# CR123A battery (circuit?) question - any explanation for this behavior?



## selfbuilt (Jun 21, 2011)

_*UPDATE:* Scroll down this thread for a discussion, but the gist of the findings are that the Scorpion V2 is driven high enough on Max to trip the PTC safety circuits of most primary CR123A cells, when run over a sustained period.  Although external cooling helps delay this effect, it is still not something you routinely want to do. 

The second point is that there is a marked difference in the behaviour of made-in-the-USA Duracell/Panasonic cells compared to made-in-China Titanium Innovation cells. The Duracell/Panasonic cells appear to heat up far more quickly than the Titanium Innovations cells in this situation (and thus trip their PTCs earlier). Again, scroll down for a greater discussion, with comparative data from my testing and HKJs._

In some of my high-output lights tested on 4xCR123A, I have noticed an interesting step-down pattern at various points into the run. For example, see the Thrunite Catapult V2 SST-50 and Olight M31 SST-50 runs in this review: 







Most lights don't show this behavior, and I always thought it was some sort of thermal shut-down sensor in the circuit in those lights (i.e. responding to increased temperature due to the resistance of CR123As). 

It seems the Thrunite Scorpion V2 is showing the same behavior, but it is quite variable depending on the battery brand. I note that this light is not reported as having a thermal sensor.

Here is a comparison in the Scorpion V2 on Max using my standard Titanium Innovations CR123As and Panasonic made-in-USA CR123A, with and without external cooling (i.e. a small fan near the light). Note the Scorpion V2's LED should be driven ~2.5A on max (in its continuously-variable mode).






The Titanium Innovation cells perform consistently for a lot longer - with cooling, there was no sign of a step-down (and even without cooling, it only happened near the end of the run). 

Cooling also didn't make much of a difference on the Panasonic runs - except I got barely ~5 mins to step down without it, and ~6 mins with it.  The only real difference cooling seems to make is in the rate of the recovery phase.

So it would appear that the Panasonic cells can't handle the current load and heat up faster than the Titanium Innovations cells (or their PTC circuits kick in faster?). This is turn either triggers some sort of stepdown circuit/resistor, or causes some sort of battery "hiccup". 

Thrunite informs me that they use a resistor which varies with temperature, so that when the temperature is high, the resistor will drive the current lower. As the temp drops in the CR123As (i.e. while being driven less hard), output gradually recovers. That makes sense to me on the recovery side, but I don't quite see why the drop-off would be so rapid. :thinking:

Any ideas as to what is going on here? I'm also curious as to the rather large difference between the two brands.

_EDIT: I should add that the ambient room temperature rose during the course of the day as I was doing these runtimes, which may be a contributing factor between the brands (although I would think a small one). It was ~22C room temp for the cooled Titanium Innovation cells, ~23C for the uncooled TI cells, ~24C for the uncooled Panasonic, and ~25C for the cooled Pannies._


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## SilverFox (Jun 21, 2011)

Hello Selfbuilt,

Interesting graphs...

In multi cell use, the cells can behave differently depending upon how hot they get. As the cell heats up the PTC can slow down the current it delivers. As things cool off, the current can recover.

It would be interesting to take 4 cells and test them together as a battery to see if the voltage swings match your light output swings.

Tom


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## selfbuilt (Jun 22, 2011)

SilverFox said:


> In multi cell use, the cells can behave differently depending upon how hot they get. As the cell heats up the PTC can slow down the current it delivers. As things cool off, the current can recover.
> 
> It would be interesting to take 4 cells and test them together as a battery to see if the voltage swings match your light output swings.


Hi Tom,

Thanks for the thoughtful reply. Thinking about it, it does indeed sound to me more like a battery response. The idea of testing multiple cells as one battery is very interesting. I don't have the setup, but I wonder if anyone here has already tried that?


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## MichaelW (Jun 22, 2011)

In BatteryGuys's data mining SilverFox's cr123 data, didn't the Panasonic brand cr123 favor energy density over power density, and TI favor power over energy? [I was wondering why Zebralight posted runtimes of the H31Fw with Panasonic cells...]

