Disc-Shaped Aircraft - National University of Singapore

Transcription

Disc-Shaped Aircraft
Submitted by:
Chew Farhana Hassan
U025539Y
Department of
Mechanical Engineering
In partial fulfilment of the
requirements for the Degree of
Bachelor of Engineering
National University of Singapore
Session 2005/2006
Abstract
ABSTRACT
A disc-shaped aircraft has the potential to be a highly manoeuvrable remotecontrolled aircraft. The aim of this project was to design, build and test a disc-shaped
aircraft that makes use of no control surfaces, and can travel in any direction, unlike
conventional aircrafts which can only move in 5 directions – straight ahead, left, right,
up or down. This paper breaks down the design process into the conceptual,
theoretical and detailed phases. Computational fluid dynamics were made use of to
come up with a conceptual design of the aircraft, and a shift of the centre of mass is
employed to provide directional control. Flight tests were carried out to test the
design, and although not all the objectives were met, recommendations are made to
further improve on the design.
Figure: Disc-shaped aircraft
Department of Mechanical Engineering
I
Acknowledgements
ACKNOWLEDGEMENTS
The Author wishes to express her heartfelt thanks to the following persons for the
critical roles that they have played from the birth of the project till the end.
A/P Gerard Leng Siew Bing, Project Supervisor, for providing crucial guidance and
supervision during the course of the project;
Encik Ahmad Bin Kasa, Mr Cheng Kok Seng, Ms Amy Chee and Ms Priscilla Lee,
staff of Dynamics and Vibrations Laboratory, for their invaluable support and endless
help throughout the project;
Staff of the Fabrication Support Centre for their advice on the construction of the
model.
Lim Jing Liang and Spencer Soh for their invaluable help during flight-testing.
Thank you very much.
II
Table of Contents
TABLE OF CONTENTS
ABSTRACT
I
ACKNOWLEDGEMENT
II
CONTENTS
III
LIST OF FIGURES
VI
LIST OF TABLES
VIII
LIST OF SYMBOLS
IX
1.
Introduction
1
1.1
Objectives
2
1.2
Organization of Thesis
2
2.
Literature Review
3
3.
Conceptual Design
6
3.1 Justification
6
3.2 Potential Roles
6
3.3
Prototypes
7
3.3.1
Prototype A
7
3.3.2
Prototype B
8
3.3.3
Final Prototype
9
3.4
Draft Design
10
3.4.1
10
Shape of Outer Body
III
Table of Contents
4.
5.
3.4.2
Counter-Rotating Shafts
10
3.4.3
Shape of Housing for Components
11
3.4.4
Propulsion System
12
3.4.5
Determination of Angle of Attack
12
Theoretical Design
13
4.1
13
Initial Weight Estimation
4.2 Dimensions / Shape
13
4.3
Preliminary Computational Fluid Dynamics
14
4.4
Propulsion Evaluation
16
4.5
Directional Control
19
4.5.1
Uni-Directional Control
19
4.5.2
Multi-Directional Control
20
Detailed Design
21
5.1
Fabrication of Prototype
21
5.1.1
Mainframe & Shaft
21
5.1.2
Directional Control
22
5.1.3
Body
23
5.1.4
Propellers
24
5.2
Detailed Weight Analysis
25
5.3
Propellers / Motor Chosen
26
IV
Table of Contents
5.4 Flight Test
26
5.5
27
Evaluation & Qualification
6.
Conclusion
28
7.
Recommendations
29
References
30
Appendix A: Velocity and Pressure Plots of Various Shapes
32
Appendix B: Details on Components Used
36
Appendix C: Froude’s Momentum Theory
38
Appendix D: Material Selection
42
Appendix E: Experiment to determine Thrust
44
V
List of Figures
LIST OF FIGURES
2A
Cross-section of a Chakram
3A
Top View of Prototype A
3B
Co-Axial Propeller & Body on Shaft
3C
Co-Axial Rotating Propellers
3D
Pressure and Velocity Plots of Chosen Chassis Shape
4A
Dimetric View of Prototype
4B
Velocity and Pressure Plots of the Prototype
4C
Graupner 500 and Promax 400s in Frame
4D
Stability of Aircraft in Hover Position
4E
Shift in C.G. of Prototype
5A
Mainframe and Bearing & Shaft
5B
Servo Mounted on Frame
5C
Determination of Height of Propellers
5D
(a) Flat Disc Cut Out with Inner Radius;
(b) Up-Close of Chamfer;
(c) Final Product
5E
Propellers connected to shaft and chassis
A1
Velocity and Pressure Plots for a Sphere
A2
Velocity and Pressure Plots for an Ellipse
A3
Velocity and Pressure Plots for a Sphere + Cylinder
A4
Velocity and Pressure Plots for a Sphere + Cone
B1
Electronic Speed Controller – 30
B2
Futaba Receiver
VI
List of Figures
B3
Servo Motor
B4
Lithium Battery
B5
Promax 400 Motor
B6
Futaba Transmitter
C1
Diagrammatic Representation of a Propeller
E1
Graph of Force vs. Extension
E2
Experimental Set-Up
E3
Thrust generated by Propellers
VII
List of Tables
LIST OF TABLES
3A
Differences between Fixed- and Rotary-Wing Aircrafts
4A
Initial Breakdown of Mass of Prototype
4B
Possible Motor / Propellers using Froude’s Momentum Theorem
5A
Breakdown of Mass of Final Prototype
A1
Comparison of Computed Drag Force
C1
Mechanical Properties of Various Materials
VIII
List of Symbols
LIST OF SYMBOLS
a
Inflow Factor
A
Area (m2)
AoA
Angle of Attack (°)
C.G.
