1. Introduction
Drones are also regarded as unmanned aerial vehicles (UAV) these machines are selfpropelled robots, and quadcopters are fourrotor UAVs with easy controllability and simple design [1] [2]. They possess a distinct ability to manoeuvre in congested zones, and vertical takeoff and landing capabilities [1] [3]. Quadcopters are equipment with some mechanisms to grasp objects and deliver them to the required destination [4]. The capability makes the quadcopter suitable for various applications and tasks such as search and rescue, delivery and other industrial applications [5]. The interest in autonomous robotic platforms in recent decades offers several advantages such as reduced costs, and flight performance improvements [6]. There are essential features to autonomous systems; these include but are not limited to efficient energy sources, structural hardware, computing hardware, sensors and actuators, and autonomous software which are generally divided into remotely piloted and autonomous vehicles [7]. This trend has led to less human supervision and more intelligence of the machines to effectively perform tasks and execute timely decisionmaking [7] [8] [9].
Quadcopters are part of the future drone industries with so much potential for applications, their popularity is also due to their relative cost, more torque, higher topographical advantage and more convenience [5] [10] for blades fixed on a frame with two blades having clockwise and the two having counterclockwise rotor motions [1] [11], it is a lightweight and high thrust generating capacity motors, which increase its weight lifting capability. The copter is controlled by altering the speed of one or more rotors [2] [4], the upward and downward motion is achieved by increasing/decreasing the rotor’s speed, and forward/backward, left/right movement is achieved by different control strategies by the rotor speed.
The rapid design and development of UAVs of different sizes, shapes and capabilities with improved functionalities was due to the advancement of flight control and integrated circuit (IC) technologies [9] [12]. The use of UAVs was initially for military applications [13], recently, civilian applications are on the rise with use in search and rescue, agriculture, shipping and delivery of packages, image collection and mapping, monitoring of large infrastructures and giving feedback to ensure quality decisionmaking [6] [8] [14]. For example, quadcopters are used in agriculture to spray pesticides, monitor livestock on the farm to improve farm security, ship and deliver parcels to required destinations, monitoring of large projects such as oil and gas, pipelines, roads, bridges, power grids and many more [6] [15] [16] [17] [18].
The Design concept for the quadcopter was based on [1], with some modifications [19] [20], the quadcopter propellers are attached to the brushless DC motors which are mounted on the ends of the frame [21]. Because of its characteristics, there’s so much research on quadcopters to cater for several applications [22]. A study was conducted to design and fabricate a solar quadcopter, the design adopted the use of finite element analysis to understand the morphology of the structure of the frame upon the addition of load to the copter [3], while it highlighted the component of the copter. Some authors developed a lightweight quadcopter for transporting goods while recording flight time which increases as weight is increased [20] [23].
Despite the attributes mentioned about UAVs, implementation, testing and operating such machines has been challenging, achieving such requires effective coordination, control mechanisms, reliable communication systems, and intelligence to navigate through various terrains. As such this paper presents a pragmatic template for developing a quadcopter to perform one of the attributed tasks of UAVs for the shipping and delivery of parcels using a conceptual design approach.
2. Materials and Methods
The components used in the design consist of the frame, brushless DC motors, electronic speed controller, four propellers, video camera, sensors and flight controllers (Table 1) [4] [22] [23].
Table 1. Material Selection Process.
S/N 
UAV Parts 
Material Performance Requirement 
Probable Material 
Final Material Selection 
Justification 
1 
Frame 
Ductility, tensile strength, toughness, cost effective, and lightweight 
Aluminium, steel, titanium, thermoplastics 
Thermoplastics 
Corrosion resistance, toughness, affordability, good strength, and low density 
2 
Motors 
Efficiency, reduction in heat generation, lightweight, and low noise 
Magnets of iron, copper, cobalt alloys, aluminium 
Alloy with aluminium 
Absorbability of heat by aluminium, lightweight 
3 
Propeller 
Stability, spinning rate, Air density, efficiency 
Wood, fiber glass, carbonfiber, reinforced plastics 
Reinforced plastics 
Low cost, lightweight, high strength, flexibility, Absorbability of impacts. 
4 
Flight Controller 
Stability, processability of commands, compatibility 
Sensors such as gyroscope, accelerometer, barometric pressure (barometer), compasses (magnetometer) 


