CASI Free Flight Glider Competition
Aircraft Design Report
By the
University of Toronto
Free Flight Glider Team
Aircraft Design Report
The
University of Toronto
Free Flight Glider Team
Team Members:
Terri Chu
Jeff Kwan
Nicolas Lee
Jay Loftus
Eric Ng
Leo Ng
Sarah Razzaqi
Rav Singh
Andrew Sun
Danny Yen
i
EXECUTIVE SUMMARY
The University of Toronto's entry for this year's CASI free flight competition
builds upon last year's successes. The improved Zephyr II employs carbon fibre/foam
wing, carbon fibre fuselage, and balsa wood empennage, while it retains a conventional
configuration from the original Zephyr.
The limiting factors in the success of the original Zephyr were the lift
characteristics, and the robustness of the aircraft. To improve the aerodynamic
characteristics, the airfoil of Zephyr II was changed to a modified SA7038 and the
wingspan was increased by almost a metre. The component integration methods were
also improved to make Zephyr II more robust, and thus it would give more consistent
performance. In addition, more refined techniques of analysis in aerodynamics, flight
dynamics and structural mechanics facilitated the design optimization process.
Overall, the performance of Zephyr II has increased without sacrificing
robustness. With improved design and construction methods, our team expects Zephyr II
will not only outperform its predecessor, but its competitors as well.
ii
Table of Contents
1 Introduction ................................................................................................................. 1
1.1
Design Philosophy .............................................................................................. 1
1.1.1
Problem Definition...................................................................................... 1
1.2
Design Factors .................................................................................................... 2
1.2.1
Competition Criteria ................................................................................... 2
1.2.1.1 Self-imposed Constraints ........................................................................ 2
1.2.2
Design Approach ........................................................................................ 3
2 Glider Design .............................................................................................................. 3
2.1
Aerodynamics and Stability ................................................................................ 3
2.1.1
Aerodynamic Surfaces Sizing ..................................................................... 4
2.1.2
Airfoil modification .................................................................................... 4
2.1.3
Finite Wing Correction of XFoil Analysis.................................................. 6
2.1.4
Longitudinal Stability ................................................................................. 7
2.1.5
Longitudinal Motion Simulation................................................................. 8
2.2
Glider Structure and Construction ...................................................................... 9
2.2.1
Material Selection ..................................................................................... 10
2.2.1.1 Wing Material ....................................................................................... 10
2.2.1.2 Fuselage Material: ................................................................................. 11
2.2.1.3 Empennage Material: ............................................................................ 11
2.2.1.4 Cargo Bay Material: .............................................................................. 11
2.2.1.5 Nose Cone Material: ............................................................................. 11
2.2.2
Structural Design ...................................................................................... 12
2.2.2.1 Wing...................................................................................................... 12
2.2.2.2 Fuselage ................................................................................................ 12
2.2.2.3 Empennage ............................................................................................ 12
2.2.2.4 Cargo Bay ............................................................................................. 12
2.2.2.5 Nose Cone ............................................................................................. 12
2.2.3
Wing Structural Analysis .......................................................................... 13
2.2.3.1 Experimental ......................................................................................... 13
2.2.3.2 ANSYS Analysis .................................................................................. 13
2.2.4
Construction Method ................................................................................ 14
2.3
Systems Integration ........................................................................................... 15
2.3.1
Wing Mounting ......................................................................................... 15
2.3.2
Cargo Carriage .......................................................................................... 15
2.3.3
Tow Hook ................................................................................................. 15
2.3.4
Empennage Mounting/Dethermalizer ....................................................... 16
2.3.5
Nose Cone ................................................................................................. 16
3 Design Alternatives ................................................................................................... 17
3.1
Canard Configuration........................................................................................ 17
3.2
Flying Wing Configuration ............................................................................... 17
3.3
Biplane Configuration ....................................................................................... 17
4 Future Considerations ............................................................................................... 18
4.1
Mechanically Assisted Wire Cutter .................................................................. 19
4.2
Computer or Microcontroller Controlled Motorized Wire Cutter .................... 19
4.3
3D Motion Simulator ........................................................................................ 20
5 References ................................................................................................................. 21
iii
6
Appendix A: Load Calculations................................................................................ 22
6.1
Wing Loads ....................................................................................................... 22
6.1.1
Flight Loads: ............................................................................................. 22
6.1.2
Launch Loads: ........................................................................................... 22
6.1.3
Impact Loads:............................................................................................ 22
6.2
Fuselage Loads.................................................................................................. 22
6.3
Empennage Loads ............................................................................................. 23
6.4
Cargo Bay Loads............................................................................................... 23
6.5
Nose Cone Loads .............................................................................................. 23
7 Appendix B: Drawings ............................................................................................. 24
iv
Nomenclature
Symbol Definition
Angle of attack

Induced drag factor

Downwash

Fraction of dynamic pressure at the tail relative to the wing
t
Glide angle


Air density

Correction factor for C L calculation
Unit
rad or degree
rad or degree
rad or degree
kg/m3
AR
CD
C D ,i
Aspect ratio
Drag coefficient
Induced drag coefficient
CL
C L
Cl _ 2 D
Lift Coefficient of a finite wing
Curve slope of lift coefficient of a finite wing
Lift coefficient of an infinite wing
Cm
C mo
C.G.
L.E.
M
MAC
MGC
N .P.
