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UNIVERSITY COLLEGE
UNIVERSITY OF NEW SOUTH WALES
School of Aerospace Civil and Mechanical Engineering
INVESTIGATION INTO THE REDUCTION OF THE DRAG AREA
OF A PARAMOTOR
By
Jon Longbottom
7 October 2006
SUPERVISOR: Alan Fien
A THESIS SUBMITTED FOR THE FINAL YEAR SUBJECT ZACM4020 AERONAUTICAL ENGINEERING PROJECT AND
THESIS AS PARTIAL FULFILMENT OF THE REQUIREMENTS OF BACHELOR OF ENGINEERING IN
AERONAUTICAL ENGINEERING
A
ABSTRACT
An experimental investigation and evaluation of the inefficiencies of a typical paramotor was
conducted. The aim of this experiment was to attempt to overcome the high drag associated
with a paramotor in order to improve the glide ratio during unpowered flight.
Initial baseline data was found from measuring the in flight performance of a typical
paramotor while in gliding flight. Previously published glide ratio results with a windmilling
propeller were found to be incorrect, with no change in glide ratio between a windmilling or
braked propeller. This report found the glide ratio of a paramotor at 6.4 ± 0.5:1, compared
to 8.2:1 with the same wing on a paraglider, however the error margin was high due to
instability of the local atmosphere. The attitude of the paramotor frame changed from
vertical when thrust was produced to typically 23o reclined from perpendicular in accelerated
glide. Surface airflow visualisation was also conducted which resulted in a greater
understanding of airflow over the paramotor and pilot.
Wind tunnel testing was completed to determine the major contributors to the drag of a
standard paramotor while in gliding flight. The measurements were taken at 0, 8, 16, 24 and
32o angle of incidence. These results would be of benefit to both high and low hook-in
paramotors. There was a 27% reduction in drag area when a low hang point paramotor
changed attitude during accelerated glide. The most significant individual drag contributors
were the frame and netting, with the reserve parachute container, motor and propeller having
little effect on the overall drag area. A folding propeller would have no benefit if the standard
frame and netting were retained.
Redesigning of high drag area components was conducted with the majority of effort placed
on the paramotor frame, netting and fuel tank. Each of the components was replaced with
alternatives which produced less drag and retained full functionality. The revised paramotor
design was retested, resulting in a 17% reduction in drag area. The results obtained were less
than desired. It was concluded that it would be more cost effective to remove the netting on
the existing paramotor and replace it with smaller diameter Dyneema netting. This would
create a small but worthwhile reduction in drag with potential thrust gains.
B
DISCLAIMER
This thesis has been written in partial fulfilment for the requirements for the degree of
Aeronautical Engineering. It is the result of a period of research and analysis by the author
while a student of the University of New South Wales. Views expressed do not represent the
views of the University College, or the University.
C
TABLE OF CONTENTS ABSTRACT...........................................................................................................................................................A TABLE OF CONTENTS......................................................................................................................................C NOMENCLATURE..............................................................................................................................................F GLOSSARY.......................................................................................................................................................... G 1. INTRODUCTION............................................................................................................................................ 1
What is a Paramotor? ................................................................................................................................... 1 Aims............................................................................................................................................................... 3 Scope ............................................................................................................................................................. 4 Limitations..................................................................................................................................................... 5 Summary........................................................................................................................................................ 6
2. LITERATURE REVIEW ........................................................................................................................... 6 Introduction ................................................................................................................................................... 6
Aerodynamic Forces in Gliding.................................................................................................................................. 6 Aerodynamic drag ...................................................................................................................................................... 6 Drag Polar .................................................................................................................................................................. 7 Basic Soaring Theory ................................................................................................................................................. 8 A Paraglider Polar Curve............................................................................................................................................ 9 Previous Drag Experimentation on Paragliding Harnesses....................................................................................... 10 Wing Loading of the Paraglider ............................................................................................................................... 13
3. EVALUATION OF CURRENT PARAMOTOR DESIGN ................................................................... 14 Introduction ................................................................................................................................................. 14
3.1 SURFACE AIRFLOW EVALUATION EXPERIMENT ................................................................................... 14 Aims............................................................................................................................................................. 14 Introduction ................................................................................................................................................. 14 Procedure .................................................................................................................................................... 15
Camera Mount - Manufacture .................................................................................................................................. 15 Surface Airflow Suit................................................................................................................................................. 15
Results ......................................................................................................................................................... 15 Discussion ................................................................................................................................................... 17 Conclusion................................................................................................................................................... 19
3.2 DESIGN AND MANUFACTURE OF PROPELLER BRAKE ........................................................................... 19 Background ................................................................................................................................................. 19 Method......................................................................................................................................................... 20
3.3 GLIDE RATIO TESTING......................................................................................................................... 22 Aims............................................................................................................................................................. 22 Introduction ................................................................................................................................................. 22 Procedure .................................................................................................................................................... 22 Results ......................................................................................................................................................... 23 Discussion ................................................................................................................................................... 26 Conclusion................................................................................................................................................... 27
3.4 PARAMOTOR CROSS SECTION VISUALISATION ................................................................................... 27 Aims............................................................................................................................................................. 27 Introduction ................................................................................................................................................. 27 Procedure .................................................................................................................................................... 27 Results ......................................................................................................................................................... 28 Discussion ................................................................................................................................................... 28 Conclusion................................................................................................................................................... 29
4. EVALUATION OF A DUCTED FAN PARAMOTOR ......................................................................... 29 Introduction ................................................................................................................................................. 29
Ducted fan theory ..................................................................................................................................................... 29 Concept of a ducted fan paramotor........................................................................................................................... 33
D
5. SCALE MODEL PARAMOTOR ............................................................................................................ 34 Introduction ................................................................................................................................................. 34
Determination of the scale factor.............................................................................................................................. 34 Scale model of standard paramotor .......................................................................................................................... 35 Low turbulence wind tunnel ..................................................................................................................................... 37
6. WIND TUNNEL TESTING ..................................................................................................................... 37 6.1 CORRECTIONS AND CALCULATIONS ................................................................................................... 37
Introduction ................................................................................................................................................. 37 Calculations................................................................................................................................................. 38
Initial method of calculating frontal area.................................................................................................................. 38 Final method of calculating the frontal area. ............................................................................................................ 38
6.2 COMPONENT BREAKDOWN DUE TO DRAG – EXPERIMENT 1 .............................................................. 39 Aims............................................................................................................................................................. 39 Introduction ................................................................................................................................................. 39 Procedure .................................................................................................................................................... 39 Results and Calculations ............................................................................................................................. 39 Discussion ................................................................................................................................................... 40 Conclusion................................................................................................................................................... 42
