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AIP Conference Proceedings 2226, 020001 (2020); https://doi.org/10.1063/5.0002285 2226, 020001

© 2020 Author(s).

Energy consumption comparison of static

pitch propeller and variable pitch propeller

using maximum thrust equation approach in

small scale electric unmanned aerial vehicle

Cite as: AIP Conference Proceedings 2226, 020001 (2020); https://doi.org/10.1063/5.0002285

Published Online: 22 April 2020

R. Stevenson, C. Chandra, J. Christon, W. Wiryanto, R. Virginio, and W. Adiprawita

Energy Consumption Comparison of Static Pitch Propeller

and Variable Pitch Propeller Using Maximum Thrust

Equation Approach in Small Scale Electric Unmanned

Aerial Vehicle

R Stevenson1,a), C Chandra1, J Christon2, W Wiryanto1, R Virginio3 and W

Adiprawita3

1Faculty of Mechanical and Aerospace Engineering, Bandung Institute of Technology, Indonesia

2School of Life Science and Technology, Bandung Institute of Technology, Indonesia

3School of Electrical Engineering and Informatics, Bandung Institute of Technology, Indonesia

a)Corresponding author: rafaelstevensong@gmail.com

Abstract. Variable pitch propeller is being implemented in a small-scale electric Unmanned Aerial Vehicles

(UAV)21 to improve efficiency of energy consumption, especially in a cruise flight condition of UAVs. The pitch value

of the variable pitch propeller is determined with an equation that depends on two main variables which is the UAV’s

airspeed and RPM of the UAV’s motor. In this paper, the energy consumption of a variable pitch propulsion system

during a UAV’s cruising condition is being compared with the energy consumption of a cruising condition of a UAV

using a fixed pitch propeller. As a result, the variable pitch propeller propulsion system is proven to be more efficient

than a fixed pitch propeller propulsion system.

INTRODUCTION

Currently the development and usage of Unmanned Aerial Vehicle or UAV are increasing rapidly. The use of

the UAV itself only began in the 1980s for military purposes and only began to be used for various public purposes

in the 2000s. Thus, since a lot of UAVs are used for various purposes, research in the field of UAVs has also

improved and the progress of research has improved.1 The main component of energy consumption from a UAV

is the propulsion system, so to develop an energy-efficient UAV, research in the field of propulsion systems will

be discussed in this paper. This paper discusses the use of variable-pitch propellers for efficient energy

consumption in electric based UAVs. For the past century, variable-pitch propeller has been developed by aviation

pioneers and various types of variable-pitch propellers are being patented by aircraft researchers and

manufacturing companies. Even in this modern aviation era, variable-pitch propeller remains a focus point in

aircraft engine in order to improve fuel efficiency and performance.2 However, in a small scale electric UAV 21with

fixed wing configuration, the usage of this variable pitch propeller is commonly for acrobatic stunts that demands

extreme maneuvers of thrust and its control, such as using reverse thrust.3 The research done in this paper focuses

on the use of variable pitch propellers in fixed-wing small scale electric UAVs type for more efficient flight

performance. This research is done to introduce a variable pitch propeller use from a maximizing thrust to achieve

efficiency perspective that has not been done by any researchers. The variable pitch propeller equation used in this

research depends on two main variables which are airspeed and the motor RPM of the vehicle. Hence, the pitch of

the propeller would adapt to an optimum value depending on the attitude of the vehicle using an STM32F103C8

microcontroller that would control the pitch value as an open loop control system. The result of static pitch

propeller and the use of variable pitch propeller will then be evaluated based on the energy consumption of the

propulsion system.

7th International Seminar on Aerospace Science and Technology – ISAST 2019

AIP Conf. Proc. 2226, 020001-1–020001-10; https://doi.org/10.1063/5.0002285

Published by AIP Publishing. 978-0-7354-1985-8/$30.00

020001-1

PROPELLER THEORY AND MAXIMUM THRUST PITCH EQUATION

Propeller is considered as a strongly twisted wing. The cross sections of the propeller are essentially of the

same shape as those of a wing, with well-rounded leading end and sharp trailing end. Airplane wings and propellers

have something in common: They are both made up of airfoil sections designed to generate an aerodynamic force.

