Ken,
STRIKEOUTS ADDED NOV 30TH BY THE AUTHOR
The number of cells has no bearing on how long the battery will run a given motor! The only thing that determines how long the battery will run a given motor! The only thing that determines how long the battery will run the motor is the milliamp rating. The first two sentences are not correct. See Tim Wescott's post three posts down. The C rating also doesn't have anything to do with how long the motor run will be.
The purpose of the C rating is to tell you how many amps the battery will comfortably deliver. This matters because every motor is rated for a maximum amperage draw. The battery must be able to deliver at least the maximum amp rating of the motor. To determine if the battery has the capacity to deliver the amount of amperage the motor will draw you multiply the milliamp rating times the C rating. So, a 2,200 mah battery (which is the same as 2.2 amps) with a 30 C rating will deliver 2.2amps x 30C = 66 amps. So, any battery with a 2,200 mah 30C rating can support a motor with a peak amperage draw of 66 amps. The formula for how many amps the battery will deliver at any given moment stays the same regardless of how many cells the battery has (amps x C rating = amps the battery can deliver). So, a 5,000 mah (5 amps) battery rated for 20C will deliver: 5 amps x 20C = 100 amps. Also, a 5,000 mah battery rated at 30C will deliver: 5 amps x 30C = 150 amps. So, a 5,000 mah battery at 20C or 30C is way beyond what you need. As I said, the number of cells (voltage) does not determine how much juice a battery can store or deliver.
To repeat, how long the battery will run the motor is not dependent on how many cells the battery has. Flight times are only dependent oon the milliamp rating if the battery. Also, how big a battery is needed to power your motor is not dependent on the number of cells, but rather the milliamp rating and the C rating of the battery. Now, the manufacturer will tell you how many cells the motor was designed to run on. The manufacturer will tell you the minimum and maximum number of cells the motor was designed to operate with. If you want to burn up or shorten the life of a motor that is rated for a maximum of 4 cells, try running it on 6 cells. It won't last long, if at all.
So, if you want the same run time and want to go from a 4S battery to a 3S battery, the milliamp rating should stay the same and the C rating should stay the same. In other words a 2,200mah 4S 30C battery will give the same run time as a 2,200mah 3S 30C battery [As Tim's post below demonstrates, they won't be exactly equal. In the example he gives there is an 8% difference going from a 5S to 6S battery.] And both a 3S and 4S battery rated at the same 2,200 mah and 30C have the same capacity to deliver the same 66 amps to the motor. Interesting enough, most 2,200 4S batteries will be the same length as a 3S 2,200. The only difference will be the 4S will be one cell thicker.
However, voltage determines thrust. You will never get anywhere near as much thrust using a 3S as you were getting from the 4S no matter how big a milliamp rated battery you use no matter how big a milliamp rated battery you use [See Tim's post below.] or how high a C rating you use.
Now the only way to know how many amps the motor is actually drawing is to buy a Wattmeter and check it for each different prop you use (every different prop diameter, pitch and manufacturer will draw a different amount of amps for a given motor/battery combination). In fact, if you attach a scale to the tailwheel to measure the thrust, the watt meter will be able to tell you which prop gives the most thrust for the least amperage draw (longest flight time.) I checked the You Tube reviews of different wattmeters and the one that reads accurately at different voltages is the "Watts-Up." I just checked and it is available on Amazon for $29.95 but wasn't at Tower Hobbies, Horizon Hobbies, or Hobbyking). This is the one I bought since I was building a lot of Flite Test foam board RC models and was using non-standardized motor, prop combinations.
If you don't want to get bogged down in the weeds with a watt meter, use combinations of motor, prop, ESC, and battery one of the suppliers recommends. And if you just want to risk it, run the motor for a while and check to see if the motor, ESC, or battery gets hot. It's not unusual for these items to get a little warm, but they shouldn't burn you to touch them. Also, if your battery swells, or the shrink wrap on your ESC bubbles, you were drawing too much current.
Each electric motor has a Kv [See Tim's correction 3 posts down] rating which stands for kilovolts which means how many rpms in a perfect world the motor will spin a reasonable prop for every volt the battery can deliver. So, a 1,000 Kv motor on a 3S battery will deliver 1,000 Kv x 11.1 volts (a 3S battery) = 11,100 rpm. The reason a 4S battery will give you a lot more power is that for every volt increase the rpms will increase whatever the Kv rating is. Thus, the same 1,000 Kv motor on a 4S battery increases to 14,800 rpm (1,000 Kv x 14.8 volts = 14,800 rpm).
Now what may seem odd is that you must run a smaller diameter pitch prop on a 4S battery than on a 3S battery or the motor will draw a lot more amps. In other words, if you change from a 3S battery to a 4S battery and don't decrease the diameter of the prop, you will burn things up. But since you are thinking of decreasing the voltage by going to a 3S from a 4S you will want to increase the diameter or the pitch of the prop from what you were using on the 4S battery to properly load the motor. [These statements are not true. See Tim's post below.] Again, a wattmeter is the only way to know if the motor is loaded properly (not too few and not to many amps).
Incidentally, since I have a watt meter, I have found that the range of props the motor manufacturer says you can use may overload the motor (and thus the ESC as well) under certain prop/battery combinations. So, even if you use a prop recommended by the motor manufacturer there is a possibility you may be overloading the motor/ESC. The only way to tell for sure is with a watt meter.
Hope this helps,
Joe Ed Pederson