6.3 EFFECT OF FUEL TANK PLACEMENT ON TOTAL DRAG AREA.............................................................. 42 Aims............................................................................................................................................................. 42 Introduction ................................................................................................................................................. 42 Procedure .................................................................................................................................................... 43 Results and Calculations ............................................................................................................................. 43 Discussion ................................................................................................................................................... 44 Conclusion................................................................................................................................................... 44
6.4 DRAG AREA VARIATION CAUSED BY REMOVAL OF PROPELLER AND RESERVE PARACHUTE ............. 44 Aims............................................................................................................................................................. 44 Introduction ................................................................................................................................................. 45 Procedure .................................................................................................................................................... 45 Results and Calculations ............................................................................................................................. 45 Discussion ................................................................................................................................................... 46 Conclusion................................................................................................................................................... 47
6.5 COMPONENT BREAKDOWN DUE TO DRAG – EXPERIMENT 2 ............................................................... 47 Aims............................................................................................................................................................. 47 Introduction ................................................................................................................................................. 47 Procedure .................................................................................................................................................... 47 Results and Calculations ............................................................................................................................. 48 Discussion ................................................................................................................................................... 48 Conclusion................................................................................................................................................... 49
6.6 TESTING OF ANNULAR AEROFOILS ..................................................................................................... 49 Aims............................................................................................................................................................. 49 Introduction ................................................................................................................................................. 49 Procedure .................................................................................................................................................... 49 Results and Calculations ............................................................................................................................. 51 Discussion ................................................................................................................................................... 52 Conclusion................................................................................................................................................... 53
6.7 USE OF FAIRED FORCE BALANCE ARM............................................................................................... 53 Aims............................................................................................................................................................. 53 Introduction ................................................................................................................................................. 53 Procedure .................................................................................................................................................... 53 Results and Calculations ............................................................................................................................. 54 Discussion ................................................................................................................................................... 55 Conclusion................................................................................................................................................... 55
7. REDUCTION IN DRAG AREA BY CHANGE OF NETTING CONFIGURATION........................ 56 Aims............................................................................................................................................................. 56 Introduction ................................................................................................................................................. 56 Background ................................................................................................................................................. 56
Netting Drag on Standard Paramotor........................................................................................................................ 56
E
Calculations................................................................................................................................................. 57 Theoretical Drag....................................................................................................................................................... 57
Discussion ................................................................................................................................................... 58 Alternatives to existing netting................................................................................................................................. 58 Method of netting attachment................................................................................................................................... 60
Conclusion................................................................................................................................................... 60 8. CONCLUSION.......................................................................................................................................... 61 REFERENCES.................................................................................................................................................... 63 APPENDIX A - CLIENT BRIEF ...................................................................................................................... 65 APPENDIX B - PROJECT SPECIFICATION................................................................................................ 65 APPENDIX C- EXAMPLE OF A STANDARD PARAMOTOR................................................................... 66 APPENDIX D – SURFACE AIRFLOW VISUALISATION EXPERIMENTS ............................................ 67 APPENDIX E – PROPELLER BRAKE DESIGN AND MANUFACTURE................................................. 74 APPENDIX F – GLIDING FLIGHT EXPERIMENTATION........................................................................ 75 APPENDIX G – SCALE WIND TUNNEL MODEL DEVELOPMENT....................................................... 80 APPENDIX H – CORRECTION FACTORS AND CALCULATIONS........................................................ 84 APPENDIX I – WIND TUNNEL CALIBRATION ......................................................................................... 90 APPENDIX J – COMPONENT BREAKDOWN DUE TO DRAG - EXPERIMENT 1............................... 90 APPENDIX K – EFFECT OF FUEL TANK PLACEMENT ON DRAG AREA ....................................... 105 APPENDIX L - DRAG AREA VARIATION CAUSED BY REMOVAL OF PROPELLER AND RESERVE PARACHUTE ............................................................................................................................... 115 APPENDIX M – COMPONENT BREAKDOWN DUE TO DRAG AS A RESULT OF WIND TUNNEL TESTING EXPERIMENT 2............................................................................................................................ 123
CALCULATIONS............................................................................................................................................... 143 APPENDIX N - WIND TUNNEL TESTING OF ANNULAR AEROFOILS.............................................. 147 APPENDIX O - FAIRED FORCE BALANCE ARM.................................................................................... 167 APPENDIX P – PROPOSED DESIGN........................................................................................................... 176
10 STEP DESIGN PROCESS ............................................................................................................................... 176 PROPOSED DESIGN........................................................................................................................................... 179
APPENDIX R – PARAMOTOR CROSS SECTION VISUALISATION.................................................... 190 APPENDIX S - PROJECT TASK OUTLINE................................................................................................ 196 APPENDIX T – TASK BREAK DOWN STRUCTURE ............................................................................... 196 APPENDIX U – PROJECT GANTT CHART ............................................................................................... 196 APPENDIX V – PROJECT MILESTONE CHART ..................................................................................... 196 APPENDIX W – RISK ASSESSMENT.......................................................................................................... 196
End ......................................................................................................................................................................... 196
F
NOMENCLATURE
A Geometric aspect ratio of aircraft.
AoA Angle of attack.
AoI Angle of incidence.
jA Exit area of duct.
pA Propeller disk area.
aC Intake velocity.
DC Drag coefficient.
,D pC Parasite drag coefficient.
,DC ∞ Wing profile drag coefficient.
jC Velocity of air post propeller disk.
LC Lift coefficient.
2LC
kAπ Induced drag coefficient.
F Net thrust.
ISA International Standard Atmosphere.
m•
Mass flow of air through propeller disk.
ap Intake air pressure.
jp Pressure at exit area of duct.
gV Glide velocity between thermals.
sV Sink rate velocity.
ScV Sink rate velocity while circling in a thermal.
V∞ Local airflow vector.
pη Propulsive or Froude efficiency.
G
GLOSSARY
AGL Above Ground Level
DHV Deutschen Hängegleiterverbandes e.V. The largest type certification testing
facility in the world to assess safety and airworthiness of paraglider and
paramotors. The ratings are 1 beginner, 1/2 intermediate, 2 advanced, 2/3 serial
competition, load–prototype competition (load tested only).
Speedbar A flight control system to change the AoI of the wing in flight by weight shift
through a pulley system operated by the legs. Half bar is half accelerated
flight.
Soaring To maintain height in the air without flapping of the wings or using power.
TAS True air speed.
1
1. INTRODUCTION
What is a Paramotor?
In 1964, Domina Jalbert invented a double sided fabric wing called the Ram Air Para Foil, US
patent No. 3285546 (Knake, 1986). This design was unique as it used the higher pressure at
the stagnation point to inflate the aerofoil, creating a lifting surface. This became the common
aerofoil wing for parachuting with a glide ratio of 3:1. During the 1970’s mountain climbers
began using the parachutes as a rapid means of descent from mountains and the new sport was
called paragliding or free flight (as opposed to powered flight).
Paragliding is undertaken by foot launching from an elevated area or by towing from the
ground to an altitude then released. The pilot is then able to soar to increase flight time.
Technology rapidly progressed and these parachuting canopies evolved into aspect ratios of
up to seven and maximum glide ratios of 9.8:1, with a faired harness for the pilot. The
advantages of free flying are the lack of noise from a motor, mastering the skill of gliding
unassisted by a power plant and the challenge of extracting the maximum lift from the local
atmospheric conditions. The disadvantages include having an appropriate launch site on a
mountain and having only a very narrow window of opportunity for launch as wind speed and
direction are critical.
Pilots began adding a motor to the paragliding wings. Initially powerful engines were needed
to provide the thrust needed to overcome the drag associated with early paramotor wings. As
paragliding wings evolved and became more efficient a lightweight power plant was used to
enable self launching and sustained flight (fig 1). The possibilities for flight are increased as a
paramotor can be launched on a small flat field if the conditions are right. Existing paramotor
or standard designs (typical specifications are shown in appendix C) are optimised to operate
for the majority of the flight with thrust delivered by the power plant. However, the increased
noise and vibration in close proximity to the pilot is a disadvantage of the paramotor. In
comparison with a paraglider, which undertakes flight after launching from a mountain or
being towed aloft, the lift to drag ratio is reduced for the paramotor due to the more upright
seating position and the frame and propeller creating additional drag.
