Quadcopter Design and Dynamics [email protected] 2: Quadcopter Design and Dynamics Page: 2...
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Lecture 2: Quadcopter Design and Dynamics Page: 1
Lecture 2
Quadcopter Design and Dynamics
Lecture 2: Quadcopter Design and Dynamics Page: 2
Objectives of this Lecture
• The objectives of today’s lecture are:
To help you understand the various frame designs, and
their advantages/disadvantages.
To help you understand the various components in a
multicopter.
This will help you design and build your own multicopters.
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What We Will be Covering
• Multicopter Frame Design
X-frame. Y-frame, hexacopter, octocopter, etc.
• Multicopter components
Frame components, motors, speed controllers, propellers,
flight controllers, batteries, battery eliminator.
• Multicopter dynamics
Mathematical models.
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MULTICOPTER FRAME DESIGN
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• Common Frame Designs
Multicopter Frame Designs
X-Frame Y-Frame H-Frame
Hexa-Frame Octo-Frame
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Multicopter Frame Designs
• Frame design affects stability
Y-frame has less roll and yaw stability than X, hexa and
octo frames.
H-frame has less pitch stability.
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Multicopter Frame Designs
• Frame design affects reliability.
• Quadcopter flip of death
Most often caused by a failure in one motor
(In this video the failure was caused by rain)
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Multicopter Frame Designs
• In Hexa and Octo frame designs, other more power can be
added to other propellers to balance out a failed motor.
Note: APM 2.6 does not support this feature.
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Multicopter Frame Designs
• Hexacopter and Octocopter frames provide much heavier
lifting capacity.
Smaller high-speed props also produce less vibration.
Very popular with video production companies.
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Frame Size
• Multicopter frame size is
measured in millimetres.
Measurement is taken from
centre of a propeller spinner, to
the centre of the spinner of the
propeller directly opposite.
A 450-sized quadcopter measures
45 cm across.
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MULTICOPTER COMPONENTS
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Components of a Multicopter Frame
• Centre Plates
Usually made of plastic or carbon fibre.
Used in pairs to hold the arms.
Holds the battery, flight controller, flight radio and other
electronics.
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Components of a Multicopter Frame
• Arms
Usually made of nylon, plastic or carbon fibre.
Holds the motors and electronic speed controllers.
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Components of a Multicopter Frame
• Power Distribution Board
Distributes power and control signals to the motors.
Many multicopter designs use a printed circuit board
integrated with the centre plate.
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Components of a Multicopter Frame
• Skids
Long skids useful for mounting cameras under the
multicopter.
Long skids tend to get caught on the ground causing the
multicopter to flip.
Short skids.
Easier to take off and land. Less chance of flipping.
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Active Components - Motors
• Motors
Types of Motors
Brush motors
A commutator is used to reverse the current in the rotor to make
the rotor spin.Brushed motors overheat more easily and are less
efficient.
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Active Components - Motors
Brushless motors
No brushes. Uses a generated AC voltage to reverse rotor
polarity causing it to spin.
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Active Components - Motors
Inrunner Motors
These are brushless motors, and the spindle is connected to an
internal rotor that spins. Inefficient at high speeds, requires
gearbox.
Outrunner Motors
Also brushless. The casing itself spins.
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Active Components - Motors
• Motors are rated according to continuous draw current,
and kV.
Continuous draw current, in amps.
Tells you how much current the motor uses in normal
operation.
Kv – Measures the number of revolutions per minute per
volt.
E.g. a 1000Kv motor produces 1,000 RPM per volt.
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Active Components - Motors
• We can find the maximum power of a motor:
P = I x V
Here I is the continuous draw power of the motor, and V is
the maximum voltage of your battery.
• This in turn affects what you can do with your multicopter.
E.g. higher power is required for acrobatics.
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The Importance of kV
• Due to the way it is built, a lower Kv motor has higher
torque.
This allows the motor to spin larger propellers and provide
larger lifting capacity.
• A higher Kv motor has lower torque but is more reactive.
You would use a smaller propeller with a high Kv motor.
Smaller propellers react much faster to changes in current
to the motor, providing better control.
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Active Components - Motors
• To summarize:
Motors with larger continuous current draw produce more
power and let you lift heavier objects.
Motors with smaller Kv let you lift heavier objects.
Motors with larger Kv react faster to changes in control
input.
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Active Components - ESC
• An Electronic Speed Controller (ESC) lets you control the
RPM of your motor.
• Selecting a speed controller is simple:
Must match the voltage of your battery. Usually stated as
an “S” value (see later)
Must exceed the current draw of your motor (rated in
Amps)
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Active Components - ESC
• The ESC provided with your F450 frames have the
following specifications:
Battery voltage : 2S to 3S (7.4v to 11.1v)
Sustained current: 30A
Burst current for 10s: 40A
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Batteries
• Almost all multicopters
operate using LiPo
batteries.
Batteries are rated with 3
values:
S value – Determines
maximum voltage output.
mAh value – Determines
capacity of the battery.
C value – Determines
maximum current draw.
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Batteries
• S value:
This tells you the number of cells in the battery.
2S -> 2 cells
3S -> 3 cells
Each cell produces approximately 3.7 volts.
2S battery produces 7.4v, 3S battery produces 11.1v, etc.
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Batteries
• Milli-amp Hours (mAh)
This measures the battery’s charge
storing capacity.
In a 2700 mAh battery, you can draw
2700 milliamps for one hour, or 1 milliamp
for 2700 hours.