When the step down occurs, remove the cells and take their temperature. See how much cooler the tail cell is than the head cell.
It would be better if you were able to take an IR photo... or use an IR pyrometer


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## selfbuilt (Jun 22, 2011)

MichaelW said:


> When the step down occurs, remove the cells and take their temperature. See how much cooler the tail cell is than the head cell. It would be better if you were able to take an IR photo... or use an IR pyrometer


Don't have an IR camera, so here is what I tried (and my results). For these tests, I used a thermal probe connected to my DMM, as well as measuring voltage and battery capacity using the ZTS meter.

I am out of Panasonics, so I used some of my Duracell made-in-USAs (in my previous testing, I found these to have virtually identical output discharge patterns to the Panasonics). My Duracells are a little older, 3-2018 expiry date (the Panasonics were 4-2019).

I labelled the cells and loaded them into the light and started the run, without cooling. 

Around 3 mins into the run, the output started dropping fast. I immediately removed the tailcap, and measured the temperature of each cell in two places as follows: 1) starting at the positive contact button of the front-most cell (near the head), 2) the negative contact plate of the front cell, 3) the positive contact button of the rear cell, and 4) the negative contact of the rear. I left the probe on the cell until the temp reading stabilized (about 2-3 secs each). After the first pass, I immediately did a second pass in the same order to see how fast they were cooling (less than 30 secs from the start of the first to the start of the second).

From front to back: 68.4C/56.4C, 51.9C/46.3C.
Second pass: 58.3C/50.3C, 49.9C/43.9C

Clearly, the front cell was a lot hotter. There is also a clear gradient from front to back.

After letting cool for 5 mins back to near room temp. I measured resting voltage as follows:

Front cell: 2.986V
Back cell: 2.966V

Stupidly, I hadn't thought to measure the voltage beforehand (doh), but all my other cells from this batch measure 3.235-3.240 at rest, when fresh.

Interestingly, despite the lower resting voltage of the back cell, it continues to give me a capacity reading under load with the ZTS meter at 100%. The front cell, in contrast, consistently gives me a 80% capacity reading.

Let me know what you can deduce from all that ... :wave:


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## MichaelW (Jun 22, 2011)

I should have put an emoticon with regards to an IR camera, seeing as a high quality one is 5-10 thousand dollars.
It would be interesting to see just how HOT a cr123 [PTC protected] gets when shorted.
Maybe Inova was on to something with the reverse insertion of cr123 cells, keeping the PTC away from the heat source...


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## HKJ (Jun 22, 2011)

To find the reason for the "strange" curve I did a runtime run where I monitored the battery voltage. The two possible results where (When the brightness drops):
1) The battery voltage will raise, because the light is reducing current drain due to a temperature sensor.
2) The battery voltage will fall, because the battery is reducing output, probably due to a PTC resistor.

Here is the result:






The 2xCR123 drops to 4 volt when the light is turned on, after 6 minutes the battery voltage drops to 3 volt, i.e. it is the battery that is reducing the current.

This test was done without any cooling and I suspect that is the reason I only got 6 minutes before it dropped (With cooling I got 10 minutes), but I got a longer runtime.

Here is the curve from the original runtime test:


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## jasonck08 (Jun 22, 2011)

Keep in mind that a cells chemical resistance (the resistance of the electrolyte) can change quite a bit depending on the temperature of the cell internals.

I've seen the voltage on some 18650 cells during a constant current discharge sag to 3v, then the voltage increases all the way to 3.2v before beginning to drop again.

If you have access to a bench power supply it would be interesting to see if you could power the light at a constant voltage and observe the behavior, to see if its possible that its the driver that is contributing to these strange curves.


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## HKJ (Jun 22, 2011)

jasonck08 said:


> If you have access to a bench power supply it would be interesting to see if you could power the light at a constant voltage and observe the behavior, to see if its possible that its the driver that is contributing to these strange curves.



You can see some curve done with a bench power supply on that light in my review of it. These curves are not at a constant voltage, but a voltage sweep and explains the curves for both LiIon cells, but not for 2xCR123.


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## mrlysle (Jun 22, 2011)

While I don't know squat, about squat, it makes sense to me that the cell closest to the emitter would definitely behave differently because of it being a higher temp, from heat conduction from the emitter. Then there would be a temp gradiant as the heat moves its way down the cell and into the other cell. Probably all sorts of resistance changes going on in both cells, but the cell closest to the emitter would change the most, and the fastest?


