Content Comparison

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However, now that energy will not be dropping, I think keeping weight as low as we relatively can is actually an important factor to consider. MS15’s battery cells already had the most minimal gravimetric and volumetric energy density that we possibly could have had with commercially widely available options (5Ah, 21700 form factor). So weight-wise, our greatest room for improvement lies in the overhead weight added from the rest of the battery system instead of the battery cells.

Comparing P45B and 50S

In our entire electrical system, power inputted into the system is equal to the power used by the system, this is true by the law of conservation of energy.

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The electrical system gets power from the batteries, solar array, and regen braking. Those powers inputted into the system are consumed by the motors, PCBs, losses, and probably some other things. This is probably a big simplification but it probably covers most of the power consumed (with the rest being negligible here).

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Solar power is the only power we are able to get externally. Battery power is limited, we start with full SOC but the only way to get new energy in is from solar. So the value of battery power tells us the net power of the car (the battery makes up for whatever power the solar can’t). If the battery is providing power we know we are running energy negative, if the battery is gaining power we know we are running energy positive, and if the battery is neither providing nor gaining energy we know we are running energy neutral.

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Since I am interested in comparing the battery power consumption for different p-counts, I am interested in ΔPbat. For the purpose of comparing different parallel configurations, the only values that will make a difference should be power consumed by motors and power loss from pack internal resistance. I will assume solar, regen, PCB power consumption, and all other power loss aren’t dependent on parallel count (I’m going to assume no difference in cooling for now since trying to find actual amount of cooling needed is too tricky to do without doing testing). Based on this assumption, when calculating ΔPbat, Psolar, Ppcb, Plosses (that aren’t IR losses) and Pregen would all be cancelled out.

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This being the case, I’ll still try to include the main power consumers that I can easily find values for so that Pbat is still somewhat in the correct ballpark:

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Power consumed by the motor can be represented using all the power our car needs to overcome to move (acceleration, drag, rolling resistance, gravity when on a gradient). I will also assume a 90% efficiency as a constant.

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For power loss from internal resistance, the power loss can written using P=I^2R.

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Using KCL, we can write

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And then we can further write

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Each component of motor power are

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Plugging all of them in, we get

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These are the main equations I will use to calculate battery power consumption, battery heat production, battery energy consumption, and total heat generation.

How much Heat Generation is Acceptable?

A lot of teams ran a passive pack with no cooling during WSC. Ideally we would also do the same for MS16, but it’s not an option due to reg change forcing some form of forced air cooling on all battery packs (and it must be turned on whenever the pack is connected). However, this doesn’t stop us from having a pack that is functionally passive for all intents and purposes, with “fans” playing an unimportant role for cooling.

Air cooling is pretty complicated in that it is not easy to make cooling uniform for all cells. Based on those two factors, I think we should (in-principle) aim for a p-count that allows us some weight savings (since we’ll have to have fans and ducts anyway, we don’t get to reduce design complexity by running no cooling) while also aiming for a p-count that generates very little heating such that we don’t have to worry about serious module hotspots complicating our design or bottlenecking our driving later on.

So first I’m going to try to figure out what the point of diminishing returns is for increasing p-count (at what point are we adding p-count without actually increasing thermal safety?

Ideally we would have power draw data for the whole 7 day race, but we don’t. And we didn’t have telemetry to log our FSGP current profile. So I’ll try to do some sort of simple model with some big assumptions.

The equation for heat production in Watts from IR loss is

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A typical tour day is 9 hours, from 9am to 6pm. I will take Psolar from a calculator for solar insolation that I found online from UNM’s website. I’ll use data for the coordinates of Nashville as a constant for solar insolation. Based on this website, the more South-West we move in the states, we should be getting more sunlight throughout the race week. So my Psolar value should be more conservative than what we actually get.

