Let's talk about charging on long distance travel?

CappyJax

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The Model 3 LR will charge at 250 kW, the curves and data you are looking at are out of date.
An 85 kWh battery charging at 250 kW is ~3C.
C is not the battery capacity, but is a measure of the discharge/charge rate relative to it's maximum capacity. A 100 kWh battery charging at 100 kW would be a 1C rate.
This is absolutely correct. C is definitely NOT the capacity of the battery in units of ampere-hours.
 

ajdelange

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"...the C- rate, derived from the ratio of the cell capacity C (Ah) to current I (A)"

Linden, David "Factors Affecting Battery Performance" in Linden's Handbook of Batteries, Fifth Edition, Ed. Kirby W Beard McGraw Hill 2019

The rate is thus the current normalized by the capacity e.g. a 100 Ah battery discharged at a 10 A rate is discharging at a rate of r = I/C = 10/100 = 0.1 . Note that the units of r are inverse hours. It represents the number of complete discharges per hour.

But the ratio can also be written R = C/I which is in units of hours and represents the number of hours it takes to discharge the battery. In this case it takes 10 hours to discharge a 100 Ah battery at a 10 A rate.

When we say we are going to charge or discharge a battery at currrent I = rC it is clear from the context that the I/C form of the ratio is being used.

It is so easy to check on these things. Why won't people do that?
 
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ajdelange

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Maybe this will help. I have a boat with a fuel tank capacity G = 60 gallons. If I burn fuel at cruise at the rate of 0.1G how long can i cruise. The number 0.1 is the rate of fuel consumption in units of "per hour". Thus 0.1G means the fuel flow is 0.1*60 = 6 gph but we don't really need to know that. We know right away that we will empty the tank in 1/0.1 = 10 hrs if we drain it at 0.1G,

Now all I have to do is change G to C with "fuel" quantity in ampere hours rather than gallons and flow rate is ampere hours per hour (equal to amperes) rather than gallons per hour and I'm talking about my BEV, not my boat. At a current consumption rate of 0.1C I can cruise for 10 hr.
 

CappyJax

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Maybe this will help. I have a boat with a fuel tank capacity G = 60 gallons. If I burn fuel at cruise at the rate of 0.1G how long can i cruise. The number 0.1 is the rate of fuel consumption in units of "per hour". Thus 0.1G means the fuel flow is 0.1*60 = 6 gph but we don't really need to know that. We know right away that we will empty the tank in 1/0.1 = 10 hrs if we drain it at 0.1G,

Now all I have to do is change G to C with "fuel" quantity in ampere hours rather than gallons and flow rate is ampere hours per hour (equal to amperes) rather than gallons per hour and I'm talking about my BEV, not my boat. At a current consumption rate of 0.1C I can cruise for 10 hr.
We already new what C was. But now that DunRider told you what it was, you are now trying to explain it back to us? You said "C is the capacity of the battery in ampere hours." Which is 100% categorically wrong. A 100kWH battery can have a C rating of 1. A 50Wh battery can have a C rating of 20. It has absolutely nothing to do with the capacity of the battery in ampere hours.
 

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Technically aj is correct, but in reality it is just a different way to express the relationship. The numbers wind up the same.
Model 3 LR has a pack with a nominal voltage of 350 and a capacity of 230 Ah.
If you are charging/discharging at 714 amps (250 kW, 350 v), the C rate is 3.1 (714/230)
If you divide the 250 kW charge rate by the pack capacity of 81 kWh, you get a C rate of 3.1
 

CappyJax

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Technically aj is correct, but in reality it is just a different way to express the relationship. The numbers wind up the same.
Model 3 LR has a pack with a nominal voltage of 350 and a capacity of 230 Ah.
If you are charging/discharging at 714 amps (250 kW, 350 v), the C rate is 3.1 (714/230)
If you divide the 250 kW charge rate by the pack capacity of 81 kWh, you get a C rate of 3.1
That doesn't change the ampere hour rating of the battery. If you discharge the battery a 3C you get 690 amps for 20 minutes which is the exact same thing as 230Ah.
 

ajdelange

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This is something engineers and scientists do all the time. One ampere, written 1 A, flowing for an hour transfers 3600 coulombs, That just happens to be a convenient sized chunk of charge if you are talking about modest amounts of current though it's often more convenient to speak in terms of ampere hours irf you are an engineer, If you are concerned with smaller currents the milliampere, written 1 mA and equal to 3.6 coulombs per hour is often more convenient, When talking about batteries we are often more interested in the chemistry than whether the battery under consideration is a button cell in the lab or an assembly of thousands of 2170s. In such applications a convenient unit of charge is one battery-full, and the current written as 1 C meaning 1 battery full per hour however many ampere hours that happens to be. That makes it easy to see that, for example, if the RWD and AWD have 100 kWh batteries which I charge with current 0.1 C (about what an HPWC on a 60A circuit can do) then it will take 10 hrs to charge them fully. If I put in a second battery for the TriMotor then capacity is doubled and it is clear that the current from a single HPWC is reduced to 0.05 C and that it will take twice as long to charge.