Re
S
Coefficient of moment about wing’s ¼ chord
Coefficient of moment about wing’s ¼ chord at   0
Centre of gravity
Leading edge
Mass
Mean aerodynamic chord
Mean geometric chord
Natural point
Reynolds number
Area
kilogram
metre
metre
a
ao
Curve slope of lift coefficient of a finite wing
Curve slope of lift coefficient of an infinite wing
Free fall acceleration due to gravity
Altitude
Length of “x” or Location of “x” from tip of aircraft nose
rad-1 or degree-1
rad-1 or degree-1
m/s2
metre
metre
Time
second
g
h
lx
t
 w
 t
Variable associates with the wing / wing-body
Variable associates with the tail
v
rad-1 or degree-1
m2
1
INTRODUCTION
The goal of the CASI Free Flight competition is to give students a chance to apply
their book-learned knowledge to the designing, building and flying of a model aircraft.
Free Flight encourages students to be problem solvers and innovators by imposing
constraints on the design that the team must work within in order to be successful.
The University of Toronto Free Flight Glider Team is comprised of ten
undergraduate students drawn from various engineering disciplines including aerospace,
mechanical and electrical. Nearly half of the team has returned from previous years’
glider teams to take up core positions within the group.
This year’s entry (Zephyr II) builds upon the performance of last year’s 2004
entry. It was the intention of the group to increase the payload capacity and flight time of
Zephyr II without sacrificing robustness. To do this, the hot-wire foam cutting process for
wing construction had to be refined. More advanced analysis and modeling techniques,
including the use of XFoil to optimize the airfoil, have also been added to our design
tools. Our longitudinal motion simulator was custom designed and programmed in
house.
Backed by these rigorous analysis methods, improved manufacturing techniques,
and most importantly, the dedication of all of the members of the flight team, we are
confident that Zephyr II will perform to our expectations with consistent competitive
flights.
1.1
DESIGN PHILOSOPHY
1.1.1 Problem Definition
The team must design and build a heavier than air aircraft, which is tow-launched
and which is capable of sustaining flight for the maximum amount of time while carrying
maximum payload. Each flight of the glider will be scored according to the formula:
FlightScore  P  t 2 *10 4
The formula suggests that there will have to be a tradeoff made between flight time and
payload carried. Ideally, the team would optimize flight time to 75 seconds, and no
more, while carrying as much payload as possible. In reality, the team must design the
1
airfoil and structure such that the plane is capable of at least a flight time of 75 seconds,
while carrying a significant amount of payload.
In the past, designs which have carried close to 1kg and which achieved flight
times of 60 seconds or more have been quite successful. This is not to be used as a
design objective, merely a benchmark.
1.2
DESIGN FACTORS
1.2.1 Competition Criteria
The fundamental, and perhaps most limiting, constraint on the design of the
aircraft is that the entire aircraft must fit inside a 2x2x1m box. This constraint most
significantly affects the design of the wing, in that the size, planform and dihedral are
limited. Also, the stability of the aircraft is impacted by this constraint, as the
longitudinal moment arm is restricted.
The new requirement to include a nose with a radius of curvature of at least 2
inches significantly affects the aerodynamics of the glider.
The mandatory inclusion of a dethermalizing mechanism has the potential to add
considerable weight to the aircraft, along with increasing the complexity of the systems
integration.
1.2.1.1 Self-imposed Constraints
1.2.1.1.1 Funding
A major obstacle faced each year by the UofT team is the uncertainty surrounding
the funding of the glider project. For the past two years, the team has been able to count
on the generous support of the UofT Engineering Society, but the exact amount of
sponsorship is generally not known until mid-March to April. As such, the team set a
modest budget of approximately $600 (based on experience), and designed within this
constraint.
1.2.1.1.2 Weight
Another significant self-imposed constraint was to minimize the weight of the
glider. Thus material selection, structural design and construction were all carried out
2
with this in mind. As a benchmark, the team aimed to have a glider with a weight
comparable to last years (approx 900g), even though this year’s glider will be 15% larger.
However, along with the constraint to minimize weight comes the complimentary
constraint to ensure that the glider can survive hard landings and maintain the
repeatability of the configuration. That is to say factors such as wing alignment,
empennage integrity, angle of attack etc. should remain constant from one flight to the
next. The lack of repeatability between flights was a major challenge of last years
design, and could well have been the reason the team did not fare better in the flight
competition.
1.2.1.1.3 Stability
Finally, static and dynamic stability of the aircraft is vitally important in an
uncontrolled glider such as we have here. The configuration of the glider, which affected
both the location of the centre of gravity and the neutral point, was motivated by the
desire to design a stable plane.
1.2.2 Design Approach
Over the last two years the UofT Free Flight team has gained a considerable
amount of knowledge and expertise in the designing and building of model gliders. The
team has chosen to build on the work of previous years, while also striving to be
innovative in solving the problems with earlier designs and the constraints imposed by
new competition rules. The team goal was to strike a balance between using tried and
true techniques and new innovating.
2
2.1
GLIDER DESIGN
AERODYNAMICS AND STABILITY
In this section of the report, the methods of aerodynamics and stability analysis of
Zephyr II are summarized. Aerodynamic surfaces were designed based on a trade-off
between aerodynamic, structural and fabrication considerations, while under the
constraints imposed by the rules. Airfoil section used in the original Zephyr was redesigned and the associate aerodynamic characteristics were determined. The results
3
were then used for stability calculation, and were inputted into the longitudinal motion
simulation code for more detailed study.
