Weight of the quadcopter

M = 1.5 kg

g = 9.81 m/s

From Equation 3.1b

W = mg = F_p

W = 1.5 × 9.81 = F_p

W = 14.715 N = F_p

Total weight of the quadcopter, W = 14.715N

1. Thrust of the propeller

Number of propellers = 4

M = 1.5kg

Number of the motors = 4

From the Equations 3.2. and. 3.3

Thrust = $\frac{4}{1}\times m$

Thrust = $\frac{4}{1}\times 1.5$

Thrust = 6 N

Thrust per motor = $\frac{m}{4}=\frac{1.5}{4}=0.375\text{N}$

Thrust = 6 N

Thrust per motor = 0.375

1. Torque required to drive the propeller

R = 130 mm = 0.13 m

F_p = 14.715 N

From Equation 3.9T = F_p × r

T = 14.715 × 0.13

T = 1.91 Nm

T = 1.91 Nm

2. Centrifugal force required for propellers

M = 1.5 kg

D = 260 mm

N = 11000 rpm

$W=\frac{2\pi N}{60}$

$r=\frac{D}{2}$

$r=\frac{260}{2}$

r = 130 mm

r = 0.13 m

From Equation 3.10

$F_c=\frac{M{v}^2}{r}$

v = wr

$v=\frac{2\pi N}{60}\ast r$

$v=\frac{2\times 3.132\times 11000}{60}\times 0.13$

$v=\frac{8984.95}{60}$

v = 149.7rev/sec

$F_c=\frac{M{v}^2}{r}$

$F_c=\frac{1.5\times {149.7}^2}{0.13}=\frac{33637.3}{0.13}$

F_c = 25.8748.1 N

v = 149.7 rev/sec

F_c = 25.8748.1 N

3. Power required for the propellers

π = 3.142

N = 11000 RPM

T = 0.868 Nm

(as calculated above)