Centre of Gravity
E
Young’s Modules (Gpa)
F
Force (N)
FD
Drag Force (N)
g
Acceleration due to gravity = 9.81ms-2
h
Height from Centre of Lift to C.G. of Moving Mass (m)
k
Spring Constant
m
mass (kg)
p1
Pressure at inlet (Pa)
p2
Pressure just before propeller (Pa)
p3
Pressure just after propeller (Pa)
p4
Pressure at outlet (Pa)
patm
Atmospheric Pressure = 101325 Pa
P
Power (W)
t
Time (s)
T
Thrust (N)
v
Design Flight Velocity (ms-1)
V1
Inlet velocity (ms-1)
V2
Velocity before Propeller = Mean Velocity of Propeller Slipstream (ms-1)
V3
Velocity after Propeller = Mean Velocity of Propeller Slipstream (ms-1)
IX
List of Symbols
V4
Outlet Velocity of Propeller Slipstream
W
Weight (N)
x
Displacement from Original Position
ρair
Standard Air Density = 1.2256 kgm-3
η
Effieciency
X
Introduction
1. INTRODUCTION
This project was initiated with the purpose of creating an aircraft, capable of providing
economical surveillance support and intelligence gathering for both civilian and noncivilian use, especially in tight situations i.e. within buildings.
In the current situation, robots have been used in tight situations for the purpose
mentioned above. However, such robots are costly in nature and have several limitations.
Firstly, being land bound, a robot would not be able to enter a compound where the sole
point of entry is situated above the ground. Only an aircraft capable of taking off and
maintaining a stable flight would be able to overcome such a scenario.
Next, robots are incapable of providing a bird’s eye view that is critical to a decision
maker for choosing the best option. A bird’s eye view of the current situation would
provide better information about the situation as compared to a specific and narrow view
provided by a robot.
Lastly, rough terrains and obstacles create barriers and impede the movement of a land
bound robot. This is extremely undesirable when information and intelligence have to be
gathered quickly. The problem is made worse when a considerable distance needs to be
covered.
As such, a remotely controlled aircraft capable of elevating, negotiating tight corners and
maintaining a stationary position is necessary.
1
Introduction
1.1 OBJECTIVES
Following below are the objectives of this project necessary to create the right aircraft to
suit the role mentioned above.
z Vertical Take-Off / Land
z Stable Hovering Flight
z Relatively Straight, Level Flight
z No control flaps – vectored lift
1.2 ORGANIZATION OF THESIS
This thesis is divided into 7 Chapters and they are organized as follows:
Chapter 1 gives an Introduction on the subject matter.
Chapter 2 is a Literature Review on the dynamics of a rotating disc in flight.
Chapter 3 is the conceptual design of the aircraft, and the initial phases and calculations
involved in designing the prototype.
Chapter 4 is the Theoretical design where theory is applied to get a more accurate design
for the next phase, which is fabrication.
Chapter 5 is the Detailed Design, where the fabrication takes place.
Chapter 6 is the Project Conclusion.
Finally, Chapter 7 gives the recommendations for future study.
2
Literature Review
2. LITERATURE REVIEW
The idea for a circular flying wing was first developed in the 1930s and 40s, and by the
1950s, a circular Vertical Take-Off/Land (VTOL) aircraft was developed. This Avrocar
made use of nozzles and jets to control its direction. [1]
However, due to the scarcity of further information on disc-shaped aircrafts, other
sources were considered in order to better understand the dynamics involved in flight of a
disc.
In these contemporary times, flying discs have been recognized as a recreational item in
the minds of many, mainly as FrisbeesTM. As such, little consideration has been placed to
thoroughly understand the dynamics of a disc in flight. Below, I shall be highlighting
some of the few experiments that had been carried out.
In the 1960s, several tests have been performed at the NASA Langley Research Centre.
Mugler and Olstad carried out a series of tests to investigate the aerodynamic
characteristics of a lenticular shape at transonic speed [2]. Concurrently, NASA also
conducted an extensive study of general lifting bodies suitable for re-entry. The results
were unsatisfactory and the projects were later abandoned. [3]
Next, research has also been done by the military, hoping to exploit the properties of a
disc in flight. In 1968, a paper was published by Paul Katz in the Israeli Journal of
Technology [4]. With his main focus on the stability criteria and flight trajectories, his
research was done with the hope of producing a possible candidate to replace artillery
shells.
3
Literature Review
An experiment performed by 2 Japanese researchers had shed much light on the airflow
over a Frisbee. In Kyushu University, 1989, Nakamura and Fukamachi had made use of
the method they had developed earlier (smoke wire method) to produce the article
“Visualization off Flow past a Frisbee” in 1991 in the journal Fluid Dynamics Research
[5]
Lastly, an article, published in a renowned British journal New Scientist (1990), deserves
special mention. The author, Macé Schurmanns (a former Swiss disc-throwing champion)
uncovered the history of Frisbees, and made a successful attempt to explain its
aerodynamic forces and their overall flight dynamics. [6]
Understandably, only minimal information could be extracted from Scientific Journals
for use in this project. Hence, in order to grasp a thorough understanding, unconventional
sources were also consulted, one of which was ancient weapons and tools, one of which
was the Chakram.
