Strojniški vestnik - Journal of Mechanical Engineering 69(2023)11-12, 444-454 Received for review: 2023-04-11
© 2023 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2023-09-15
DOI:10.5545/sv-jme.2023.601 Original Scientific Paper Accepted for publication: 2023-09-19
*Corr. Author’s Address: PSG College of Technology, Coimbatore, Tamil Nadu, India, tamilselvanganesan98@gmail.com 444
Aerodynamic Analysis of Mathematically Modelled Propeller  
for Small UAV Using CFD in Different Temperature Conditions
Ganesan, T. – Jayarajan, N.
Tamilselvan Ganesan
,*
 – Niresh Jayarajan
PSG College of Technology, Department of Automobile Engineering, India
Unmanned aerial vehicle (UAV) usage has witnessed a significant rise owing to its cost-effectiveness and versatile applications. However, the 
design techniques for UAV propellers, encompassing aerodynamic and structural analysis, have received limited attention from researchers. 
A well-designed propeller can effectively reduce battery consumption and enhance overall efficiency. This study focuses on mathematically 
designed propellers and compares them with advanced precision composite (APC) Slow Flyer propeller blades in terms of thrust coefficients, 
power coefficients, and efficiency. The investigation includes the utilization of tetrahedron meshing in simulations, employing the standard 
k–ω (k–omega) model. To evaluate the accuracy of the blade element theory (BET) in predicting thrust, the simulation data is compared 
with BET results. Furthermore, the study encompasses experimental testing to validate the simulation findings. The findings demonstrate 
that the mathematically modelled propeller outperforms the APC Slow Flyer propeller across all ranges of revolutions per minute (rpm). 
When comparing the results of both methods, BET exhibits an error difference of 10 % in higher rpm ranges, but this error diminishes as 
the rpm decreases. This study contributes a novel design technique for modelling propellers using mathematical formulas and provides a 
comprehensive comparison of their aerodynamic properties with existing propellers, utilizing both BET and computational fluid dynamics 
(CFD) methods, along with experimental validation.
Keywords: unmanned aerial vehicle, propeller, computational fluid dynamics, blade element theory, mathematical design
Highlights
• Design the propeller based on the mathematical model generated using the Eppler E63-based airfoil due to the amount of lift 
it generates to increase the UAV thrust and efficiency.
• Perform the CFD analysis for these propellers in various temperature conditions and generate the results.
• Compare the designed propeller with the APC Slow Flyer, which is among the most commonly used in 10’ UAV propellers.
• Blade element theory has been used to verify the results generated from the analysis and noted the error difference between 
these two.
0  INTRODUCTION
Unmanned aerial vehicles (UAVs) play a vital role 
in defence missions, encompassing remote sensing, 
surveillance, and data collection in challenging 
environments with varying temperatures [1]. The 
lifespan of a drone is crucial in such missions, as 
numerous operational factors significantly impact 
its performance and structural integrity [2] to [4]. 
Rotor blades serve as fundamental components of 
drones and most UAVs, with operational temperature 
being a crucial parameter in their design. However, 
a comprehensive database on UAV performance 
in harsh environmental conditions is still lacking, 
which is critical for evaluating battery lifespan and 
thrust prediction in relation to weather conditions. 
Our primary objective is to gather data on propeller 
performance under cold temperatures for preliminary 
research on the impact of environmental factors on 
UA V propulsion systems [5] to [9].
In recent years, several experiments have been 
conducted on small UAVs and their power systems. 
Brandt and Selig [10] focused on propellers for 
small unmanned aerial vehicles, creating a reference 
database that emphasizes thrust generation in windy 
conditions and propeller behaviour in low Reynolds 
flow conditions. Scanavino et al. [11] proposed 