2
Figure 1. Time lapse photography of a paramotor self launching (Goin.2005).
A paramotor is also unique in recreational aviation as the aircraft can be stored in minimal
space, such as the boot of a car and can be quickly assembled and flown from an area the size
of a cricket field. Due the fact that it is a foot launched vehicle, it can be legally flown below
500 ft AGL unlike other aircraft, however it shares other airspace restrictions. A typical high
mount paramotor is shown in figure 2 with the important components labelled.
Figure 2. Component identification of a standard paramotor (Goin.2005).
The forces imposed on the paramotor during flight are similar to other aircraft (fig 3),
however they differ in that the wing and propeller of the paramotor are only attached by lines
in tension. The pilot warps the wing (as per the Wright Bros. aircraft) in order to steer the
aircraft with the brake toggles. If the brake toggles are pulled down simultaneously the wing
camber is increased in order to create more lift. The angle of incidence of the wing is
controlled indirectly by the length of the paraglider lines and can be adjusted by either: a)
releasing the trimmers which lengthens the rear most suspension lines (thereby increasing the
trim speed by 10% by weight shift) or b) by use of the speedbar. The speedbar is operated by
an extension of the pilot’s legs which shortens the length of the forward suspension lines
(thereby increasing the trim speed by up to 25% by weight shift). The thrust from the motor
controls the ascent and descent rates.
3
Figure 3. Overview of forces encountered during flight in a paramotor. (Goin.2005).
Aims
The aim of this project is to investigate the feasibility of reducing the drag of a paramotor, in
order to increase the lift to drag (L/D) ratio in gliding flight when the motor is not producing
thrust. This will be broken down into the following segments:
(1) Obtaining experimental results of lift to drag ratio and surface airflow visualisation of
a typical paramotor while gliding.
(2) Wind tunnel model testing to determine the major contributors to drag of a standard
paramotor while in gliding flight.
(3) Further wind tunnel testing to investigate the individual contributors to drag of a
paramotor and determine the feasibility of the reduction of the drag of the individual
components, and to redesign the affected components to individually have a lower
drag coefficient than the baseline paramotor.
(4) Evaluate the revised complete paramotor design in the wind tunnel to determine if a
lower drag can be achieved gliding when compared to a standard paramotor design
when overall interference drag between the components is included.
There is a desire for a redesigned paramotor that is capable of a high L/D ratio in order to soar
efficiently as a glider after launching from flat land under its own power. Standard paramotors
are designed for sustained flight with an engine providing the thrust for the duration of the
flight, but the L/D ratio is low while undergoing unpowered flight, which is detrimental to
effective soaring characteristics. This is shown as a simplified schematic in figure 4.
4
Figure 4. Top box shows flight schematic of a standard paramotor, indicating the poor glide ratio in unpowered flight requiring more thermal lift to cover the same distance. Middle box shows a schematic representation of free flight off an elevated launching area. Lower box shows desired flight schematic launching from flat land in a paramotor with improved glide ratio.
Scope
It is necessary to perform a qualitative and quantitative analysis of the contributors to drag in
the flight of a standard paramotor. The experiments utilised a standard paramotor to obtain
actual flight data and used a scaled paramotor model in a low turbulence wind tunnel to obtain
drag data. All flight trials were undertaken above Lake George, NSW or in the vicinity of
Michelago, NSW within airspace restrictions. During the flights, still images were taken of
positioned wool tufts for surface airflow visualisation and a data recording instrument was
used to record flight details. These results were used to obtain an accurate measurement of
the L/D ratio of a paramotor.
An accurate full sized representation of a paramotor and manikin was created using the
CATIA software, depicting the position of the aircraft and pilot during flight. Based on the
3D CATIA rendering, a scaled model was constructed for low turbulence wind tunnel testing.
Various configurations were measured for drag in order to determine the individual
contributions of various components to total drag.
The problem. A paramotor is inefficient when gliding creating poor soaring performance.
Typical paraglider soaring flight
What is desired. A paramotor that has similar flight characteristics to a paraglider.
5
Using the results of the analysis, a revised paramotor designed to minimise the drag in order
to increase the L/D ratio of a paramotor in flight was designed in CATIA and evaluated at
10% scale in the low turbulence wind tunnel. The wing was not modified in this project.
Limitations
The collection of data during paramotor flight was limited to the accuracy of the flight data
recording instrument, an Aircotec Top Navigator. This instrument is an integrated GPS
receiver that is able to store the flight path to a high accuracy for later analysis. The influence
of the local atmosphere provided the largest errors in measuring the glide slope. To reduce the
error rate, all flights were undertaken in nil wind conditions and a stable air mass. The flight
testing occurred south of Michelago where there were minimal flight restrictions below
10,000 ft in order to create a longer gliding flight in order to create a longer data sample.
In order to remove any variations caused by piloting inputs in flight glide test results, the
piloting was done with control positions to achieve the best glide. There are two methods of
yawing a paraglider. The first method is the application of brake control inputs, which warps
the wing on the side the turn is to be initiated, creating greater lift and therefore drag on that
side. As a result the glider turns in that direction. The other method is weight shifting by the
pilot in the harness to create an uneven load on the wing and thus initiate a turn to the side of
the harness with the greatest weight. Weight shifting is more efficient as the aerofoil is not
deflected from its optimal shape. In order to achieve the straightest glides during the
experiments the pilot used only weight shift.
The wind tunnel paramotor representation was limited to a scaled replica of a PAP 1400
paramotor. This model was chosen as it has won three out of five recent paramotoring world
championships and is at the forefront of conventional paramotor design. It is also the model of
paramotor that was flown by the pilot in order to collect base line data from which the scale
model was constructed. The limited space inside the wind tunnel prevented research on a
larger model due to the close proximity of the test section walls creating wall interference
effects. This reduced the possible size of the model and increased error in the experimental
process due to difficulty of creating an accurate 10% scale model.
6
Summary
This initial chapter provided a brief introduction to paragliding and paramotoring, and
identifies the reasons for the choice of thesis topic. It also provided an outline of the aims and
the scope of the research to be carried out. The limitations of the thesis project were also
discussed with the means of reducing the experimental error.
2. LITERATURE REVIEW
Introduction
Aerodynamic Forces in Gliding
The forces acting on an aircraft in power off glide are lift (L), drag (D) and weight where
thrust is zero (Anderson, 2000, p 391). During equilibrium unaccelerated glide the sum of
forces is zero. These individual forces cancel down to 1tan ( )LD θ−= , where θ is the glide angle.
The weight of the paramotor has no bearing on the L/D ratio of the aircraft, but changes the
glide velocity; the higher the weight the greater the velocity (Thomas, 1999, p 44).
Stall velocity will also increase with a rise in weight; these factors will intensify landing
difficulties due to higher approach and stall speeds. These factors and the fact the power plant
has to be carried by the pilot during takeoff and landing make it essential that the paramotor
weight be kept to a minimum. This leaves only the drag force to be manipulated during this
thesis in order to improve the glide ratio.