Here is the matlab script I will run for heat generation and power consumption when considering the whole race (scenario 1):

Here is the matlab script I will run for considering short term high power scenarios (scenario 2):

50S vs P45B Scenario 1

The first scenario I will consider will be a 36S8P configuration based on the specs of the Samsung INR21700-50S cell (max charging temp of 50 deg C). I will also assume this configuration will give a total car mass of 296kg. I am assuming that the P45B configuration will have no problem helping us reach our target 300kg total car mass, and that the difference in weight between the two battery packs will be 3.5kg (2kg for battery difference, 2kg for overhead weight, I think this should be reasonable…).

The datasheet for the 50S is a little rough because it gives a lot of different numbers for max charge temp and talks about “re-charge release” and “discharge release” (I’m not able to confirm what they actually mean, Samsung never responded to my emails), I am going with 50 deg C because if you scroll down to “Pack Design Guidelines” Samsung says to not exceed 50 deg C charge temperature range and 80 deg C discharge temperature range. I think it’s better to err on the safer side and go with 50C. This also matches the max charge temp for 50G, which is a higher cycle count cell that has a lower discharge rate. 50S has a higher discharge temperature cutoff of 80 deg C vs. the 50G’s 60 deg C cutoff which makes sense since the 50S is designed for power tools and the 50G seems more designed for e-mobility, appliances, EVs, and things that don’t need as much power density. Power cells probably don’t absolutely need to have a high charge operating temp since the actual heavy power draw would be when it’s discharging, so I think it checks out.

This pack should run the hottest since it has the lowest parallel count. I will assume the car runs at a constant speed of 80km/h and with constant solar.

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The total heat generated by finding the area under the curve of the graph is 4.52Wh, which is equal to 0.97 deg C rise in temperature using Q=mCT.

This seems quite good, and I think it shows that we can run 36S8P without any huge cooling concern to be honest.

Doing the same script with modified variables for P45B (36S9P, 0.09mOhm DCIR per cell, 300kg total car mass), the heat generated using area under the curve is 2.63Wh, which translates to 0.50 deg C. The temperature rise was cut by roughly half compared to the 50S.

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50S vs P45B Scenario 2

For Scenario 2 I will consider a 15% grade uphill scenario at 34.2km/h (9.5m/s) with no solar because this seems like a plausible scenario and since it also requires almost ~5000W, which is the maximum power that the motor can take.

First for the 50S:

Here is the first scenario for 5 minutes at nominal cell voltage

Enter time in minutes5
Total Mass: 296
Acceleration: 0
Velocity: 9.5
Grade: 0.15
Voltage: 129.6
Cell DCIR: 0.014
Parallel Count 8
Form Factor: 21700
Heat Energy Generated: 7.2539 Wh
Total Race Temperature Rise: 1.5606 deg C
Battery Power Consumed: 4904.4201 W
Total Battery Power Consumed: 408.7017 Wh
Current: 37.8427 A

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How much Heat Generation is Acceptable?

A lot of teams ran a passive pack with no cooling during WSC. Ideally we would also do the same for MS16, but it’s not an option due to reg change forcing some form of forced air cooling on all battery packs (and it must be turned on whenever the pack is connected). However, this doesn’t stop us from having a pack that is functionally passive for all intents and purposes, with “fans” playing an unimportant role for cooling.

Air cooling is pretty complicated in that it is not easy to make cooling uniform for all cells. Based on those two factors, I think we should (in-principle) aim for a p-count that allows us some weight savings (since we’ll have to have fans and ducts anyway, we don’t get to reduce design complexity by running no cooling) while also aiming for a p-count that generates very little heating such that we don’t have to worry about serious module hotspots complicating our design or bottlenecking our driving later on.

So first I’m going to try to figure out what the point of diminishing returns is for increasing p-count (at what point are we adding p-count without actually increasing thermal safety?

Ideally we would have power draw data for the whole 7 day race, but we don’t. And we didn’t have telemetry to log our FSGP current profile. So I’ll try to do some sort of simple model with some big assumptions.