2.1.1 Aerodynamic Surfaces Sizing
Since the dimensions of glider are limited by the rule’s size constraint, the length
of the wing span is set at 2.90 m (sum of all wing panels’ lengths). To ensure roll
stability, the dihedral angle is specified to be 15º from previous experience. The wing’s
planform is determined based on a trade-off between aerodynamic performance,
structural strength and fabrication considerations. The mean aerodynamic chord (MAC)
and its location are approximated by those of the mean geometric chord (MGC). The
method followed was given in Ref 1 for a multi-panel wing planform with each section
having distinct tapering ratio and dihedral angle. The geometry of the wing is
summarized in Table 1a.
The sizing of the empennage was based on recommended tail volume ratios found
in Ref 2. The geometry of the tail was determined with stability and ease of fabrication in
mind after studying numerous glider designs found in Ref 3. The design of the
empennage was modified slightly after performing various aerodynamic and structural
analyses. The geometries of the empennage are provided in Table 1b and Table 1c.
Wing geometry
Airfoil Section
Customized
SA7038
Area
0.5205 m2
Aspect Ratio
15.9
Dihedral
15º
Root Chord
0.20 m
Tip Chord
0.13 m
MAC
0.18 m
Span
2.90 m
Sweep (L.E.)
None
Tapering Ratio
0.66
Horizontal tail geometry
Airfoil Section
Flat plate
Table 1a
Table 1b
0.095 m2
4.27
None
0.15 m
0.15 m
0.15 m
0.64 m
None
1.0
Area
Aspect Ratio
Dihedral
Root Chord
Tip Chord
MAC
Span
Sweep (L.E.)
Tapering Ratio
Vertical tail geometry
Airfoil Section
Flat plate
Area
Aspect Ratio
Dihedral
Root Chord
Tip Chord
MAC
Span
Sweep (L.E.)
Tapering Ratio
0.027 m2
1.51
None
0.15 m
0.12 m
0.13 m
0.20 m
25.4º
0.77
Table 1c
2.1.2 Airfoil modification
Instead of choosing a completely new airfoil section, our team decided to modify
the airfoil section used for previous year’s entry, SA 7038, for Zephyr II. The goal was to
4
improve the glider performance by manipulating the camber and thickness. Progress is
being made in extending our analysis to include fully inverse design. Different
combinations of camber and thickness were analyzed using XFoil (Ref 4). The cross
section of the improved airfoil, SA 7038 t9 c5 (Note: t9 denotes 9% thickness, and c5
denotes 5% camber), is shown in Fig 1. In Fig 2-4, a comparison of the 2D airfoil
aerodynamic characteristics of the original SA 7038 and the improved SA 7038 t9 c5 is
given. Fig 2 shows that SA7038 t9 c5 generates more lift than SA 7038 throughout the
entire test range. Fig 3 shows that there was no significant increase in drag due to our
Fig 1
modification. Fig 4, however, indicates that due to the increased camber, the nose down
pitching moment has increased. Thus, a larger downward force is required from the tail to
provide the trimming moment. This has a negative effect on the glider’s performance
since it decreases the overall lift and increases induced drag from the tail. Nevertheless,
in later section of this report, the stability calculations and our self-developed
longitudinal motion simulation code showed that the increase in trim drag was small. In
terms of maximizing points, the gain in lift due to our modification more than offset the
increase in trim drag.
XFoil 2D Analysis: Cl Comparsion,
Re=100,000
XFoil 2D Analysis: Cd Comparsion,
Re=100,000
Xfoil 2D Analysis: Cm Comparsion,
Re=100,000
0.1400
0.0000
-10
1.4000
0.1200
0.1000
0.0600
0.4000
0
5
10
15
-0.0400
0.0800
Cm
SA 7038
SA 7038 t9 c5
Cd
Cl
0.9000
-5
-0.0200
SA 7038
SA 7038 t9 c5
-0.0600
-0.0800
0.0400
-10
-5
-0.1000
-0.1000
0
5
10
15
0.0200
20
-0.1200
0.0000
-0.6000
-10
Angle of Attack (deg)
Fig 2
-5
0
5
10
Angle of Attack (deg)
Fig 3
5
15
20
-0.1400
SA 7038
SA 7038 t9 c5
Angle of Attack (deg)
Fig 4
20
2.1.3 Finite Wing Correction of XFoil Analysis
Before the aerodynamic data from XFoil can be used in the longitudinal motion
simulation code, correction for finite wing effects had to be made. The effects to be
accounted for include:
1.
2.
dC L
a.
d
Induced drag caused by wing tip vortices
Decrease in lift curve slope, C L 
The expression for 3-D lift coefficient, CL, was calculated using equation (2.2.2.1), which
can be found from Ref 5 and Ref 7 :
a0
dC L
(2.2.2.1)
a
d
1  (a0 AR)(1   )
where a0 was the lift versus α slope in 2-D. The parameter τ for a uniformly tapered wing
was obtained from data provided in Ref 7. However, no data of τ for a multi-panel wing,
like Zephyr II’s, could be found in our technical literature survey. Therefore, our team
proposed the following original approximation method.
Fig 5
Suppose there exists an equivalent uniform taper wing such that its finite wing
aerodynamic coefficients are the same as the multi-panel wing in question. Our
estimation method assumes that such wing will have the same planform area, MAC and
same span as the original multi-panel wing. Thus, the aspect ratio is also guaranteed to be
the same. By equating these values and solving the associated quadratic equation, the root
chord and tip chord, and thus tapering ratio, of the equivalent uniform taper wing can be
obtained. Using this newly found tapering ratio, τ in equation (2.2.2.1) can be estimated
from Ref 7. To correct for the finite wing effect, equation (2.2.2.2) is applied.
a
Cl _ 2 D
(2.2.2.2)
a0
The results of the finite wing correction on CL for SA7038, SA7038t9c5 and the
CL 
horizontal tail using (2.2.2.2) are given in Fig 6-8 respectively.