a comparison between blade element theory and 
experimental results obtained from extreme weather 
conditions using a 15’ × 5’ carbon fibre propeller. 
Another significant contribution was made by 
Russell et al. [12], who analysed the performance of 
five commercial UAVs in a wind tunnel under static 
conditions, providing a comprehensive overview 
of their overall performance. That article includes 
information about the experimental analysis, test 
matrix, and results obtained from laser scanner 
measurements. However, when it comes to UAVs 
in harsh environments, few papers describe the 
performance of these vehicles. Precision Hawk [13] 
conducted environmental experiments on multi-rotor 
and fixed-wing propellers in partnership with the 
Automotive Centre of Excellence. Unfortunately, no 
experimental data from these studies have been made 
available for investigation. More recently, research 
on propellers has focused on ice accretion conditions 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)11-12, 444-454
445 Aerodynamic Analysis of Mathematically Modelled Propeller for Small UAV Using CFD in Different Temperature Conditions 
[14] to [17], exploring the aerodynamic performance 
of propellers at various water content and operational 
temperature levels. The goal of this characterization 
was to develop a new anti-ice propeller component 
that would reduce power consumption. A passive 
solution based on surface wettability and hydrophobic 
materials has been proposed.
The UAV industry has only recently begun 
providing end users with information on flying 
recommendations in extreme circumstances [18] 
and [19]. For instance, the Alta 8 flying handbook 
by Freefly Systems includes a table that shows the 
maximum take-off weight as a function of temperature 
and altitude. However, beyond conventional flying 
conditions, data are often based on projections, real-
world experiments, and user input.
In our research, we focus on designing propellers 
using numerical formulas to optimize their efficiency. 
We specifically employ high lift, low drag airfoils that 
are well-suited for low Reynolds numbers, such as 
the Eppler E63 airfoil. By utilizing the airfoil’s data 
coordinates and implementing a spline interpolation 
technique, we design propellers based on these 
numerical values using computer aided design (CAD) 
software. Subsequently, the propellers undergo 
comprehensive analysis of various aerodynamic 
properties, including thrust, lift, and drag, through the 
utilization of computational fluid dynamics (CFD) 
simulations. To ensure controlled conditions, we 
employ a specialized climate-controlled facility to 
collect precise experimental data. The experimental 
results are then compared with the CFD simulations, 
as well as benchmarked against industry-leading 
propellers such as the 10’ APC propeller and the 
classic NACA 4412 propeller. By combining both 
experimental and computational approaches, our 
primary objective is to provide a comprehensive 
analysis of the performance of these mathematically 
designed propellers.
1  ENVIRONMENTAL CONDITIONS
Testing the propeller in harsh environmental 
conditions is one of this experiment’s main objectives. 
Propeller thrust data will be useful for UA V objectives 
and will increase reliability while flying in extreme 
environmental conditions. For this experiment, the 
pressure is kept constant during propeller testing in 
various temperature environments. The temperature 
of the environment influences air density called the 
isobaric test as shown in Table 1. 
Table 1.  Isobaric test conditions
Temperature [ºC] Pressure [hPa] Air density [kg/m³]
42.5 989 1.0924
33.3 990 1.1256
29.3 990 1.1405
24.8 990 1.1577
18.1 983 1.1760
-13.5 978 1.3124
-20.3 978 1.3477
-25.7 978 1.3771
-28.4 977 1.3909
-34.5 974 1.4221
2  DESIGN OF PROPELLER
2.1  Design of Optimal Rotor Blades
The rotation of a propeller blade creates turbulence, 
which reduces its efficiency. To maintain balance 
and maximize efficiency, propellers are typically 
designed with two blades. Adding more blades 
brings diminishing returns as the blades become 
Fig. 1.  Methodology