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Batteries
• C Rating
This is the maximum safe continuous discharge rate of
your battery.
To find discharge rate, multiply the C rating by the
capacity.
E.g. maximum current discharge for a 25C, 2700 mAh
battery is 25 x 2700 = 67,500 mA or 67.5 A.
Discharging higher than this will cause your battery to heat
up, bloat, and possibly explode.
• Thus if you are using an 80A ESC, a 25C 2700 mAh battery
would be insufficient.
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Propellers
• Propellers are rated using two values:
Diameter in inches.
Pitch in inches
• A 10x4.5 propeller for example has a 10” diameter, and
“travels forward” 4.5 inches with each revolution.
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Propellers
• Propellers can be clockwise or counter clockwise.
Every quadcopter would use 2 clockwise and 2 counter-
clockwise propellers.
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Propellers
• Propellers can be made
of:
Plastic
Cheap.
Suffers from aero-
elasticity, can lose
efficiency and cause
vibrations.
Carbon fibre
More expensive.
Rigid, less vibrations
and less aero-elasticity.
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Propeller Power Requirements
• The amount of power a motor must put out to turn a
propeller is given by the following equation:
𝑾 = 𝒌 × 𝑹𝟑 × 𝑫𝟒 × 𝑷
R = propeller RPM, D = propeller diameter inches, P = propeller
pitch in inches, and W is power required.
• k is a factor that depends on:
Design of the propeller
Blade thickness, width, airfoil profile, etc.
A typical value is 5.3 X 10-15
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Propeller Power Requirements
• This equation tells us:
Increasing propeller diameter results in a large increase in
motor power requirement.
This in turn means drawing much more power from your
ESC and battery.
Increasing propeller pitch results in a small increase in
power requirement.
And of course, more RPM = more power needed.
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Propeller Power Requirements
• E.g. specification:
1000 Kv motor at 11.1v = 11,100 rpm
10” propellers with 4.5” pitch
• Power requirement:
5.3 x 10-15 x 11,1003 x 104 x 4.5 = 326.18W
Current draw = 326.18 / 11.1 = 30A.
• Your ESC must be able to supply at least 30A of power,
and if you are using a 3700 mAh battery, you need a rating
of at least 9C.
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Propeller Power Requirements
• Lets take the exact same specifications, but this time we use
a 12” propeller with the same 4.5” pitch.
W = 5.3 x 10-15 x 11,1003 x 124 x 4.5 = 676.37W
I = 676.37 / 11.1 = 60A
• A 2” change in propeller diameter has increased current
draw by double!
Your ESC must be able to supply 60A or it will overheat.
If your battery has a capacity of 3700 mAh, it must now
have a discharge capacity of at least 17C.
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Propellers and Thrust
• You can also estimate thrust from a propeller using the
following equation:
𝑭 = 𝟒. 𝟑𝟗𝟐𝟑𝟗𝟗 × 𝟏𝟎−𝟖. 𝑹.𝑫𝟑.𝟓
𝑷. (𝟒. 𝟐𝟑𝟑𝟑𝟑 × 𝟏𝟎−𝟒. 𝑹. 𝑷 − 𝑽𝟎)
• D is propeller diameter in inches, R is propeller pitch in
inches, R is RPM. This gives us thrust F in newtons.
• This equation is only an approximation. It assumes an air
density of 1.255 kg/m3, the “standard” air pressure at sea
level.
It also ignores the propeller profile.
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Example
• You are designing a quadcopter which will carry 4kg (40N)
in total.
• Your total thrust needed is generally taken to be twice the
weight of your quadcopter, i.e. 80N.
Too little thrust and your quadcopter is unresponsive.
Too much thrust and your quadcopter is too twitchy.
• Since there are four propellers, each prop must generate
80/4 = 20N of thrust.
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Example
• We make the following assumptions:
We continue to use 1000 Kv motors.
We continue to use 3S batteries, producing 11.1v
Maximum RPM is therefore 11.1 x 1000 = 11,100 rpm
Our propeller pitch is fixed at 4.5”
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Example
• It is too difficult to derive D from the thrust equation given
earlier, so what we will do instead is to use the equation to
generate thrust for propeller sizes from 7” to 12”
Prop Dia (inches) Thrust (N)
7 4.410413032
8 7.038029408
9 10.62881641
10 15.36866424
11 21.45411088
12 29.09179268
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Example
• From here we see that an 11” x 4.5” propeller is ideal. The
power required at full RPM is:
W=5.3 x 10-15 x R3 x D4 x P
= 478 watts
• Given we are using a 3S battery producing 11.1v, current
draw is 478/11.1 = 43A.
• So we know we need an ESC that can supply 43A
sustained.
• If our battery capacity is 6000 mAh, we need a battery
rated at least 8C (8 * 6000 = 48A)
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Flight Controllers
• Unlike airplanes, multicopters are unstable.
If you apply equal thrust to all propellers, your quadcopter
is very likely to flip over at the slightest disturbance.
• A flight controller is required to keep the multicopter
stable.
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Flight Controllers
• In addition to stabilization, modern flight controllers
include:
Return to Launch : Fly back autonomously to starting point
and land.
Loiter : Stay in one place at a fixed altitude.
Mission Planning: Fly autonomously through various GPS
waypoints, before coming back to land.
Telemetry: Transmit important data like flight speed,
direction, altitude, battery life, etc.
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QUADCOPTER DYNAMICS
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Quadcopter Control
• Pitch, Roll and Yaw are accomplished by varying the speed
of the motors.