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Overview
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 Fast precise and affordable accelerometers are a key technology for these flying platforms. Their development was initially driven by their use for air bags in cars, and now increasingly bv their use in consumer devices such as mobile phones. Accelerometers are key because unlike standard helicopters, which use complex mechanics to allow stable flight, they use fast on board motor control to take care of stability. This mechanical simplicity is also their main attraction, Quadcopters can navigate in three dimensions using only four moving parts. The high realibilty of brushless motors make them simpler more reliable alternative to many traditional flying platforms. Hexacopters pack more rotors into a given size to provide more power.
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Tricopters
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Are cheap, easy to build, least stable, not as robust, low lifting power and flight time because the motors have to run faster to keep it the air hence heavier battery drain. No engine out capability, in the event of one of the three motors failing it will drop and crash.
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Quadcopters
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Mechanically simpler than Tricopters. While they weigh much the same they have about 1/3 more lift. They are usually more stable, not having servo issues and are capable of staying airborne longer. They can either lift larger batteries or fly more economically because the weight is spread across four motors. No engine out capability, again in the event of one of the three motors failing it will drop and crash.
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Hexacopters
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All the goods the good features of the Quadcopters, plus more lifting capabiity. As a bonus they add limited engine out capability, a Hexacopter can loose any single engine and still land, it will loose yaw control and if it looses one or both engines on the neutral torque bar it could even continue flying unaffected. The downside is that they are larger and a little more pricier, especially if running pricier motors.
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Octocopters
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They are heavier, all the good things features of the Hexacopters, plus true engine out ability. Loosing any one of the motors will enable it to fly as normal. This is what you fly if you need horsepower and reliability.
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Velocity and maneuverability
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It depends on the weight to lift ratio. If the machine weighs say 2 Kg and each of the four motors generates 625g of thrust (4*.625 = 2.6Kg), then the ratio is 2.5/2 = 1.25, which is not really good. However if the Quadcoter weighs 2 Kg and each motor generates 1Kg of thrust, then the lift to weight ratio is 4:1, which means plenty of power and speed for acrobatics.
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Flight Control
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 Rotors of motors 1 and 3 rotate clockwise, while rotors of motors 2 and 4 rotate anticlockwise, yielding opposing torques for control.
Each rotor produces both Thrust and Torque about its centre of rotation, as well as a Drag force opposite to the vehicle’s direction of flight.
If all the rotors are spinning at the same Angular velocity, with rotors 1 and 3 rotating Clockwise and rotors 2 and 4 rotating Anticlockwise, the net aerodynamic Torque and hence the Angular acceleration about the Yaw axis is exactly zero, which implies that the Yaw stabilizing rotor of conventional helicopters is not needed.
Yaw is induced by mismatching the balance in aerodynamic torques ie by offsetting the cumulative thrust commands between the counter-rotating blade pairs. Angular accelerations about the Pitch and Roll axes can be caused separately without impacting the Yaw axis. Each pair of blades rotating in the same direction controls one axis, either Roll or Pitch, increasing thrust for one rotor while decreasing Thrust for the other will maintain the Torque balance neede for Yaw stability and induce a net Torque about the Roll or Pitch axes. This way, fixed rotor blades can be made to maneuver the quad rotor vehicle in all dimensions. Translational acceleration is achieved by maintaining a non-zero pitch or roll angle.
In other words .... Having established that the North-South motors rotate Clockwise and the East-West motors rotate Anticlockwise.
For the Quadcopter to hover, all the torques generated by the 4 motors RPM have to be balanced.
For the Quadcopter to turn, increase one pairs RPM and decrease the other pairs RPM, in doing so the Thrust remains constant.
To pivot the Quadcopter, say on the East-West axis, assuming that both the North-South motors are turming at 50% of maximum RPM (whatever that may be), decrease the North motor say 45% of maximum RPM and increase the South motor to 55% of maximum RPM.
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