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)11-12, 444-454
446 Ganesan, T. – Jayarajan, N.
[21]. The equation for determining the inflow angle 
Eq. (3) as follows:
 



tan
1
2
3
. (3)
The blade angle is the angle between the chord 
of the propeller blade and the plane of rotation. It is 
measured at a specific position along the length of the 
blade. The blade angle is the sum of the inflow angle 
and the angle of attack of the propeller, as stated in Eq. 
(4). To maintain a relatively constant angle of attack 
(AOA) along the length of the blade, the propeller 
blade twists along its length. This twist is necessary 
because the blade speed is significantly higher at the 
tip compared to the base.
Blade angleI nflow angleA ngleo fa ttack         . (4)
2.2  Reverse Engineering the APC and NACA Propellers
The APC Slow Flyer 10’ propellers are widely used in 
small UAVs and are manufactured by APC. They are 
two-bladed propellers that have become popular in the 
UAV industry. Another commonly used propeller in 
the past is the NACA 4412 propeller. Both propellers 
have a diameter of 0.254 m and a fixed pitch.
Fig. 2.  Sectional airfoil structures of APC
The APC propeller incorporates a combination 
of NACA 4 and 5 series airfoils, as depicted in Fig. 
2, while the NACA 4412 propeller is based on a 
single airfoil bearing its name. To obtain detailed 
information about the propeller profiles, a 3D scanner 
called ATOS 2M was used. This scanner can capture 
the product part in the form of images or drawings, a 
process known as ‘reverse engineering’. The scanning 
process involves mounting the scanner on a tripod for 
scanning large parts, or it can be operated manually. 
By obtaining a reference point from the rotating 
table, the entire propeller is scanned. The scanned 
blade profiles of the APC and NACA propellers 
were exported to IGES format, providing valuable 
data as shown in Fig. 3. The three distinct designs of 
closer together, further decreasing efficiency. While 
a tri-blade or quad-blade configuration can provide 
additional thrust, the benefits are less pronounced. 
Therefore, most propellers used in small UAVs have 
two blades. In this research, a 10’ propeller is chosen 
as it is widely used in small UAV applications. To 
enhance accuracy, each blade of the propeller is 
divided into 18 sections, resulting in a total of 32 
sections for the complete propeller design. This 
segmentation allows for precise control over chord 
length and blade angle at each section. The propeller 
models are created using a set of formulas that 
define parameters such as chord length, tip speed 
ratio, air flow angle, and blade angle. The propellers 
are modelled in methods as shown in Fig. 1. These 
formulas ensure the propeller is designed with optimal 
characteristics for efficient performance.
The tip speed ratio (TSR), denoted as λ, 
represents the ratio of the tangential speed of the 
propeller blade tip to the wind velocity. It is a crucial 
parameter in propeller design as it directly influences 
various aspects of performance. When the tip speed 
increases, it can result in increased noise generation 
and vibrations within the propeller system. The 
formula for calculating the tip speed ratio is expressed 
in Eq. (1) as follows:
 


 Blade tips peed
Wind speed
r
v
, (1)
where ω is rotational speed [rad/s], r radius at the 
point of computation [m], R radius at the tip [m], and 
v wind velocity [m/s].
The chord length of a propeller refers to the 
distance between its leading and trailing edges in the 
direction of the wind. Increasing the chord length of 
a propeller can lead to improved efficiency. This is 
because a propeller with a larger width offers a larger 
surface area for interaction with the air. According 
to Newton’s Third Law, a propeller can push back a 
greater number of air particles in a single rotation, 
resulting in a greater reaction force that propels the 
vehicle forward. Therefore, increasing the chord 
length contributes to enhanced propeller performance 
[20]. The calculation of the chord length is determined 
by utilizing Eq. (2) as follows:
 Chordl ength
R
Cl r


 

56
2
2
2
.
.

