The 2:1 Rule of Thumb - Not good for the CF
The 2:1 thrust-to-weight ratio is a popular rule of thumb. That is, at 100% throttle, you want your combined propeller thrust to be capable of lifting two times the weight of the craft. While this rule ensures the quadcopter is very maneuverable, I've found it to be too conservative for the CF: total weight is 19 grams, but it can barely lift 10 grams of payload, instead of the additional 19 grams required by the rule.
For Maximum Flight Time
For the CF, the thrust/weight ratio is more a matter of preference, depending on how much flight time you're willing to sacrifice for maneuverability. For heavy payload, camera/fpv applications, flight time is more important than maneuverability. For these applications, you may only need enough thrust to keep the CF hovering, with some ability to climb occasionally. The next logical question becomes "how big of a battery should I load the CF with before the weight of the battery counteracts the extra thrust that it provides?" The answer to this question is in this study on Optimal Battery Capacity. Here's a summary of the study: Maximum flight time is achieved when battery weighs twice as much as the weight of the copter without batteries. Beyond that, any more battery capacity is cancelled out by its added weight. That said, inefficiency of the motors and battery energy/weight density won't allow us to fly a 13 gram CF with a 26 gram battery-- A 4-motor CF can only carry about 10-15 grams of battery weight. But the principle does still hold true up to a theoretical 26 gram battery: Despite the weight increase, a bigger battery will allow the CF to fly for longer.
Best Compromise Between Flight Time & Maneuverability
But a CF loaded with a heavy battery does impact maneuverability. The study also shows there is a point of optimum compromise between weight and thrust (maneuverability): "The best compromise is for batteries that weigh about 83% of the airframe. For this mass fraction, about 87% of the most optimal flight time is still achieved and this with only 61% of the total weight." Thus for a 13 gram CF, the most efficient compromise between flight time and maneuverability is ~11 grams of total battery weight (83% X 13 grams).
Using an After Market Battery
For example, here's an 11 gram 400mAh 25C battery that could work on a CF once the connector is swapped out. To determine flight time, actual testing has always been way more accurate for me than using math/formulas (I'm not an electrical engineer!). The connector on this new battery is different than the stock battery, but you can take the connector from your stock battery and use it on the new battery: use a needle or xacto blade to carefully lift/pry the plastic prongs upward and the wire leads will slide out of the plastic connector.
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Ordering New CF Battery Connectors
If the new battery's connector won't allow you to disconnect and pull out the metal leads, you'll have to just cut the wires and create new metal leads and feed them into the connector from your CF battery or use a new CF battery connector. You can purchase new JST-ZHR-2P battery connectors from segor.de that will fit into the CF battery port. You'll have to send them an email with the number/type of connectors you want (don't forget to order 2 metal wire clamps for each 1 connector so you can clamp them around the ends of the wire before inserting them into the plastic connector).
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UPDATE:
An easier way to get the correct battery connectors is to use the pre-assembled plugs for sale on eBay:
Mini. Micro JST Connector plug ZH 1.5 2-Pin w/.Wire x 10 sets
Battery for Double-Motor Configuration
See the thread on Double-Motor Configuration for background on this modification. Doubling the motors increases power output, allowing you to carry a larger payload/battery. A regular 4-motor CF can lift a maximum of 10-15 grams of battery and/or payload. Based on testing, a double motor CF (8 motors, 21 gram empty weight) can lift 15-20 grams of battery and/or payload. Under the same principles described above, the best time/thrust compromise (83% X 21g) for a non-payload, double motor CF, is ~17 grams of battery, which falls within the 15-20 gram limit. Here's a 600mAh, 15 gram battery and here's a 650 mAh battery, weight unknown.
Looking forward to thoughts from the rest of the group!