This electric thing is a huge balancing act. First off lets establish that as voltage decreases, apmerage increases (it's how all electrical systems work). Also the higher the current draw, the more heat. Heat is energy, energy that's wasted in the form of radiation and not thrust, thus an efficienty loss. Also battery's have two voltages we are concerned with, an at rest voltage, and an under load voltage. The slower we drain the batteries the more time we can fly. Also the longer we can maintain higher under load voltages means longer periods of burst power.
The idea behind the 12 cell set up is to increase voltage which in return lowers amperage (current). Current is what provides us the raw power we are looking for( the more current the more power). The question is how much raw power, and better yet, how long is that raw power available to us.
To make it simple, view your battery as a pinched garden hose with the water turned all the way on, yet the water supply is being pumped from a five gallon bucket(mah). With a low voltage setup (6S) you have to open the pintched hose 1/2 way to get the same same water pressure (current) as a high voltage (12s) that's opened only 1/4 of the way. As you can see, the five gallon bucket will run out much quicker with the low voltage setup than the high volage one.
Put another way, on a 6s setup, your battery's are working much harder to supply current as compared to a 12S setup. Lower current draw that yeilds the same power (thrust) makes for a more efficent system. Remember this is all a blacning act, right. With a higher cell count pack (12s) used on the same motor as the 6s setup, the rpm's of the motor would double and send the current draws (amperage) throughout the roof. To maintain balance, the winding is changed in the motor to a lower KV, thus maintaining the same rpm's as the 6s setup. In the end you have the same power, (maybe a little more depending on the actual motor wind) but you gain efficienty which equates to longer flight times, longer burst power, and less wear on your battery packs. But there is more, battery packs and weight.
In order to maintain a proper flying weight, you might have to buy different packs. Example, I already have like 10 5000mah 6s packs. I use them in several of my planes and multirotors. I plan to test 2 of the 5000mah packs as 12s setup in my plane, but if the weight is too much I will be forced to buy a bunch of smaller (3700mah) 6s packs. I made this decision going into the build and before I ever bought the motor. It took me a whole to wrap my head around the implications of a 12s system, but I the end I felt the reward was worth having to buy different packs. I have even thought of buying a bunch of 3s and making custom packs.
Lastly I just want to say I am no expert. I am just an old ham radio guy thats been playing with electritiy sice i was a kid. What I wrote above is my understanding of things, if I provided wrong or inaccurate information I hope someone will step in and set me straight. So there you have it, a long winded answer for what in my case could of simply been said, "because it's just better"
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