 (2)
The inflow angle is the angle formed between the 
axis of the propeller and the direction of the airstream. 
It plays a significant role in the propeller equation 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)11-12, 444-454
447 Aerodynamic Analysis of Mathematically Modelled Propeller for Small UAV Using CFD in Different Temperature Conditions 
propellers as shown in Fig. 4 are made using the CAD 
design software.
3  TURBULENCE SIMULATION MODEL
3.1 Selection of Flow Domain
The flow region and numerical predictions were 
conducted using ANSYS software. The design CAD 
models were imported into ANSYS Fluent, where the 
geometry was created. To ensure accurate simulations, 
a domain was built around the propeller that extended 
taller than the propeller itself. This was done to prevent 
the wall boundary, which is closer to the propeller, 
from heating up quickly due to the airflow generated 
during propeller rotation. Additionally, the domain 
was carefully chosen to avoid any recirculation within 
the domain, as recirculation can introduce variations 
Table 2.  Propeller design parameters for E63 airfoil
S. No r / R Tip speed ratio In flow angle Chord length [mm] Angle of attack Blade angle
1 0.10 0.754 35.338 18.495 5.60 40.938
2 0.20 1.508 22.376 17.826 5.04 27.416
3 0.25 1.885 18.638 17.318 4.76 23.398
4 0.30 2.262 15.906 15.838 4.48 20.386
5 0.35 2.639 13.841 15.181 4.20 18.040
6 0.40 3.016 12.234 14.998 3.92 16.155
7 0.45 3.393 10.952 13.898 3.64 14.592
8 0.50 3.770 9.908 13.367 3.36 13.268
9 0.55 4.147 9.042 12.611 3.08 12.122
10 0.60 4.524 8.313 11.806 2.80 11.113
11 0.65 4.901 7.691 11.647 2.52 10.215
12 0.70 5.278 7.155 11.032 2.24 9.395
13 0.75 5.655 6.688 10.674 1.96 8.648
14 0.80 6.032 6.278 10.378 1.68 7.958
15 0.85 6.409 5.914 10.323 1.40 7.314
16 0.90 6.786 5.591 10.533 1.12 6.711
17 0.95 7.163 5.300 10.093 0.84 6.140
18 1.00 7.540 5.038 9.697 0.56 5.598
a)           b) 
Fig. 3.  Data from ATOS 2M: Chord and blade angle of: a) APC propeller, and b) NACA 4412 propeller
a)       b)      c) 
Fig. 4. a) Mathematically modelled E63 propeller, b) APC Slow Flyer, and c) NACA 4412 propeller

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)11-12, 444-454
448 Ganesan, T. – Jayarajan, N.
in the results. The domain boundary was extended 
higher than normal and designated as the rotating 
domain, as illustrated in Fig. 5. A static environment 
was created around this rotating domain. Before 
commencing the simulation, the geometry was 
prepared with the appropriate environment settings, 
including airflow conditions and Boolean operations 
for specific regions.
Fig. 5.  Flow domain dimensions in [mm]
3.2  Mesh Generation and Dependency Test
Mesh generation must ensure high-quality meshes that 
balance calculation accuracy and computation time. If 
the element size of the mesh is too large, the solution’s 
final precision will be compromised. Conversely, if 
the element size is too small, the computation time 
will significantly increase. Therefore, an optimal 
element size must be determined to achieve accurate 
and efficient simulations. Initially, the computational 
domain was aligned using a line surface-to-body 
sequence. Given the large size of the propeller 
surface and its curvature, efforts were made to reduce 
curvature effects, particularly through surface splitting 
and merging techniques. 
A mesh dependency study was conducted in the 
CFD simulation to determine an appropriate mesh 
size. The study focused on evaluating thrust and drag. 
Fig. 6 illustrates that consistent results were obtained 
with a mesh consisting of more than 2.5 million 
elements. To accurately capture the behaviour of the 
viscous sub-layer, mesh refinement was applied to all 
sides of the rotating domain, which was constructed 
around the propeller blade boundaries. The boundary 
criterion was determined by selecting the appropriate 
named selection for the primary part. Table 3 provides 
details of the node and element sizes for the propeller. 
Furthermore, Fig. 7 showcases the computational 
domain and the results of the meshing process. To 
achieve better simulation results, tetrahedral meshes 
were employed for both the propeller and its rotating 
domain. The mesh size of the rotating domain was 
intentionally kept smaller than that of the static 
domain, which served as a boundary wall. Proper 
naming conventions were applied to all faces and 
domains using named selections to ensure clarity and 
organization throughout the simulation process.
Fig. 6.  Results of CFD mesh dependency test
Fig. 7.  Tetrahedron mesh generation
Table 3.  Mesh size of each propeller
Propeller Node Element
E63 451628 3215652
NACA 452587 3368426
APC 458564 3224153
3.3  Turbulence Model Properties
The CFD simulation involved three distinct blade 
rotation speeds: 4000 rpm, 6000 rpm, and 6500 rpm. 
The free stream velocity was determined at the intake 
boundary, while the outflow was set at the outlet 
boundary. All walls within the domain were assigned 
as non-slip boundaries. Turbulence modelling played 
a crucial role in achieving accurate simulation results, 
and six different turbulence models were considered. 
The selection of the turbulence model was based on 
its ability to closely match experimental data. The 
chosen turbulence model in this investigation was the 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)11-12, 444-454
449 Aerodynamic Analysis of Mathematically Modelled Propeller for Small UAV Using CFD in Different Temperature Conditions 
k-omega normal model, which exhibited the lowest 
percentage difference compared to the other models 
(1.1249 %). The k–omega turbulence model is widely 
used to capture the effects of turbulent flow conditions 
and belongs to the Reynolds-averaged Navier-Stokes 
(RANS) family of turbulence models. It involves 
solving two transport equations for turbulent kinetic 
energy (k) and turbulent dissipation rate (omega). 
These equations account for historical effects such as 
convection and turbulent energy diffusion, providing a 
comprehensive representation of turbulence. 
Kinetic energy equation:
 