The equation for heat production in Watts from IR loss is P = I^2R, but if I make it a function of bunch of things like car speed, mass, gradient, etc, then it comes out like this. I took the Voltage part out cause it looked neater like this and also cancelled out with some things.

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A typical tour day is 9 hours, from 9am to 6pm. I will take Psolar from a calculator for solar insolation that I found online from UNM’s website. I’ll use data for the coordinates of Nashville as a constant for solar insolation. Based on this website, the more South-West we move in the states, we should be getting more sunlight throughout the race week. So my Psolar value should be more conservative than what we actually get.

Here is the matlab script I will run for heat generation and power consumption when considering the whole race (scenario 1):

Here is the matlab script I will run for considering short term high power scenarios (scenario 2):

50S vs P45B Scenario 1

The first scenario I will consider will be a 36S8P configuration based on the specs of the Samsung INR21700-50S cell (max charging temp of 50 deg C). I will also assume this configuration will give a total car mass of 296kg. I am assuming that the P45B configuration will have no problem helping us reach our target 300kg total car mass, and that the difference in weight between the two battery packs will be 3.5kg (2kg for battery difference, 2kg for overhead weight, I think this should be reasonable…).

The datasheet for the 50S is a little rough because it gives a lot of different numbers for max charge temp and talks about “re-charge release” and “discharge release” (I’m not able to confirm what they actually mean, Samsung never responded to my emails), I am going with 50 deg C because if you scroll down to “Pack Design Guidelines” Samsung says to not exceed 50 deg C charge temperature range and 80 deg C discharge temperature range. I think it’s better to err on the safer side and go with 50C.

This pack should run the hottest since it has the lowest parallel count. I will assume the car runs at a constant speed of 80km/h and with constant solar.

...

The total heat generated by finding the area under the curve of the graph is 4.52Wh, which is equal to 0.97 deg C rise in temperature using Q=mCT.

This seems quite good, and I think it shows that we can run 36S8P without any huge cooling concern to be honest.

Doing the same script with modified variables for P45B (36S9P, 0.09mOhm DCIR per cell, 300kg total car mass), the heat generated using area under the curve is 2.63Wh, which translates to 0.50 deg C. The temperature rise was cut by roughly half compared to the 50S.

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The difference in power consumption in Scenario is shown below.

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I did an actual comparison of the two arrays by just running the script two times, saving one of the arrays in a separate variable, and then subtracting the two arrays for the difference:

ans =

Columns 1 through 10

4.8328    4.9403    5.0306    5.1052    5.1656    5.2133    5.2500    5.2775    5.2971    5.3105

Columns 11 through 20

5.3192    5.3242    5.3269    5.3281    5.3284    5.3285    5.3285    5.3285    5.3281    5.3271

Columns 21 through 30

5.3246    5.3197    5.3114    5.2985    5.2794    5.2527    5.2168    5.1701    5.1108    5.0375

Columns 31 through 37

4.9486    4.8426    4.7182    4.5744    4.4103    4.2254    4.0192

So it seems like the 50S configuration would save 5.3W of power at most under Scenario 1 compared to P45B. 5.3W is like 1.5X a Noctua IPPC 3000 fan at max power….

50S vs P45B Scenario 2

For Scenario 2 I will consider a 15% grade uphill scenario at 34.2km/h (9.5m/s) with no solar because this seems like a plausible worst case scenario and since it also requires almost ~5000W, which is the maximum power that the motor can take.

