# the effects of Cd, speed, temperature on range



## ModFather (Apr 3, 2016)

Here is a post on a different forum that I find fascinating (since I am the type who is fascinated by statics and analytical validation)
*********

I've been wondering just how much the extremely low goal of Cd=0.21 (drag coefficient) for M3 was going to make, especially when compared to, say, the Chevy Bolt. I found a great start on figuring it out here:
Chevy Bolt EV Range
I used this to calculate ranges at different Cd to see how much difference would it make since the Bolt has a terrible Cd of 0.31, particularly at speed. The result from my calculation is quite intriguing! The article mentioned above is geared mostly towards higher speed results, so the formula results are not that accurate at low speeds, but I was interested to know the effects of Cd, which really only come into play above say 35 mph. The formulas result in the Bolt getting 238mi at constant 65mph. If I ONLY change the Cd and put the M3 value of .21 the range at constant 65 mph goes to 306mi. So, while the Bolt may have lower resistance tires and a more efficient motor, the M3 should be able to cruise on the freeway with significantly reduced aerodrag. This is just to show the impact, not to say the same numbers will apply to the M3.








****************
Although the chart above is difficult to read, in essence the more efficient Cd of the model 3 compared to the Cd of the Bolt should give approximately 25% increase in range at 60/65mph given all other factors are equal.

If you click on the link in red above, it opens the page to some technical data that show the effects of speed and temperature on EV range. It even includes some references to the MS. I will let the mathematicians on this Forum speak to the veracity of the calculations, but if true, the results are eye opening.


----------



## John (Apr 16, 2016)

Did you factor in the fact that the frontal area of the cars is different?
Drag force = Cd x Area x (air density and constants) x velocity squared

So when you hear that car has a "low Cd," you should immediately wonder what its frontal area to go along with that is. A car with a very low Cd but a huge frontal area won't get as many miles from a certain size battery and motor as one that is substantially smaller.

Model 3 actually wins on both, so it's a double-whammy.

Bolt: 164″ L x 70″ W x 63″ H (max rectangular frontal area for comparison roughly = 4410 in2)
Model 3 (est) : 184.1 x 74.2 x 56.5 in (4192 in2)

Bolt factor: 4410 * .31 = 1367
Model 3 factor: 4192 * .21 = 880

So for the same battery size and motor efficiency and speed, Model 3 would go 1367/880 = over 1.5x as far.


----------



## EVfusion (Mar 10, 2017)

John said:


> Did you factor in the fact that the frontal area of the cars is different?


 Thanks for your post, John - very informative.
Weight also needs to be factored in - don't know how the Bolt and M3 compare. But once drag, frontal area and weight are all factored in, I expect the Model 3 will deliver some impressive range numbers. Can't wait to know what they actually are.


----------



## ModFather (Apr 3, 2016)

John said:


> Did you factor in the fact that the frontal area of the cars is different?


Just to be clear John, these are not my calculations, someone else did them. I recommend that you click on the link in red to see the mathematical methodology. With your talent in math, I think you can define the numbers better than I can. And please share with us your opinion of the results.


----------



## mkg3 (May 25, 2017)

John said:


> ......
> Bolt: 164″ L x 70″ W x 63″ H (max rectangular frontal area for comparison roughly = 4410 in2)
> Model 3 (est) : 184.1 x 74.2 x 56.5 in (4192 in2)
> 
> ...


What you've shown is the difference in drag force and not range. The calculation is correct, assuming that the input values for both vehicles are right and the air density drops out, if one assumes the same condition. The simplified comparison, however, does not directly equates to distance.

As you know, there are more variables, such as rolling resistance (different tire and wheel sizes, friction coefficient of tires), and mass/weight of the vehicle plays a big factors in determining the range, given any particular velocity.

It is clear, however, that the drag force will less for Model 3, assuming that the CDs compared both have induced and skin friction drag components. (induced drag force will be much less than Bolt, but skin friction drag probably will be higher for Model 3 as it will likely have greater wetted area.)

I do find the claim bit aggressive to obtain CD=0.21 (but it is Tesla so would expect nothing less). Looking at the CD for Model S at 0.24, to get lower than that is a significant challenge, given Model 3's lower fineness ratio (length/height).


----------



## John (Apr 16, 2016)

I think the cars are probably fairly similar in weight, and so assuming they use the same tires, the rolling resistance will be pretty similar. I don't know the weight of Model 3 (the Bolt is 3,580 lbs; Model S starts a 4,469, so 80% of that would be the same as Bolt's weight).

Even if there was a weight difference, the relationship between weight and rolling resistance is milder than you'd think (in other words, if the weight increases by 20%, the rolling resistance increases to a lesser degree.








Source: http://bit.ly/2swvW4L


----------



## John (Apr 16, 2016)

It would be interesting if the ~300 mile range car spotted in San Mateo yesterday was just a 60 kWh model...
But it's hard to believe that they would estimate 215 miles for the base model and be that far off.
So I suspect it was the larger battery model, and that although the small battery Model 3 could go 300 miles at 45mph, it only goes ~215-240 miles EPA.


----------



## mkg3 (May 25, 2017)

John said:


> I think the cars are probably fairly similar in weight, and so assuming they use the same tires, the rolling resistance will be pretty similar. I don't know the weight of Model 3 (the Bolt is 3,580 lbs; Model S starts a 4,469, so 80% of that would be the same as Bolt's weight).
> 
> Even if there was a weight difference, the relationship between weight and rolling resistance is milder than you'd think (in other words, if the weight increases by 20%, the rolling resistance increases to a lesser degree.....


You've missed my point. Rolling resistance was a simply an example of other factors that determines range. There are plenty of others that I did not list. I'm sure you know, such as final drive, electronic controller, SW for current management and so on. Not intended to be a complete list.

The only point is to say that to directly apply less drag X % = X % more range. Its not directly applicable.


----------



## John (Apr 16, 2016)

The importance of all of those "back of the envelope" calculations faded for me a bit when we saw the first indication of ACTUAL range from the display spotting in San Mateo, which seemed to indicate ~310 miles of range in the big battery version.


----------



## ModFather (Apr 3, 2016)

mkg3 said:


> The only point is to say that to directly apply less drag X % = X % more range. Its not directly applicable.


I think the original point was that less drag equals more range if all other factors are the same but may not correlate directly in this specific case between the Bolt and TM3 because of the variables you so rightly point out.


----------

