In the previous post of the series, I outlined some basic information about this study. In this post, I’ll start diving in to the data to see what it tells us about LiPo characteristics. I’d recommend you give part 1 a read to familiarize yourself with the method I used to collect data.
A word on how to interpret the graphs below: Each trendline represents a single battery discharged from 100% down to about 20% in 20 second intervals at a fixed load resistance. Each graph has a legend to indicate which line is which. For example, “45C #1 3.7 Ohm” refers to one of the 45C batteries I named “#1”, using a load resistance of 3.7 Ohm.
Also, you need to know Ohm’s Law to get the most out of this data. Ohm’s Law states “Voltage equals current times resistance” or V = I*R. The larger the load resistance used, the larger the current draw will be.
Finally, keep in mind that I’m primarily looking for relationships between variables, and not specific numbers. The batteries I’m using were chosen for very specific reasons (discussed in part 1), but this is not a review of those batteries. The relationships discussed apply to all LiPo cells.
LiPo State of Charge
The term “State of Charge” refers to how much energy is left in the battery on the current charge cycle. It’s directly related to the battery capacity rating. A 300mAh battery at 100% state of charge has 300mAh worth of current stored. At 50%, it’s only got 150mAh left, and so on. It turns out most properties of a LiPo change as a function of state of charge, and it makes for the most useful x-axis value for most of these graphs.
Unfortunately, state of charge can’t be directly measured, but it can be computed from current draw and time. Amp-hours consumed is (Current Draw in Amps * Duration in seconds) / (60 seconds/min * 60 mins/hour). Multiply by 1000 to get milliamp-hours. Keeping a running sum of milliamp-hours consumed allows state of charge to be computed.
It turns out the state of charge vs time relationship is very close to linear. This is why it makes a good x-axis value. It takes less time to discharge a battery with a very small load resistance than it does a large load resistance. Plotting voltage, current, etc against state of charge (instead of elapsed time) normalizes this time discrepancy while remaining linear with respect to time.
LiPo Resting Voltage
Resting voltage is the voltage across the battery terminals when the circuit is open (the battery isn’t connected to anything). This measurement is commonly used as a simple fuel gauge for a LiPo cell. Some common guidelines are 4.2V = 100%, 3.8V = 50%, and 3.7V = 20%. It’s also widely accepted that a LiPo cell experiences permanent damage if it’s discharged below 3V, and to protect against this you should usually never discharge past 20%. Here’s what the data says:
I notice a few things about this graph:
- The curves are highly consistent across all batteries tested, including both 20C and 45C, regardless of how fast they were discharged.
- The voltage-to-percentage guidelines mentioned above seem to match up pretty well.
- The resting voltage falls off a cliff right after the 3.7V/20% mark. This characteristic is the basis for the rule of thumb that you shouldn’t deplete your battery past 20% capacity. As you can see, after the 3.7V/20% point, the voltage will plummet below 3.0V pretty quickly.
- Note: I pushed 20C #3 over the edge in order to show the voltage drop off in the data. You shouldn’t do this, and I almost certainly damaged that battery in the process. But hey, what’s one battery for the sake of science??
There’s one other observation that’s pretty subtle, but worth pointing out. Take a close look at where the curves cross the 3.7V mark. Lower load resistances reach 3.7V at higher states of charge. This is most obvious on the “45C #1 0.5 Ohm” test where it crosses 3.7V well before 20%.
Does that debunk the 20% discharge rule? Not quite. Here’s what’s going on: There’s a small portion of current that’s lost inside the pack itself due to inefficiencies. As the current draw increases, more and more current is lost inside the pack itself. As current draw increases, this loss also increases. So, the 0.5 Ohm test isn’t actually crossing 3.7V at ~25%. Instead, the calculated state of charge is slightly optimistic because it doesn’t account for current loss. There are two practical applications of this:
- The method I’m using to calculate state of charge is the exact same way it’s done by flight controllers with a current sensor. So, if you’re relying on a current sensor and battery capacity in mAh to decide when to end your flights, I’d recommend not pushing it all the way to 20%. If you’ve been consuming current at a high rate, there’s a good chance the battery fuel gauge is a bit optimistic.
- I believe this measurement error could actually be used to compare efficiencies of LiPo cells. I’ll look in to this idea more in a future post.
LiPo Load Voltage & Voltage Sag
Load voltage is the voltage that matters the most, because it occurs when the battery is connected to something and delivering current. Take a look at the load voltage graph.
You can see that each curve matches the shape of the resting voltage curves pretty well, but the amplitude is lower. This discrepancy (the difference between resting voltage and load voltage) is called “voltage sag”. Here’s a graph of voltage sag vs state of charge.
Note that voltage sag is proportional to current draw. The higher the current draw the more the voltage drops. There also appears to be three sections to the curve (more obvious as the current draw increases): Voltage sag decreases slightly from 100%-80%, remains relatively constant from 80%-20%, and then increases again after 20%.
