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Theoretical maximum speed over distance in P85D and other charting hypotheticals

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randompersonx

Member
Oct 10, 2014
522
32
Orlando, FL
#1
It seems that Tesla's calculations of 285 Miles of range on the P85D are assuming an efficiency of 300WH/Mile. I have used this to estimate WH/Mile for speeds from 55 MPH -> 155MPH (top speed of vehicle).

This chart also assumes that you would only ever use 80% of the charge of the battery, the 10% is out for a safety factor and battery damage, and the top 10% is out because of slow charging and battery damage.

As far as charging locations, we are assuming that superchargers would be built at whatever spacing is necessary for these hypothetical speeds (Obviously, the case for 155MPH with 40 Mile spacing is unrealistic, but it's interesting to see the numbers anyway).

Perhaps someone on the forum already knows the answer to this, but what is the maximum sustained energy draw rate that the P85+ can handle? Has anyone maintained 1000WH/Mile for more than a few minutes? I am assuming that if you attempted the 155MPH for 40 Miles test, you would ultimately get throttled way before 40 miles due to sustained power draw limitations.

Ultimately though, this suggests that 85MPH is the ideal speed and a spacing of approximately every 130 miles is ideal (in reality, having spacing of half this number is better as it will allow for more choices -- so one every 65 miles).

Would love any commentary :)

- - - Updated - - -

optimal-p85d-speed.png
 
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#6
There's an article in Green Car Congress with fuel consumption data at high speed for several ICE cars. Most cars tested couldn't go 155 mph, but looks like fuel consumption was about 2.5 - 3.5 times higher at 155 mph than at 65 mph for a pair of BMW 5-series gasoline and diesel cars. Your P85D estimate indicates 5.7 times more energy usage at 155 mph compared to 65 mph. Does it make sense that P85D energy consumption would increase by a factor of 5.7 at 155 mph compared to 65 mph, while ICE fuel consumption would increase by only a factor of 2.5 - 3.5?
 
#7
CalDreamin said:
There's an article in Green Car Congress with fuel consumption data at high speed for several ICE cars. Most cars tested couldn't go 155 mph, but looks like fuel consumption was about 2.5 - 3.5 times higher at 155 mph than at 65 mph for a pair of BMW 5-series gasoline and diesel cars. Your P85D estimate indicates 5.7 times more energy usage at 155 mph compared to 65 mph. Does it make sense that P85D energy consumption would increase by a factor of 5.7 at 155 mph compared to 65 mph, while ICE fuel consumption would increase by only a factor of 2.5 - 3.5?
Click to expand...

I am assuming that at 65 MPH the majority of the energy is used to defeat wind resistance, and that AC, Stereo, Lighting, etc is a small % of total power usage at that speed. I am also assuming linear efficiency of the inverter/motor. Wind resistance increases with the square of speed, so since 155 is more than twice as fast as 65, yes, I would expect that much more energy.

Keep in mind that ICE cars are VERY inefficient at all speeds, and therefore their efficiency curves may do some unexpected things (like, becoming more efficient as the load becomes more difficult -- especially so for a turbocharged car)
 
#8
The proposed P85D chart indicates:
range at 65 mph is about 72% of the range at 55 mph
range at 75 mph is about 54% of the range at 55 mph

There's a blog post by Elon and JB about the range of Model S 85 as a function of speed. Eyeballing the chart:
range at 65 mph is about 84% of the range at 55 mph
range at 75 mph is about 71% of the range at 55 mph

Tesla's range calculator indicates that range at 65 mph is 85% of the range at 55 mph, which is consistent with the Elon/JB blog post.

I think the proposed P85D chart is too pessimistic about the effect of speed on range.
 
#10
richkae said:
I have an old spreadsheet that was modeled on Roadster spreadsheet available on a Tesla blog a few years ago.
My numbers are:


View attachment 62954
Click to expand...
This seems a more realistic to me. The range calculator on the Tesla website estimates 240 miles @ 70 mph on the 85 kWh battery with 19" wheels @ 70F without the heat on (thus, approximately 354 wh/mi). Granted, the actual mh/mi is truthfully lower, as you have to account for the ~10% "bricking protection charge" (76.5 kWh / 319 wh/mi = 240 miles).

Edit: The dual motor P85D configuration likely alters this math quite a bit, as the calculator hasn't been updated for the D models. However, the P85D range penalty over the P85+ is minimal (~4%).
 
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#11
randompersonx said:
I am assuming that at 65 MPH the majority of the energy is used to defeat wind resistance, and that AC, Stereo, Lighting, etc is a small % of total power usage at that speed. I am also assuming linear efficiency of the inverter/motor. Wind resistance increases with the square of speed, so since 155 is more than twice as fast as 65, yes, I would expect that much more energy.

Keep in mind that ICE cars are VERY inefficient at all speeds, and therefore their efficiency curves may do some unexpected things (like, becoming more efficient as the load becomes more difficult -- especially so for a turbocharged car)
Click to expand...
The wind resistance increases with the square of the speed, so that if you need 12 kW at 55 mph, you'll need 48 kW at 110 mph. At 110 mph, your figures suggest around 93 kW.