First for the 50S:

Here is the first scenario for 5 minutes at nominal cell voltage

Enter time in minutes10minutes5
Total Mass: 296
Acceleration: 0
Velocity: 9.5
Grade: 0.15
Voltage: 129.6
Cell DCIR: 0.014
Parallel Count 8
Form Factor: 21700
Heat Energy Generated: 147.50772539 Wh
Total Race Temperature Rise: 31.12135606 deg C
Battery Power Consumed: 4904.4201 W
Total Battery Power Consumed: 817408.40337017 Wh
Current: 37.8427 A

Here is a another scenario for 5 10 minutes at 3.0 nominal cell voltage

Enter time in minutes5minutes10
Total Mass: 296
Acceleration: 0
Velocity: 9.5
Grade: 0.15
Voltage: 108129.6
Cell DCIR: 0.014
Parallel Count 8
Form Factor: 21700
Heat Energy Generated: 1014.44565077 Wh
Total Race Temperature Rise: 23.24731213 deg C
Battery Power Consumed: 49424904.72054201 W
Total Battery Power Consumed: 411817.89344033 Wh
Current: 4537.76598427 A

Here is a scenario for 10 5 minutes at 3.0 cell voltage

Enter time in minutes10minutes5
Total Mass: 296
Acceleration: 0
Velocity: 9.5
Grade: 0.15
Voltage: 108
Cell DCIR: 0.014
Parallel Count 8
Form Factor: 21700
Heat Energy Generated: 2010.89124456 Wh
Total Race Temperature Rise: 42.49472473 deg C
Battery Power Consumed: 4942.7205 W
Total Battery Power Consumed: 823411.78688934 Wh
Current: 45.7659 A

Next for the P45B:

Here is a scenario for 5 10 minutes at 3.6 0 cell voltage

Enter time in minutes5minutes10
Total Mass: 300296
Acceleration: 0
Velocity: 9.5
Grade: 0.15
Voltage: 129.6108
Cell DCIR: 0.009014
Parallel Count 98
Form Factor: 21700
Heat Energy Generated: 420.25548912 Wh
Total Race Temperature Rise: 04.813814947 deg C
Battery Power Consumed: 49324942.1347205 W
Total Battery Power Consumed: 411823.01127868 Wh
Current: 3845.05667659 A

Next for the P45B:

Here is a scenario for 10 5 minutes at 3.6 cell voltage

Enter time in minutes10minutes5
Total Mass: 300
Acceleration: 0
Velocity: 9.5
Grade: 0.15
Voltage: 129.6
Cell DCIR: 0.009
Parallel Count 9
Form Factor: 21700
Heat Energy Generated: 84.51082554 Wh
Total Race Temperature Rise: 10.627681381 deg C
Battery Power Consumed: 4932.134 W
Total Battery Power Consumed: 822411.02230112 Wh
Current: 38.0566 A

Here is a scenario for 5 10 minutes at 3.0 6 cell voltage

Enter time in minutes5minutes10
Total Mass: 300
Acceleration: 0
Velocity: 9.5
Grade: 0.15
Voltage: 108129.6
Cell DCIR: 0.009
Parallel Count 9
Form Factor: 21700
Heat Energy Generated: 68.12785108 Wh
Total Race Temperature Rise: 1.17196276 deg C
Battery Power Consumed: 49544932.6025134 W
Total Battery Power Consumed: 412822.88350223 Wh
Current: 4538.87590566 A

Here is a scenario for 10 5 minutes at 3.0 cell voltage

Enter time in minutes10minutes5
Total Mass: 300
Acceleration: 0
Velocity: 9.5
Grade: 0.15
Voltage: 108
Cell DCIR: 0.009
Parallel Count 9
Form Factor: 21700
Heat Energy Generated: 126.25561278 Wh
Total Race Temperature Rise: 21.34381719 deg C
Battery Power Consumed: 4954.6025 W
Total Battery Power Consumed: 825412.76718835 Wh
Current: 45.8759 A

Here is the battery power consumption difference between the two packs for each scenario:

3.6 cell voltage (nominal voltage)

Battery Power Consumption Difference: 4932.134W - 4904.4201W = 27.7139W

3.0 cell voltage

Battery Power Consumption Difference: 4954.6025W - 4942.7205W = 11.882W

Summary

Going with a P45B pack seems to have a very clear advantage over the 50S when it comes to high current thermal performance. But we aren’t likely going to be dealing with a lot of high current scenarios during race, and Scenario 1 results seem to show that a 50S pack will operate perfectly fine with only a ~1 deg C temperature rise. Even if we consider short transient scenarios where a high current draw is necessary, I think simply running a few fans at a higher RPM would be enough to cool the cells below 50C.