Fig 2A: Cross-section of a Chakram [7]
The ancient Indians have been using the Chakram[7] as a weapon and tool for hundreds
of years. The profile of a typical brass Chakram can be seen in Figure 2A above. The
shape of the Chakram enables it to hold its stable position over relatively long distances.
The Chakram, although similar in shape and size to the Frisbee, is actually more efficient
in that respect.
4
Literature Review
Since this is a powered flight, however, it will be slightly different from a Chakram in
that it need not depend solely on the speed and angle of release. Because of this, the
principles behind coaxial rotored helicopters are also studied. [8]
Making use of the principles of an airfoil providing lift, and that of a gyroscope providing
stability, derived from the way the Chakram and Frisbee operate, a conceptual design can
be drawn up.
5
Conceptual Design
3. CONCEPTUAL DESIGN
3.1 JUSTIFICATION
The advantages in building a Vertical Take-Off / Land (VTOL) vehicle can be
summarized as below:
Table 3A: Differences between Fixed- and Rotary-Wing Aircrafts
Rotary Wing
zStationary
zSmall
Surveillance possible
launching area
Fixed Wing
z
No Stationary Surveillance
z
Large launching area
z
High noise
z
Lower noise
z
Usually higher profile
z
Lower profile
As can be seen, the VTOL vehicle has a smaller launching area, enabling it to lift off in a
shorter amount of time. Also, rotary wing vehicles can hover, enabling stationary
surveillance. However, there are disadvantages as well. Rotary wing aircraft usually have
a higher noise signature, and they tend to have a higher profile as well. However, in
developing this UFO, the profile shall be lower as compared to typical rotary wing crafts.
3.2. POTENTIAL ROLES
The potential roles that can be played by this would be as follows
(i)
Surveillance in interior of buildings
(ii)
Surveillance in built-up areas
6
Appendix E
3.3 PROTOTYPES / INITIAL DESIGN
3.3.1 PROTOTYPE A
Figure 3A: Top View of Prototype A
The first prototype that made use of no control flaps was Prototype A. Prototype
A consists of four propellers located at the four corners of the aircraft as shown in
Figure 3A above. In order to travel in a specific direction, opposite propellers
increase or decrease thrust respectively. This would cause the aircraft to tilt and
thus move off in a specified direction.
This is convenient as one needs only control the thrust in order to control the
direction, however, it comes with many disadvantages.
It would be rather unstable, and even with a gyroscope placed in to stabilize the
flight path, too much thrust might cause the whole aircraft to flip. This would be
especially apparent in outdoor conditions. Further more, with four motors being
controlled independently, should one motor fail, the whole aircraft would be
rendered unstable, and come to a crash. Hence a better design needs to be
evaluated. This leads us to Prototype B.
7
Appendix E
3.3.2 Prototype B
Prototype B is very similar to the current design, except that instead of two
propellers, it made use of only one propeller. To counter-act the moment
generated by this propeller, the body would rotate in the opposite direction,
connected to the same shaft driven by the single motor, as seen in figure 3B
below.
Figure 3B: Co-Axial Propeller & Body on Shaft
For the shape of the outer ring, a cross sectional shape was first determined.
Based on the findings earlier, a regular airfoil would not do, as the ring would be
rotating, and thus after rotating through 180°, what used to be the leading edge
would now be the trailing edge. As such, a Göttingen 795 Airfoil, obtained from
the UIUC coordinates database [9], was used as a reference. It was reflected about
its midplane to give a cross section. This cross-sectional area was treated as a
wing, and by making use of CosmosFlow and Solidworks, flow visualizations
were carried out to determine that the best configuration for such an airfoil was
15°.
8
Appendix E
However, with only a single motor driving both shafts, it proves ineffective, and
the torque is unevenly distributed since the propeller and the body draw different
ratios of power from the motor. It would prove extremely challenging to obtain an
exact solution such the torque drawn by the body is the same as that drawn by the
propeller.
Furthermore, the profile of the Göttingen 795 is extremely thin, and for an aircraft
of this size, would mean the body would be very brittle. If rotating, it would break
upon contact, and not only would the aircraft be deemed unstable, flying pieces
could hurt someone in the vicinity.
3.3.3 FINAL PROTOTYPE
This leads us on to our final prototype that consists of a coaxial shaft with two
propellers contributing to the lift of the aircraft. The design of the final prototype
is outlined in the next section.
9
Conceptual Design
3.4 DRAFT DESIGN OF FINAL PROTOTYPE
3.4.1
SHAPE OF OUTER BODY
The shape of the outer body would be based on that of an airfoil, rotated about a
centre, to give a disc vaguely resembling that of a Chakram.
3.4.2
COUNTER-ROTATING SHAFTS
By Newton’s third law of motion, when the propeller rotates, a counter-moment
would result in the body and the body would counter-rotate. To prevent this from
occurring, a shaft would be made with two components allowing the propeller to
rotate, and another propeller to counter-rotate in the opposite direction. This
enables the main chassis to remain stationary so that surveillance equipment can
be mounted on it.