6
Zephyr II's SA7038 3D Aero. Coeff.
at Re=100,000
Zephyr II's SA7038t9c5 3D Aero.
Coeff. at Re=100,000
1.4000
1.4000
1.2000
1.2000
1.4000
1.2000
1.0000
1.0000
Cl
Cd
Cm
Fitting line
0.8000
0.6000
0.4000
-10
Zephyr II's Horiz. Tail 3D Aero.
Coeff. at Re=90,000
0.6000
0.4000
0.2000
0.2000
0.0000
-5 -0.2000 0
0.0000
5
10
15
20
-10
-5
0.8000
0.6000
0.4000
0.2000
0.0000
-0.2000 0
5
10
15
20
-15
-10
-0.4000
-0.4000
-0.6000
-0.6000
Angle of Attack (deg)
Fig 6
Cl
Cd
Cm
Fitting line
1.0000
Cl
Cd
Cm
Fitting line
0.8000
-5
-0.2000
0
5
10
15
-0.4000
Angle of Attack (deg)
Fig 7
-0.6000
Angle
of Attack (deg)
Fig 8
To properly represent the drag acting on the wing, equation (2.2.2.3) was used to
calculate the induced drag (Ref 5):
C L2
(2.2.2.3)
1   
AR
In equation (2.2.2.3), the induced drag factor,  , was estimated from data found in Ref 5
C D ,i 
and Ref 6 using the equivalent uniform taper wing mentioned above. Due to Zephyr II’s
large aspect ratio, extrapolation was required to obtain an estimate of  . As a reminder,
the CL used in (2.2.2.3) was obtained from equation (2.2.2.2). Results of the drag
coefficients with the appropriate C D ,i has been added and plotted along with CL and C m
in Fig 6-8. Currently, our team is researching the necessity for C m correction. If such
correction is required, an analysis from a vortex-lattice code may be needed.
2.1.4 Longitudinal Stability
To achieve longitudinal stability, two conditions must be satisfied (Ref. 8):
1.
Positive static margin
2.
Positive pitching moment at zero angle of attack ( C mo  0 ).
Positive pitching moment can be satisfied by adjusting the angle of the horizontal
tail. To guarantee that there is a positive static margin, an estimation of the location of the
centre of gravity (C.G.) and the neutral point (N.P.) is required. From Table 2, the C.G. is
found to be located at 0.55 m from the tip of the nose.
Using the definition of N.P., one can easily derive (2.2.3.1) to find the N.P.’s
location.
l np  1 C L C L w l w  C L t 1    lt S t S  t 
7
(2.2.3.1)
where C L  C L w  C L t 1    S t S  t and   is to be estimated with
USAF DATCOM method outlined in Ref 8’s appendices. The location of the N.P. was
calculated to be at 0.64 m behind the tip of the nose. Thus, yielding a static margin of
0.50 and the first longitudinal stability condition is satisfied. Following the method
outlined in Ref. 8, in order to satisfy the second condition ( C mo  0 ), only a minimum of
1º downward horizontal tail angle is required. Thus, Zephyr II can easily be set to be
statically stable in longitudinal motions.
Dist of components' CM to tip of nose (m)
Component's mass (kg)
Wing
0.55
0.4
Vertical Tail
1.45
0.03
Horizontal Tail
1.4
0.03
Fuselage
0.7
0.1
Nose
0.06
0.07
Ballast
0.1
0.085
De-Thermalizer
0.7
0.03
Payload
0.55
0.2
Total weight
0.945
CG location from tip of nose
0.55
kg
m
Table 2
2.1.5 Longitudinal Motion Simulation
The development of the longitudinal motion simulation code using C++ began
before last year’s competition and it was finally tested and verified in Jan 2005 before the
construction of Zephyr II. The purpose of the simulation code is to serve as an economic
mean to try out different glider configurations and airfoil sections. The theory of the
simulation is based on Ref. 8. The operation of the simulation is outlined in Fig.9
Fig. 9
8
During initialization, the necessary data such as aerodynamic coefficients, glider’s
configurations and initial conditions are entered. Then, using a time marching method,
the forces, velocities and position of the glider are calculated through successive
integrations.
As a demonstration of Zephyr II’s longitudinal stability, a simulation was run for
the stress case in which Zephyr II pre-maturely detached from the tow hook at 40m
altitude at a remarkably low air speed of 5m/s and 3º pitch up angle (none are steady
conditions). Fig 10 shows an initial height loss due to low airspeed, but the oscillation in
the glider’s altitude eventually flattens out and the flight path stabilizes. Fig 11 illustrates
the fluctuation in the glider’s air speed settles as the oscillation in motions dampens out.
Finally, Fig 12 shows the pitching motions as a function of time and demonstrates Zephyr
II’s natural stability in its attitude.
Air speed vs. Time
Airspeed (m/s)
Height (m)
Height vs. Time
60
40
20
0
20
40
60
10
5
0
0
80
20
40
Time (sec)
Time (sec)
Fig 10
Fig 11
Angle (deg)
Ang Vel.(deg/s)
0
15
20
10
0
-10 0
-20
-30
60
80
Euler Pitch Angle and Ang Velocity
20
40
60
80
Euler Pitch Ang.
