Electric RC planes, boats and cars use batteries and Electronic Speed Controls (ESC) to control the motor. The ESC has two sets of leads, one runs to the motor, the other set to the battery pack. While it can be advantageous to solder the motor to the ESC, the same is not true for the battery. LiPo battery packs are rechargeable and need to be removed from the RC vehicle before charging. Some LiPo packs come with a connector already installed, others with nothing but a pair of wires.
What is an ESC?
ESC stands for Electronic Speed Control. Either the flight controller or radio receiver sends signal to the ESC, and the ESC drives the brushless motor by providing the appropriate level of electrical power.
The ESC thinks it is connected to a LiPo battery because it was programmed that way. Low Voltage Cut off (LVC) reduces power to the motor when the voltage drops to a pre determined level (usually 3V per cell for LiPo) to prevent damage to the battery. If you are not using a LiPo you need to disable this functionality. In the manual for the ESC there is a programming procedure which can disable this.
A 3s lipo is 12.6v fully charged, a fully charged 12v lead acid is higher then that, so the ESC probably thinks you connected a 2200mah 3s lipo. The LVC for a 4s would be 3v x 4 = 12v. When your motor starts pulling amps the voltage drops. It will quickly drop below 12v with how many amps you are trying to pull. This will trigger the LVC which will drastically reduce power to the motor.
ESC refresh rates vary. For multi-rotors, given the balance of multiple motors critical to the craft's ability to stay airborne, high refresh rates are more important than many other hobbies where ESCs are used.
The only other major factor to consider is an ESC's maximum current rating, which must exceed the current draw to each motor. Generally, 30 A for medium/large quads and 10 to 12 A for a small quad is plenty.
Clearly, those are high current draws. But such is the nature of multi-rotors. A medium-sized hex can easily pull 40 A on a steep ascent. As a result, hefty batteries are a necessity for decent flight times.
The industry standard is lithium-ion polymer (LiPo) batteries. Relatively lightweight, compact, and offering high discharge rates, LiPos are well-suited for multi-rotors.
There are three to consider as you start perusing the cyber-aisles of LiPo batteries. The first is voltage. A single cell supplies a nominal voltage of 3.7 V (4.2 V at full charge). Each additional cell wired in series adds 3.7 V to the nominal voltage of that pack. Cell counts are denoted by the number of cells followed by "S". A cheap 2s lipo batteries, therefore, is a battery of four 3.7 V cells at a summation of 14.8 V.
LiPo packs also have C ratings that indicate the maximum rate at which a pack can be discharged, with C standing for capacity. A 20C pack can be discharged at a rate 20 times its capacity.
Capacity, therefore, is the third important factor. It's measured in milliamp-hours (mAh). Let's say our 20C pack has a capacity of 4000 mAh. Given what we know about C ratings, we can do the math and determine its maximum discharge at up to 80,000 mA, or 80 A. Similar to ESCs, you need a discharge rate that's higher than the combined draw current of your motors.
How to Connect ESC to a LiPo Battery
Following the instruction to connect ESC to Your Lipo battery
Instructions
Strip about a quarter inch of insulation off each of the four wires. Place a 1-inch long piece of heat shrink tubing on each wire. Place the heat shrink as far from the bare end of wire as possible.
Solder the connectors to the wires. Make sure the prongs and sockets align properly to keep the polarity correct. Once the solder has cooled slide the heat shrink tubing over the solder. Use a match or lighter or even your soldering iron to shrink the tubing tight.