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I like to know are there simple equations to find how much motor power is needed to lifting 1 KG with a quad rotor? Also if we use gas powered engine, how can we find a relation between lifting weigh and fuel consumption?

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In order to lift the weight of $mg$, you need at least a trust $T=mg$. The trust of a quadrotor with four identical motors is given by $T=4 k_T \omega^2$, in which $k_T$ is a parameter that depends on your motor/rotor and $\omega$ is the angular velocity. From this, you can estimate at which $\omega$ your motor has to operate. Additionally, to this, you will have to overcome the air drag due to rotation of the blades. This air drag needs to be overcome by a torque $M=4k_M \omega^2$. So you have to check if your motor does supply this torque $M$ at $\omega$. So if you combine this information you can estimate your power by $P=M\omega$. Remember that this is just a lower bound and you should rather select a better motor in order to allow a certain level of agility.

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The thrust to weight ratio of your quadcopter should be at least 2 to for a decently manoeuvrable quadcopter.

For example, if your quadcopter has mass m, then your motors need to provide a total thrust of m*g to hover. Look for motors that can provide a thrust of mg/4 each (assuming 4 rotors) at 50% throttle.

Most motor manufacturers today actually provide performance statistics of their motors with various prop sizes so finding the right motors should not be too difficult.

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