The difference between the geometry of a propeller blade and that of a wing consists mainly that the orientation

of the profiles of a propeller changes considerably as one proceeds from the hub toward the blade tip. Fig. 1 shows

the shape of a propeller used in UAVs.20

FIGURE 1. Fixed Pitch Propeller

From the airfoil theory, the dimensionless quantity advance ratio J plays an important role in the angle of attack

of the propeller where the angles of attack of all blade sections are uniquely determined by J when the shape of

the propeller is given. The advance ratio J could be represented in the form:20

(1)

where is the aircraft’s relative airspeed(m/s), n is the number of revolutions per second of the propeller (),

and d is the diameter of the propeller (m). The propeller’s thrust T (N), which is the force in the direction of the

propeller axis can be written in the following way:

(2)

Where is the non-dimensional thrust coefficient and is the air density(kg/m3). The propeller’s thrust T

equals to the product of and the thrust coefficient, which depends on the shape of the propeller, on the

advance ratio J, and on the Reynolds number. Another important quantity is the resulting moment, with respect to

the propeller axis, of the forces that the air exerts on the propeller. This moment is known as the propeller torque

and will be denoted by Q. According to the laws of similarity, the formula Q has an analogous structure to T but

contains an additional factor which has the dimension of a length. If the propeller diameter d is taken as this factor,

the torque is

(3)

Where the torque coefficient depends on J, Reynolds number and the shape of the propeller. The work which

is done by the torque Q is called the propeller power and will be denoted by P. The propeller power P appears as

(4)

Where the is the power coefficient and the propeller power depends on the shape of the propeller, the

advance ratio and the Reynolds number. Another notation that is going to be discussed is the propeller efficiency.

The efficiency of the propeller could be measured from the ratio of power output to power input

(5)

Where TV is the product of Thrust and the Velocity of flight measures the power that is available for the

propulsion of the airplane and P is the power that must be transmitted to the propeller in order to obtain the desired

angular velocity. The efficiency of the propeller could be expressed in , and J as

(6)

A plot of propeller efficiency from Eq. (6) is illustrated in figure 2.20

020001-2

FIGURE 2. , , J and efficiency plot

Based on quantitative analysis, the main result of the experiment is that the values of and and therefore

, depend essentially on three parameters, the solidity of the propeller, the relative distance of the representative

element expressed in and the blade setting which is the angle of the blade against the plane rotation of the

propeller. Therefore, from equation (6), we could express and plot the propeller’s efficiency against the advance

ratio J and with various blade setting angle as shown in Fig. 3 below.6

FIGURE 3. Efficiency with various angle plot

Based on the method of representative blade element, the blade setting angle of the propeller could be the

representative of a propeller’s general information about the shape of the characteristic curves called the propeller’s

pitch p (inch) . The propeller’s pitch p is also defined as the distance travelled by a propeller in one revolution.

The propeller theories and terms mentioned earlier are going to be used to explain the main equation used for the

variable pitch propeller control in this paper. The term variable pitch propeller means that the propeller has the

ability to modify the blade setting of all blade sections along the propeller by the same amount while on the ground

or in flight.20

There are many attempts done by researchers to definementioned in Eq. (2). analytically but this requires

detailed knowledge of the propeller’s geometry and instead another relation of the propeller’s thrust is developed

from the simple momentum theory and proven from experimental data. The alternative thrust model could be

represented as10,8

(7)

From Eq. (7), we could have the Dynamic thrust equation where the freestream airspeed is being considered

into the momentum theorem and could be represented as10,8

(8)

Where p is the propeller’s pitch (in), V is the flight’s airspeed and N is the revolution per minute of the propeller.

is the coefficient constant and is the power constant, both to be determined empirically that is obtained from

experimental data to fit the model and the number 0.0254 and 60 are the results of the variables’ unit conversion

factor due to the use of inch and minute to present the propeller’s thrust T in Newton. From Fig. 3, it could be seen

that in a certain flight condition of the propeller which is expressed by the propeller’s freestream airspeed V in the

advance ratio J equation, to achieve the maximum efficiency of that certain flight condition there is a certain value

of blade angle setting and therefore propeller’s pitch p that fulfills. From Eq. (5) the propeller’s efficiency

depends on the Thrust T, vehicle’s airspeed V and the power transmitted to the propeller P. Therefore, we can

achieve a maximum efficiency by achieving a maximum thrust T in certain condition of the vehicle’s airspeed V