Aerodynamic drag
The resistance to motion as a result of aerodynamic drag is expressed as:
2
2
1Aerodynamic Drag = (Anderson, 2001, p. 64)2Where:
= the air density or mass per unit volume through which the object is travelling.
V = the relative velocity. = the objects drag coeff
D
D
V SC
C
ρ
ρ
∞ ∞
∞
∞
icient (not neccesarily constant - Reynolds numbers effects).S = the reference area of the object.
The desired result of experimentation is qualitative data to assess the impact of configuration
changes and the most useful term to express these results is drag area. ‘Flat plate drag area
21( )2D
D C SVρ
= is useful in cases where an area of reference is not obvious (such as, for
7
instance, in the case of a motorcycle) or where several component parts are combined in some
system' (Hoerner , 1965, p 1-8).
Relative velocity is the dominant force as it is a squared term. The total aerodynamic drag on
an object at 0o AoA is divided into two components: pressure drag and skin friction drag
(Anderson, 2001, p. 63). Therefore there are two different types of shapes in aerodynamics, a
blunt body where most of the drag is pressure drag and a streamlined body where most of the
drag is friction drag (fig 5). As the flat plate and cylinder have high pressure drag they are
blunt bodies. The current standard paramotor is a blunt body; initial efforts will concentrate
on reducing the pressure drag around the pilot.
Figure 5. A comparison of relative shapes in terms of skin friction and pressure drag. The effects of different
Reynolds numbers are also shown (Anderson, 2001, p. 64).
Drag Polar
Drag on an aircraft is comprised of differing factors, ‘those which vary with lift and those that
do not… the nondimensional coefficient form of this representation is the drag polar’ (Brandt
et al., 2004, p 130).
The drag polar is: 2
, , ,(assumes and are constant)LD D p D D p
CC C C C kkAπ∞= + + (Cone, 1964,
p14). Where 2LC
kAπ is the induced drag coefficient concerned with the lift produced by a 3D
8
wing, changing the lift is outside the scope of this thesis. ,DC ∞ is the aircraft drag coefficient.
(Babinsky, 1999, p 421) states ‘An analysis of paraglider performance has revealed that wing
section drag is the most significant contribution to overall drag’ (fig 6). This is largely made
up of the profile drag of the paraglider wing section and lines maintaining the paraglider’s
wing shape.
Figure 6. Paraglider drag broken down into separate elements and plotted against flight velocity
(Babinsky, 1999, pp 422-423).
The importance of reducing parasite drag is emphasised by Cone, (1964, p 17) who states
‘The parasite drag coefficient ,D pC plays an important role in determining the sinking
velocity of a sailplane and should always be reduced to its lowest possible value. The parasite
drag coefficient can be reduced by eliminating as much fuselage and emplanage area as
possible and by paying strict attention to such drag-producing details as fuselage wing
junctures, canopy contour and fairing, control gaps, miscellaneous protuberances, and the
prevention of all areas of separated flow’. The equivalent areas on a paraglider are line drag,
pilot drag, pilot-paramotor junctures, cage protuberance and areas of separated flow.
Basic Soaring Theory
To maximise the potential for good paramotor soaring flight a reduction in the sink rate in
glide and/or increase in glide airspeed is required. Thomas (1999) states an optimised
sailplane (same principles as a paraglider) is designed for ‘a low sink rate ScV while circling, a
low sink rate sV while gliding between thermals and a high inter thermal glide speed gV .
Modifying sV and gV are within the scope of this thesis by reducing the overall drag. The
effect of this is shown (fig 7). If the glide gradient has a large negative value the paramotor
will be forced to land rather than climb up in the next rising air mass.
9
Figure 7. A closer examination of figure 4, in order to maximise soaring flights, gV should be maximised,
sV minimised (Thomas, 1999, p 62).
A Paraglider Polar Curve
The L/D ratio will increase as the pilot’s drag decreases and the glide speed will increase
slightly as pilot drag decreases (fig 8). The best glide velocity is where a line drawn from the
origin is tangent to the drag polar curve; this is in the vicinity of 38km/hr for the experimental
wing, an Ozone Rush (an intermediate classed glider).
Approximate Drag Polar for Ozone Rush DHV 1/2 Paraglider
-3
-2
-1
00 5 10 15 20 25 30 35 40 45 50 55
True Air Speed in km/hr
Dec
ent V
eloc
ity in
m
/s
Drag Polar Curve For ParagliderBest Glide VelocityStall VelocityMinimum SinkBest Glide Velocity-no brake positionFully Accelerated
Figure 8. An approximation of the drag polar for the paraglider wing to be used during experimentation, note this is during paragliding flight at correct wing loading. A compilation of two graphs by the author based on drag polar projections from the Para 2000 website (Florit, 2006).
10
A sailplane drag polar has been used as an example as the principles involved are the same as
a paramotor (fig 9). When wing loading is increased the polar moves down and to the right,
however the minimum flight path angle remains constant as does the intersection with the
polar. To achieve the best L/D ratio, the glider will have a higher velocity and descent rate.
The glide angle will change due to increased parasite and profile drag (Babinsky, 1999,
p 421). As DoC is increased the drag polar will move to the right and thus the tangent point
will move. The net result will be a deteriorated glide angle and decreased interthermal
performance. For the soaring paramotor pilot this means flying at minimum sink speed while
ascending in a thermal (approximately 30 km/hr), then a higher interthermal glide speed by
weight shift (approximately 45km/hr) when bridging thermals.
Figure 9. Left. Drag polar for a sailplane showing the effect of changing the wing loading. minγ is minimum flight path angle, note it remains constant, and the polar moves down and to the right with increased wing loading (Thomas, 1999, p. 46). Right. As DoC is increased the minimum glide angle is increased and interthermal flight performance is reduced (Thomas, 1999, p. 44).
Previous Drag Experimentation on Paragliding Harnesses
Wind tunnel tests with two types of harness and multiple seating and limb positions (fig 10)
showed that the position of the legs and arms have a major influence in the overall drag. The
contributors to increased drag in order of their decreasing difference in effect are the chest,
arms, legs and a profiled helmet (fig 11). The posture in the experiment most similar to the
piloted paramotor being evaluated for the thesis studies is the classic style harness with
stretched legs at an equivalent flat plate area of 0.41m2. This posture has the arms with
elbows out at 90o to the body and airflow, with forearms perpendicular to the ground.
11
Figure 10. Left. The photograph shows wind tunnel testing being undertaken with a pilot in a classic style paragliding harness (Belloc, 1999, p 1). Right. This is a side view drawing of the wind tunnel testing with the pilot in a reclining position and in a competition type harness showing the location of the force balance to measure the resultant drag (Belloc, 1999, p 1).
Classic Style Harness Equivalent Drag Area SCd
0.53
0.380.29
0.380.28 0.32
0.42 0.41 0.410.35 0.30
0.23
0.43 0.40
00.10.20.30.40.50.60.7
Che
stex
tend
ed
Stan
dard
Post
ure
1
Stan
dard
+cr
ouch
ing
Elbo
ws
onth
e ris
ers
Cro
ssed
arm
s
Leng
then
edar
ms
Stan
dard
post
ure
2
Cro
ssed
legs
Stre
tche
dle
gs
Legs
toge
ther
Tran
sitio
nal
mov
e
Tran
sitio
nly
ing
Stan
dard
post
ure
3
Prof
iled
helm
et
Chest Arm Leg Transition Helmet
Position Identifier
Equi
vale
nt F
lat P
late
Dra
g A
rea
in S
quar
e M
eter
s
Figure 11. This graph has been translated and redrawn by the author from the original French graph by Dr Herve Belloc (Belloc, 1999, p. 4). It details the drag results in the equivalent flat plate drag area found during experimental testing of standard type unpowered harnesses. Note due to the poor resolution of the scanned original figure, the error bars have been estimated at 10%.
