Fun With Math - ICE Cooldown vs EV Charging

Random math I thought I would share.  I did this because of a discussion on another forum that started from a comment along these lines:

"It sure is nice my EV doesn't make heat my garage up a bunch when I park it in there after a drive, unlike my ICE car"

I ran some ballpark numbers to compare the two.

Assumptions:

• Level 1 Chargers have an efficiency ranging from 74.2 to 83.8% and draw 1400 Watts
• Level 2 Chargers have an efficiency ranging from 87.20 to 89.40% and draw 6600 Watts
• ICE Car #1 Represents a powertrain that is approximately 350lbs of Aluminum and 30 lbs of water.  
• ICE Car #2 Represents a powertrain that is approximately 450lbs of Iron + 75lb of Aluminum and 30lbs of water
• Chassis represents 2500lbs of steel at ambient outdoor temp (this is just a reference point - this is not factored into any other equations).
• All components in the ICE powertrain are at 195F when the vehicle is turned off.
• The Chassis is at 95F when the vehicle is turned off.
• The garage environment is 75F

Results are shown in the form of Energy Released in kJ (heat added to the garage environment the vehicle is parked in).  Obviously this does not represent the actual cooling rate of the ICE powertrain and how that may impact the temperature of the garage in the short term.

As a function of charge time:

As a function of charge delivered:

I guess technically the EV isn't warming up the garage, the charger is. But that is a technicality. Now park them both side by side in a garage and observe where the cat sleeps.

In reply to slefain :

If you set that up, the cat will sleep elsewhere.

30lb is a lot of water.  Most modern cars run around 12-15lb of coolant (not water, must be careful here).

And yes, it feels a little weird to be discussing something normally considered as a volume, in terms of its weight or mass.

Knurled. said:

30lb is a lot of water.  Most modern cars run around 12-15lb of coolant (not water, must be careful here).

Indeed, but they also run some oil as well.  I lumped the liquids together and used water as it is kind of a worst-case for the ICE.

In reply to ProDarwin :

Good point!

It's worth noting that a Level 2 charger will fully charge the biggest EV battery on the market from dead flat in 12 hours, so that is an extreme case. It would be really interesting to show the ICE cooling down - I think the ICE powertrain masses are low, because you also have 150-ish lbs of transmission and potentially another 100 lbs of differential that's running warm plus the very (very) hot cats and exhaust.

The real question is - where do they cross over? 

Keith Tanner said:

It's worth noting that a Level 2 charger will fully charge the biggest EV battery on the market from dead flat in 12 hours, so that is an extreme case. 

I need some clarification here.  A level 2 charger is called 6.6kw, and 89% equivalent.  Is 6.6kw being delivered after the efficiency loss?  Or before.  If after, it will deliver 79.2 kWhr in 12 hours.  If before, it will deliver 70.5.  No EVs will accept that level of charge (P100 Tesla)?  I know Tesla has their own charging protocols, but I don't know efficiency numbers for those.  Either way, the lines cross way way before that point, so its not that important anyway.

Keith Tanner said:

I think the ICE powertrain masses are low, because you also have 150-ish lbs of transmission and potentially another 100 lbs of differential that's running warm plus the very (very) hot cats and exhaust.

I think that depends on the car.  My car certainly does not have a 150lb transmission or a 100lb diff.  In my Saturn, those two things combined are like 75lb.  A V8 RWD car would have more mass for sure.  I can factor those in.  The real question is what does the gearset (steel) weigh compared to the case (aluminum)?

What's a typical exhaust weigh?  Say a stock Miata, because I know you know.  I can double that for a Mustang or something.  What do you think the average temp is for all of the mass in the exhaust system?  

The exhaust will be interesting.  Steel (and iron) has a low heat capacity compared to aluminum which is why the lighter Aluminum engined ICE is actually dumping more heat out in the initial graphs.

Keith Tanner said:

The real question is - where do they cross over? 

I don't understand.  Its shown on the charts where they cross.

My Tesla reports a 7.2 Kwh charge rate with the supplied charger, and it's sucking down 32A at 230V. That's the only data point I have.  There are Model S Teslas with a 100 Kwh battery - I'm assuming that's the biggest one that's present in any sort of numbers. Most people run them between 20 and 80%.

2019 Miatas have a 95 lb transmission without fluid (2 qt). V8 Miatas and Cameros have a 145 lb transmission - again, no fluid. The rear diff on a 1.8 Miata is 80 lbs when full of fluid. I think you're underestimating your Saturn. 