020001-3

and power transmitted to the propeller P.20 To achieve a maximum thrust at every condition, we can find the

maximum value of thrust of the propeller from Eq. (8) by finding the first derivative against pitch p equals to zero

and obtain the pitch of the propeller needed for the maximum thrust denoted by . After the process of first

derivative of Eq. (8) equals zero we obtain the maximum thrust pitch equation as seen in Eq. (9) below.

(9)

Equation (9) is used as the equation for the variable pitch propeller’s pitch value determination to achieve the

maximum thrust as proposed to achieve better efficiency.

HARDWARE AND SOFTWARE DESIGN

The variable pitch propeller Eq. (9) is to be tested on a small-scale electric UAV where the variable-pitch

propeller mechanism could be fitted safely and the implementation of the variable-pitch propeller equation using

a microcontroller and actuated by servo and linkages to drive the variable-pitch mechanism.

Testing Airframe

The model airframe used for testing the variable pitch is the Skywalker 1680. It is a pusher-configuration model

plane and has a 4-channel control. The design of the variable pitch propeller mechanism is also the reason why we

chose the Skywalker 1680 as the motor is installed above the tail boom to avoid damage between the propeller and

the ground when landing. The following figure 4 and figure 5 are the Skywalker 1680.

FIGURE 4. Front View of Skywalker 1680 FIGURE 5. Back View of Skywalker 1680

Variable Pitch Propeller Electrical and Programming System

The variable pitch propeller electrical diagram of the system is shown in Fig. 7 below.

FIGURE 6. Flowchart of Electrical System

The variable pitch propeller actuator uses Kingmax CLS6111HV servo which is a servo suitable for the variable

pitch mechanism shown in Fig. 7. The microcontroller used to implement the variable pitch propeller pitch

equation is STM32F103C8T6. This microcontroller is programmed to be able to calculate the pitch for the variable

020001-4

pitch propeller and sends Pulse Width Modulation signal to the servo and the microcontroller does this pitch

alteration during flight.

FIGURE 7. Kingmax CLS6111HV servo

FIGURE 8. STM32F103C8T6 Microcontroller

The main function of the STM32F103C8T6 microcontroller is to obtain optimum pitch that results in maximum

thrust in a certain point according to Eq. (8). The data that must be obtained include V which is the vehicle’s

airspeed and N which is the revolution per minute or RPM. The sensor used to obtain airspeed data is 12C-

MS4525D0 that is connected to Pixhawk, while the sensor used to obtain RPM is the HW BQ2017 RPM sensor.11

The basic concept of the microcontroller processing is shown below.

FIGURE 9. Flowchart of Basic Program Concept

In obtaining the airspeed data, the utilization of MAVLink is crucial in the program coded in the

microcontroller. MAVLink, or Micro Air Vehicle Link, is a communication protocol in UAV that is used to

transmit data and command from UAV to GCS (Ground Control Station) or vice versa.12,13 The data and command

sent is packed into a kind of messaging packet called MAVLink message. The format and specification of the

MAVLink message is shown in Fig. 10.

FIGURE 10. MAVLink Message Content13

020001-5

Before obtaining the airspeed data, a message ID containing airspeed data must first be determined. Message

ID is used to define the meaning of the payload data. Different message IDs define different payload data.14 To

test the suitability of the message ID used, pitot tubes and airspeed sensors which are connected to Pixhawk via

the I2C port are used. The air is passed to the pitot tube, then the airspeed data in the GCS is matched with the

airspeed data in the serial monitor. In this case, the software used as the GCS is Mission Planner.15 The message

ID that is used to obtain the airspeed data is VFR_HUD (# 74). Using the method described, it is evident that the

airspeed data in the serial monitor approaches the airspeed data listed in the GCS. This means that VFR_HUD is

the appropriate message ID to get airspeed data.

