Appendix C. Internal Resistance (IR) and Estimating the Health of Your Lipos

At some point in this hobby you'll become concerned about the 'health' of your lipos and something called ESR (Effective Series Resistance), also known as the battery pack's IR (Internal Resistance).  Lots of opinions of what 'good' numbers are versus 'bad' ones.  Obviously, lower numbers are always better.  But, as batteries age and are cycled their internal resistance increases, so where do the upper limits lie?

I'm not going to give a dissertation about lithium polymer chemistry and all of the things that affect internal resistance - there's plenty of interweb info out there for that.  It's been stated many times that the internal resistance value of a cell/pack is an excellent indication of it's overall health, with lower values always being better.  However, larger 5000mAh cells need their IR to be down near 3-4  milli-ohms to be considered healthy, while smaller 200mAh cells can operate just fine around 100 milli-ohms or more.  That's quite a spread - how do you know what a good IR reading is for your particular cell or pack?

The answer is complicated unfortunately.  Lots of things can and do affect IR.  Temperature, equipment used to measure IR, cables, connectors, C rating of cells/packs and their age, battery chemistry, usage, storage, etc.  And, the phrase "Good IR reading" is subjective as higher IR cells may not perform well in high-current applications but are perfectly fine when subjected to lower-current usage.  Lots of discussion, opinions and facts on the RC forums will illustrate this clearly.

Fine, but I just want to be able to evaluate future IR readings and hopefully prevent what happened in the video from happening again, especially on my larger helis.  What happened in the video?  Well, at some point, after the start of the flight, the battery's ability to power the heli ended and caused a crash.  That's kind of vague, subjective, and hard to dissect or analyze.  However, I've quantified some things, established a few assumptions, and in doing so may have actually come up with something useful.

Defining Stuff

Let's say the heli crashed because LVC (Low Voltage Condition) was detected by the ESC causing it to shut down.  LVC has often been defined (when using lipos) as when the voltage of the pack's individual cells drop to 3.2V.  

Lipo cells are normally charged to 4.2V.  Typically, a fully charged cell will drop to 4.0V when first connected to the heli (under load, at the start of the flight).  Also typically, the pilot will fly until the cell drops to 3.7V (under load, at the end of the flight).  The cells will 'rest' after being disconnected from the heli and their voltage will rise, typically to 3.8V.  We'll use a halfway pack voltage of 3.85V (halfway between 3.7V and 4.0V) in the calculations below.

We'll also assume that 80% of the pack's mAh are used, and that 20% is left unused to prevent damage.  And we'll assume the C rating of the pack is appropriate for (can support) the chosen flying style.

Finally, let's establish some flying styles and RPM scenarios, which will be used to calculate average (or peak) current draw:

• High RPM, Smack 3D, Collective Punch-Outs, etc. will use 80% of the lipo in 3 minutes.
• Medium RPM, Sport, Aerobatics, Loops, etc. will use 80% of the lipo in 5 minutes.
• Low RPM, EZ Circuits, Collective Management, etc. will use 80% of the lipo in 7 minutes.

With all of this, we can work backwards from LVC for a given flying style - and calculate the IR of the pack that will cause LVC - for a bunch of different sized lipos.  These will be BALLPARK values, based on all of the assumptions above - YMMV.  They will clearly indicate RANGES of values you need to be aware of if you want to avoid hitting LVC during a flight.  

Disclaimer:  You (or I) won't be able to tell the exact IR value when your cells/packs will fail, but you will know when they are getting close, or within a RANGE OF VALUES where problems will occur.

Example - 3S 2200mAh Pack, Med RPM, 5 Minute Flight

So the story problem is written like this:  

          Find the IR of a 3S 2200mAh pack that will cause LVC during a 5 minute flight.   

