Drone Physics



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The Flight Physics of Quadcopter Drones
Physics
The Rotors on the quadcopter drone act like wings. They create lift by rotating at fast speeds, which pulls the air downwards and pushes the quadcopter drone in the air.

If the lift cancels out with the acting force of gravity, then the net force becomes zero and the quad hovers in midair.

A directional thrust makes the quadcopter to move in that direction.

A decrease in lift makes the Drone to lower its height.

Drone Flight Setup:
- Two adjacent motors rotates in the opposite direction.
- Two opposite motors rotates in the same direction.
 
For example, motors 1, 3 rotates Clockwise. While motors 2 and 4 rotate counter-clockwise. The reason behind this is that physics claims to be that the stability of the net force acting on a body should be zero.

Thus, if all the rotors were to rotate in the same direction, the result would be a net Torque causing the complete Quadcopter drone to rotate.


Image Source: Wired

Terminology
The terminology of drone movement is the exactly the same as used when describing naval movement. I will use these terms to explain the motions of our drone.



Image Source: Hackernoon

Roll: Moving to left or right with respect to the front of the drone. (The drone moves side to side.)

Pitch: Moving the drone forward or backwards.

Yaw: Pivoting or turning from the left or right. (The drone rotates around the center.)
Image Source: Quadcopterflyers

 Take Off
In order to take off the ground, you need a net upward Force. The motors generate lift that is greater than the force of gravity, making the drone take off.



Image Source: Hackernoon

Hovering
Understanding how drones hover is easy. First, motors create lift. Second, the lift should equal the force of gravity on the system. Therefore, the lift and force of gravity cancel out. Which makes the quadcopter drone hover in mid-air.

Roll
To Roll to the Left, the lift is increased on the motors on the Right. The drone must also decrease the lift on the motors on the Left.




Image Source: Hackernoon

If you wish to roll right, you do the exact opposite. The lift is increased on the motors on the left. The drone must also decrease the lift on the motors on the right.



Image Source: Hackernoon

Pitch
To make the drone pitch forwards (move towards) to you. The power applied to the motors rear motors is increased. This generates a forward net force which makes the Drone’s nose to pitch downward. You also have to decrease the power applied to the two front motors to keep the angular momentum conserved.



Image Source: Hackernoon


The exact opposite is done to make the drone pitch backwards (move away) from you.

Yaw
To make the drone Yaw (rotate) clockwise. You must increase the lift on the anti-clockwise moving motors.You also have to decrease the lift on clockwise rotating motors.

The reason behind this is to keep the both the upward and downward net force equal to zero. There is also a resulting anti-clockwise torque. The drone rotates clockwise to conserve the Angular Momentum.



Image Source: Hackernoon

Computerized Components:
Each movement the drone makes is possible by changing the rotational rate of one or multiple motors. In order to change the rotational rate of one or more rotors, you will need a controller that can up or lower the voltage to each motor. Thus, you will need one controller per each motor to move the drone as you desire.

You can also have some type of computerized control system to move the drone. This is done by easily moving around a joystick and letting the computer handle the rest. An accelerometer and gyroscope built into the drone can assist in creating ease and stability of flight. It achieves this by adjusting the power to each rotor every minute. If you add a GPS in the mix, there is no need for human control. Basically, adding a computer into the mix simplifies it.

Equations:
Multiple physics equations are at play when dealing with drones.Which includes:
- Lift (Ascends the drone)
- Force of Gravity (Pulls down the drone)
- Thrust (Moves the drone forward)
- Drag (Resistance when the drone moves forward)
- Voltage

In the example below, If the lift = force off gravity, and the thrust = drag. The drone moves forward at a constant speed.

Image Source: kiss png

Lift Equation:


L = ½ ρ v2 A CL
L = Lift

ρ = Density of Air

v = Velocity

A = Surface area

CL = Coefficient of Lift

 
Force of Gravity Equation:

FGravity = m g

m = mass

g = gravity (9.8 m/s2)

 
Thrust Equations:

FThurst = A ΔP

FThurst = ½ A ρ ( Vf2 - Vi2 )


ΔP = Change in  Pressure
A = area of propeller disks

ρ = Density of air ≈ 1.2 kg/m3

Vf = Final Velocity
Vi2 = Initial Velocity

Drag Equation:

D = ½ ρ v2 A CD

D = Drag

ρ = Density of Air ≈ 1.2 kg/m3

v = Velocity

A = Surface area

CD = Coefficient of drag


Voltage Equations:

V = I R
    or
V = P / I

V = Voltage
P = Power
I = Current


Jared Maltos
Physics 211 - F04
University of Alaska Fairbanks
Fall 2018