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## brightnorm (Jun 22, 2011)

selfbuilt said:


> ...I am out of Panasonics, so I used some of my Duracell made-in-USAs (in my previous testing, I found these to have virtually identical output discharge patterns to the Panasonics). My Duracells are a little older, 3-2018 expiry date (the Panasonics were 4-2019)...


 Selfbuilt, I always assumed that Duracells were a superior brand, which is why I always bought either Surefire or Duracell.

Should I revise my thinking about this?

Brightnorm


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## candle lamp (Jun 23, 2011)

HKJ said:


> To find the reason for the "strange" curve I did a runtime run where I monitored the battery voltage. The two possible results where (When the brightness drops):
> 1) The battery voltage will raise, because the light is reducing current drain due to a temperature sensor.
> 2) The battery voltage will fall, because the battery is reducing output, probably due to a PTC resistor.
> 
> ...


 
You did it. HKJ! 
Thanks for your effort. :twothumbs

1. Could you please explain what PTC resistor is. And is it in CR123A batteries only?
2. The graph says that the current draw per CR123A is (2.6~2.7)/2=1.3A? when the light is turned on?
3. The conclusion is that the battery voltage will fall, because the battery is reducing output, probably due to a PTC resistor?
4. In my view, CR123A is not suitable to high mode of Scorpion V2.

Thanks for your detailed answer in advance.


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## HKJ (Jun 23, 2011)

candle lamp said:


> 1. Could you please explain what PTC resistor is. And is it in CR123A batteries only?



PTS is shorthand for Positive temperature coefficient (Resistor) and is a resistor that increase resistance with rising temperature. They are often used as fuses with automatic reset and in other applications where you wish to limit current.
LiIon cells also uses them as a security. With protected LiIon you have the protection circuit in *addition* to the PTC.
Like fuses you can get them with different current limit. High ambient temperature (Like just behind the led in a flashlight) can reduce the current limit of the PTC.



candle lamp said:


> 2. The graph says that the current draw per CR123A is (2.6~2.7)/2=1.3A? when the light is turned on?


No, because they are in series each cell has the full current, i.e. up to 2.7 ampere.



candle lamp said:


> 3. The conclusion is that the battery voltage will fall, because the battery is reducing output, probably due to a PTC resistor?



The battery voltage is first falling from 6 to 4 volt due to the heavy load, later on it is dropping to 3 volt, probably due to the PTC.



candle lamp said:


> 4. In my view, CR123A is not suitable to high mode of Scorpion V2.


 
I did write something like that in my review. You have to only use full brightness for a minute or two at a time.


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## selfbuilt (Jun 23, 2011)

brightnorm said:


> Selfbuilt, I always assumed that Duracells were a superior brand, which is why I always bought either Surefire or Duracell. Should I revise my thinking about this?


Well, if this effect is the result of the battery limiting output (and HKJ's results strongly suggest that it is), then the question becomes why and how. As discussed here, the most likely explanation is the excessive heat near the head of the light is triggering the PTC in the front-most cell.

If that is the case, then the question becomes why the difference between the brands? I don't profess to know much about the specifics of the PTCs or internal chemistry of the various brands, but it seems to two general categories of answers are possible (with overlap between them). To wit, are the Panasonic/Duracells heating up faster than the Titanium Innovations cells (and thus triggering the PTC earlier?), or is the PTC more sensitive on those cells (and thus responding to a lower temperature?). Of course, some combination of both may be occurring.

I'm curious as to what the battery experts here think about those possibilities. Depending on the explanation (and one's perspective), the early triggering of the PTC could be good sign (i.e. safety first, the cells are not taking any chances), or bad sign (i.e. less able to sustain high drain due to high heat). Note I am talking about a question of degree here - if this is due to PTC tripping, then I've certainly seen it happen on Titanium Innovation cells as well as the others (just less quickly, perhaps).

I'm not qualified to say what is going on here, but I have done a lot of runtimes over years, with both types of cells, and have some subjective observations. Specifically, I started out testing using only Duracell or Surefire (and later Panasonics, when I found them to be equivalent). Beginning a year and a half ago, I switched completely to Titanium Innovation cells (due mainly to their much lower cost and their good performance, especially at high drain). I easily burn through 250+ cells a year, mainly at max and near-max levels (as an aside, CR123A batteries are the major expense I incur in my testing, so my annual costs are now in the low hundreds with the TI cells, not high hundreds with the others! ). Over all that time, I can tell you my *subjective* impression is that the Titanium Innovation cells typically come out of the lights cooler than the Duracell/Surefire/Panasonics. But I have never directly measured that head-to-head ... let me try it here and see what happens with the TI cells. I'll be back ...