Furthermore, to obtain RPM data, an ESC RPM sensor is used which can detect voltage changes in brushless

motor cables. In order for STM32F103C8T6 to get the RPM value, an interrupt system is used in the program.

Using the interrupt system, the STM32F103C8T6 microcontroller can calculate the number of signals sent by the

ESC RPM sensor in a given period so that the RPM data is obtained from the motor at a certain time.16 After

obtaining airspeed and RPM data, the data is substituted into the pitch formula in Eq. 8 to obtain the optimum

pitch value. This pitch value is then converted to PWM using the pitch-PWM conversion formula. Later, the

converted PWM value is sent to the servo of the Variable Pitch Propeller which will then move according to the

PWM sent. In addition, there are several operational modes programmed into the microcontroller, which are:

1. Static, where the servo is set so that the pitch is constant at a certain PWM value. In this case, because the

propeller used is 11 x 7, then the pitch of the propeller is 7 inches, so based on the PWM-pitch conversion

formula, the PWM value used in this mode is 1052 ms.17

2. Static pilot, where the pitch can be adjusted freely through the transmitter. The microcontroller receives

PWM input from the flight controller via MAVLink message which will then be sent again to the servo so

that the pitch can change as PWM input from the transmitter.

3. Dynamic, where the pitch will change according to the pitch formula. Briefly, the pitch will change

automatically following changes in airspeed and RPM. At this stage, the airspeed and RPM data is taken

and then processed so as to produce a pitch that is converted to PWM.

Variable Pitch Mechanism

The Variable Pitch Mechanism is connected to the motor’s shaft by using a shaft coupler. In addition, a pair of

blades is installed therefore the Variable Pitch Propeller’s diameter become 11 inches. Afterwards, the Variable

Pitch Propeller is connected by a linkage to a servo therefore the pitch of the Variable Pitch Propeller could be

modified by the servo as shown in Fig. 11 and 12.

FIGURE 11. Installation of the Variable Pitch Propeller with Motor, Servo, and Blade

FIGURE 12. Illustration of Variable Pitch Propeller which can change its pitch value on flight by using a push-pull rod

driven by servo

Pitch of the Variable Pitch Propeller is set by a servo with PWM range between 900 - 1500 microseconds.

Minimum PWM value will result pitch value of 3.998 inches and maximum PWM value will result pitch value of

25.211 inches.

020001-6

METHODOLOGY

Propeller pitch data measurement

From Eq. (9) the propeller’s pitch obtained is in inch, where the servo used as the variable pitch mechanism

actuator sends data in Pulse Width Modulation or PWM. Therefore, we need to find the pitch value converted to

PWM value so the servo could use PWM signals to appoint the intended pitch value to the variable pitch

mechanism. This correlation is needed for STM32F103C8T6 to convert the pitch value calculated from Eq. (9) to

a signal (PWM) to move the servo arm. Eq. (10) shows the formula used to calculate the pitch of the propeller

manually4 as can be seen below

(10)

Where pitch is the pitch value of the propeller at a certain state in inch, D is the diameter of the propeller in

inch, h is the height of the blade cross section at 75% of diameter in cm (the difference between height at leading

edge and height at trailing edge), and w is the width of the blade cross section at 75% of diameter in cm.

FIGURE 13. Blade Cross Section at 75% of Diameter

The cross section at 75% of diameter is used because the pitch at 75% of diameter generally comes close to the

effective pitch of a propeller.4 Eq. (10) can be used to estimate almost every propeller’s pitch. Some data samples

are taken to represent all pitch values on a particular PWM value. The pitch samples are taken by using Eq. (10)

by measuring variables related using calipers. Meanwhile, various PWM values are sent to the servo. The data

taken are then plotted so that the equation is obtained to convert the value of PWM servo to the pitch propeller

value. The conversion equation is implemented inside the STM32F103C8T6 microcontroller to switch the value

of pitch obtained from airspeed and RPM data into PWM. Figure 13 shows a graph of pitch to PWM conversion

with the equation used for calculation in the STM32F103C8T6 microcontroller.