Belloc* concluded that the main results were:
‘The standard harness position has an equivalent flat plate area of 0.41 2m , equivalent
to 2.5 kg drag. The cocoon position (competition) has an equivalent flat plate area of
0.2 2m a 50% reduction over standard. An intermediate glider of initial data of wing
area 28 2m , mass of 95kg, glide ratio of 7.6:1 and TAS of 36km/hr has by use of a
competition harness an improvement of the glide ratio to 8.2:1, a total drag
improvement of 14% and a speed improvement of 4.4%. Pilot drag is a key driver for
glide ratio improvement, and has little effect on speed. This improvement is [e]specially
useful for long straight flights against wind. In the case of a[n] 18km/hr counter wind,
improvement is equivalent to 90m altitude and 50 seconds time reduction for a 10 nm
ride. It may be very important to successfully take the next thermal’.
*(Belloc, 1999, translated and summarised by Caldara, 2005)
12
The intermediate glider referred to by Belloc is similar in specification to the glider to be used
for the intended paramotor experiments. While it will not be possible to achieve as a result of
this thesis an equivalent flat plate drag area of 0.2m2, a similar type of improvement is desired
between the current and future paramotor designs
A more recent study has been undertaken to find the most aerodynamic competition harness.
With careful design a classic seating position can be made to have a low overall drag
(Virgilio, 2005, p 12) (fig 12). The Ram Race harness is unique that it has an inflatable rear
cowling pressurised from stagnation points near the base of the harness, which creates
minimal separation of the airflow around the harness. The advantages of a comfortable
seating position are maintained with good piloting control and weight shift being achievable.
It does not have a forward cowling for the legs which allows easier launching and landings
with less chance of the legs being trapped with an equipment malfunction. Lastly, certain
models of competition harnesses with leg fairings have instability in forward flight with the
pilot having to hold the harness stable into the oncoming airflow to maintain low drag, which
distracts the pilot from the overall function of piloting the aircraft.
Figure 12. This graph has been translated by the author from the original Portuguese graph (Virgilio, 2005, p 18). The effectiveness of a streamlined harness to reduce flow separation can be seen in the reduced overall harness drag, the Ram Race harness is to the far right.
The method of drag calculation differed in the French (Belloc, 1999) and Portuguese
(Virgilio, 2005) studies. The French study was by force balance data recordings taken from
above the pilot and the Portuguese study was from upstream of the pilot (fig 13). The French
study reports half the drag in Newtons, as compared to the Portuguese study for a similar
harness; therefore in each study the comparative values but not the direct numerical figures
can be examined. Also, neither of the studies account for the direction of the oncoming
airflow during flight. The classic harness had a glide ratio of approximately 7.2:1. If the
Belloc experimental method had accounted for this by inclining the harness to the required
Comparison of Drag
Drag (N
)
13
angle, then the drag achieved could have been lower due to V∞ not being perpendicular to the
torso. The experimental error is reduced in proportion to the level of harness drag.
Figure 13. Showing the method of obtaining drag results on full scale test subjects. Note the cords running horizontally forward into the wind tunnel attached to a force balance at the other end. The harness and leg position is optimised for a horizontal oncoming airflow, not glide ratio (Virgilio, 2005, p 15).
Due to the thoroughness of the French and Portuguese studies, no attempt was made to
evaluate the effect of differing pilot positions in the proposed wind tunnel experimentation
using full scale test subjects. Instead, a manikin was manufactured in the position adopted by
the pilot during actual flight testing.
Wing Loading of the Paraglider
A paramotor with the engine not operating exhibits similar flight characteristics as a
paraglider except for a higher wing loading. Wing loading is the aircraft’s weight divided by
the wing area, which increases as a result of the added weight of the paramotor. The higher
wing loading may result in the flexible paraglider wing distorting because of the maximum
take off weight exceeding manufacturer’s specifications, therefore the wing may not generate
as much lift and will also create more drag. The intake at the stagnation point near the
maximum AoA flares open and creates a separation bubble at the leading edge of the upper
wing surface and the cell centres of the flexible wing may distort (Babinsky, 1999, p 426) (fig
14). The net result of both of these deficiencies is increased separation of airflow and reduced
overall lift.
14
Figure 14. Detail of points of airflow separation of a flexible paraglider wing due to distortion at high angles of
attack (Babinsky, 1999, p 426).
While not expressly stated by Babinsky, it is plausible that a flexible wing when placed under
a load higher than the designer had intended could deform and create a similar situation.
Therefore a paramotor at a higher than specified weight rating with equal drag to a paraglider
harness may not be able to achieve the same L/D ratio as a correctly weighted paraglider.
3. EVALUATION OF CURRENT PARAMOTOR DESIGN
Introduction
Due to the recent arrival of the sport of paramotoring, there is limited previous research
carried out on this particular type of aircraft. As a result a body of quantitative and qualitative
data had to be obtained in order to form the baseline for alternative design comparison. This
baseline data was collected in experiments which examined surface airflow evaluation, glide
ratio measurement, the effect of a windmilling propeller, angle of incidence (AoI) during
glide and finding the contributors to drag in the wind tunnel.
3.1 SURFACE AIRFLOW EVALUATION EXPERIMENT
Aims
The aims of this experiment were to:
(1) Gain a greater understanding of the airflow over the existing paramotor.
(2) Gather information to enable an accurate wind tunnel model to be built.
Introduction
There has been little emphasis on improving the glide ratio of a paramotor, and there is a need
to investigate the effect of airflow interaction between the pilot and paramotor which may
15
potentially have a dramatic effect on aircraft drag. This experiment sought to identify any
obvious indicators.
Procedure
Camera Mount - Manufacture
To record the airflow over the surface visualisation suit, a digital camera was used with an
infrared remote control attached to the left hand paraglider brake toggle. CATIA images of
the camera mount can be seen in figure 15, further detail can be found in appendix D. The
camera mount was able to be rotated in flight allowing images to be taken from 0o to 90o to
the direction of travel. A 3m long boom was used to achieve acceptable focal length as
opposed to a close range fisheye lens which would distort the image.
Figure 15. Scale CATIA isometric images of the camera mount, the length of the camera boom can be clearly seen. When launching and landing the camera is also stowed perpendicular to flight direction then rotated after launch in order to achieve frontal photographs.
Surface Airflow Suit
A surface airflow visualisation suit was worn by the pilot during experimentation. It consisted
of a set of disposable white overalls with attached red wool tufts. The hood was removed to
allow access to the reserve parachute in case of an emergency. The pilot's helmet, paramotor
netting and frame were also evenly covered in short strips of fluorescent surveyors’ tape. The
surveyors’ tape was changed after the initial experiment to red wool as the tape did not
provide sufficient clarity in the photographs.
Results
Images taken during experimentation are shown in figures 16 to 19. These are only a small
sample of over 200 photographs taken during the course of the experiment; these particular
example are shown as representative views at 0, 45 and 90o to direction of flight, other images
are shown in appendix D.
