Quadcopter Design and Dynamics [email protected]/uav/uav-lect2.pdf · Components of a...

Lecture 2: Quadcopter Design and Dynamics Page: 1

Lecture 2

Quadcopter Design and Dynamics

[email protected]

mailto:[email protected]


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.


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.


MULTICOPTER FRAME DESIGN


• Common Frame Designs

Multicopter Frame Designs

X-Frame Y-Frame H-Frame

Hexa-Frame Octo-Frame



• Frame design affects stability

Y-frame has less roll and yaw stability than X, hexa and

octo frames.

H-frame has less pitch stability.



• 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)



• 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.



• Hexacopter and Octocopter frames provide much heavier

lifting capacity.

Smaller high-speed props also produce less vibration.

Very popular with video production companies.


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.


MULTICOPTER COMPONENTS


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.



• Arms

Usually made of nylon, plastic or carbon fibre.

Holds the motors and electronic speed controllers.



• Power Distribution Board

Distributes power and control signals to the motors.

Many multicopter designs use a printed circuit board

integrated with the centre plate.



• 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.


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.



Brushless motors

No brushes. Uses a generated AC voltage to reverse rotor

polarity causing it to spin.



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.



• 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.



• 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.


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.



• 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.


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)


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


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.


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.


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.


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.


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.


Propellers

• Propellers can be clockwise or counter clockwise.

Every quadcopter would use 2 clockwise and 2 counter-

clockwise propellers.


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.


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



• 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.



• 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.



• 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.


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.


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.


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”


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


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)


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.


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.


QUADCOPTER DYNAMICS


Quadcopter Control

• Pitch, Roll and Yaw are accomplished by varying the speed

of the motors.

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