FIGURE 14. Graph of PWM and Pitch

The graph in Fig. 14 is obtained from using logarithmic approximation. Finally, in accordance to Fig. 14, it is

found that the conversion formula is

(11)

020001-7

Where the pitch value calculated from Eq. (8) is in inch and could be converted to PWM values to be sent to

the servo by using Eq. (11).

K2 Propeller Constant

The K2 value needed in the pitch equation of the variable pitch propeller is obtained using the Thrust

Benchmarking System Instrument.10 Using this, it is determined that the K2 value for an average 11-inch propeller

is 3.5.

Variable Pitch Equation Plot

Equation (8) used in the variable pitch mechanism is being plotted as below.

FIGURE 15. Graph of Airspeed, RPM, and Pitch for Maximum Dynamic Thrust

The two main variables in determining the pitch value are RPM of the motor and the UAV’s airspeed [see Eq.

(9)]. The relationship between pitch to the motor’s RPM and the UAV’s airspeed are being plotted as below.18

From the graph in figure 15, it could be seen that the pitch desired for maximum efficiency depends on RPM and

airspeed in a trend of the pitch equation used for the variable pitch propeller. 18 It is shown that the characteristics

of the equation meet our expectations as on a constant RPM the pitch will increase as the airspeed increases and

also for a constant airspeed, the pitch will decrease as the RPM decreases.

RESULTS AND DISCUSSION

Data retrieval is done on 7 test flights with each test flight alternating between static pitch propeller and variable

pitch propeller in a same flight path to achieve as similar flight condition as possible in the flight controller’s

autopilot mode in a set constant airspeed. Energy data is obtained from the power meter and the calibrated power

module of the pixhawk autopilot. Airspeed data is obtained from the I2C airspeed sensor. Comparison of energy

consumption is done by normalizing the value of energy consumed with the aver age airspeed during flight by

dividing the Energy data from the flight log by airspeed squared. This normalizing method is used based on Eq.

(5) and (8) where the energy is proportional to the airspeed squared. Table 2 shows that the variable pitch propeller

use less energy than the static pitch propeller in a similar flight condition where the mean airspeed and flight paths

are similar. The validity of the data is proved with the statistical method of finding the p value through t test with

a p value of 0.00017 where this value is less than 0.05 which proves the significance of the variable pitch propeller

against the static pitch propeller. Observations were made on energy consumption which can be seen in the Table

1.

020001-8

TABLE 1. Comparisons of Static and Variable Pitch Propellers with respect to Energy Used

Flight

Propulsion System

Mean Airspeed (m/s)

Energy Used

1

Static Pitch Propeller

24

31.094299

Variable Pitch Propeller

24

23.846943

2

Static Pitch Propeller

17

85.711696

Variable Pitch Propeller

17

73.821626

3

Static Pitch Propeller

17

82.8356782

Variable Pitch Propeller

17

73.422042

4

Static Pitch Propeller

17

98.694567

Variable Pitch Propeller

17

82.308997

5

Static Pitch Propeller

17

84.499308

Variable Pitch Propeller

17

73.504983

6

Static Pitch Propeller

17

79.148062

Variable Pitch Propeller

17

71.885882

7

Static Pitch Propeller

17

68.633226

Variable Pitch Propeller

17

60.182542

CONCLUSION

In this paper, variable-pitch propeller system is being made to be used for small scale electric UAVs. The

system has operational modes that are used for a safe method of testing. The equation used in these systems is

obtained from the derivation of the dynamic thrust equation derived against the propeller’s pitch to obtain the

maximum thrust at certain airspeed and motor’s RPM in order to achieve better propeller efficiency. The equation

is being used on the designed variable pitch propeller mechanism and has given proof of positive results to

improvements of propeller’s efficiency for small scale electric unmanned aerial vehicle on cruise flight condition.

On further testing and improvements, usage of a folding propeller with better airfoil section, chord and pitch

distribution would provide the propeller used in the variable pitch propeller mechanism a better aerodynamic

performance and thus be a more suitable propeller to be used for further efficiency improvements by implementing

the variable pitch propeller equation for optimum pitch performance to achieve better efficiency.

ACKNOWLEDGEMENT

This work is supported by Aksantara UAV Research and Development Team of Bandung Institute of

Technology, Indonesia

020001-9

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