16
Figure 16. Image of paramotor gliding with half speedbar, local area of reversed airflow is clearly seen behind the pilot and aft of the pilot’s toes.
Figure 17. Frontal image of paramotor during glide with half speedbar.
Laminar flow through frame netting.
Local region of turbulent flow behind pilot’s feet.
Wool tufts show extent of turbulence behind pilot.
Inclination of paramotor is not perpendicular to horizon during glide.
With application of speed bar attitude of pilot and frame changes in relation to
17
Figure 18. Left. Image of paramotor climbing under full throttle with half acceleration by use of the speed bar. Note paramotor frame is perpendicular to horizon when engine is creating thrust. Right. Image of paramotor gliding, half accelerated by use of the speed bar. Note the angle between vertical and the frame is at 23o.
Discussion
The photographs in figures 16 to 18 have been labelled to more effectively enable pertinent
points to be shown. Common points are that the region of turbulence during glide is behind
the pilot’s upper torso and a significant proportion of the body behind the feet. The soles of
the boots especially when the speedbar is applied represent a bluff body where most of the
drag is pressure drag. The large pressure drag region is due to flow separation off the sharp
edged boot tread. Laminar airflow occurred through the paramotor netting, generally over the
frontal half of the pilot and the pilot’s helmet. Further modification will occur to increase the
amount of laminar airflow.
The difference in attitude between a paramotor with full thrust and a paramotor gliding (fig
18) hold the most important findings. As shown earlier in figures 7 and 8, in order to achieve
a greater cross country soaring distance the interthermal velocity must be increased. This
interthermal velocity is approximately 45km/hr and is affected by use of the speedbar. When
the pilot places the pressure on the speedbar this applied a force forward of the carabineer
pivot which rotates the paramotor and pilot backward (fig 19).
18
Figure 19. Image of paraglider gliding, half accelerated by use of the speed bar.
There are several variations in the types of paramotor harnesses (fig 20). The standard
paramotor used for experimental testing is a low hook-in type with swing arm. The high
hooking attachment type harnesses have the centre of gravity well below the carabineer hook
in point and the application of thrust or speedbar on the paramotor has little change in
attitude. These types of harnesses generally have poor
weight shift characteristics; weight shift is the loading
of one side of the harness in order to turn the
paraglider wing without use of the brake toggles.
Therefore the high hook-in type harness is not
preferred for pilots seeking soaring flight.
The low hook-in harness with swing arm has a
significant change in attitude of the pilot and
paramotor with varying thrust, the centre of gravity (C
of G) of the paramotor is at the same height as the
carabineer pivot (fig 20). Therefore as thrust is applied
the propeller disk becomes perpendicular to the
ground. When gliding because the C of G is behind
the pivot point this causes rotation of the paramotor to
approximately 20o attitude. With application of the
speed bar the upwards force forward of the pivot
Red arrow points to the carabineer pivot point. Green arrows show routing of the speed bar. As the speed system is depressed the force applies a lifting force forward of the pivot point. This and the lack of thrust produced during glide changes the attitude of the paramotor and pilot to approximately 23o from perpendicular.
Figure 20. Types of paramotor harness configurations.
19
causes the attitude to change further to approximately 23o.
Before this experimentation was conducted, the attitude of a paramotor was during
accelerated glide was unknown. This experiment showed the average attitude of the
paramotor was 23o. This had implications for the method of mounting the scale model in the
wind tunnel at such a reclined AoI, as the effective frontal area of the model was significantly
reduced. Therefore a similar reduction in drag was a possibility.
Conclusion
This experiment set out to gain a greater understanding of the airflow over the existing
paramotor in both accelerated glide and full throttle. Also further information about the
paramotor's attitude during glide was sought. It was found that the attitude with respect to the
horizon changes from 0o when thrust is produced to typically 23o in half accelerated gliding
flight.
3.2 DESIGN AND MANUFACTURE OF PROPELLER BRAKE
Background
The effect of a windmilling propeller could have a large influence of the overall L/D ratio of a
paramotor. In relation to paramotors, Goin, 2005, p. 220 states:
‘A windmilling prop has dramatically more drag than a stationary one…. Expect a 10 to
20% decrease in glide performance with a windmilling prop (clutched units), 2 to 4%
decrease with a stopped prop and no change for an idling prop (no clutch)’.
Due to the slow forward velocity of the paramotor with windmilling propeller during glide it
is similar to an autogyro. At the commencement of glide the paramotor had the engine idling
with the centrifugal clutch disengaged. The propeller rpm then achieves a balance between the
stored kinetic energy of the rotating propeller, the rotor disk extracting power from the local
airflow and the frictional drag created by rotation of the reduction gearbox. If the propeller is
in an equivalent state of autorotation to a helicopter or forward flight of an autogyro the drag
effects are large. ‘A much lower descent rate is possible in forward flight, however the rotor
flow state in autorotation is similar to that of a bluff body of the same size, so it is not
surprising that comparable drag forces are produced’ (Johnstone, 1994, p 110).
20
An overlay of an autorotation diagram (Johnstone, 1994, p 111) scaled to the size of the
paramotor propeller is shown in figure 21. If autorotation rpm is achieved, the net torques in
the outer two circles must be equal. At the beginning of autorotation the collective in a
helicopter is reduced to a slightly positive angle to maintain rotor rpm; this is a fundamental
difference to a paramotor, as a paramotor has a fixed pitch propeller and its attitude may be
high, resulting in a stalled rotor. The attitude will decrease rotation speed, thereby increasing
the centre stall region and reducing the accelerating torque region causing reduced drag.
Figure 21. Windmilling propeller energy regions shown when rotational speed is equivalent to autorotation to a helicopter, scaled to actual paramotor dimensions for 1.25m diameter propeller. Note diameters of differing regions are not to scale. Rotor blade in autorotation taken from (Johnstone, 1994, p 111).
Method
A method to allow the propeller to be held fixed, windmilling or producing thrust had to be
designed. To the best of the author’s knowledge a propeller brake has not been fitted to a
paramotor before. Several designs were conceived, however the final design utilised a disk
brake fitted to the output flange with a mechanically operated calliper mounted to the
reduction gearbox to stop rotation. This design allowed for a lightweight brake that the pilot
operated during flight and that the motor could overpower if emergency thrust was required.
The design was developed using CATIA and was converted into MasterCAM (appendix E).
The calliper components were created using the SACME computer aided wire cutter from
0.100” 7075 T-6 aluminium alloy. The calliper was not corrosion treated due to the short
expected life span of the components. Modified bicycle components were used in the
assembly of the calliper; a brake pad was the friction element and the front derailleur shifter
operated the brake (fig 22 and 23).
21
Figure 22. Left. Image of propeller brake calliper after 15 flight hours. The calliper was removed and inspected for fatigue. No defects were evident. Right. Image of propeller brake as fitted to the Top 80 paramotor engine. This image was taken after 10 hours operational use, the control cable has been covered in heat shielding to reduce radiated heat effects from the expansion chamber.
Figure 23. Image of propeller brake as fitted to the Top 80 paramotor engine showing brake control on left hand underarm bar. The brake controller is a modified front derailleur control from a bicycle. Several ground test runs were carried out after the brake was assembled; these involved
ground runs of 30 minutes at maximum throttle to ensure security of components, application
of the brake at idle, maximum rpm at full rotation and maximum throttle from idle. The
detrimental effects of the brake were a qualitative reduced thrust and increased noise level; a
Brake control lever.