Figure 3C: Co-Axial Rotating Propellers
10
Conceptual Design
3.4.3
SHAPE OF HOUSING FOR COMPONENTS
The components will be housed in a chassis that will also in future house the
surveillance equipment. This shape should reduce drag – in terms of flow
separation and skin friction, and as such, Computational Fluid Dynamic (CFD)
analysis was carried out by making use of SolidWorks and COSMOSFloWorks.
(a)
(b)
Figure 3D: (a) Pressure and (b)Velocity Plots of Chosen Chassis Shape
This shape was chosen as the best for the chassis, since this results in the least
wake or turbulence. Even though the skin friction drag is not the lowest, the
difference is negligible compared to the drag force caused by the turbulence and
wake of the other shapes (Appendix A). Furthermore, it was large enough to
house the electrical components needed for flight.
Fins were added to stabilise the chassis and also to enable the aircraft to stand on
its own when left stationary just before launch.
11
Conceptual Design
3.4.4
PROPULSION SYSTEM
The best propulsion configuration needs to be determined for the system.
Furthermore, no control flaps will be employed in this and thus an efficient
directional system needs to be put in place too.
An electric motor is chosen rather than a combustion engine due to various
factors. The cost of the fuel is high, and the operability of the aircraft with a liquid
propellant would be affected. Furthermore, with a liquid propellant, the weight
would be dynamically changing, and this could affect the stability of the aircraft.
As such, an electric motor was decided upon.
Evaluating the different motors available on the market due to cost and size
considerations, the motors were finally narrowed down to two choices – the
Promax Speed 400 and the Graupner Speed 500.
3.4.5
DETERMINATION OF ANGLE OF ATTACK
The angle of attack needs to be determined for optimum travel by making use of
computational fluid dynamics.
From the results, an angle of attack of 15° was chosen. The turbulence on the
underside of the “wing” can be neglected.
12
Theoretical Design
4. THEORETICAL DESIGN
4.1 INITIAL WEIGHT ESTIMATION
Table 4A: Initial Breakdown of Mass of Prototype
Component
Mass
Wireless Receiver
30g
Electronic Speed Controller
21g x 2
ESC-30 x 2
=42g
71g x 2
Battery x 2
=142g
Body + Motors
350g
Servo Motor
18g
Large Propeller
77g
Small Propeller
39g
Total
698g
*Refer to Appendix C for detailed components
4.2 DIMENSIONS / SHAPE
The preliminary dimension was chosen to be that of a standard Frisbee. In addition to
that, the shape was chosen to be one similar to that of a Chakram. However, we must bear
in mind that a Chakram has no propulsion, whereas this aircraft does, hence the problems
associated with a Chakram can be somewhat overcome.
13
Theoretical Design
4.3 PRELIMINARY COMPUTATIONAL FLUID DYNAMICS
With the propellers in place, we again made use of computational fluid dynamics to come
up with various angles of attacks, to determine the lift and drag generated.
The assembled diagram with all the components in place is are follows:
Figure 4A: Dimetric View of Prototype
From the CFD computations, when the prototype is moving upwards with a velocity of 5
ms-1, the theoretical Drag Force calculated = 1.224 N
14
Theoretical Design
Figure 4B: (a) Velocity and (b) Pressure Plots of the Prototype
15
Theoretical Design
4.4 PROPULSION EVALUATION
By making use of the Weight and Drag calculated earlier, the minimum thrust can be
calculated.
Min Thrust = Total weight + Total Drag
= W + FD
= 0.698 x 9.81 + 1.224
= 8.07 N
By making use of Froude’s momentum theory [11] (Appendix C), the theoretical sizing
of the propulsion can then be obtained to see if the Graupner 500 and the Promax 400 are
suitable for use with each of the propellers.
Given that T = 7.56 N, Design velocity v = V1 = 5 ms-1, ρair= 1.2256 kgm-3 and area of
propeller A = πr2 = 0.2463 m3 we can substitute in the following equation:
T = ρA2V12(1+a)(2a)
Hence (a2 + a)
= T / (2ρA2V2)
= 0.535
Solving for a, we get a = 0.386
Efficiciency η = 1 / (1 + a)
= 1 / 1.386
= 0.722
16
Theoretical Design
Therefore, based on Froude’s momentum theory,
η
=
Pdisc =
Pinput/ Pdisc
Pinput / η
=
T*V*(1+a)
=
55.9 W << 96W
The theoretical rating of the Promax is 96W, and this value obtained is higher than the
Power calculated using Froude’s momentum theory above. In a similar manner, the
Power required for the Graupner and different configurations of the Promax were
calculated and tabulated below to show the plausible configurations.
Table 4B: Possible Motor / Propellers using Froude’s Momentum Theorem
Motor Type
Prop
A of disc
Diameter
(m2)
(m)
T
(N)
(a2 + a)
a
Pdisc
(W)
Single
0.28
0.246
8.07
0.535
0.386
55.9
Promax 400
0.35
0.385
8.07
0.342
0.270
51.2
Single
0.28
0.246
8.07
0.535
0.386
55.9
Graupner 500
0.35
0.385
8.07
0.342
0.270
51.2
0.28
0.246
4.04
0.267
0.219
24.6
0.35
0.385
4.04
0.171
0.149
23.2
2 Promax 400s
Can be
used?
;
;
;
;
;
;
These results were then checked against the results from the thrust experiment, and we
once again see that it is plausible to use either of the motors.
