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What Determines My Robot's Operating Time?
This length of time you wish the robot to operate between recharging is determined primarily by the motors you choose, the robot's total efficiency, the battery pack and the obstacles (including terrain) your robot encounters. The most common practice when designing a custom robot is to include all the parts necessary for the desired functionality (motors, motor controllers etc.), and then choose a battery pack no heavier than the weight you set aside for the batteries in your design.
The capacity of the battery pack you choose essentially decides the total time your robot will operate between recharges. Keep in mind that if you want the robot to operate for a long time, your battery pack will either be heavier or need to be high capacity for the same size (costlier). For small robots, an operating time of 30 minutes to two hours is common. For medium sized robots, an operating time of ~1 hour is common. For large robots, the operating time can vary tremendously given the components and type of power supply selected.
A 2000mAH ( = 2.0 AH) battery pack can power a robot with two drive motors drawing 1A each continuously for up to 1 hour. Similarly, it can power a robot with two drive wheels each consuming 0.5A for 2 hours (0.5 * 2 * 2). Usually, higher capacity battery packs are physically larger.
An important note is that battery packs rated at a specific capacity are not always intended to be used at the maximum discharge rate. For example, a battery pack rated at 5AH should not necessarily be discharged at 5A for 1 hour. It is suggest to add 20 to 40 percent extra capacity whenever possible, so if your project requires 5A continuously, you should select a pack rated at 5AH * 1.4 = 7AH. Remember to always check the rated peak discharge rate as motors that are starting up consume significantly more current (around stall current) when starting than when in operation.

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