Note that I referred to the battery as a 100 kWh battery rather than a 259.7 Ah battery. When we are talking about charging etc as owners/drivers we don't really want to be bothered with Ah and so we assume that each Ah will be delivered at some nominal voltage V and speak of the capacity of the battery in units of watt hours, calculated by multiplying the capacity in Ah by V. This, of course, represents an approximation as the battery voltage is not constant but we don't need precision that would satisfy Mr. Spock, Thus a battery with capacity C = 100 kWh charged at a rate of 10 kW is charging at 0.1 C and will charge in 10 hours. Obviously using the symbol C for capacity in both cases can lead to confusion but the context should be clear and in either case 0.1 C represents the same amount of stress, performance etc on the battery. That's the beauty of doing things this way,
 

CappyJax

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This is something engineers and scientists do all the time. One ampere, written 1 A, flowing for an hour transfers 3600 coulombs, That just happens to be a convenient sized chunk of charge if you are talking about modest amounts of current though it's often more convenient to speak in terms of ampere hours irf you are an engineer, If you are concerned with smaller currents the milliampere, written 1 mA and equal to 3.6 coulombs per hour is often more convenient, When talking about batteries we are often more interested in the chemistry than whether the battery under consideration is a button cell in the lab or an assembly of thousands of 2170s. In such applications a convenient unit of charge is one battery-full, and the current written as 1 C meaning 1 battery full per hour however many ampere hours that happens to be. That makes it easy to see that, for example, if the RWD and AWD have 100 kWh batteries which I charge with current 0.1 C (about what an HPWC on a 60A circuit can do) then it will take 10 hrs to charge them fully. If I put in a second battery for the TriMotor then capacity is doubled and it is clear that the current from a single HPWC is reduced to 0.05 C and that it will take twice as long to charge.

Note that I referred to the battery as a 100 kWh battery rather than a 259.7 Ah battery. When we are talking about charging etc as owners/drivers we don't really want to be bothered with Ah and so we assume that each Ah will be delivered at some nominal voltage V and speak of the capacity of the battery in units of watt hours, calculated by multiplying the capacity in Ah by V. This, of course, represents an approximation as the battery voltage is not constant but we don't need precision that would satisfy Mr. Spock, Thus a battery with capacity C = 100 kWh charged at a rate of 10 kW is charging at 0.1 C and will charge in 10 hours. Obviously using the symbol C for capacity in both cases can lead to confusion but the context should be clear and in either case 0.1 C represents the same amount of stress, performance etc on the battery. That's the beauty of doing things this way,
C has absolutely nothing to do with the ampere-hour rating of the battery. Nothing you said changes that fact.
 

electruck

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OMG people... let's pick nits here.

C-rate, or simply "C", is defined as the discharge rate of the battery relative to it's maximum capacity (ie, it is a normalized quantity) thus, by definition, "1.0 C" is indeed equal to the max capacity of the battery.

May this dead horse RIP... please.
 

ajdelange

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[Edit]Removed by author, Not intended that it should post.
 
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PoorPilot

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Just goes to show you that all arguments end up being decided by who has the biggest “C”.

That was a joke...
 

ajdelange

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I ignore people who repeatedly vector the discussion away from relevance so I don't have to waste time responding to "noise".They are never convinced even though it usually very obvious that they are dead wrong. So I didn't see all the posts until today when the "ignore" feature didn't work until I logged in. Though I know I will not convince anyone I do want it to be very clear to the general readership that when speaking of charge and discharge rate C is indeed the capacity of a battery in ampere hours as the textbook definition of the rate makes clear: "...the C- rate, derived from the ratio of the cell capacity C (Ah) to current I (A)" Given that the textbook definition specifies not only that C is the capacity of the battery and that its units are Ampere hours I just don't understand how a rational person could come to the conclusion that C means something else.

OMG people... let's pick nits here.
I'm afraid we do need to for a bit.

C-rate, or simply "C", is defined as the discharge rate of the battery relative to it's maximum capacity (ie, it is a normalized quantity) thus, by definition, "1.0 C" is indeed equal to the max capacity of the battery.
As the definition says C rate is derived from the ratio of the charge rate and charge current. Thus C rate is not simply C which is an amount of charge. Thus if the battery is a 200 Ah battery being charged at a 10 amperes the charge rate is 10 amperes divided by 100 ampere hours and is equal to 0.1 per hour. 1C is a current in units of amperes. The capacity is in units of ampere hours. While the number may be the same the dimensions attached to the numbers are not. 100 apples are not equal to 100 oranges.

C rate is a number, in inverse hours (a rate) which is multiplied by the capacity, in ampere hours to calculate a current: 1 per hour times C ampere hours = C amperes.

May this dead horse RIP... please.
It can if people (most people, anyway) understand the above. But I would like to keep it alive for a bit longer (whether people do or not) because the C notation can also be very useful in discussing battery life as related to range in BEVs. A battery cell degrades as it is charged and discharges. At some point it's capacity reaches some number beyond which we think it is no longer useful in a BEV though it is now being recognized that there may still be plenty of life left in these batteries for other uses. Whatever that limit degradation is for a BEV (5% loss of capacity perhaps?) it is clear that the loss increases with number of times that battery is charged and discharged. While the rate depends on depth of charge/discharge, rate of charge/discharge and, doubtless a whole bunch of other things, it is clear that the useful life of the battery can be expressed in units of C. How that relates to time and how that relates to distance driven relate to how fast we go through C's.

For example the EPA range of my X is 351/C that is 351 miles per full charge. Note that for calculations like this we scale by an average battery voltage so that C is in units of kWh ( C *= V/1000). I'm told that the battery life in my car is 500,000 miles. Thus the life of my battery is 500000/351 equal to 1424.5C. Note that the 1424 is a function of the cell chemistry.
If someone comes up with a cell chemistry that can handle 2848C (which we fully expect them to do pretty soon) before degrading to the same limit level) it's pretty clear that this battery would go 1,000,000 miles in my car. It's also easy to see how far it would go in a car that had a range of 300 mi/C.

I don't know whether anyone else besides me has any interest in any of these aspects of BEV's but I someone does it's clear that he can be helped by normalizing to C in his calculatons. But clearly he has to understand what C is and that means ignoring the noise.
 
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