17
Theoretical Design
A single Promax Speed 400 weighs 90g, and a single Graupner Speed 500 weighs 160g,
which is a huge 56% increase in weight. When mounted onto a frame for counterrotation, the two Speed 400 motors weigh 195g while the Graupner Speed 500 assembly
weighs 216g. This differential is rather sizeable, especially since now the two propellers
can rotate independently of each other.
Furthermore, with 2 motors in place, the weight distribution is symmetrical aiding in the
stability of the aircraft.
(a)
(b)
Figure 4C: (a) Graupner 500 in Frame and (b) Promax 400s in Frame
Thus it would be more feasible to make use of two Promax Speed 400s for producing the
required torque.
18
Theoretical Design
4.5 DIRECTIONAL CONTROL
4.5.1. UNI-DIRECTIONAL CONTROL
By making use of a shift in C.G, we can enable the aircraft to change directions.
Theoretically, the aircraft will be in stable equilibrium when the C.G. of the
aircraft is directly underneath its centre of lift. Hence, if the C.G. is shifted, it will
tilt into a new position.
=
Center
of mass
(a)
(b)
Figure 4D: Stability of aircraft in hover position
In Figure 4D(a), we can see the aircraft in a straight-up/hover position. The C.G.
and the Lift are in a straight line. Should the aircraft tilt, as in Figure 4D(b), the
anti-clockwise righting moment, as taken about the C.G., caused by the lift and
the components of the plane would serve to stabilize the aircraft, and thus push it
back to its equilibrium position (Fig. 4D(a)). Similarly tilting it the other way
would yield a clockwise righting moment.
19
Theoretical Design
Figure 4E: Shift in C.G. of Prototype
The C.G. of the aircraft is shifted slightly by virtue of shifting the components of
weight. By assuming that all the weight of the aircraft acts through its C.G., as in
Figure 4E, we can see that there is now a couple generated about the C.G. of the
aircraft. This will cause it to tilt until the C.G. is directly beneath the centre of lift
once again as seen in Figure 4E(b).
In this way, we can enable the aircraft to move in a single direction.
4.5.2. MULTI-DIRECTIONAL CONTROL
In order to enable the aircraft to move in any direction, one of the propellers just
needs to be slowed down a little. This will create a differential torque and cause
the body to rotate. In this way, the aircraft can now travel in any direction
required.
20
Appendix E
5. DETAILED DESIGN
5.1 FABRICATION OF PROTOTYPE
The main steps taken in fabricating the final prototype are detailed in the following
paragraphs.
5.1.1 MAINFRAME & SHAFT:
The mainframe is made out of acrylic sheets, as after cost, weight and machining
considerations, it was the most viable option. The detailed process of material
selection is included in Appendix D.
Circular shapes were cut out from acrylic sheets and then joined together with
carbon rods and screws to create a mainframe to hold the motors and propellers
and body together. Holes were cut out so the motors could be fitted in, and space
was left at the bottom to house the electronic components.
Ball bearings were then press-fitted into the centre (Figure 5A(b)), and the shaft
was placed through there.
Figure 5A: (a) Mainframe and (b) Bearing & Shaft
21
Appendix E
5.1.2 DIRECTIONAL CONTROL:
The servo motor was mounted in the configuration shown in Figure 5B, to enable
the shift in the C.G. As the servo rotates, it causes a shift in the pinion gear, which
in turn moves the rack horizontally.
Figure 5B: Servo Mounted on Frame
The servo subtends an angle of 105° and thus making use of a gear with radius
1.5cm, we find that the shift caused would be 2.75cm. Since an angle of attack of
15° is ideal when moving in any direction, the servo should be mounted 10.3cm
below the centre of lift.
tan15°=2.75 / h
h = 2.75 / tan 15°
15°
= 10.26cm
2.75cm
Fig 5C: Determination of Height of
Propellers
22
Appendix E
5.1.3 BODY:
Out of Styrofoam discs, the following shapes were manufactured by sanding
down the edges so the profile has a cross-section as shown in Figure 5D.
Figure 5D: (a) Flat Disc Cut Out with Inner Radius;
(b) Up-close of Chamfer; (c) Final Product
The body is then attached to the main shaft / mainframe via an acrylic block with
carbon rods attached.
23
Appendix E
5.1.4 PROPELLERS:
Ball bearings were fitted onto the propeller to ensure it rotates in an even manner.
Carbon rods were fitted through the propeller, and a gear was attached to the
larger propeller, which the smaller propeller was mounted onto the shaft directly.
This enables both to rotate independently of each other. Figure 5E shows this
configuration.
Figure 5E: Propellers Connected to Shaft and Chassis
24
Appendix E
5.2 DETAILED WEIGHT ANALYSIS
Table 5A: Breakdown of Mass of Final Prototype
Component
Mass
Wireless Receiver
30g
Electronic Speed Controller
21g x 2
ESC-30 x 2
=42g
71g x 2
Battery x 2
=142g
Motor Frame (Promax)
195g
Servo Motor
18g
Body
60g
Large Propeller
77g
Small Propeller
39g
Total
564g
*Refer to Appendix D for detailed breakdown of components
With this, we once again double check against Froude’s momentum to find out that the
Power needed is <<< 96W.