Load voltage is also where you start to see the difference between batteries of different current draw ratings come in to play. Here’s the load voltage and the voltage sag of the 20C battery compared to the 45C battery at the same load resistance – the 20C battery sags quite a bit more. Also note that the drop off point of load voltage happens a bit later on the 20C battery than the 45C battery. This is worth exploring more, and might also have to do with cell efficiency: could be a good metric for comparing different batteries.
LiPo Current Draw
Recall that Ohm’s Law states that for a fixed resistance, voltage and current are proportional. With that in mind, there aren’t really any surprises in the current curves.
I shared this chart of expected/theoretical current draws in part 1, and you can see the measured current matches up pretty well. It’s slightly lower across the board, which is due to voltage sag (lower voltage means lower current).
|Load Resistance||Expected Current Draw at Nominal Voltage (3.7 V)||C Rating of Expected Current Draw (assuming 300mAh capacity)|
|0.5 Ohm||7.4 Amps||24.67 C|
|0.9 Ohm||4.11 Amps||13.7 C|
|1.3 Ohm||2.85 Amps||9.48 C|
|1.9 Ohm||1.95 Amps||6.49 C|
|3.7 Ohm||1 Amp||3.33 C|
And here’s the comparison between the 20C and 45C batteries. Again, not shocking: the 20C battery supplies less current. This makes sense, given the higher voltage sag and Ohm’s Law.
The third variable in Ohm’s Law is resistance. Since the premise of this experiment was to test batteries under a set of fixed, constant load resistances, you might not expect this graph to be interesting. You’d be wrong. Here’s the graph of total circuit resistance (calculated by R = V/I):
Two things: First, the actual resistance is higher than what I measured the load to be. Second, the resistance increases as the state of charge decreases. This is due to a LiPo property called Internal Resistance (or IR for short), which describes a resistance that occurs inside the cell itself. IR is the most important property, and it turns out it’s the hardest to measure. Part 3 of this series discusses internal resistance in depth. For now, just know that it exists and it changes over the discharge of the battery. It’s also responsible for voltage sag.
Finally, you can see that the 20C battery appears to have a higher IR than the 45C battery, which explains the larger voltage sag and lower current supply.
Since we’re talking about a power delivery system, I’d be remiss not to mention Power. Power (in watts) is defined as voltage times current. We’ve already looked at voltage and current independently, so again, there are no surprises in the power curves.
Summary And Practical Applications Of LiPo Characteristics
So what does all of this mean for you, the consumer of LiPo batteries? Here are some key applications.
Application #1: Voltage and current decrease as you deplete your battery. The effects depend on the application. For electric motors (in general) decreased voltage means decreased RPM (speed or thrust) and decreased current means decreased torque (rotational force). This explains why your aircraft/vehicle becomes sluggish as the battery is depleted.
Application #2: Some batteries are better than others. This is mostly due to Internal Resistance (coming in Part 3 of this series) but there are other factors, like efficiency and the shape of the voltage/current curves. I plan on dedicating a post to discuss some key metrics to look for when comparing batteries.
Application #3: It’s not that straightforward to tell when you should stop and change batteries. You’ve basically got two choices: monitor voltage and stop before 20% (3.7V) resting voltage, or use a current meter and count mAh consumed (also stopping before 20%). Monitoring voltage isn’t straight forward, because you want to pay attention to resting voltage not load voltage. If you want to have a beeper go off (or a low volt warning in an OSD) you need to do some testing with your batteries to figure out what load voltage at what throttle position corresponds to 3.7V. This changes from battery to battery, and it also changes over the lifecycle of a single battery. For this reason I strongly prefer using a current sensor. However, keep in mind what I said about current monitors up in the “Load Voltage” section: They don’t account for current loss so the remaining capacity is over-estimated towards the end of the cycle. For this reason, I’d aim to shoot for 30% or 25% instead of pushing it all the way to 20%.
Application #4: Quadcopter PID tuning. I think most of us tune with full batteries. After seeing this data, I might wait until the 90% or 80% mark to start tuning. The idea here is that voltage and current drop off at a much faster rate from 100%-80%, and then level off to be fairly linear from 80%-100%. Voltage and current factor directly in to the responsiveness of the motors (via RPM and torque, respectively). By tuning on a full pack, you’re actually optimizing for a pretty small portion of the battery cycle. If you tune with your battery at 80%-90% you might end up a little bit over-tuned on a full pack, but have a tighter feel for the remainder of the battery. Now, I haven’t actually tested this idea out, but it sounds good to me on paper. I’ll have to try it out and report back.
In part 3 of the series, I’ll drill deeper into the Internal Resistance of a LiPo cell. We’ll talk about what it is, how to measure it, and how to use it to compare batteries for health and quality.
Got any questions or comments? See any trends in the data that are interesting that you think are worth highlighting? Let me know in the comments below. And don’t forget to follow @thejumperwire on Instagram, Twitter, and/or Facebook for post notifications and other tips!