Ang. Velo
Time (sec)
Fig 12
2.2
GLIDER STRUCTURE AND CONSTRUCTION
In this section we will determine the glider structure and composition, based on
our design objectives. In terms of determining structure and composition the most
important criteria are the following: strength, weight, cost and experience. For strength,
our glider must withstand loads associated with launch, flight and landing. For weight,
9
our glider should be as light as possible and definitely less than 900g. For cost, our total
glider cost should be less than $600. Finally, our team must be experienced, or at least
confident, with the construction method and materials that we use.
Objectives
Main Wing
Fuselage
Empennage
Cargo Bay
Nose Cone
Miscellaneous
Max Load†
15 Nm
680 MPa
n/a
9N
45 MPa
n/a
Max Weight
500g
100g
100g
100g
50g
50g
Max Cost
$350
$50
$50
$50
$50
$100
Experience*
4
2
3
1
1
n/a
†
See ‘Appendix A: Load Calculations’ for the derivations
*A rating from 1-5 of how important experience with the materials and construction is, for a given part of
the glider (5 being most important).
Table 3
In addition, during construction we will attempt to minimize excess weight and
maximize the accuracy of construction. In this way our glider will perform as close to our
theoretical predictions as possible.
2.2.1 Material Selection
In this section we want to choose materials for each part of the glider in order to
meet the previously stated objectives.
Material Properties
Material
Cost [$/kg] Density
[kg/m3]
Aluminum
Steel
Carbon
Fibre
Balsa
Spruce
2
0.6
240
2700
7750
1570
Elastic
Mod.
[GPa]
73
207
190
1
0.7
200
400
3.4
10.8
Tensile
Strength
[MPa]
90
380
810
Yield
Strength
[MPa]
48
207
200
Specific
Yield
Strength
0.018
0.027
0.13
n/a
76
22
40
0.11
0.10
Note: The highlighted entries are the ‘best’ for that column.
Table 4
2.2.1.1 Wing Material
From the material properties we can clearly see how carbon fibre has the best
strength to weight ratio (specific yield strength). A carbon fibre wing would be the
10
lightest possible for a given strength. And although the cost of carbon fibre is much more
than the cost of the other materials we plan on using at most 400g, which will cost only
$95. Furthermore, our team is experienced with carbon fibre construction, since our
glider wings last year were of the same construction.
2.2.1.2 Fuselage Material:
For the lightest fuselage for a given strength we will again use carbon fibre. In
fact, discarded carbon fibre golf club shafts can be obtained for free and are suitable for
our fuselage.
2.2.1.3 Empennage Material:
Since the empennage will experience very small stresses and moments, strength is
a minor issue, so we will choose the lightest material, balsa wood, for its construction. In
addition, members of our team are familiar with balsa wood construction. Keeping the
empennage light is also important in maintaining a positive static margin.
2.2.1.4 Cargo Bay Material:
For the cargo bay we will use an aluminum can since they are light, cheap, and
strong enough for a tow hook. We will also use foam to create an aerodynamic shape
around the cargo bay.
2.2.1.5 Nose Cone Material:
We will use foam for the nose cone, in order to meet the nose cone requirements.
An aluminum sheet embedded in the nose cone will prevent the fuselage from puncturing
the nose cone when the glider hits the ground.
Final Material Selection
Main Wing
Fuselage
Empennage
Cargo Bay
Nose Cone
Carbon Fibre
Carbon Fibre
Balsa Wood
Aluminum with Foam
Foam with Aluminum
Table 5
11
2.2.2 Structural Design
This section contains the finalized structural design of the wing, fuselage, and
empennage.
2.2.2.1 Wing
The wing will be composed of a foam core, with a balsa wood trailing edge, with
a carbon-fibre/epoxy outer shell weighing 5.8oz/1800in2 (0.142kg/m2).
Fig 13 – Wing Cross Section
2.2.2.2
Fuselage
The fuselage will consist of a pre-made carbon fibre shaft with a 1cm2 crosssection.
2.2.2.3 Empennage
The empennage and horizontal stabilizer will be made of a frame of balsa wood,
coated with heat-shrinking plastic wrap like Monokote.
Fig 14 - Empennage
2.2.2.4 Cargo Bay
The cargo bay will be constructed from an aluminum cylinder to house payload,
with foam for aerodynamic shaping.
2.2.2.5 Nose Cone
The nose cone will be made of foam, with an aluminum sheet to prevent the
fuselage from puncturing it, upon impact.
12
Fig 15 - Nose Cone
2.2.3 Wing Structural Analysis
2.2.3.1 Experimental
Based on our moment loading on the wing (Appendix A: Load Calculations), the
most likely location for wing failure is mid-span. Thus, we will focus our analysis at that
location.
We used the glider wing from last year to perform the structural analysis, since
this year’s glider wing is of similar construction. We applied a measured force 28 cm
from the center line, until the breaking point. The wing began to buckle at 32 lbs (140N)
of applied force, or a moment of 39Nm. Clearly, our wing from last year was able to
easily withstand the 15Nm from launch. This year we plan on reducing the weight of the
wing by eliminating the spruce spars, and carbon fibre trailing edge of last year’s design.
2.2.3.2 ANSYS Analysis
A finite element structural analysis was performed on the wing using ANSYS.
The model was constructed using 1774 4-node shell elements representing half of the
wing cantilevered at the root. It was loaded with a uniform upward pressure on all
surfaces, as a conservative approximation of the actual lift the wing will experience. The
total lift load was set at 21.582 N, to represent a 1 kg plane under a 4.4g pull-up, as
specified in (Ref 9). Under this load case, the maximum von Mises stress was
determined to be slightly less than 50 MPa, which is lower than the carbon fibre wing’s
yield stress of 200 MPa. The stress distribution on the upper and lower wing surfaces is
shown in Figure 16
13
Figure 16
2.2.4 Construction Method
The main glider wing is manually cut out of foam using a manual hotwire.