25
Appendix E
5.3 PROPELLERS / MOTOR CHOSEN
In order to determine the best configuration of the motors, an experiment was carried out
to show the different thrusts for each configuration. (Appendix E)
Again, we remain with our choice of Promax Speed 400 since it is lighter compared to
the Graupner Speed 500, and the additional power provided by the Graupner 500 does
not justify the 56% increase in weight.
5.4 FLIGHT TEST
The aircraft managed to lift off and hover for a few seconds before losing lift and falling.
This is possibly due to the initial push caused by the ground effect.
The body managed to rotate and tilt to move off. However, the uneven rotation of the
propellers caused the main chassis to rotate as well, causing the aircraft to be unstable
and thus tip over.
26
Detailed Design
5.5 EVALUATION & QUANTIFICATION
A reason for the instability and rotation of the aircraft is the fact that the two counterrotating propellers are of different sizes even though they are of the same pitch. This
would cause differential torques and the body would rotate to counter-act this.
This problem was only discovered during the final flight test phase, when it was too late
to change the whole design, Furthermore, there was a problem in obtaining 2 identical
propellers of opposite orientation, and not enough time to fabricate it.
A possible solution for this would be to have the propellers rotate at different speeds – the
smaller one at a faster speed than the bigger one. This would enable the torques to
balance out. However, this might lead to insufficient thrust, hence the motors need to be
re-evaluated.
The lift created by the propellers is not substantially higher than the lift required for the
aircraft to lift off. Thus even if it were possible to move off in a direction, the aircraft
would not be able to move very fast.
Also the profile was higher than initially expected due to the addition of a motor and
another battery. This would increase the drag and thus affect the performance of the
aircraft.
Hence, due to the inherent instability of the aircraft, video surveillance was not possible
at this time.
27
Conclusion
6. CONCLUSION
From the simulations, reports are generated to give value of drag. However, these are
merely theoretical values, and experiments need to be carried out to find out the
experimental values as well. However, due to the unavailability of resources, the
theoretical drag could not be verified by experimental means, as it was not possible to do
wind tunnel testing.
Due to the number of components that needed to be housed in the chassis, the profile of
the prototype was higher than was expected. This could have contributed to increased
drag, and thus affected the performance of the aircraft.
Even though the prototype managed to hover, it was not able to maintain steady flight.
This meant that directional control could not be achieved, as the body rotation could not
be stabilized. This was due to the difficulty in obtaining two propellers of the same size
and pitch that rotated in different directions.
28
Recommendations
7. RECOMMENDATIONS
From the simulations, reports are generated to give value of drag. However, these are
merely theoretical values, and experiments need to be carried out to find out the
experimental values as well. However, due to a constraint of time and resources, the
theoretical drag could not be verified by experimental means, as it was not possible to do
wind tunnel testing.
Due to the number of the components, the profile of the aircraft was increasing.
Furthermore, due to stability issues, the C.G. had to be kept somewhat constant. In order
to ensure a lower profile, it would be a better idea for the components to be housed in the
outer body. This way, the aircraft would have a lower profile. The outer shell would have
to be sturdier to house the electronic components though. This also comes with more
issues that need to be evaluated – greater instability since the weight is now further from
the centre of mass and rotation of the aircraft.
The propellers that were obtained, although of the same pitch, were of different sizes. In
an ideal situation, they would be of the same size, rotating in opposite directions. In this
way, each propeller counter-acts the torque produced by the other, in addition to
generating more lift. Hence it is recommended that two 35cm propellers be used instead.
Another possible solution for this would be to have the propellers rotate at different
speeds, enabling the torques to balance out. However, this might lead to insufficient
thrust, hence the motors used may need to be re-evaluated
Once the stability issues are solved, a video can be attached to provide real-time
information.
29
References
REFERENCES
1. Murray D.C. The Avro VZ-9 Experimental Aircraft – Lessons Learned. AIAA-903237, AIAA, AHS & ASEE Aircraft Design, Systems & Operations Conf.,
Daytona OH. Sept 1990
2. Mugler, John P. Jr, and Walter B. Olstad. Static Longitudinal Aerodynamic
Characteristics at Transonic Speeds of a Lenticular-Shaped Re-entry Vehicle.
3. Ware G. M. Investigation of the Low-Subsonic Aerodynamic Characteristics of a
Model of a Modified Lenticular Re-entry Configuration. NAA TM-X-756, Dec
1962.
4. Katz, Paul. The Free Flight of a Rotating Disc. Israel Journal of Technology,
Volume, 6, No. 1-2, 1968. Pp. 150-155.
5. Nakamura Y, and N. Fukamachi, Visualization of the flow past a Frisbee. Fluid
Dynamics Research, Volume 7, No. 1, January 1991, pp.31-35
6. Schurmans, Macé. Flight of the Frisbee. New Scientist, Volume 127, No.1727, 28
July 1990, pp. 37-40
7. Ted Bailey, “Chakram” http://www.sonic.net/~quine/tbailey/Chackrum.html
8. Raymond W. Prouty, “Helicopter Aerodynamics”. Phillips Publishing, Potomac,
Md., 1985.
9. UIUC
Airfoil
Co-ordinates
Database
http://www.aae.uiuc.edu/m-
selig/ads/coord_database.html
30
References
10. Alan Adler, “The Evolution & Aerodynamics of the Aerobie Flying Ring”
http://www.aerobie.com/Products/Details/RingScientificPaper.htm
11. Dietrich Kuchemann and Johanna Weber, Aerodynamics of Propulsion, McgrawHill Book Company, Inc. 1953
12. Potts J.R. and Crowther W.J.: The flow over a rotating disc-wing. RAeS
Aerodynamics Research Conference Proc., London, UK, Apr. 2000.