A 2019 Miata has a 50 lb stock exhaust including the manifold (tubular steel instead of the more common cast iron) and the cats. Those cat are hot by design - somewhere around 500F. The temperature of the exhaust will drop as you head back, but the muffler is can be too hot to touch after a normal drive.

I'm thinking primarily of my M5, which radiates a stupendous amount of heat for a long time after a normal drive. Oddly, our Grand Cherokee seems to radiate far less even though they're very similar cars if you squint - V8 engines, two less cats in the GC (I think), basically RWD. Maybe it's the black paint on the M5.

The EV numbers seem reasonable. I think the ICE is a little oversimplified and underestimated in the example, and of course it's going to flatline eventually. That's the crossing point I was thinking about, where the EV charging inefficiency equals to total thermal mass of a hot ICE. Maybe I'll do an empirical test with the M5 and the 3 :)

In reply to Keith Tanner : I suspect it's air flow during the drive, greater airflow under the car and exhaust components on the Grand Cherokee means less retained heat upon parking.  Just a WAG on my part I've noticed the same phenomenon with my 'vettes and my Truck.  I'll go further and say my Z06 stays hotter when parked than my '85.

I can get behind that theory. That M5 is definitely packaged tightly and airflow is a lot more controlled.

Keith Tanner said:

My Tesla reports a 7.2 Kwh charge rate with the supplied charger, and it's sucking down 32A at 230V. That's the only data point I have.  There are Model S Teslas with a 100 Kwh battery - I'm assuming that's the biggest one that's present in any sort of numbers. Most people run them between 20 and 80%.

2019 Miatas have a 95 lb transmission without fluid (2 qt). V8 Miatas and Cameros have a 145 lb transmission - again, no fluid. The rear diff on a 1.8 Miata is 80 lbs when full of fluid. I think you're underestimating your Saturn. 

A 2019 Miata has a 50 lb stock exhaust including the manifold (tubular steel instead of the more common cast iron) and the cats. Those cat are hot by design - somewhere around 500F. The temperature of the exhaust will drop as you head back, but the muffler is can be too hot to touch after a normal drive.

I'm thinking primarily of my M5, which radiates a stupendous amount of heat for a long time after a normal drive. Oddly, our Grand Cherokee seems to radiate far less even though they're very similar cars if you squint - V8 engines, two less cats in the GC (I think), basically RWD. Maybe it's the black paint on the M5.

The EV numbers seem reasonable. I think the ICE is a little oversimplified and underestimated in the example, and of course it's going to flatline eventually. That's the crossing point I was thinking about, where the EV charging inefficiency equals to total thermal mass of a hot ICE. Maybe I'll do an empirical test with the M5 and the 3 :)

Understood on the Tesla charging.  I don't think that impacts the numbers significantly, but it is a good datapoint.  Is the 20-80% a representation of charge on a 100kW battery, or does tesla call the range typically used on the battery '100kW'?  Your charger is reporting a 7.2kw charge rate but only drawing 7360 watts.  Given the other efficiency values I found, I'm guessing less than 7.2kw is actually reaching the battery.

I checked on forums and the Saturn trans (with diff) weighs 69lbs.  I've shipped one before in a Fedex box which is where the 75lb estimate comes from.  They are not heavy.  A quick google shows a D-series honda trans a few pounds lighter.  I think a lot of small FWD cars are in this ballpark.  Regarding the diff, does a Tesla, Leaf, Bolt, etc. have a traditional diff?  If so, the mass here should not be counted.

I'll toss in the exhaust numbers.  We could say the average temp is around 400F?  450F?  The cat forward is really high, but after the cat the temp drops off quickly, and the muffler is a large chunk of mass around... 150F?

The difference between the M5 and GC is interesting.  I'm guessing a lot has to do with the engine weight on the M5 (aluminum), which is going to have a large heat capacity and also radiate the heat quicker than the iron block in the GC.

I put a gas fireplace in my garage.

Tesla battery ratings are at 100% capacity, but they recommend you don't charge past 80% for daily use for the health of the battery. It's a user-settable setting and anything above 80% is identified as "trip". So our 75 Kwh battery will stop charging at 60 Kwh, and of course we never roll in with the battery empty. And the car reports charging rates, I'd be surprised if it was trying to calculate losses in the rest of the system.