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## HKJ (Jun 23, 2011)

I agree with selfbuild thinking about the PTCs. Does the Panasonic shut down at a lower temperature or do they heat faster?

What could be interesting is doing fully logged runs with both Panasonic and Titanium cells. With fully logged I would also log the temperature at the front of the cell closest to the led. I have another DMM on order and with some programming I will be able to log 4 channels in a few weeks.
I also need to get some titanium cells, I wonder if I can get them in EU (Please answer that on PM).

As I wrote above, it will be a couple of weeks before I can do anything, if somebody else can do it sooner, please do it.


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## selfbuilt (Jun 23, 2011)

Wow, the Titanium Innovations run was interesting. oo:

Using the same method I posted in #5, I redid the temp analysis with the Titanium Innovation cells. Note that these cells did not trip, so I simply stopped the run at the point when the Duracells began to drop in output (~3.5 mins into the run). Here is a summary of the comparisons:

Voltage at start: 
Duracell: ~3.240V
Titanium Innovations: ~3.245V

Voltage at end:
Duracell Front/Back: 2.99V/2.97V
Titanium Innovations Front/Back: 2.99V/2.99V

ZTS battery capacity:
Duracell Front/Back: 80%/100%
Titanium Innovations Front/Back: 100%/100%

Temperature (first pass, after 3.5 mins runtime):
Duracell Front Cell Top/Bottom, Back Cell Top/Bottom: *68.4C/56.4C, 51.9C/46.3C*
Titanium Innovations Front Cell Top/Bottom, Back Cell Top/Bottom: *43.0C/42.2C, 42.5C/42.4C*

Holy cow, there's a HUGE difference in the heat of the these cells at this point in time (i.e. when the Duracell's PTC apparently tripped). The Titanium Innovation cells are LOT cooler than the Duracells.  More than than, there is basically no gradient on the Titanium Innovation run (i.e. just ~42-43C across the batteries).

It looks like my earlier subjective assessment is born out here - the Titanium Innovations cells are NOT getting anywhere near as hot as the Duracell (and presumably Panasonic cells), at least not as quickly. This presumably explains the output graph differences - it is likely taking a lot longer for the Titanium Innovation cells to reach a temperature when the PTC is engaged.

This is a very simple analysis, but the differences between these runs is quite large. As a result, I am quite comfortable concluding that the Panasonic/Duracell cells are heating up faster. Of course, the question of whether the PTC engages earlier remains to be decided. I will do a longer-term run with the TI cells, to see if I can get them to trip and quickly measure the temp (will be tricky to time it, but I will give it a try). I am curious as to what HKJs more detailed analysis will bring, but these preliminary findings are fascinating so far.


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## selfbuilt (Jun 23, 2011)

Ok, I won't be trying this again. :sweat:

I ran the light without cooling on the Titanium Innovation cells until the PTC apparently engaged (occurred a little after ~20 mins into the run, as before on these cells). _Keep in mind this is a not exactly fair comparison to the Duracells at 3.5 mins, as the longer run gave everything a lot more time to heat up._ Here are the temps: (first pass is immediately upon removing from the light as the drop in output began, second pass is ~25 secs later).

Duracell (3.5min) first-pass, from front to back: 68.4C/56.4C, 51.9C/46.3C.
Duracell (3.5min) second-pass, from front to back: 58.3C/50.3C, 49.9C/43.9C

Titanium Innovations (20min) first-pass, from front to back: 80.6C/73.6C, 72.4C/70.3C.
Titanium Innovations (20min) second-pass, from front to back: 77.6C/71.3, 69.4C/66.6C

_I don't believe you can draw any real conclusions about the temperature at which the PTC engaged this way._ It's possible both types of cells responded at the same point - but because the Duracell/Panasonic ramped so much more quickly, they also dropped more quickly (i.e. by the time I got everything out of the light and measured it). As you can tell from the later TI run, the temp of the cells remained elevated longer (as you would expect from the more gradual increase in heat of the light and batteries). As such, it is really impossible to know what internal temp triggered the PTC throttle-down.