5 
Battery 
Rechargeability, replaceability, low cost, availability, ability to store energy for long, light weight, high discharge rate to power 
Lithium polymer (LiPo), Lithium ion (Liion), Lithium iron Phosphate (LiFePO_{4}) 
Lithium Polymer 
High energy density 
3. Kinematic Structure of the Quadcopter
The kinematics structure of the quadcopter refers to the air and motion that enters for movement of the quadcopter [24]. The rotors are mounted on the far ends of the frame of the quadcopter. The rotors are controlled by the motors that drive the propellers, the flight controller controls the speed and direction of the motors which are equipped with microcontrollers that receive input from ground sensors and commands from the control centre. The camera is mounted on the copter to provide smooth shorts, while the wireless communication allows the copter to send wider footage to the control centre on the ground which can be monitored and analyzed.
3.1. Conceptual Design
This methodology was adopted in the designing of the quadcopter, which is the identification of required problems through summary, establishing functional structures, selection of appropriate working principles and unifying these problems into a working structure. It answers the following question; has the problem been sufficiently clarified, is the conceptual design needed or has known solutions permit the embodiment design, to what extent should the conceptual design be developed? [25] [26] Figure 1 shows the steps in performing conceptual design.
3.2. Design Considerations
The design factors considered in this endeavour were based on simplicity, aesthetics, costeffectiveness, parcel size and other engineering properties relevant to the development of a quadcopter [10] [19] [20] [25] which form part of the conceptual design process shown in Figure 1.
3.3. Design Calculations
Thrust calculations
The form normal to the propellers required to provide the motion to the quadcopter, the force is generated by the rotors which span at the certain angular velocity is given by the equation:
$T=\frac{\pi \ast {D}^{4}\ast \rho \ast v\ast \Delta v}{4}$
(1)
Figure 1. Steps to conducting conceptual design [25].
where: T = thrust (N), D = Propeller diameter (m), ρ = air density (kg/m^{3}), v = velocity of air (m/s), ∆v = velocity of air accelerated by the propeller.
Total mass lifted by the quadcopter: the total mass (M) is given by the equation:
$M=\frac{T}{a}$
(2)
where:
M = total mass (kg), T = thrust, a = acceleration due to gravity = 9.81 m/s^{2}.
Force Analysis: the forces applied on the rod are given as thrust, centrifugal forces and the movement created by the propeller [24]
$Fc=mR{w}^{2}$
(3)
where, Fc = centrifugal force, m = mass of the propeller (kg), R = Radius of the Propeller (m), w = angular speed = $\frac{2\pi N}{60}$
.
Lift and Weight analysis: the focus is to reduce the weight by increasing the lifting capability of the flight system given by [1]:
$W=\text{required}\frac{\text{RPM}}{\text{referenceRPM}}\ast \text{referenceweight}$
(4)
Propeller Length to Weight Ratio is given by [4]:
$y=\text{required}\frac{\text{weight}}{\text{referenceweight}}\ast \text{referencepropellerlength}$
(5)
$\text{Lift}\left(\text{kg}\right)=\frac{\left(W\ast {D}^{4}\ast {N}^{2}\right)\frac{p\ast 24}{cf\ast 29.9}}{2.2}$
(6)
where cf = lift coefficient.
Duration of Flight: Duration of flight is given by [1] as
$\text{Duration}=\text{capacityof}\frac{\text{battery}}{\text{max}\text{.currentdrawnbymotor}}$
(7)
Power required is given by,
$\text{Power}\left(W\right)={K}_{p}\ast {d}^{4}\ast P\ast {N}^{3}$
(8)
where, K_{p} = propeller constant = 1.11, p = pitch of the propeller.
4. Results and Discussions
4.1. Design Calculations
Table 2. Design specification and assumptions.
S/N 
Item Names 
Values 
1 
Source of Power 
Battery (1800 MAh) 
2 
Type of motor used 
Brushless DC (BLDC) 
3 
Mass of the Quadcopter 
1.5 Kg 
4 
Battery Voltage 
11.1 V 
Table 3. Design calculations.
Initial Data 
Calculations and Sketches 
Results 
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 = $\frac{m}{4}=\frac{1.5}{4}=0.375\text{\hspace{0.17em}}\text{N}$