With the variation in ICE vehicle types, it sounds like you'll have to pick a specific configuration. Miatas and Saturns have pretty similar power levels, but the transmission/diff weight is quite different due to the FR vs FF drive types. Of course, you throw power into the mix and numbers go way up. Even an inline vs V configuration is going to have an effect, as that will double the number of cats. Given the wide range in battery capacities for EVs, you should really pick a specific EV as well - the Model 3 would be the obvious choice but even it comes with three different battery options.

We also have to take the heat loss rate of the garage into account :) Seriously, in winter a charger might heat the garage more slowly than the garage sheds heat while a hot ICE will spike the temperature before it sags back down again. Same thing in an air conditioned garage in summer, the ICE might overwhelm the AC for a while. That would certainly give a person the impression the car is heating up the garage more than the charger's slow release.

Keith Tanner said:

My Tesla reports a 7.2 Kwh charge rate with the supplied charger, and it's sucking down 32A at 230V. That's the only data point I have.  There are Model S Teslas with a 100 Kwh battery - I'm assuming that's the biggest one that's present in any sort of numbers. Most people run them between 20 and 80%.

Since we are doing math here, and units matter, kWh is an energy amount, not a charging rate.  Based on your 32 A@230 V, that's just over 7.3 kW. 

Whereas 7.2 kWh isn't going to get you very far if it uses a 100 kWh battery, as it's 25,9 MJ when the battery is rated at 360 MJ.

(and what letters you caps also matters- W = Watt- a person's name, so it's cap'ed, as is J Joule.  kilo is not (1000x) Mega is (1,000,000x).  And hour is almsot always hr.  Again, units matter, which means how the letter is placed matters...)

edit- according to NIST- it also matters that there is a space between the number and it's unit.  I ALWAYS miss that. So it's 32 A instead of 32A.  

Can you show the time on the ice examples as well? The don't instantly dump all their heat but I suspect it is pretty quick at the beginning.

The poster who got you to do all this is probably feeling that initial heat dump. PLUS ice cars tend to keep running the fans after shutdown so you FEEL the hot air in the garage, furthering the misconception.

Robbie said:

Can you show the time on the ice examples as well? The don't instantly dump all their heat but I suspect it is pretty quick at the beginning.

The poster who got you to do all this is probably feeling that initial heat dump. PLUS ice cars tend to keep running the fans after shutdown so you FEEL the hot air in the garage, furthering the misconception.

For a body where it's just losing heat that is has- with out adding any more- the heat loss is an exponential decay.  The heat flow depends on the temperature difference, so as the body gets closer to ambient, the slower the heat release. (works the same for the opposite direction)

Keith Tanner said:

We also have to take the heat loss rate of the garage into account :) Seriously, in winter a charger might heat the garage more slowly than the garage sheds heat while a hot ICE will spike the temperature before it sags back down again. In summer things would get interesting if the garage has stabilized to ambient.

Not just winter, sounds like the original idea person lives in a hot area and has an at least partially air conditioned garage.

In reply to alfadriver :

I agree, really you just have to add a "bull nose" to the front of the ice graphs...

Heat transfer rate wasn't part of this modeling (as stated in the original post).  This was just a simple heat transfer calculation for curious minds.  Calculating rate of transfer for something like that would be orders of magnitude more difficult.  I'm also not going to model the heat loss of a garage.  There are a way too many variables here.

Keith Tanner said:

Given the wide range in battery capacities for EVs, you should really pick a specific EV as well - the Model 3 would be the obvious choice but even it comes with three different battery options.

Well, as the graphs show, most of those differences in capacity are well beyond the point where they cross.  They won't impact heat transfer rate, only total heat transfer and you can simply stop earlier on the graph.  Heck, on the second graph I don't show anything beyond 40kWhr delivered anyway :P

I went back to run some additional numbers.  The Miata and Econobox (Saturn, or similar) actually have nearly identical numbers because so much more of the powertrain weight in the Miata is Iron vs. Aluminum in the Saturn.  So I made 2 distinct cars.  Again, the numbers are not perfect.

Econobox:  250lbs of Aluminum, 50lbs of Iron @ 195, and a 75lb Exhaust system at 400F

M5:  450lbs of Aluminum, 150lbs of Iron @ 195F, and a 150lb Exhaust system at 400F

The econobox results in roughly the same values as previously (aluminum went down, but super hot steel exhaust went up).  

The M5 releases considerably more heat.