Several foam wing sections are cut using airfoil templates as guides for the hotwire. Each
section was then glued together by epoxy and coated with carbon fibre using the vacuum
bag method.
The cargo bay of the glider is made out of an aluminium cylinder cut to size.
Epoxy and balsa wood fillets are used to fix the cylinder to the fuselage. The rest of the
cargo bay, including the planform for the wing, is cut out of foam using a manual
hotwire.
The empennage was constructed using a balsa wood truss which is coated with
heat shrinking plastic wrap. The empennage is connected to the cabin with the graphite
shaft fuselage.
The nose cone is made of a hemisphere of foam, with a tapered trailing edge, and
a small aluminum insertion.
Only after careful consideration of the objectives of our glider design, we
determined the most suitable materials, and structural design to use. The carbon fibre
wing and fuselage will have the largest strength to weight ratio. The aluminum and foam
cargo bay will be cheap, strong and light and can support the tow hook. The balsa
empennage will be light and the foam nose cone will conform to requirements.
14
2.3
SYSTEMS INTEGRATION
2.3.1 Wing Mounting
In the mounting of the wing, the team has decided to continue to use elastic bands
to secure the wing to the fuselage, allowing the wing to pop off on impact, which
prevents significant damage. This technique has worked well for the past two years, thus
there was no need to change it. However, the team did suffer some problems with wing
alignment in previous designs. To solve this problem a small piece of balsa wood was
mounted in front of the wing in order to align it with the empennage. This is a simple
and light solution, which successfully addresses the repeatability constraint identified
earlier.
2.3.2 Cargo Carriage
The cargo carriage is located under the fuselage, exactly at the centre of gravity of
the glider. The carriage is simply an aluminum can, with a foam cap for safety, and foam
fairing for aerodynamic purposes. The payload itself is a small cylindrical disk of lead
shot and epoxy. This payload comes in a range of weights and sizes appropriate for this
particular glider. Cylindrical foam disks are used as plugs of sort to ensure that the
payload is secure in the container during flight and upon impact.
2.3.3 Tow Hook
The dynamics of the glider during tow are actually quite difficult to analyze,
constraining a degree of freedom of the aircraft makes the analysis more complicated.
However, in depth theory of tethered aircraft is not really necessary for our purposes,
instead we identified two possible cases for tow hook placement. In all cases the tow
hook must be placed ahead of the cg for stability considerations. First, for the tow hook
mounted closer to the nose the tow will be slower but the glider should come off the hook
at a level attitude. However, this method runs the risk of placing the tow hook too far
ahead such that the nose is pulled down during tow. The second option is to mount the
took just barely in front of the cg, which results in a much faster climb rate. There are
two potential risks with this method. One, the cg of the aircraft could change over the
15
course of the competition and the tow hook might end up aft of the cg. Two, with such a
large nose up angle during tow there is the potential for the glider to stall on tow, thus
losing a lot altitude during the initial stages of the flight. We decided to go with the
second option of placing the tow hook just in front of the cg, and have analyzed the
aerodynamics sufficiently to ensure that the glider won’t stall as it comes off the hook.
2.3.4 Empennage Mounting/Dethermalizer
The empennage mounting is very similar to the wing mounting, but there exists
the added complexity of the dethermalizer mechanism. It was imperative to allow the tail
to pop off on impact, in a similar manner to the wing. Thus the empennage is mounted
onto the fuselage via elastic bands as well. There is a small hinged board attached to the
fuselage on which the empennage sits. On impact, the elastics come off and the
empennage pops off the board. The dethermalizer is a small mechanical timer; a radio
control activated device was deemed to be too heavy. There is a pin on the timer that is
connected via a string to the board on which the empennage is mounted. When 75
seconds of flight time has elapsed, the pin pops out creating slack in the string, which
allows elastics connected to the empennage to pitch the tail down. There is a stop in
place, which restricts this pitch down to 45 degrees. This is a simple, effective and
innovative solution to the new mandatory dethermalizing constraint.
2.3.5 Nose Cone
In order to ensure the safety of all participants, it was necessary to include a round
foam nose cone in the design of the glider. The presence of a bulbous nose at the front of
the glider will wreak havoc with aerodynamics, thus it was important to try and minimize
its impact. A 2-inch radius semi-circle was attached to the front of the fuselage, then a
foam fairing of sorts was mounted behind the cylinder on the fuselage to reduce the
potential for flow separation around the nose. A small metal plate was placed at the tip of
the golf shaft fuselage before the foam semi-circle nose in order to distribute the load on
impact and prevent the fuselage from piercing the foam nose. The foam fairing is a
simple technique that will greatly improve the glider aerodynamics. In addition the metal
plate to distribute load is a clever way to avoid the problems of the fuselage piercing the
nose cone as encountered by other teams in last year’s competition.
16
3
3.1
DESIGN ALTERNATIVES
CANARD CONFIGURATION
The advantage of a canard configuration is that the trim surface produces positive
lift to the aircraft, instead of negative in the case of a conventional configuration.