     

Use Figure 1 to solve the problem.  We'll be finding the value of Rint using Ohm's Law.  Ignore Vpin1 and Vpin2 for now (assume they are 0V):

Figure 1.  Simplified Circuit for DC Analysis

   1)  2200mAh x 80% = 1760mAh   <-- This is how many mAh will be used in 5 minutes

   2)  3.85V x 3 = 11.55V   <-- This is the voltage of the pack used in the calculations (Vbatt)

   3)  3.2V x 3 = 9.6V   <-- This is the value of LVC used in the calculations

   4)  1760mAh / 5min = 352mAh/min   <-- This is how many mAh per minute will be consumed

   5)  352mAh/min * 60min = 21.12A   <-- This is the average current (I) drawn during the flight

   6)  (11.55V - 9.6V) / 21.12A = .092 Ohm   <--  This is the IR of the pack (92 milli-Ohm)

   7) .092 Ohm / 3cells = .031 Ohm/cell   <-- This is the IR per cell (assuming all 3 cells are equal)

Another way to state this is "A 3S 2200mAh pack with an IR in the range of 92 milli-ohms will cause LVC if the flying style results in a current draw of 21.12A or greater."  (see Figure 3).  So, if my iCharger displayed a pack IR within 10-20% of 92 milli-ohms (remember range, YMMV) I would suspect that this pack might not be suitable for a medium RPM 5 minute flight.

Obviously, you need to have an idea of how many mAh you're actually using and what your average current draw is during your timed flights.  This same 92 milli-ohm pack might be fine, however, for 7 minute flights, where the current draw is only 15.09A (see Figure 4).

IR is Known - Solve for Current (I)
You can also calculate the current draw that will cause LVC for a particular pack with a known IR.

Let's say you have a 2S 800mAh pack with an IR of 102 milli-ohms:

   8)  (2 x 3.85V - 2 x 3.2V) / 102 milli-ohm  = 12.75A

So if anytime during a flight the current increases to 12.75A (remember range, YMMV) then that 102 milli-ohm pack will cause LVC to occur.  See line #8 of Figure 2.

Here are Some Charts
Using the above simplified circuit and equations, I've prepared three spreadsheet/charts that calculate IR values that will cause LVC for various lipo batteries and current draws.  Red (Figure 2) is for high RPM/Smack 3D.  Green (Figure 3) is for medium RPM/Sport.  Blue (Figure 4) is for for low RPM/EZ flying.  You can use these charts, or calculate your own with your own custom values, to get an idea of where your lipos are health-wise.  Remember, these are ballpark ranges, YMMV, but at least figure these ranges are 10-20% wide.

Figure 2.  IR Values vs. 3 Minute Discharge

Figure 3.  IR Values vs. 5 Minute Discharge

Figure 4.  IR Values vs. 7 Minute Discharge

As you can see, the Red calculated IR values appear to fall in line with what many of the forum estimates are for 'Good IR' values, and most of the forum pilots are interested in 3D flying and high performance (I said most, not all).  The IR of a cell's electrode is inversely proportional to it's surface area.  Good thing because larger packs typically can only tolerate smaller IRs because of  the large amounts of current that will be pulled.  Smaller packs typically can tolerate the higher IRs because of smaller amounts of current.  The Green and Blue charts show that as your flying style eases up the exact same lipos can have higher IR values before becoming 'unusable'.

So what happens is the internal resistance of the cell 'steals' voltage away from what the helicopter sees.  The higher the current and/or resistance, the more it steals.  This causes LVC to occur sooner than it should.  Conversely, when charging the pack (and current is flowing in the opposite direction) the internal resistance of the cell 'adds' to the voltage of the cells, which causes the charger to see a higher voltage prematurely, thus thinking the cell is charged before it really is.

Another take-away from all of this is "Good IR Values" will also depend on the capacity, or size, of the lipo cell.  Smaller 'good' cells will have higher resistances when compared to larger 'good' cells.

1.25mm "Pico" Connectors (Molex) Used on Micro/Nano Aircraft.

One last thought - those tiny 1.25mm 'Pico' connectors used on ultra-micro or nano aircraft.  They suck.  They often have higher values of series resistance (thus, non-zero values for Vpin1 and Vpin2) due to their small contacts and weak spring forces.  These values end up adding to the battery's IR voltage drop to make power problems even worse.  They also make it more difficult to measure the IR of the cell, even with an iCharger.  Given those facts you may decide keeping up with these packs is best done on a performance evaluation basis.  After all, if those tiny aircraft hit LVC and 'auto-land' the damage will most likely be very minimal.