 




















t
k
x
uk
u
x
k
x
kk
x
j
ji j
i
j
jj
   




 



	


. (5)
Specific dissipation rate:
 


 












tx
u
k
u
x
k
xx x
j
ji j
i
j
d
jj j
  

 




2
 















	






 k
x
j
, (6)
Table 4.  Simulation parameters
Parameters Values
Time Transient
Time step 0.015
Number of Time Step 100
Max Iteration per time step 40
Viscous model k–omega, Normal
Fluid medium Air
Inlet velocity 15 m/s
Type of flow Transient
Air density 1.225 kg/m³
Pressure-velocity coupling Simple scheme
Gradient Least squares cell based
Interpolating scheme (momentum) Second-order upwind
Interpolating scheme  
(specific dissipation rate)
Second-order upwind
The k–omega model is particularly suitable for 
near-wall treatment and offers improved performance 
for complex boundary layer flows with adverse 
pressure gradients and separations, such as in external 
aerodynamics and turbomachinery applications. 
The simulation parameters used in the study are 
summarized in Table 4, ensuring the accuracy and 
reliability of the simulation results.
The simulation of the propeller employed 
a second-order upwind interpolation scheme. In 
computational physics, an upwind scheme is a 
discretization method used to solve hyperbolic 
equations and approximate the derivatives in a flow 
field. To better understand its function, let us consider 
the one-dimensional (1D) advection equation, Eq. 
(7). The advection equation is commonly used when 
analysing the movement of fluid through a passage.
1D advection equation:
 






u
t
a
u
x
0. (7)
The advection equation represents the propagation 
of a wave with a specific velocity along the x-axis. It 
is commonly used to analyse one-dimensional linear 
advection. Let us consider a standard grid point i in 
a one-dimensional domain. In this domain, point 
1 has two directions: towards the negative infinity 
side (upwind) and towards the positive infinity side 
(downwind). If the velocity is positive, the wave 
propagates towards the right side. In this case, the left 
side of point i is referred to as the upwind side, while 
the right side is called the downwind side. An upwind 
scheme is characterized by having a higher number of 
∂u/∂x data points on the upwind side. In the case of 
the first-order upwind scheme, a 2-point grid data is 
used in the Taylor series approximation. However, the 
second-order upwind scheme employs a combination 
of 3-point backward difference and 3-point forward 
difference in the data points, as depicted in Eqs. (8) 
and (9). This method offers improved accuracy due 
to its reduced diffusivity compared to the first-order 
upwind scheme.
3-point backward difference:
 u
uuu
x
x
i
n
i
n
i
n
 



 34
2
12
, (8)
3-point forward difference:
 u
uuu
x
x
i
n
i
n
i
n
 

 