Brake assembly fitted to reduction drive gearbox.
22
‘ripping’ cavitation-type noise occurred around the disk. If the propeller brake was to be used
in a future concept a redesign would need to occur; possibly the use of a propeller spinner
would reduce airflow disturbance around the propeller disk brake.
3.3 GLIDE RATIO TESTING
Aims
(1) Determine the glide ratio of a paramotor in standard configuration.
(2) Determine a difference in the glide ratio between a windmilling and a vertically fixed
propeller.
(3) Determine the rpm of a windmilling propeller in glide.
(4) Determine the drag polar of a paramotor.
Introduction
The experiment to determine glide angle was critical to the thesis. The assumption that had
developed during previous flights was that a paramotor had significantly reduced glide ratio
compared to a paragliding harness. The results of this experiment would determine the effect
of a paramotor on glide ratio. Also the contribution to glide as a result of a fixed or
windmilling propeller were investigated to confirm the validity of previous data showing a
20% reduction in glide with a windmilling propeller (Goin, 2005, p. 220). The rpm of a
propeller during clutched gliding flight was of interest as the rpm reached would determine
the amount of drag produced.
Procedure
The initial gliding flight was undertaken over two blocks of testing separated by several
months; a total of 25 flights were performed. The initial flight block consisted of over 10
flights during February 2006, but due to the unfavourable adiabatic lapse rate creating too
much vertical movement of the air, there was difficulty in obtaining an accurate glide ratio.
Dawn flights are generally considered to be the most stable part of the day, but recorded
thermal movements of up to 2.5m/s, created inaccuracies in glide. The decision was made to
suspend data gathering flights until early winter in order to obtain a stable air mass.
The second block of flights proceeded with less vertical air mass movement however during
the two month time period there was a prevailing westerly jet stream and the typical valley
23
inversions to the east of the Great Dividing Range did not occur. As a result the anticipated
still air mass did not eventuate, but due to time constraints, testing continued with greater
levels of error than desired.
The Aircotec Top Navigator (fig 24) that was used as the primary flight data recording
instrument, is a combination of a three dimensional GPS with pressure altimeter, vertical
accelerometer and temperature sensor to record the location of thermals. An external true air
speed (TAS) probe was attached to this instrument to increase the recorded velocity accuracy
to 0.25± m/s (Aircotec, 2006). The TAS probe was stabilized using a small weight and
shuttlecock type arrangement, which was suspended on a 2m cable below the paramotor to
ensure the sensor was aligned with the oncoming airflow. The probe was deployed when
sufficient altitude was reached after launch. With the motor operating the airspeed recordings
were inaccurate due to proximity of the TAS probe to the propeller. Prior to the
commencement of flight testing, the instrument was sent to Austria for recalibration with a
new TAS probe purchased to ensure the integrity of the data being recorded.
Figure 24. Left. Aircotec Top Navigator. (Aircotec, 2006) Right. True air speed (TAS) probe. (Aircotec, 2006)
The Top Navigator calculates the drag polar of a particular paraglider setup if glide is
recorded at three velocities; minimum sink, best glide and maximum speed. However local
wind speed must be less than 2 km/hr for this to be accurate. As mentioned previously the
weather conditions did not allow the drag polar to be accurately measured.
Results
The TN Complete software was used to graph and analyse the data recorded. On this
particular data gathering flight a maximum of 6,000 ft altitude was reached due to an upper
24
level westerly wind on that particular day (fig 25). Flights were made to 10,000 ft when
weather conditions allowed.
Figure 25. Flight path data recorded 5/5/06 on Top Navigator overlaid onto Google Earth software, high altitude perspective with plumb line from flight path. To minimalise experimental error, each glide alternated between a windmilling propeller and
a vertically braked propeller. In figure 26, between M1 and M2 the propeller windmilled and
was braked between M3 and M4. Also glides into and with the prevailing breeze were
undertaken with the results averaged out. In Appendix fig F.5 in the lowest graph it can be
seen that before and after the milestones there was considerable variation in vertical velocity.
This was due the pilot doing a 360o turn pre and post glide for the GPS to calculate the wind
velocity and direction. The longitude and latitude for each milestone was found via GPS
reading; this data was then used in Geoscience Australia’s webpage which uses a Vincenty
formulae calculator to give an ellipsoidal distance on the mean Australian surface between
two points. The error between the mean land surface and the flight altitude for ellipsoidal
distance is less than 1%. A table of sample calculations is shown in Appendix F.
25
Figure 26. An example of the
format of the flight path data
recorded 5/5/06 on Top Navigator
GPS. The top left hand corner is a
summary of the flight, the box to
the right is the instantaneous flight
details at the time shown by the
vertical purple line at milestone
M14. The blue pointer on the dial
shows direction of travel with the
red tip the local wind velocity and
direction.
The first graph gives the altitude in
metres in the Y axis, time on the X
axis (common for all graphs). The
complete flight is plotted. The
difference in colour is the colour
trace from thermal sensor.
The middle graph shows the
vertical velocity, with the Y axis
showing m/s.
The lowest graph is horizontal
velocity with the Y axis shown in
km/hr (as is typical for
paragliding).
26
Of the 25 flights undertaken only 6 flights had accurate data, the final average glide ratios
were 6.4 0.5 :1± for a windmilling propeller and 6.5 0.5 :1± for a vertically braked propeller.
During glide testing the rpm of the windmilling propeller was tested. When at best glide (38
km/hr) the pilot turned around and counted propeller rotations using a wristwatch as a timer.
The average windmilling propeller in glide was120 20± rpm. This rpm could be significantly
increased when increasing the local velocity, for example while in a steep descending spiral,
and rpm could be made to slow down during the search for stall manoeuvre.
Discussion
To determine the lift to drag ratio of a paraglider the German magazine ‘Gleitschirm’ uses a
standard harness and pilot for the paraglider to be evaluated and compares the glide to a
reference paraglider wing and weighted pilot (always the same for each test); they claim a
L/D ratio of relative precision +/- 0.1 and consistency across their tests (Gleitschirm, 2006,
translated and summarised by author, 2006). However, whether the absolute reported
numbers are accurate remains unknown, as it all depends on whether the initial absolute L/D
ratio value for the reference wing was accurate. Other magazines use similar methods; the
only test available on the wing used in this experiment was conducted by Vol Libre, which
tested the Ozone Rush at 8.2:1 glide ratio. In the context of this thesis, the average glide
ratios were 6.4 0.5± :1 for a windmilling propeller and 6.5 0.5 :1± for a vertically brake
propeller. It would seem the paramotor has an approximately 20% decrease in glide
performance from published figures. However due to the poor local conditions and the lack
of a known reference paraglider the experimental glide results should be dealt with a healthy
degree of scepticism.
There appears to be little difference between the glide ratios of a windmilling propeller and a
brake propeller. As a result the scale model can have a fixed vertical propeller for further
experiments and will remain relevant to a windmilling propeller.
The experimental result of the propeller windmilling during glide at approximately 120rpm at
an AoI of 32o is vital for further understanding of the problem. The offset of the propeller
disk to the oncoming airflow on a paramotor can be compared to a power-off autorotative
descent with forward airspeed for a helicopter. At the commencement of glide for the
experimental paramotor, the engine was idling and the centrifugal clutch disengaged. The
27
propeller rpm achieved a balance between the stored kinetic energy of the rotating propeller,
with the rotor disk extracting power from the local airflow and the frictional drag created by
rotation of the reduction gearbox.