Nevertheless, this does not guarantee an overall lift increase in the aircraft. The
downwash from the canard reduces the local angle of attack of the wing, and therefore,
the lift as well. To study the effect of the wing being “unloaded” by the canard’s
downwash, the following method can be used. The downwash can be estimated by USAF
DATCOM method. If the downwash is assumed to be of the same width as the span of
the canard span, Schrenk’s method (Ref 7, Ref 9) can be used to calculate the lift
deficiency. However, our team’s previous experience with canard has found that such
configuration is prone to failure because performance of the aircraft is quite sensitive to
the sizing of the aerodynamic surfaces. Idea of a canard configuration was abandoned
during the early stage of our design process.
3.2
FLYING WING CONFIGURATION
Recent research by NASA and Boeing in the blended wing body (BWB) concept
spurs general interest in the flying wing configuration. Combining the wing with fuselage
has the potential to reduce weight while maintaining the aircraft’s cargo storage space.
However, cargo storage space is not a critical constraint to our glider. Thus, the merit of a
flying wing is limited for our purposes. In addition, in order to generate a nose down
moment to trim the aircraft, sweep back and twisting of the wing and/or a reflex airfoil
section are required. None of these wing features are aerodynamically favorable, and they
are difficult to construct.
3.3
BIPLANE CONFIGURATION
Despite years of neglect, our team’s recent interest in biplanes prompted us to
investigate such a configuration. With the span of the glider limited by the rules, biplane
appears to be an attractive alternative in reducing induced drag from the wing. The
method of our analysis followed that given in Ref 9 and Ref 10. Better theoretical lift
17
coefficient can be obtained following Ref 11 and Ref 12. Given the lift coefficient,
induced drag coefficient can be calculated from Ref 13.
Three cases were tested in our analysis:
1. Basic monoplane based on last year’s Zephyr configuration
2. Biplane with 2 full size wings, both wings same as the one used in case 1
3. Biplane with 2 wings having chord length half of the one used in case 1
To simplify calculation, we assumed
1. The wing is the aerodynamically dominant part on the glider (i.e. trim force
assumed to be small)
2. Glider is under steady condition throughout the flight (i.e. net force is zero,
constant velocity, etc)
Following these assumptions, expression of flight time can be easily derived from force
balance and basic kinematics equation.
1/ 2
 S C 2  C 2 
L
D


2
gM


where   tan 1 D L  and h is the initial altitude of the glider.
h
t 
sin 
(4.3.1)
Using the lift and drag coefficients obtained from the method outlined in Ref 10,
it was found that monoplane (case 1) and biplane with 2 full size wings (case 2) had
similar flight durations (147sec and 145sec respectively under the assumed ideal
conditions). However, biplane with 2 half size wings (case 3) yielded a substantially
longer flight time than the other 2 cases (337sec under the assumed ideal conditions).
Thus, case 3 has the potential to carry more cargo than the other two cases. This "halfsize" configuration will be the focus of our future research.
Although biplane is aerodynamically favorable, reduction in individual wing size
increases the structural load. A finite element analysis, similar to the one given earlier, is
required to determine the feasibility of biplane for future competitions.
4
FUTURE CONSIDERATIONS
In the course of constructing the glider, the most important tool was the wire
cutter. The wire cutter was simply a long wooden handle with wire running across it,
connecting to a power transformer. This vital tool used to cut through foam would
18
lengthen and lose tension when heated. The lost in tension causes the wire to drag along
the surface of the foam, creating undesirable grooves. The process of cutting required
two people, one person on either side to hold the wire cutter steady. Much time and
material was spent for practicing with the wire cutter. The construction of the glider can
be drastically improved in aspect of quality and speed if we had better method of cutting
the foam. Two options are worth considering for the future: mechanically assisted and
computer or microcontroller controlled motorized wire cutter.
4.1
MECHANICALLY ASSISTED WIRE CUTTER
Mechanically assisted wire cutter is basically two highly flexible mechanical arms
mounted on a platform, with the wire held between them. In essence, a mechanically
assisted wire cutter is similar to current crude wire cutter; it will still require two people
to operate most of time. However, there are four important differences.
1. Adjustable distance between the two ends that holds the wire, to ensure constant
tautness even when heated.
2. Mechanical arms assistance minimizing tremors in user’s hands allow for
smoother cutting of foam.
3. Allow for more precise cutting when following a template because the wire cutter
mechanical arms are mounted on platform.
4. Allow for single person operations by locking the two mechanical arms to move
in synchronization when there is an obvious symmetry in shaping the foam.
With this device, the foam cutting time and learning curve would be dramatically
shortened. The greatest challenge of building such construction is determining the
amount of flexibility of the mechanical arms. Not only the joints cannot be too loose or
tight, but the number of joints is also important factor in creating an ideal arm. Such task
will require much time in research and development.
4.2
COMPUTER OR MICROCONTROLLER CONTROLLED MOTORIZED WIRE CUTTER
The principle of a computer or microcontroller controlled motorized wire cutter is
similar to the current foam cutting method except the hot-wire cutter will be guided by
stepper motors. The dimension of the airfoil section will be entered into the control
software, and the path of the stepper motors will be calculated automatically. This type of
wire cutter has all the advantages of the mechanically assisted wire cutter plus three
additional points:
19
1. Minimized human errors by minimizing human involvement.
2. Very precise foam cutting.
3. Automatic adjustment for tautness of wire.
This is much more ambitious task than the previous type of wire cutter.
Constructing such contraption will likely require more than a year of development. Aside
from the previously mentioned mechanical challenge, there will be electrical and
software challenges. Controlling this device will require a microcontroller or a computer,
depending on the interface of the user and the device.
Both types of wire cutter will be a definite improvement over the current tool.