As an aside, I will say the light was a LOT hotter to the touch when getting these cells out (compared to the 3.5min Duracell runs, where the light was still relatively quite cool to the touch).  Also, the wrapping of the cells had opened up near the positive terminals - slightly on rear cell, considerably on the front cell. Needless to say, I will not be doing any more of these runtimes without cooling!

The only way to know for sure what is going on would be to directly measure the temperature of the front cell while the light is operation, and see directly when the PTC engage. Given the wide time disparity here, my simple method doesn't really tell us much. As the more detailed analysis is beyond my capability to measure, hopefully HKJ (or someone else here) will be able to do it.

*So, to summarize all of the above:*

the Duracell (and presumably Panasonic) cells heat up FAR more quickly than the Titanium Innovations cells in this setup.
it is possible the Titanium Innovation cells are also tripping at higher heat levels, but the only real way to know is to directly measure temp under operation. This is beyond my ability at this point in time.


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## brightnorm (Jun 23, 2011)

Fascinating. My layman's conclusion is that I can replace my Duracells and Surefires with
the cheaper Titanium Innovations and incur no runtime penalty, but with a possible compromise of safety. Is this accurate?

Brightnorm


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## selfbuilt (Jun 23, 2011)

brightnorm said:


> Fascinating. My purely pragmatic layman's conclusion is that I can replace my Duracells and Surefires with the cheaper Titanium Innovations and incur no runtime penalty, but with a possible compromise of safety. Is this accurate?


The former statement seems reasonable (i.e. runtime performance), but I don't think you can infer the latter yet (i.e. possible safety).

I have certainly also seen Duracell and Energizer wrappings open up near the positive terminal, on runs driven at very high levels. Again, I probably push cells as hard as anyone here, given all the max output runtimes over the years. In the literally hundreds of cells I have blown through of all types, there has been nothing that has caused me any greater concern on the Titanium Innovation cells. In fact, the opposite is the case - I have experienced a number times when Duracell/Surefire/Panasonic cells were too hot to hold coming out of the light, whereas this is the first time I have found that on TI cells (and I would say I have blown through a roughly equal number of each).

I think we need to wait for direct measurement of temperature at the time of PTC engagement to say anything more.

But on the general subject of safety, I think its important to remember that you should aim to never push a cell to the point the PTC needs to engage. I will definitely make this point clearer in my reviews from now, given the likely conclusion that this is what is happening here. And again, in my case, this is why on CR123A, I ALWAYS do runs under a cooling fan, and NEVER do unsupervised runs. Common sense needs to prevail in all battery handling. :candle:


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## HKJ (Jun 23, 2011)

selfbuilt said:


> Temperature (first pass, after 3.5 mins runtime):
> Duracell Front Cell Top/Bottom, Back Cell Top/Bottom: *68.4C/56.4C, 51.9C/46.3C*
> Titanium Innovations Front Cell Top/Bottom, Back Cell Top/Bottom: *43.0C/42.2C, 42.5C/42.4C*



Very interesting, now the question is why does the Duracell heat up? Is it:
1) Because the chemistry is not designed for the current.
2) Because the PTC is selected for a lower current (PTC works by heating up and then disconnect when they get hot)?

Or is it a combination of 1) and 2).




brightnorm said:


> Fascinating. My purely pragmatic layman's conclusion is that I can replace my Duracells and Surefires with the cheaper Titanium Innovations and incur no runtime penalty, but with a possible compromise of safety. Is this accurate?



It looks like the Titanium cells are better at high current or at least high temperature, but we do not know if this involves any safety compromises.

I have found a few Titanium cells (I suppose they have been included with a light, but because I am mostly using LiIon, I have not used the cells). I am going to do some test with the battery alone, i.e. no flashlight, only a resistor. This way I can log current, voltage and temperature at the same time


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## selfbuilt (Jun 23, 2011)

HKJ said:


> I have found a few Titanium cells (I suppose they have been included with a light, but because I am mostly using LiIon, I have not used the cells). I am going to do some test with the battery alone, i.e. no flashlight, only a resistor. This way I can log current, voltage and temperature at the same time


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## SilverFox (Jun 23, 2011)

Hello Selfbuilt,

My "best guess" is that there is a difference in the chemical formulation.