It seems to me like your consumption increases by the square of the energy use over distance at the given speed, or in other words, the cube of the speed. As such it's waay too pessimistic.
 
#13
Interesting stats. The Tesla is certainly not the optimum vehicle for someone who routinely drives on the unrestricted portions of the autobahn. However due to thermal limitations I doubt you could drive 155mph for any extended period of time anyway. For conditions we see in the USA, and much of the rest of the world, is a pretty good fit. For me (not an owner yet) the majority of time would not exceed 120 miles in a day, which according to this graph I could make even if going 100. But several times a year will do take vacations or visit children where trips will be 350-600 miles in one day, which is where the careful planning comes into play.
 
#14
Kbsilver said:
Interesting stats. The Tesla is certainly not the optimum vehicle for someone who routinely drives on the unrestricted portions of the autobahn. However due to thermal limitations I doubt you could drive 155mph for any extended period of time anyway. For conditions we see in the USA, and much of the rest of the world, is a pretty good fit. For me (not an owner yet) the majority of time would not exceed 120 miles in a day, which according to this graph I could make even if going 100. But several times a year will do take vacations or visit children where trips will be 350-600 miles in one day, which is where the careful planning comes into play.
Click to expand...
If there are Superchargers in reasonable places on the drive, it might not require much planning - drive for a few hours, have late breakfast/lunch, drive some more.If the stations aren't there, it's a little harder...Walter
 
#15
mgboyes said:
Your energy usage numbers are much too high for a RWD Model S let alone a D with different front and rear gear ratios. Suggest you read values from this chart and go from there (blue data is from Tesla; red extrapolated)


View attachment 62958
Click to expand...

My reading of these extrapolated numbers on this chart shows a range of 60 miles at 125, which is the same as on my spreadsheet. It does look perhaps that the low end of my chart is pessimistic (75-105), and the high end (>125MPH) might be optimistic.
 
#16
Yggdrasill said:
The wind resistance increases with the square of the speed, so that if you need 12 kW at 55 mph, you'll need 48 kW at 110 mph. At 110 mph, your figures suggest around 93 kW.

It seems to me like your consumption increases by the square of the energy use over distance at the given speed, or in other words, the cube of the speed. As such it's waay too pessimistic.
Click to expand...

There is common confusion here between energy and power. In the Tesla world, the common units for energy are Watt-hour (Wh) or kiloWatt-hour (kWh), and the common units for power are Watts (W) or kiloWatts (kW)

For pure aerodynamic drag, the aerodynamic force goes up as the square of speed. Energy is distance times force, but the power required is speed times force. From that, for aerodynamic losses, the energy to cover a particular distance (Wh/mi or Wh/km) goes up as the square of speed, but the power needed to go that speed goes up as the cube of speed.

  • Energy - Wh/mi or Wh/km goes up as speed[SUP]2[/SUP]
  • Power Required - kW goes up as speed[SUP]3[/SUP]
 
#17
Cottonwood said:
There is common confusion here between energy and power. In the Tesla world, the common units for energy are Watt-hour (Wh) or kiloWatt-hour (kWh), and the common units for power are Watts (W) or kiloWatts (kW)

For pure aerodynamic drag, the aerodynamic force goes up as the square of speed. Energy is distance times force, but the power required is speed times force. From that, for aerodynamic losses, the energy to cover a particular distance (Wh/mi or Wh/km) goes up as the square of speed, but the power needed to go that speed goes up as the cube of speed.

  • Energy - Wh/mi or Wh/km goes up as speed[SUP]2[/SUP]
  • Power Required - kW goes up as speed[SUP]3[/SUP]
Click to expand...
Aw, man! You're absolutely right. That's what I get for posting before breakfast.
 
#18
I do not have any special expertise in this topic, but I do note that the folks behind EVTripPlanner helpfully provide some charts that establish their assumptions. They include both a range calculation at various speeds and an estimated Wh/mile. I understand that a number of people have found their calculations to be accurate, but I myself am in no position to vouch for the accuracy. I did make a chart to illustrate the difference between your conclusions:

Capture.PNG
 
#19
LetsGoFast said:
I do not have any special expertise in this topic, but I do note that the folks behind EVTripPlanner helpfully provide some charts that establish their assumptions. They include both a range calculation at various speeds and an estimated Wh/mile. I understand that a number of people have found their calculations to be accurate, but I myself am in no position to vouch for the accuracy. I did make a chart to illustrate the difference between your conclusions:

View attachment 62985
Click to expand...

Thanks for that. Their estimated ranges seem to be based on 100% charge -> 0% empty, whereas mine is based on 90% charge -> 10% empty. That's a big part of the difference on the "estimated range" sheet.

On the "Estimated WH/mile" sheet, Has anyone actually tested to confirm their numbers?

Ultimately, I want to know what those numbers are, so if others have already done that work -- great :)
 
#20
There's only about 76kWh between 100% and 0% (i.e. between full and empty on the charge bar in the middle of the dashboard). The rest is reserved by Tesla for zero mile protection, anti-bricking, battery life management etc.

That's what evtripplanner's numbers will be based on.

If yours are based on 80% of the whole battery capacity of 85kWh then you're actually working with 89% of a "full range charge".
 
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