or 71% of your battery, meaning you need to continue charging from 72% to 81% after I've left. You're well into the battery's taper, but I'll be generous and say you're still getting 60kW. So, charging the extra 7.1 kWh you need takes 7 min 8 sec, plus 1 hour drive time puts you in at 1:07:08.

So, driving at 100 MPH comes in slower, contradicting the "charge speed = drive speed" rule. Not only was average charge speed irrelevant (the first 71% could have been done on L2 and it wouldn't have changed the results), but even the ending charge speed (60kW = 206 mph charge) didn't match the optimal drive speed.

 

[The Duke]

Your math is correct. But your consumption figures are not what I get. You have a much larger delta between 90 and 100 MPH for battery use.
Tesla Model S P85 At 125 MPH For 12 Minutes - Video

 

[csanders90D]

I'm not sure what I'm supposed to get from that video, it's claiming 840 Wh/mi, even higher than my formula's estimate of 746. However he's also accelerating and decelerating frequently, which harms efficiency.

Going from 90 to 100 increases your aero losses by 23% (as square of speed). Rolling losses and other power (AC, etc.) are unaffected, but aero is by far the biggest power hog at these speeds. How much of a delta do you see between 90 and 100? I'd be happy to calibrate my model with more real data.

 

[The Duke]

I'm not sure what I'm supposed to get from that video.

Just an end point with real world data. I will try to get 5 mins at 90 which is easy enough, 5 mins at 100 is a lot harder.