13. E L Houghton and P W Carpenter, Aerodynamics for Engineering Students, John
Wiley & Sons, Inc. New York 1993.
14. Anderson, John David, Jr. Computational Fluid Dynamics: The Basics with
Applications McGraw-Hill, New York, NY, 1995
15. Callister, William D. Jr. Materials Science and Engineering, An Introduction.
John Wiley and Sons, Inc., 2003.
16. Seah Kar Heng. Manufacturing Processes. The McGraw Hill Education, 2004.
31
Appendix A
APPENDIX A: VELOCITY AND PRESSURE PLOTS OF VARIOUS SHAPES
Figure A1: Velocity (top) and Pressure (bottom) Plots for a Sphere
32
Appendix A
Figure A2: Velocity (top) and Pressure (bottom) Plots for an Ellipse
33
Appendix A
Figure A3: Velocity (top) and Pressure (bottom) Plots for a Sphere + cylinder
34
Appendix A
Figure A4: Velocity (top) and Pressure (bottom) Plots for a Sphere + Cone
35
Appendix A
Table A1: Comparison of Computed Drag Force
Highest
Lowest
Skin Friction Drag
Form Drag
Total Drag
Hemisphere +
Cylinder + Cone
Hemisphere +
Cylinder
Hemisphere +
Cylinder
Hemisphere +
Cylinder
Hemisphere +
Cylinder + Cone
Hemisphere +
Cylinder +
Cone
Sphere
Sphere
Sphere
Ellipse
Ellipse
Ellipse
36
Appendix B
APPENDIX B: EQUIPMENT USED
1. Speed Controller: ESC-30
Weight
:
Power Source :
Dimensions :
20g
8.4V 1500mAH Lithium Cell
26x16x6
. .. . . .Figure B1: ESC-30. . . .
2. Futaba 6-Channel Micro Receiver FP R116FB
6 Channels
Weight
:
Dimensions :
Frequency
:
30g
50x32x20
29.75 MHz
Weight
Dimensions
Torque
Speed
16g
24x25x14
2.4kg.cm
0.14 sec / 60°
. ..Figure B2: Futaba Receiver. . .
3. Super Micro Servo S2414
.
:
:
:
:
. .Figure B3: Servo Motor. . .
4. Lithium Polymer Battery
Output Voltage
Capacity
Weight
Dimensions
:
:
:
:
8.4V
1500mAH
71g
73x36x12
.Figure B4: Lithium Battery.
37
Appendix B
5. Promax Speed 400 Motors
Output Voltage
Diameter
Weight
Length
Shaft diameter
Max Amperes
Max Model Wt
:
:
:
:
:
:
:
7.2V
28mm
90g
38mm
2.3mm
8.0 A
793g
..Figure B5: Promax 400 Motor. .
5. Futaba Transmitter T9ZAP
…..Figure B6: Futaba Transmitter…..
Features
• 3 modes:
o Aircraft
o Helicopter
o Glider
• 1024 High Resolution
• 9 Channels
• 10-Model Memory
• Up to 8 Flight Conditions for Each Model
• Ball Bearing Control Sticks with Adjustable
Length and Tension
• Programmable Transmitter Switches
• Large Liquid Crystal Display (LCD) with
Adjustable Contrast Screen
• Automatic System Power-off
• Built-in Tachometer
6. Master Airscrew Propellers
Master- Airscrew – 3-Blade Series
NACA airfoils, true pitch, accurately balanced
Constructed of glass-filled Nylon
Provides greater thrust at lower RPMs
11” x 7” and 14” x 7”
….Figure B7: 3-Blade Propeller…
38
Appendix C
APPENDIX C: FROUDE’S MOMENTUM THEORY
William Froude came up with a simple theory that helps us estimate the propulsion
needed. This theory involves considering the propeller as an infinitely thin disc
rotating in the air.
Propeller
(infinitely thin disc)
airflow
p1
V1
p2
V2
p4
V4
p3
V3
Fig C1: Diagrammatic Representation of a Propeller
We assume the pressures at the ends of the slipstream to be atmospheric pressure. As
such,
p1 = p2 = patm
---- (1)
As the propeller rotates, it imparts momentum and energy to the air entering. If we
assume the disc to be an ideal disc, the air will encounter no losses or resistance, and
as such, all the energy of the disc is thus imparted to the air. We therefore get
p2 = p3
---- (2)
Since the disc is infinitely thin, then the areas of the cross-sections before and after
the disc at 2 and 3 are the same, and hence the velocities are equal.
V2 = V3 ---- (3)
39
Appendix C
By making use of the Equation of Continuity, we get
ρA1V1 = ρA2V2 = ∂m / ∂t ---- (4)
Thus the thrust on the disc can be given by
T = V4ρV4A4 – V1ρV1A1 = ρA2V2(V4 – V1) = ∂m/∂t (V4 – V1) ---- (5)
Since V2 = V3, The thrust force is equal to A2(P3 – P2) ---- (6)
A (P3 – P2) = ∂m / ∂t (V4 – V1)
Since (∂m / ∂t) A = ρA2,
---- (7)
(P3 – P2) = ρA2(V4 – V1) ---- (8)
Since there is no work done or heat supplied between sections 1 – 2 and sections 3 –
4, we can thus apply Bernoulli’s equation. It is important to note, however, that there
is work done between sections 2 – 3, and we can therefore not apply Bernoulli’s
equation there.