21
43
2
. (9)
4  RESULTS
4.1  Efficiency
CFD simulations were performed on three different 
propellers, namely the APC Slow Flyer, NACA 
4412, and E63 designed propellers, under normal 
environmental conditions. The objective was to 
compare their respective efficiencies. In the CFD 
analysis, various parameters were calculated, 
including thrust generated T in [N], torque output Q in 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)11-12, 444-454
450 Ganesan, T. – Jayarajan, N.
[N·m], fluid density ρ in [kg/m³], propeller speed n in 
[rpm], propeller diameter D in [m], and power P [W]. 
To evaluate the performance of the propellers, several 
coefficients were derived from the CFD data. These 
include the thrust coefficient C
T
, torque coefficient C
Q
, 
power coefficient C
P
, advance ratio J, and efficiency 
η. These coefficients were computed using specific 
equations. The efficiency values for each propeller are 
presented in Table 5.  
 J
V
nD
= , (10)
 C
P
nD
t


24
, (11)
 C
P
nD
p


35
, (12)
  
JC
C
t
p
. (13)
Table 5.  Efficiency comparison on various advance ratios
Advance ratio Velocity [m/s] APC η NACA 4412 η E 63 η
0.235 2.999 0.412 0.411 0.452
0.336 4.234 0.527 0.498 0.534
0.433 5.500 0.601 0.574 0.621
0.525 6.666 0.659 0.631 0.678
0.580 7.250 0.670 0.643 0.694
0.631 7.999 0.666 0.616 0.673
0.719 9.100 0.589 0.558 0.590
Fig. 8.  Propeller efficiency comparison between E63, NACA and 
APC propellers
Fig. 8 depicts a comparison graph showcasing 
the efficiency of the three propellers. Notably, the 
propeller designed using the E63 airfoil exhibits a 
remarkable efficiency of nearly 70 % at an advance 
ratio of 0.58 before experiencing a decline. A common 
trend among all propellers is that their efficiency 
gradually decreases beyond the 0.58 advance ratio. In 
terms of initial efficiency, both the APC and NACA 
propellers demonstrate similar performance, but 
as the advance ratio increases, the APC propeller 
slightly outperforms the NACA propeller. In contrast, 
the NACA propeller, with its comparatively lower 
lift structure, exhibits the lowest efficiency among 
the three propellers. However, the propeller based 
on the E63 airfoil consistently maintains superior 
efficiency throughout the entire range. The high 
lift characteristics of the E63 airfoil contribute to 
its enhanced efficiency compared to the other two 
propellers.
4.2  Aerodynamic Numerical Solution
The numerical analysis of the three propellers focused 
on analysing their aerodynamic properties, including 
thrust, lift force, and drag coefficient. The analysis was 
conducted at various temperature settings and at three 
different speeds, resulting in a total of 30 simulations 
for each aerodynamic property. The analysis revealed 
that as the propeller speed decreases, both the thrust 
and lift force decrease as well. While this relationship 
may seem obvious, it is important to consider that 
thrust and lift force are directly proportional to the 
pressure acting on the propeller. The results clearly 
indicate that the propeller based on the E63 airfoil 
is less susceptible to pressure compared to the other 
two propellers, as illustrated in Fig. 9. This suggests 
that the mathematically modelled propeller exhibits 
superior efficiency compared to the other propellers. 
The thrust force generated by the propeller plays a 
crucial role in propelling a UAV through the air. It is 
responsible for overcoming the drag and weight of the 
drone, enabling it to maintain flight.
 Tm V   , (14)
where ṁ is mass flow rate calculated as:
  mA V   . (15)
Substitute the Eq. (14) into Eq. (15), and we get
 TA V  
2
. (16)
Fig. 10 demonstrates the thrust generated by 
different propellers under various environmental 
conditions and at three rpm ranges. The simulation 
results clearly show that the mathematically designed 
E63 propeller outperforms both the NACA and APC 
propellers in terms of thrust. This superiority is due 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)11-12, 444-454
451 Aerodynamic Analysis of Mathematically Modelled Propeller for Small UAV Using CFD in Different Temperature Conditions 
to the E63. Consequently, the APC propeller generates 
more drag than the other two propellers. When 
comparing these three propellers, the mathematically 
designed E63-based propeller demonstrates superior 
performance. The drag force can be calculated as half 
the product of the drag coefficient, air density, area, 
and the square of the velocity.
 Drag forceC AV
d