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 3.9 T = 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
$\frac{1800\text{\hspace{0.17em}}\text{MAh}}{1000}=1.8\text{\hspace{0.17em}}\text{Amp}$
$t=\frac{\text{BatterybAmpere}\times 60}{\text{MotorAmpere}}$
$t=\frac{1.8\times 60}{4.62}=\frac{108}{4.62}$
t = 23 minutes 
t = 23 minutes 
Factor of Safety (F.S) for the Quadcopter 
F.S = 1.25 
From Equation 3.8 $\sigma =\frac{{\sigma}_{ta}}{F.S}$
$\sigma =\frac{W}{A}$
$A=\frac{\pi {d}^{2}}{4}=\frac{3.142\times {0.5}^{2}}{4}$
$A=\frac{0.7854}{4}=0.196\text{\hspace{0.17em}}{\text{m}}^{\text{2}}$
$\sigma =\frac{W}{A}=\frac{14.715}{0.196}$
σ = 75.1 N/m^{2} σ_{ta} = σ × F.S σ_{ta} = 75.1 × 1.25 σ_{ta} = 93 N/m^{2} 
A = 0.196 m^{2} σ = 75.1 N/m^{2} σ_{ta} = 93 N/m^{2} 
Twisting moment for the propeller 
d = 260 mm = 0.26 m r = 130 mm = 0.13 m T = 1.91 Nm π = 3.142 τ = 22 MN/m^{2} F.S = 1.25 
From Equation 3.16 $\tau =\frac{{\tau}_{u}}{F.S}$
τ_{u} =τ × F.S τ_{u} = 22 × 10^{6} × 1.25 τ_{u} = 27500000 N/m^{2} τ_{u} = 27 MN/m^{2}
From equation 3.18b $J=\frac{\pi {d}^{4}}{32}$

τ_{u} = 27 MN/m^{2} T_{m} = 76 KNm J = 4.5 × 10^{−}^{4} M^{4}


$J=\frac{3.142\times {0.26}^{4}}{32}$
$J=\frac{0.0144}{32}$
J = 4.5 × 10^{4} M^{4}
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} m^{4} σ = 75.1 N/m^{2} 
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^{4}m^{4}
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^{4}m^{4} 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 ${T}_{e}=\sqrt{{T}_{m}^{2}+{B}_{m}^{2}}=76153.8\text{\hspace{0.17em}}\text{N}\cdot \text{m}$

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/m^{3} 
$q=\frac{1.293\times {344}^{2}}{2}=\frac{153008.4}{2}$
q = 76504.2 N/m^{2}
A = L × b A = 0.5 × 0.5 A = 0.25 m^{2}
${C}_{L}=\frac{F}{Aq}$
$q=\frac{1}{2}\rho \times {v}^{2}$
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/m^{2}
A = 0.25 m^{2}
L = 7834.03 N L = 7.834 KN 
Lift required for the drone 
= 1/2ρV^{2}AC_{L} v = 2 to 9.5 m/s (from meteorological data) A = Area = L × B = 0.5 × 0.5 = 0.25m^{2} C_{L} = 1.0 to 1.5 (for squared quadcopter depending on angle of attack, Reynolds number and other aerodynamic characteristics)
ρ = 1.293kg/m^{3} 
L = 1/2 × 1.293 × 9.5^{2} × 0.25 × 1.5 $L=\frac{43.76}{2}$
L = 21.88 N 
L = 21.88 N 
Drag required for the Drone 
D = 1/2ρV^{2}AC_{D} ρ=1.293kg/m^{3} V = 2 to 9.5 m/2 (from meteorological data) A = area = L × B = 0.5 × 0.5 = 0.25 m^{2} C_{D} = coefficient of Drag = 1.05 (for squared quadcopter depending on size, surface roughness and flow conditions) 
D = 1/2 × 1.293 × 9.5^{2} × 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} × 2πR^{2} × 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/m^{3} (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 × N^{3} × D^{4} × 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} × 11100^{3} × 10^{4} × 4.5 × 0.8 W = 260.94 watts 
W = 260.94 watts 
Maximum current drawn at full throttle 
I = w/v 
${I}_{\text{max}}=\frac{260.94}{11.1}=23.508\text{\hspace{0.17em}}\text{A}$
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 
The flight speed or aircraft speed. V_{a} = 1/2 × V_{d} 
V_{a} = 1/2 × 23.82 V_{a} = 11.91 m/s 
V_{a} = 11.91 m/s 
4.2. Discussions
The developed quadcopter presented in this study was designed to cater for costeffectiveness, simplicity and mechanical design (See Appendix 1) done using Solid Works and specifications with a brief description of the quadcopter components used in the development of drones for parcel delivery and other tasks shown in Table 2, while Table 3 displayed the mathematical equations used in the design and development of the quadcopter. The design was tested and proved to be effective and demonstrated stability and energy efficiency as per design calculations.
4.3. Recommendations
The following recommendations were proposed for further enhancement of the performance reliability and aesthetics.
The quadcopter should be equipped with weatherproofing to make it have multifunctional capabilities over varied weather conditions and also another design alternative should be considered to reduce the noise of the quadcopter.
Appendix 1: Design Drawings