P1 + ½ρV12 = P2 + ½ρV22 ---- (9)
P3 + ½ρV32 = P4 + ½ρV42 ---- (10)
Since V2 = V3 and P1 = P4 = Patm
(P3 – P2) = ½ρ(V42 – V12) ---- (11)
40
Appendix C
Substituting (11) into (6)
T = ½ρA2(V42 – V12) = ρA2V2(V4 – V1) ----(12)
V2 = ½ (V4 + V1) ---- (13)
This shows that the average of inlet and outlet flows gives the velocity through an
ideal disc.
Substituting in the value for thrust from equation (12);
Pideal = TV2 = ½ρA2(V42 – V12)V2 ---- (14)
Ptotal = ∂m / ∂t (V4 – V1) V2 + ½∂m / ∂t (V4 – V1)2 ---- (15)
Where the last term is the kinetic energy lost upon imparting into the air stream
Efficiency of a disc: η = Pinput/ Pdisc
= TV1 (from 5) / TV2 (from
= TV1 / (½ρA2(V42 – V12)V2)
= V1 / [½(V4 + V1)]
= 2 / [1 + (Vv/V1)]
= 1 / (1 + a)
---- (16)
Where the inflow factor, a = ½ [(V4 – V1) / V1 ]
From the above, we can get V2 and V4 in terms of A2 and V1:
V2 = V1(1+a)
and
V4 = V1(1+2a)
41
Appendix C
Therefore,
T = ρA2V2(V4 – V1)
= ρA2V1(1+a)[V1(1+2a)– V1]
= ρA2V1(1+a)V1[(1+2a)– 1]
= ρA2V12(1+a)(2a)
(a2 + a) = T / (2ρA2V12)
By solving for a, we can thus find the efficiency, and hence the effective power
given the power rating of a motor. And this was used in the determination of
propulsion for the aircraft.
42
Appendix D
APPENDIX D: MATERIAL SELECTION
In determining the main materials for the model, a table was used which compares the
cost, density, ease of machining and strength among others as follows:
Table C1 : Mechanical properties of various materials [15, 16]
Material
Cost/Kg
Density
(kg/m3)
Tensile
Strength
(MPa)
Impact
Strength
Young
Modulus,
E (GPa)
Corrosion
Resistance
Ease of
Machining
Electrical
conductivity
Jelutong
Wood
Aluminium
(alloy
6061, T6
condition)
Mild Steel
(alloy
1020),
hot-rolled)
$9.25
bd.ft
460
-
3
10.3
3
3
Bad
$10.37
2700
310
2
69
4
4
Excellent
$1.02
7850
380
1
207
5
5
Good
Acrylic
$3.20
1200
50-100
4
-
1
1
Bad
PVC
$1.50
12001600
10-45
5
-
2
2
Bad
Carbon
$3.50
/rod
2300
11001900
2
120-140
1
5
Average
(*1 being the best, 5 being the worst.)
Referring to the table above, the main factors we considered were density, strength and
cost. Since the aircraft would not normally be subject to impact strength, it is not that
great a consideration. Cost is a factor due to the fact that a more cost-effective approach
would be more viable in the future.
For the frame / chassis of the model, Acrylic was chosen. Acrylic is easily machined, and
thus smooth shapes may be cut out without much difficulty. It also has one of the lowest
densities, proving it to be light and useful for our purposes. Even though wood is lighter,
it is relatively more expensive and is slightly more difficult to machine. Further more, its
43
Appendix D
strength is only against the grain, and not along it. Since this aircraft would be rotating, it
is not advisable to make use of something that is more likely to fail in a certain direction.
Carbon rods are chosen for their high tensile strength and low density, which is ideal for
holding the acrylic pieces together.
However, an Aluminium rod is used as the main shaft as we require the shaft to maintain
a stiff position, and it will be undergoing a large number of revolutions. Hence it should
not deform under heat and should be able to withstand it. Since such a small amount is
required for the shaft, the price is justified due to necessity.
44
Appendix E
APPENDIX E: EXPERIMENT TO DETERMINE THRUST
Objective:
To determine experimentally the thrust force generated by different
configurations of Master Airscrew propellers
From Hooke’s Law, we know that
Force = k∆x
Hence, we carry out an experiment as set up in Figure E1,
to determine the force constant k, of a particular spring,
and the results are graphed below, in Figure E2.
Figure E2:
Experimental Set-up
Force vs Extension
30
25
20
15
y = 0.2302x
10
5
0
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
Extension / mm
Figure E2: Graph of Force vs. Extension
45
Appendix E
From this result, we find that the gradient of the graph is equal to 0.2302. We can then
connect the propeller assemblies to the springs, and measure the thrust generated when
the motors are switched on at full throttle.
Figure E3: Thrust generated by Propellers
For the Promax 400 motors and the two propellers in the configuration used in the
aircraft, the spring extended by 34 mm showing that the force generated is 7.82N and
thus it is sufficient to lift the body, which requires a total theoretical thrust of 7.56N.
46

Disc-Shaped Aircraft - National University of Singapore

Transcription

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