1
2
2
 , (17)
where C
d
 is a drag coefficient, and A is area of 
propeller.
Fig. 11.  Drag coefficient vs. temperature in three different rpms
Lift refers to the total force perpendicular to the 
incoming flow direction, whereas drag force runs 
parallel to the flow direction. Lift plays a crucial 
role in counteracting the force of gravity. From Fig. 
12, it is evident that the E63 propeller performs 
exceptionally well at 6500 rpm. The APC propeller 
demonstrates a relatively closer lift force to the E63, 
but its performance diminishes due to the significant 
drag it generates at lower rpm, resulting in minimal 
lift production. In contrast, the NACA propeller 
performs poorly compared to the other two. This is 
primarily due to the inferior airfoil properties of the 
NACA 4412 in contrast to the superior characteristics 
of the E63. Overall, the E63 consistently outperforms 
both the APC and NACA propellers.
to the E63 propeller’s utilization of the high lift and 
low drag characteristics of its airfoil structure. Despite 
the NACA airfoil structure variations along the APC 
propeller sections, the mathematically designed 
propeller consistently exhibits better blade angle 
efficiency along its entire length. This efficiency 
advantage is particularly evident at 5000 rpm, where 
the E63 propeller generates nearly twice the thrust 
force compared to the APC propeller. In contrast, 
the NACA propeller performs poorly, producing less 
than 2 N of thrust. The increased efficiency of the 
E63 propeller results in reduced battery usage, as it 
generates more lift even at lower rpm ranges.
Fig. 10.  Thrust vs. temperature in three different rpms
Drag on the propeller surface is caused by the 
velocity difference between the top and bottom 
portions. Aerodynamicists employ the drag coefficient 
to account for the complex relationships between 
geometry, angle, and flow conditions, which affect 
aircraft drag. The drag equation can be rearranged 
to solve for the drag coefficient in terms of other 
variables. From Fig. 11, it is evident that the APC 
propeller exhibits greater drag compared to the other 
two propellers. The APC propeller experiences high 
drag across all RPM ranges, primarily due to its 
utilization of a low lift airfoil structure at the tip. The 
propeller tip speed ratio being significantly higher 
than at the root contributes to the NACA series airfoil 
having higher drag coefficient values when compared 
a)       b)       c) 
Fig. 9.  Pressure acting on the propeller at 6000 rpm

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)11-12, 444-454
452 Ganesan, T. – Jayarajan, N.
Fig. 12.  Lift force vs temperature in three different rpms
4.3 Blade Element Theory
The BET offers the evaluation of propeller 
performance based on geometrical parameters, 
aerodynamic coefficients, and operating conditions 
[4], [22] to [24]. However, this theory overlooks 
secondary effects like tip vortex and radial flow, 
which can have a negative impact on total thrust 
output [25]. The distributions of airfoil profile, chord, 
and twist are represented as functions of the distance 
from the propeller hub using Eqs. (18) to (23). As the 
propeller profile varies, simulations were conducted 
using a simplified E63 airfoil for the mathematically 
designed propeller, NACA 4412 airfoil for the NACA 
propeller, and various NACA airfoils for different 
sections of the APC propeller. Comparison results 
between simulation and BET thrust force as shown in 
Fig. 13.
The angle between the thrust and lift directions is 
defined as
   . (18)
The thrust of the blade section can be written as 
   TL D  coss in ,  (19)
where
   LCAV cd r
L
1
2
2
 , (20)
   DCAV cd r
D
1
2
2
 . (21)
Therefore, the thrust equation becomes
 TA VcCC Bd r
LD
 
