## Friday, April 13, 2012

### 4pcb: 3S/370mAh Testing

Previously, I promised some PCB quadrotor testing on a 3S/370mAh battery instead of its former 2S/460mAh. They're both Turnigy nano-tech packs with a 25-40C discharge rating, so I am only trading mAh capacity for more voltage. In actuality, the 3S does store more energy (1110SmAh vs. 920SmAh to use a nonexistent unit of energy). Accordingly, it's also physically larger:

 3S/370mAh (left) vs. 2S/460mAh (right)
And, it weighs more. The 2S/460mAh weighs 30.0g, while the 3S/370mAh is 36.6g. (In both cases, this comes out to about 113Wh/kg, which seems reasonable for a small power-cell pack where much more of the weight is packaging and connector.) Generally, adding 6.6g of weight to a micro quad is going to hurt a little, but if you're going to add weight somewhere, the battery is a good place to do so.

Theorem 1: "LiPoCopter Theorem" As the ratio of battery weight to total weight (LiPoCopter ratio) of an RC helicopter/multirotor increases, it is increasingly likely to be able to fly with properly chosen motors, props, and ESCs.

Proof: Consider the extreme case: a helicopter made out of a LiPo (possibly one of these, with two rotors attached to it like a LiPo-bodied Chinook). It is certainly possible to choose a set of components {motor, prop, ESC} which will allow this to fly. As any helicopter/multirotor approaches this ratio of battery to total weight, there will be some set of components which allow it to fly.

 A respectable LiPoCopter Ratio of 26.4% (formerly 22.8%).
Of course, I don't get to choose an arbitrary set of components for 4pcb; I'm stuck with the existing motors, props, and controllers. I had a hunch that it would fly better, though, since the ESCs would very much like to see more voltage. They're rated for 7-42V, so running on 2S (7.4V) is very borderline. 3S (11.1V) gives much more margin for voltage sag under load. The weakest motor would tend to reach command saturation well before the 2S battery was dead, leading to drifting and ultimately instability.

The improvement on 3S was immediately apparent, with no additional work required. Here's a comparison of the motor commands for full-length flights on 2S and 3S:

 2S/460mAh
 3S/370mAh
In the 2S/460mAh flight, the average command to hover starts at about 200 (out of 255) and increases as the battery voltage drops, up to about 220. The problem is the front motor: after some time, it begins to saturate and when it does, it can't produce any extra thrust to counteract for disturbances. In flight, this causes the quad to pitch forward, especially on throttle-up, and makes it difficult to fly. You can see I had to land several times to let it re-stabilize. The total flight time was about 6 minutes, but the last 2-3 minutes were me fighting to keep it in the air. Usable flight time was about 3-4 minutes and even at the end of the flight, the battery was still above 7.4V (only 50% discharged).

The 3S flight is one continuous stretch of over 8 minutes in the air. The average command to hover starts at about 165 and increases to about 185 as the battery voltage drops. This leaves plenty of margin for stability, so even though the front motor command is still highest, it never saturates. The problem of uncontrollable pitch as the battery gets discharged is eliminated. One side-effect of having higher voltage is that all the gains are now too high, causing small/fast oscillations (compare the width of the lines in the above images). This should be easy to fix. After 8 minutes, all four motors start to taper off in power. And all of the battery capacity was used:

 3S/370mAh after 8 minute flight. Total voltage: 9.02V.
Luckily, I bought four of the 3S/370mAh packs, so I now have enough capacity for 32 minutes of continuous flying. Just in time for demo season.