Both will decrease time to learn and build the glider, as well as minimizing wastage of
materials. However, the amount of work that required setting up either one is not feasible
at this moment. Nevertheless, when our team’s techniques in aerodynamic analysis have
matured, these ideas will be worth considering.
4.3
3D MOTION SIMULATOR
The U of T Free Flight Glider Team is currently implementing a 3D motion
simulator in MATLAB Simulink. However, calculating the aerodynamic coefficients and
stability derivatives prove to be quite difficult using USAF DATCOM method. We are
currently attempting in estimating stability derivatives using computational fluid
dynamics (Ref 14).
20
5
REFERENCES
[1]
Jones, B., “Elements of Practical Aerodynamics”, 4th ed., John Wiley & Sons,
Inc. New York, 1950
[2]
Raymer, D.P., “Aircraft Design: A Conceptual Approach”, 3rd ed., AIAA
Education Series, 1999
[3]
Coates, A., “Jane’s World Sailplanes and Motor Gliders”, New Edition, Jane’s
Pub. Co., London, 1980
[4]
Drela, M., “Xfoil Manual”, Aerospace Computation Design Laboratory, Dept. of
Aeronautics & Astronautics, M.I.T., 2001
[5]
Anderson, J.D., “Fundamentals of Aerodynamics”, McGraw-Hill, 2001
[6]
McCormick, B.W.., “Aerodynamics, Aeronautics, and Flight Mechanics”, John
Wiley & Sons, New York, 1979
[7]
Schrenk, O., “A Simple Approximation Method for Obtaining the Spanwise Lift
Distribution”, N.A.C.A. Technical Memorandum No. 948, 1940
[8]
Etkin, B., Reid, L.D., “Dynamics of Flight: Stability and Control”, 3rd ed., John
Wiley & Sons, Inc., 1996
[9]
Hiscocks, R.D., “Design of Light Aircraft”, R.D. Hiscocks, 1995
[10]
Munk, M.M., “General Biplane Theory”, Technical Report No. 151, N.A.C.A.,
1922
[11]
Diehl, W.S., “Relative Loading on Biplane Wings”, Technical Report No. 258,
N.A.C.A. , 1922
[12]
Diehl, W.S., “Relative Loading on Biplane Wings of Unequal Chord”, Technical
Report No. 501, N.A.C.A. , 1934
[13]
Prandtl, L, “Induced Drag of Biplanes”, Technical Note No. 182, N.A.C.A. ,
1924
[14]
Park, M.A., Green, L.L., Montgomery, R.C., Raney, D.L., “Determination of
Stability and Control Derivatives Using Computational Fluid Dynamics and
Automatic Differentiation”, 17th AIAA Applied Aerodynamics Conference,
Norfolk, Virginia, AIAA 99-3136, 1999
21
6
6.1
APPENDIX A: LOAD CALCULATIONS
WING LOADS
6.1.1 Flight Loads:
We assume level flight Lift = Weight. A glider of 1 kg and a span of 3m has a
wing loading of 3.27N/m. Then the moment along the wing can be described as follows:
M  3.7  4.9 x  1.6 x 2
Moment Load [Nm]
Moment Load Along Wing During Flight
4
3
2
1
0
0.0
0.5
1.0
1.5
Distance From Fuselage [m]
6.1.2 Launch Loads:
During launch the glider is at an inclined configuration for climbing. This
increases the drag and lift of the wing substantially. We will assume that the moment on
the wing during launch is between 2 to 4 times greater than the moment on the wing
during normal flight. A maximum of moment 14.8 Nm may be experience.
6.1.3 Impact Loads:
The impact loads are highly unpredictable. Typically a wing-tip will impact the
ground upon landing, resulting in a maximum moment near the fuselage and a large
shearing force near the wing-tip. These factors will be qualitatively taken into account.
Thus we will design our wing to withstand a maximum moment in the wing of 3.8
Nm during flight and 15 Nm during launch.
6.2
FUSELAGE LOADS
The maximum loading for the fuselage will occur during landing. The glider
travels at approximately 5.5m/s (22km/hr) and upon impact could stop within 20cm. This
corresponds to a deceleration of 76 m/s2. Assuming the mass of the glider is 900g and the
22
cross-section of the fuselage is 1cm2, the corresponding load is 680 MPa. This is within
the limits of the carbon fibre properties.
Assuming constant accel. Vav = 5.5/2 = 2.75 m/s
Δt = Δd/2.75 = 0.2m/2.75m/s = 0.0727s
a = Δv/Δt = 5.5m/s/0.0727s = 75.6 m/s2
stress = ma/Area = 0.9kg*75.6m/s2/0.0001m2= 681 MPa
6.3
EMPENNAGE LOADS
The maximum loading on the empennage will occur during landing. The
empennage is attached with rubber bands to absorb any impact forces. We will adjust the
rubber band configuration to ensure that the yield strength of 22MPa of the balsa wood is
not surpassed.
6.4
CARGO BAY LOADS
The maximum loading for the cargo bay will occur during launch, through the
tow hook. From experience we can estimate the tension in the rope during launch at
approximately 3 times the glider weight. Thus the maximum load on the cargo bay tow
hook is 27N.
Force = (3)mg = 3*0.9kg*9.81m/s2= 26.5N
6.5
NOSE CONE LOADS
The maximum loading on the nose cone will occur during landing. The
calculation is similar to that of the fuselage, except the cross-sectional area is now the
contact surface (~15cm2). Thus the maximum stress is 45MPa.
23
7
APPENDIX B: DRAWINGS
24