1
2
2
  (c os sin) . (22)
To calculate the total thrust generated by the 
propeller for a specific rpm
 TT   . (23)
Fig. 13.  Thrust comparison between BET and SIM
Comparisons were made between the 
experimental data and the results obtained from 
the blade element theory. The BET technique 
generally follows similar patterns, but it significantly 
overestimates the thrust force at higher rpm, with an 
error margin of approximately 10 % to 15 % compared 
to the actual results. This indicates that there are 
interactions between the propellers that are not 
accounted for in the basic coaxial model. However, 
both the CFD approach and the BET method yield 
similar thrust predictions when approaching lower 
rpm, with differences of less than 13 % between 
the simulated data and the blade element theory. 
Notably, the accuracy improves as the rotational speed 
decreases.
4.4  Experimental Ssetup
The experimental setup for propeller thrust calculation 
involves several components. Firstly, a weighing scale 
is utilized to measure the lifting force generated by 
the propeller. The motor responsible for rotating the 
propeller is securely mounted on a wooden structure. 
A servo controller is employed to regulate the 2200 
kV brushless direct current (BLDC) motor speed and 
control its rotation. The motor is connected to a 30 
A electronic speed controller (ESC) and is powered 
by a 3S battery. As the propeller rotates, it generates 
a lifting force that is transferred to the weighing 
scale. The scale readings are carefully observed and 
recorded. To convert the readings into Newtons, a 

Strojniški vestnik - Journal of Mechanical Engineering 69(2023)11-12, 444-454
453 Aerodynamic Analysis of Mathematically Modelled Propeller for Small UAV Using CFD in Different Temperature Conditions 
suitable conversion factor or calibration procedure 
is applied, allowing for accurate measurement of the 
propeller thrust. The setup image as shown in Fig. 14 
and the result compare with the simulation values are 
tabulated in Table 6. 
Fig. 14.  Experimental setup to test the thrust
Table 6.  Error comparison of simulation thrust to the experimental 
values
Propeller rpm Thrust (Sim) Thrust (Exp) Error [%]
E63
6500 5.548 5.165 6.90
6000 5.216 4.868 6.67
5000 4.881 4.562 6.53
APC
6500 5.380 4.963 7.75
6000 4.672 4.325 7.42
5000 2.749 2.552 7.16
NACA
6500 4.627 4.289 7.30
6000 3.679 3.421 7.01
5000 1.912 1.778 7.00
The E63 propeller, designed based on a 
mathematical model, was 3D printed using ABS 
material through the process of fused deposition 
modelling (FDM). The results of the comparison 
between the UA V 10’ propeller, the novelty developed 
E63 airfoil structure-based mathematical modelled 
propeller, the NACA 4412 propeller, and the industry-
leading APC Slow Flyer were obtained through 
both CFD simulation and experimental testing. The 
analysis revealed an error deviation ranging from 6.5 
% to 7.7 % between the predicted and observed values. 
It was observed that the CFD simulations tended to 
overestimate the performance values compared to the 
theoretical predictions. However, it is important to 
note that the variation was not significantly large, and 
the results obtained from the CFD simulations were 
still reasonably comparable to the experimental data.
5  CONCLUSION
In conclusion, this research introduced a mathematical 
model for a UAV propeller, incorporating various 
airfoil structures. Experimental tests were conducted 
to evaluate the propeller’s performance in terms of 
thrust, lift, and drag. The designed E63 propeller, 
utilizing the high lift E63 airfoil structure, exhibited 
superior characteristics compared to the APC 
propeller and the NACA 4412. It generated greater 
thrust, produced higher lift force, and experienced less 
drag. The APC propeller showed good performance at 
6500 rpm but experienced a decline at lower speeds 
due to increased drag. The NACA propeller performed 
inadequately when compared to both the E63 and 
APC. The slight changes in aerodynamic properties 
observed at different temperatures had minimal 
impact on propeller performance. Comparisons 
with calculations from the BET showed satisfactory 
correlation at lower rpm ranges but increased errors at 
higher rpms. Nonetheless, the BET remains a valuable 
tool for preliminary propeller evaluation when the 
geometry is known. Overall, the mathematically 
designed propellers incorporating the high lift E63 
airfoil structure consistently demonstrated superior 
performance across various temperature ranges in 
comparison to the other propellers tested.
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