Okay, back to the original question: what is the expected range of the Nissan Leaf. We know that under EPA*4* test LA4 that it has a total range of 100 mi, assuming ideal conditions. So, I'm going to repeat some of the math I did on Facebook but not all of it, so don't be frightened.
What we know is:
Range: 100 mi @ LA4
Battery Potential Energy: 24 kWh (86.4 MegaJoules)
Tires: P205/55R16 (205mm width, 55% ratio width to height, 16" rim -> 0.31595 meters wheel+tire radius*)
Average speed of LA4: 19.6 mph**
Maximum speed of LA4: 56.7 mph
Total distance of LA4: 7.45 mi
Since we know 7.45 mi is covered in LA4 and this represents the cycle under which 100 mi is achieved, that one LA4 represents 7.45% of the total driving range of the Nissan Leaf and thus 7.45% of the battery capacity:
Total Energy Used for LA4: 1.788 093 kWh or 6,437,136 Joules
Now we know what LA4 constitutes from this: http://www.epa.gov/nvfel/methods/uddscol.txt
Specifically, we have a table that gives us the speed used in 1 second intervals.***
The question is, how can we, if possible, use that to calculate what the expected range of the Leaf is under the more realistic US06*3*, HWFET*2* or EPA75?
I think our best bet is to try and match the Leaf to the Tesla curve. The trick is, I don't know what polynomial we're trying to fit, never mind the point where the slope becomes 0. Any thoughts?
I tried calculating the Moment of Inertia for the Nissan Leaf but I now think there was a flaw in the way I summed energies. So I think curve fitting is the best bet, since we know, in general, any electric car should follow the same curve Tesla uses, with a basic scaling factor. I'm sure it's more closely related to angular acceleration, perhaps angular acceleration * the moment of inertia to get the net energy transfer. If I knew the torque required for each speed, I could work backward by calculating the power over the 1-second interval from the torque and angular velocity, which in turn would give me the energy drain (1 Watt per Second = 1 Joule of Energy).
Anyway, I hope my Moment of Inertia calculations are very wrong since I came up with 50.5 mi range under US06, never mind 60.7 for HWFET, since I need a solid 67.
Of course, if Nissan would just publish these numbers...
Any thoughts? Thanks.
* This is arrived at as follows: the 16" wheel rim diameter is halved and converted to meters to get the wheel radius: 16*0.0254/2 = 0.2032 m; add this to the tire height radius: 205mm = 0.205 m width * 55% or 0.55 = 0.11275 m. Sum the wheel radius and the tire height to get 0.31595 m total wheel-tire radius.
** Notice in the Tesla curve the optimal energy/speed ratio is around 19.6 mph!
*** The FTP, or EPA75, is LA4 + LA4[0:504], i.e. LA4 plus the first 505 seconds of LA4 repeated, which includes a second burst of 55+ mph driving in the test (the first burst peaks at second number 240 or exactly 4 minutes in). It replaces UDDS, which is the official name for LA4. EPA75 can be measured in 0.1 second intervals and therefore can give a finer grain of test data as well: http://www.epa.gov/nvfel/methods/ftp10hztable.txt
*2* HWFET or HFET is the Highway Fuel Economy [Test] Driving Schedule and also can be measured in 0.1 second intervals: http://www.epa.gov/nvfel/methods/hwy10hztable.txt
*3* US06 is known as the aggressive driving schedule, though it best matches my driving pattern because I do a lot of highway driving on my daily commute at hours where traffic is light: http://www.epa.gov/nvfel/methods/us06col.txt
*4* For all the EPA test driving suites, please visit: http://www.epa.gov/nvfel/testing/dynamometer.htm