From the Equation 3.12

$P=\frac{2\pi TN}{60}$

$P=\frac{2\times 3.142\times 868.12\times 11000}{60}$

P = 100000 2.45 W

P = 1000 KW

P = 1000 KW

Quadcopter flight time

Max motor Ampere = 4.62A

From Equation. 3.13

$\frac{1800\text{MAh}}{1000}=1.8\text{Amp}$

$t=\frac{\text{Batteryb Ampere}\times 60}{\text{Motor Ampere}}$

$t=\frac{1.8\times 60}{4.62}=\frac{108}{4.62}$

t = 23 minutes

t = 23 minutes

Factor of Safety (F.S) for the Quadcopter

F.S = 1.25

From Equation 3.8

$\sigma =\frac{{\sigma }_{ta}}{F.S}$

$\sigma =\frac{W}{A}$

$A=\frac{\pi d^2}{4}=\frac{3.142\times {0.5}^2}{4}$

$A=\frac{0.7854}{4}=0.196{\text{m}}^{\text{2}}$

$\sigma =\frac{W}{A}=\frac{14.715}{0.196}$

σ = 75.1 N/m²

σ_ta = σ × F.S

σ_ta = 75.1 × 1.25

σ_ta = 93 N/m²

A = 0.196 m²

σ = 75.1 N/m²

σ_ta = 93 N/m²

d = 260 mm = 0.26 m

r = 130 mm = 0.13 m

T = 1.91 Nm

π = 3.142

τ = 22 MN/m²

F.S = 1.25

From Equation 3.16

$\tau =\frac{{\tau }_u}{F.S}$

τ_u =τ × F.S

τ_u = 22 × 10⁶ × 1.25

τ_u = 27500000 N/m²

τ_u = 27 MN/m²

From equation 3.18b

$J=\frac{\pi d^4}{32}$

τ_u = 27 MN/m²

T_m = 76 KNm

J = 4.5 × 10⁻⁴ M⁴

$J=\frac{3.142\times {0.26}^4}{32}$

$J=\frac{0.0144}{32}$

J = 4.5 × 10^-4 M⁴

From Equation 3.18

$\frac{T_m}{J}=\frac{\tau }{r}$

$T_m=\frac{J\tau }{r}$

$T_m=\frac{4.5\times {10}^{-4}\times 22\times {10}^6}{0.13}$

$T_m=\frac{9900}{0.13}$

T_m = 76153.8 Nm

T_m = 76 KNm

Bending moment for the propeller

$I=\frac{\pi d^4}{64}$

$y=\frac{d}{2}$

d= 260 mm = 0.26 m

r = 130 mm = 0.13 m

$y=\frac{0.26}{2}$

y = 0.13 m

I = 2.24 × 10^-4 m⁴

σ = 75.1 N/m²

From Equation 3.19b

$I=\frac{\pi d^4}{64}$

$I=\frac{3.142\times {0.26}^4}{64}$

$I=\frac{0.0144}{64}$

I = 2.24 × 10^-4m⁴

From Equation 3.19

$\frac{B_m}{I}=\frac{\sigma }{y}$

$B_m=\frac{I\sigma }{y}$

$B_m=\frac{2.24\times {10}^{-4}\times 75.1}{0.13}$

$B_m=\frac{0.0168}{0.13}$

B_m = 0.13 Nm

I = 2.24 × 10^-4m⁴

B_m = 0.13Nm

y= 0.13Nm

Equivalent twisting moment for the propeller

T_m = 76153.8 Nm

B_m = 0.13 Nm

From Equation 3.20

$T_e=\sqrt{T_m^2+B_m^2}$

$T_e=\sqrt{{76153.8}^2+{0.13}^2}$

$T_e=\sqrt{5799401254}$

T_e = 76153.8 Nm

T_e= 76 KNm

T_e = 76153.8 Nm

T_e = 76 KNm

Equivalent bending moment for the propeller

T_m = 76153.8 Nm

B_m = 0.13 Nm

$T_e=\sqrt{T_m^2+B_m^2}=76153.8\text{N}\cdot \text{m}$

From Equation 3.21

$M_e=\frac{1}{2}\left[B_m+\sqrt{T_m^2+B_m^2}\right]$

$M_e=\frac{1}{2}\left[0.13+76153.8\right]$

$M_e=\frac{1}{2}\left[76153.93\right]$

M_e = 38077 Nm

M_e = 38 KNm

M_e = 38077 Nm

M_e = 38 KNm

Lift required for the Drone

v = 2 to 9.5 m/s (speed of air from meteorological data)

ρ = 1.293kg/m³

$q=\frac{1.293\times {344}^2}{2}=\frac{153008.4}{2}$

q = 76504.2 N/m²

A = L × b

A = 0.5 × 0.5

A = 0.25 m²

$C_L=\frac{F}{Aq}$

$q=\frac{1}{2}\rho \times v^2$

At 0˚ angle of attack

C_L = 0.4096

$L=\frac{0.4096\times 1.293\times 344\times 0.25}{2}$

L = 7834.03 N

L = 7.834 KN

q = 76504.2 N/m²

A = 0.25 m²

L = 7834.03 N

L = 7.834 KN

Lift required for the drone

= 1/2ρV²AC_L

v = 2 to 9.5 m/s (from meteorological data)

A = Area = L × B

= 0.5 × 0.5 = 0.25m²

C_L = 1.0 to 1.5 (for squared quadcopter depending on angle of attack, Reynolds number and other aerodynamic characteristics)

ρ = 1.293kg/m³

L = 1/2 × 1.293 × 9.5² × 0.25 × 1.5

$L=\frac{43.76}{2}$

L = 21.88 N

L = 21.88 N

Drag required for the Drone

D = 1/2ρV²AC_D

ρ=1.293kg/m³

V = 2 to 9.5 m/2 (from meteorological data)

A = area = L × B

= 0.5 × 0.5 = 0.25 m²

C_D = coefficient of Drag = 1.05 (for squared quadcopter depending on size, surface roughness and flow conditions)

D = 1/2 × 1.293 × 9.5² × 0.25 × 1.05

$D=\frac{30.63}{2}$

D = 15.32 N

D = 15.32 N

Thrust generated by the rotors

T = [(ηW)² × 2πR² × ρ]^1/3

where η = 0.8 (is taken as the efficiency)

W = Propeller power = 260.94W

D = 10’’ = 0.254m

R = 0.127m

ρ =1.22kg/m³ (density of air)

T = [(0.8 × 260.94)² × 2π(0.127)² × 1.22]^1/3

T = 17.531N

T = 17.531N

Power of the rotor

Power required W = K × N³ × D⁴ × P × η∙∙∙where K is propeller constant, it depends on the design of the propeller blade thickness, width, aerofoil profile etc.

K = 5.3 × 10^–15

N = Speed of the rotor in rpm η = 0.8 (efficiency)

D = Propeller diameter in inch = 10"

P = Pitch of the propeller = 4.5"

W = 5.3 × 10⁻¹⁵ × 11100³ × 10⁴ × 4.5 × 0.8

W = 260.94 watts

W = 260.94 watts

Maximum current drawn at full throttle

I = w/v

$I_{\text{max}}=\frac{260.94}{11.1}=23.508\text{A}$

I_max = 23.508 A

I_max = 23.508 A

Velocity of air accelerated downward

The velocity of air accelerated downward is given as.

V_d = (2Wη)/T

V_d = (2 × 260.94 × 0.8)/17.531

V_d = 23.82 m/s

V_d = 23.82 m/s

Flight of speed or Aircraft speed