In order to contextualize this comparison though, I think it is fair to also take a look at the power consumption difference between the two packs.

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I did an actual comparison of the two arrays by just running the script two times, saving one of the arrays in a separate variable, and then subtracting the two arrays for the difference:

ans =

Columns 1 through 10

4.8328    4.9403    5.0306    5.1052    5.1656    5.2133    5.2500    5.2775    5.2971    5.3105

Columns 11 through 20

5.3192    5.3242    5.3269    5.3281    5.3284    5.3285    5.3285    5.3285    5.3281    5.3271

Columns 21 through 30

5.3246    5.3197    5.3114    5.2985    5.2794    5.2527    5.2168    5.1701    5.1108    5.0375

Columns 31 through 37

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a scenario for 10 minutes at 3.0 cell voltage

Enter time in minutes10
Total Mass: 300
Acceleration: 0
Velocity: 9.5
Grade: 0.15
Voltage: 108
Cell DCIR: 0.009
Parallel Count 9
Form Factor: 21700
Heat Energy Generated: 12.2556 Wh
Total Race Temperature Rise: 2.3438 deg C
Battery Power Consumed: 4954.6025 W
Total Battery Power Consumed: 825.7671 Wh
Current: 45.8759 A

Here is the battery power consumption difference between the two packs for each scenario:

3.6 cell voltage (nominal voltage)

Battery Power Consumption Difference: 4932.134W - 4904.4201W = 27.7139W

3.0 cell voltage

Battery Power Consumption Difference: 4954.6025W - 4942.7205W = 11.882W

Summary

Right off the bat, it seems fair to say that heat generation from cruising in normal conditions (with expected solar, 0% grade driving) is almost negligible. So I think it’s fair to say that the main concern with temperature rise should be regarding those high power draw scenarios. In those situations, a P45B pack would seem to perform significantly better thermally (1/2 the temp rise and a higher temperature ceiling).

However, this is all napkin math without actual testing done. Ideally, we would have tested a P45B module and a 50S module in a wind tunnel, but I’m not too sure we have the luxury of time to do that now.

To be honest, I think it’s fair to think about the P45B as costing extra power consumption (5.3W cruising, 27.7W for high power), but providing a much higher thermal performance for the pack. Does the pack need that extra ceiling? Maybe not. But it doesn’t seem like a huge cost to pay for greatly improved thermal benefits. Having to potentially rely on fans a great deal isn’t ideal because:

1. It’s in our interest to impede the inlet to protect the pack from foreign objects or water from getting in, that would probably work against cooling/would require more fans or more powerful fans to overcome the added static pressure

2. I don’t know how reliably we can scale up module results to a pack level

3. We can definitely develop a way to scale up module results to a pack level and model cooling using a wind tunnel and test jig, but that would be time consuming, and it wouldn’t be wise to push back final cell selection that far

Additionally, a P45B pack can likely still allow us to reduce overall battery system weight from MS15 and won’t massively increase our volume and testing + manufacturing + assembly time like an 18650 pack likely will (since that would massively increase cell count).

Based on what was said above, I think going with a P45B pack is most in line with our MS16 goals of reliability and thermal safety. I wouldn’t be surprised if we eventually learn from doing full testing that a 50S pack would have worked perfectly fine, but P45B gives us a lot more assurance with thermals at a fairly small price (probably 3-4kg extra total added weight). Significantly squeezing weight for the sake of efficiency seems out of scope for this car and is something we can probably aim to do in the future when we have more time and know-how.

I don’t think I specified this above, but a 36S9P pack shouldn’t make a huge change to the volume (so space constraint should be fine) and shouldn’t present any issues with the CG.

And based on the cell selection sheet, the pack should cost $1600, so that is also perfectly within our budget.