Who is good at maths?

Hi,

I have (mostly) built a headtorch running 3 Kree XR-Es, and a buck driver with efficiency of above 85% from 11AA cells at 1.3v each (average) and a capacity of 2700mAh. Everything is in series.

I will be running the XR-Es at 0.72W, 1.36W & 3.04W.

Does anyone know how I could derive the expected length that flashlight would run before the batteries died?

I work it out that it should last at least 14hrs at .72W; 7.4 hours at 1.36W and 3.3 hours at 3W respectively.

Can anyone confirm that this sounds correct, or even better show me how to calculate the exact figure?

Thanks,

Peter.

p.s. I will even show the first teasr shot of the torch for the first good answer!

Congrats to this (mostly) completed project, Peter !
Assuming you meant to say 1.2 V (not 1.3 V) per cell.. your calculation looks good to me.

Now in the real world, you likely find that the runtime is somewhat less than calculated. The following factors are to blame for this:
- Cells rarely have the capacity that's printed on them
- Cell capacity depends a lot on the discharge current (check datasheet)
- Cell capacity derates depending on cell temperature
- You have a series-connection of cells. The lowest-capacity cell in your pack determines when u must stop charging as not to overcharge and when you must stop discharging as not to damage the weakest cell.
- The charger may not fill your cells to 100%
- Cells self-discharge, so if some time passes b/w topping them up and doing the runtime test you will not start out with a 100% charge.

Take a look at SilverFox' Battery Shoot Out . Indeed very helpful figures that explain a lot about batteries.

Aehm, an 11-cell series connection, is that a good approach for a caving-light ? I mean battery pack reliability. Not that I have any experience with this, I just think statistics: One cell (or its wiring) dies, the light is out.

Hello Peter

Good suggestions Martin did:goodjob:. I would also say, 11x single cells are very risky in an light, you have to trust.

You'll get with these cells a theoretic capacity of 35,6 Wh. I suggest 4x18650 cells with a total capacity of 32,56 Wh. (Protected ones with 2,2Ah each).

I guess you will have at last a better runtime with nearly no selfdischarge and a smaller, lighter and easyer to handle package.

Best regards

_____
Tom

Hi,

Thanks very much!

The discharge plots of the batteries I am using for a discharge rate of 0.1C which I think means 1A (please correct if I am wrong) for about 805 of the discharge cycle the average voltage is in excess of 1.3V.

I break the cells out and charge them individually which should generate a better average charge than charging them in series. It takes a long time, means the battery box has to be openable (waterproofing not easy) but it should make the difference in life length.

As reliability is paramount in caving torches, I carry a spare torch and a glow stick, As do most of my friends. If my main torch fails I probably have 5-6 spares offered to me.

I have done some serious SRT in the dark before as well!

So do my run time guesses seem reasonable?

Hmm,
not to sure about that calculator morelite. It says I should get 48hrs runtime on max. Doesn't seem correct, either that or I can fit 5 times as many LEDs!!!!

The battery case and headset has been built. All I need is my nice XR-e's to arrive from cutter and I can slot 3 of them in the Al headset.

The headset and the pack weigh a ton but they are nicely balanced so they are fine to wear on my helmet. Though i must confess, it would be more comfotable with a few less AA's but I wanted a buck converter due to the efficiency.

PeterScowcroft said:

The discharge plots of the batteries I am using for a discharge rate of 0.1C which I think means 1A (please correct if I am wrong) for about 805 of the discharge cycle the average voltage is in excess of 1.3V.

Click to expand...

0.1C is a formula. C is the rated capacity of the battery in mAh. If your batteries are 2700mAh, then 0.1C is 270mA.

Paul

http://i139.photobucket.com/albums/q312/pscowcroft/DSCN0038.jpg

my first photo. I will provide better when the design is complete. so this is the unpolished.

PeterScowcroft said:

I break the cells out and charge them individually which should generate a better average charge than charging them in series.

Click to expand...

Now think about the discharge cycle, Peter:
You have 11 cells connected in series, all of them are 100% charged. However, 100% is not always 2700mAh. One cell will be the weakest, let's say it stores 2450mAh. Towards the end of the battery run time, this weakest cell gets reversed (and consequently damaged) as the other cells yet have a higher charge.
Charging all cells in a series-connection yields better reliability. The charge is terminated when the charger notices the first deltaV-dip. This way, all cells have the charge of the weakest cell and the risk of reversing a single cell is low.

PeterScowcroft said:

So do my run time guesses seem reasonable?

Click to expand...

Without looking at the datasheets and discharge curves,
I bet they are reasonable on low and mid, maybe 25% less on high. All assuming you really have 2700mAh to start with and ambient is something like 20 deg C.

I like Long John's concept of 4x18650 cells. Superior power-to-weight !
With LiIon, one can even set up a circuit with the battery voltage just slightly higher than the LED's forward voltage (somewhat depending on LED bin). With this constellation, a linear regulator beats a step-down. On a fresh battery, efficiency is yet below the step-down. As it quickly approaches nominal 3.7 V, the efficiency is slighly better than step-down, from there on it increases to 100% where it drops out of regulation. Beyond that point, dimming at 100% efficiency. Overall efficiency is nice.