I know that the major manufacturers of CR123 cells consider a 1C load large. In the early development of some high power incandescent lights there were a few incidents with cells blowing up under close to 4C loads. The formulation may have been changed to guard against that.

Another indication that the formulation may be different is that the Titanium cells start to form a pacification layer after a couple of years of storage and the Panasonic cells don't. Whatever keeps this passivation layer from forming may result in higher cell temperature under high loads.

I wonder what the internal cell temperatures are...?

Tom


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## HKJ (Jun 23, 2011)

My first two runs are done. The temperature did not rise enough to trip the PTC, I will do another run with the cells in a plastic tube and hope this will isolate enough to trip the PTC.
The Titanium cells has a higher voltage and lower temperature during load, the final capacity is the same, but the energy is higher. This can be due to different chemical formulation as SilverFox guesses, but it can also be due to higher resistance in the PTC (it could even be differences in my connections to the cells, but because we have seen differences in the flashlight I doubt that).
















The test is done with a 0.716 ohm (including wires and meter) load and a temperature is measured with a thermocoupler mount with adhesive tape to the CR123 cell. The connections to the cell is done with a clamp with the voltmeter connected directly to the screws.


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## Justin Case (Jun 23, 2011)

SilverFox said:


> Another indication that the formulation may be different is that the Titanium cells start to form a pacification layer after a couple of years of storage and the Panasonic cells don't. Whatever keeps this pacification layer from forming may result in higher cell temperature under high loads.


 
Passivation layer?


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## 45/70 (Jun 24, 2011)

Justin Case said:


> Passivation layer?



Nit picker.

And it's "large crystalline formations", not "granules".:nana:

Dave


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## Helmut.G (Jun 30, 2011)

This is extremely interesting info, especially for anybody using primary CR123s in high power lights on the high power levels.
Thank you HJK and Selfbuilt for your measurements!


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## recDNA (Oct 25, 2015)

selfbuilt said:


> Ok, I won't be trying this again. :sweat:
> 
> I ran the light without cooling on the Titanium Innovation cells until the PTC apparently engaged (occurred a little after ~20 mins into the run, as before on these cells). _Keep in mind this is a not exactly fair comparison to the Duracells at 3.5 mins, as the longer run gave everything a lot more time to heat up._ Here are the temps: (first pass is immediately upon removing from the light as the drop in output began, second pass is ~25 secs later).
> 
> ...


In the 20 min test the TI batteries got hotter than 3.5 min Panasonic test. Why not run BOTH for 20 min? My major concern is safety. If the Duracell are hotter after 20 min I want TI. If early ptc causes Duracell to be cooler after 20 min than TI I want Duracell.

Actually I have several boxes of Surefire and no Duracell's but I am drawing an inference that Surefire is more like Duracell than TI?

This thread is fascinating. I'm surprised it ever died. Maybe someone else could continue it with more tests? I would.also be very curious about results in single cell tests. 

I noticed a Surefire heats up quickly in a sx32w in h1 2.2 amps. If I had a way to test I would try TI. Despite owning several boxes of SF I would buy TI if they run cooler in sc32w.

I have never heard of a sc32w blowing up on primary but maybe too few users with primaries.


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## Lumencrazy (Oct 26, 2015)

The difficulty here is that we are trying to answer technical issues related to battery performance indirectly. Flashlights are not analytical test instruments used for battery evaluations. Especially when comparisons are being made with different lights under varying conditions. One really needs to use the correct equipment like a calibrated DC Load in order to be able to isolate the reasons for the varying differences in battery performance under controlled conditions.


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## selfbuilt (Oct 27, 2015)

recDNA said:


> I am drawing an inference that Surefire is more like Duracell than TI?


Yes. You can see my 2013 CR123A round-up for some commentary on the source of all made-in-the-USA cells - and some direct testing results.



Lumencrazy said:


> The difficulty here is that we are trying to answer technical issues related to battery performance indirectly. Flashlights are not analytical test instruments used for battery evaluations. Especially when comparisons are being made with different lights under varying conditions. One really needs to use the correct equipment like a calibrated DC Load in order to be able to isolate the reasons for the varying differences in battery performance under controlled conditions.


+1 :thumbsup:

I certainly didn't set out to do battery testing in this thread - it was just to explore what the likely source of the issue was. It really needs someone with the right equipment and expertise to investigate further (neither of which I have).


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