The Rivers Models: Moar (Batteries)


Good lord, is it March already?  The CBR project took a huge hit, when, just as I was ready to pull the trigger on one of two decent deals on CraigsList, we got hit by a ginormous amount of snow (and how is it that “ginormous” isn’t getting picked up by my smellcheck.  Is it really a word?)  … and my trailer got totally buried (by “totally buried” I mean under literally 4 FEET of snowbank) and put me off for a few days.  By the time I was ready to do the deal, the bikes were pulled off the CL.  Both of them were on for a long time – it’s entirely possible the sellers just gave up with the Big Snow, so I’m still hopeful…  but delayed.

In the meantime, mad genius Andrew Rivers has been hard at work putting the rest of his modeling program together.  Here’s what he sent me – and do us both a favor.  Contact him here if you want to use this stuff. He’s put a crap-ton of personal time into it.  Start with the pdf of the work here: Battery Tests

All of these calculations are done as consistently as I currently know how to do them. Some of the packs required more assumptions than others due to the information I have available, but I always note when there is one that will effect performance.

I will break this down on a pack by pack basis.

———-General Notes———-

With the exception of the Volt pack, all of the mass and volume calculations do NOT account for the enclosure.

All of the Resistance values are for the loaded packs, not under C/3, so they should be more accurate than a static test as they account for temperature rise.

Full load capacity is based on both voltage sag and the approximate Peukert losses based on the discharge curves.

The same general techniques I previously sent still hold.


This is the highest capacity pack tested, at nearly 15kwh. The 380v peak and ~10kwh minimum are not conducive for this particular cell. Removing a parallel string brings the capacity down too far and reducing the number of series cells lowers the power output below the requirements.

Resistance was calculated from high discharge tests and compared with the A123 design guide.

The lower cutoff voltage and low IR both contribute to the higher EOC power relative to the other packs. The cell is operable over a 1.6v range, from 3.6-2v, which is 39.1% larger than other lithium cells with the more typical 1.15v range from 4.15-3v.


NOTE: The simulation I did for the EMRAX was based on a 91s2p pack not the 91s1p tested here. The results are still fine, it is just that this is the one that will actually fit in the bike (aka I forgot to check that when I was doing all the motor side stuff).

The resistance is based on the 30sec pulsed discharge test from the INL.

The voltage curve from 4.15-3v is based on the Hybridautocenter plots.

The LEAF allows a minimum voltage of 2.5v/cell. I previously calculated it to be 2.7v/cell but have adjusted the program appropriately for the 2.5v minimum under load.

This pack is actually pushed very hard relative to what it experiences in a LEAF. INL tests show the peak power of the pack at 0% SOC being between ~95-150KW. With 192 cells in the complete pack, this equates to 495-781W per cell.The ~240A peak draw in the leaf equates to just 3.7C peak. The CBRe is pushing similar power levels but with less than half the cells, thus the voltage sag is much higher and performance suffers.

———-RC lipo———-

The low EOC power is due to several factors. First the sag threshold is the same as the no-load LVC unlike the other cells. Also the resistance of lithium cells increases near exponentially near the end of the discharge while at the same time the voltage is dropping exponentially from the “lipo-cliff”. However this is more or less irrelevant due to full power being available for ~99% of the SOC.

Resistance was calculated from high discharge tests.

The resistance is easily the lowest of the group. Though the single cell resistance is similar to that of a single A123 cell, the 6p strings effectively drop the resistance by a factor of 3 relative to the 2p A123 strings.

In terms of both specific and volumetric power density, the RC lipo is well above the others.

The main disadvantage of this pack is the large number of connections involved. While the other packs use between 91 and 210 cells, the RC lipo requires 546 cells to achieve similar capacity. This will effectively increase the resistance of the battery on a much larger scale than the others. Thus its performance will not be as stellar relative to the others once it is assembled as the table indicates it to be.

I could assume some constant resistance per connection but that involves a lot of other consequential assumptions such as: the wire gauge is the same for all the packs, the wire length is the same for all the packs, the wires are all carrying the same amount of current (i.e. thermal conditions), and that the termination methods for the packs are all the same in terms of surface area, mechanical clamping and heat dissipation etc… So I decided against it.


The resistance is based on the 30sec pulsed discharge test from the INL.

The voltage curve from 4.15-3v is also based on INL data.

Minimum voltage on these cells is always reported as 3v/cell. However this is just the cutoff for the Volt. To be safe, I made the loaded voltage 2.7v/cell. From what I have read and calculated, this is about right but on the high side just in case.

Unfortunately there are no multiple C rate discharge tests publicly available, so the INL tests were the basis for all of the calculations. The BOC resistance was assumed to be the same as the 90% SOC value as the INL tests begin at 90% and end at 10% SOC. The EOC resistance was selected such that it continued the exponential curve begun by the INL data.

Because I have not found measurements of individual cells, both the mass and volume account for the cell frames supplied with the vehicle.

Here are the supporting charts.  Click on any of them to get the full-res:


Volt cells sag


Volt cells resistance


Volt cells power


RC lipo sag


RC lipo resistance


RC lipo power


Leaf cells resistance


Leaf cells power


A123 cells sag


A123 cells resistance


A123 cells power


Leaf cells sag



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