Conclusion
This experiment found the glide ratio of a paramotor at 6.4 0.5 :1± , however due to instability
of the local atmosphere and lack of a reference glider the margin of error was high. There
was no appreciable difference in glide ratio between a fixed and windmilling propeller,
therefore the assumption that the wind tunnel can utilise a fixed propeller and not corrupt test
results is correct. Due to the adverse local weather conditions mentioned, the drag polar of a
paramotor was unable to be measured with any degree of accuracy and is therefore not
shown.
3.4 PARAMOTOR CROSS SECTION VISUALISATION
Aims
(1) To gain further understanding of the cross sectional area exposed toV∞ .
(2) To analyse the fundamental design of the paramotor in order to develop a more
streamlined cross sectional area to reduce possible airflow separation.
(3) To determine a benchmark for future designs to compare reduced pressure drag
producing profiles.
Introduction
Airflow separation causing viscous pressure drag and interference between bodies is a major
cause of drag in a gliding paramotor. Reduction of the effects of airflow separation can be
achieved through streamlined profiles. Interference can be reduced by a thorough design to
improve placement of bodies in close proximity. As the profiles are equally as important at o o0 and 32 AoI, a method was sought to visualise the profiles at o32 AoI. CATIA software
has been used for the calculation of the profiles.
Procedure
The CATIA model of the PAP1400 paraglider with pilot used for the production of the wind
tunnel model was analysed. The model was simplified with the harness and netting removed;
28
due to the difficulty in generating these images in CATIA. The sectioning tool available in
the CATIA software was used with dissections taken in 0.1m intervals at o32 angle. This
angle was chosen as it replicates the profile area as exposed byV∞ .
Results
Screen prints from the CATIA software of the model sectioning are provided in appendix R.
Discussion
The images taken illustrate that the existing paramotor design was not developed to have a
streamlined profile at o32 AoI, as its primary task is powered flight. Several possible
redesigning features that could reduce drag include the use of vertical tubing in the cage, the
streamlining of the tank area and airbox silencer and the improvement of the aerodynamics of
the harness and the reserve chute.
Cage tubing projects at an angle that increases the effective frontal profile (appendix R, figs
R.5 and R.11). The replacement of horizontal structural elements with an increase in vertical
elements supporting the outer ring of the cage could reduce pressure drag (fig 27). At the
angle of inclination of o32 the circular tubing creates an improvement in streamline profile
due to the cross flow principal. This is due to fluid dynamic pressure forces only being
applied at the vector V∞ on the cylinder. (Hoerner, 1992, pg 3-11).
Figure 27. How an inclined circular cylinder can produce less pressure drag as a result of the cross flow principal (Hoerner, 1992, pg 3-11). Drag (and lift) coefficients (on area ‘d’ times axial length ‘l’) of circular cylinders, wires and cables; inclined against the direction of flow – at Reynolds numbers below the critical.
29
Another area of possible improvement is in the position of the fuel tank (appendix R, figs
R.9, R.10 and R.11). This area has both a separation inducing profile and tubing in close
proximity creating interference drag.
If the airbox silencer was turned at an angle of approximately o90 forward then the profile
view would become more streamlined and possibly reduce airflow separation (appendix R,
figs R.5 and R.6). Space exists behind the netting for this to occur on the current paramotor.
Alternately the air box could be redesigned to be situated over the top of the motor. This
could take the form of a cowling designed to reduce separation of the airflow behind the
upper torso of the pilot.
Conclusion
This experiment has been successful in gaining a further understanding of the cross sectional
area as exposed to the oncoming airflow. It provided a benchmark for comparison of
forthcoming thesis designs, with respect to airflow separation producing profiles. Areas of
possible improvement over the existing paramotor may be the use of more vertical and less
horizontal tubing to improve the tubing cross sectional profile. Another option would be the
redesign of the fuel tank and surrounding area to reduce separation and interference drag. A
third option would be to turn the airbox silencer approximately o90 forward to quickly and
effectively improve the profile area or if time allowed other airbox solutions could be
explored.
4. EVALUATION OF A DUCTED FAN PARAMOTOR
Introduction
A ducted fan paramotor was evaluated as an alternative to a standard paramotor as it offers
the potential advantage of a lower frontal area. This will lower the S term in the drag
equation and therefore possibly reduce overall drag. There has been a ducted fan paramotor
in the past however it was not a success due to the excessive noise produced. A re-
examination of the feasibility of a ducted fan equipped paramotor will occur.
Ducted fan theory
The paramotor used to collect experimental data was an 80cc two stroke motor driving a
1.25m diameter caged open propeller, which produced 50kg of static thrust (as determined by
experimentation). This net thrust (F) due to change in momentum is shown as
30
( )j aF m C C= −& (Saravanamuttoo, 2001, p 100). Where m& is the mass flow of air through the
propeller, jC the velocity post rotor disk and aC the intake velocity. In the case of a ducted
propeller when the air pressure post propeller disk but still inside the duct is higher than the
ambient pressure there will be an additional pressure thrust on the duct over the exit area. In
this case the equation changes to include momentum and pressure thrust is shown as
( ) ( )j a j j aF m C C A p p= − + −& , where jA is the exit area of duct, jp the pressure at area of
duct and ap the intake air pressure (Saravanamuttoo, 2001, p 100). An analysis has to occur
to find out which is more efficient use, a high exhaust velocity or more mass flow by use of
the Froude or propulsive efficiency equation 2 [1 ( )]p j aC Cη = + − . The most efficient form
of propulsion has a higher jC compared to aC but the amount should not be by too much
(Saravanamuttoo, 2001, p 101). At the cruise velocity of approximately 10.5m/s the existing
large diameter open propeller efficiently moves a large mass flow at low speed. The ducted
fan moves a smaller mass flow at a higher velocity, so increased emphasis on efficient fan/
shroud design is essential to retain a reasonable propulsive efficiency.
A potential advantage of the low speed ducted fan is it can be smaller in rotor disk area than
an equivalent open propeller for the same propulsive efficiency (Barnard and Philpott, 1995,
p 159). This is achieved as the ducted fan acts as a shroud, allowing the blades to be able to
be uniformly loaded along their length thus having a higher disk loading. The unshrouded
propeller blade tips are less loaded due to span wise flow as a result of pressure inequalities.
The shape of the duct if correctly designed can develop a thrust component of its own
(McCormick, 1999, p 232). Early studies have found even greater improvements, ‘In the
static condition a shrouded propeller produces approximately twice as much thrust as an open
propeller’ (Platt, 1948, p 1). Platt reasoned that this is due to the fixed pitch open propeller
having a large part of its area where the blade is stalled creating less overall thrust. The fact
that this is measured in the static condition is very important; at a forward velocity this thrust
advantage for the same disk area is reduced.
A ducted fan could possibly reduce the frontal area of a paramotor, resulting in a reduction of
overall drag while in gliding flight. In other air propelled vehicles that operate up to 20m/s
such as the airship and the hovercraft the ducted fan or ducted propellers are a common
configuration. In the airship, a ducted propeller has the advantages of protection to the
ground crew when ground handling, protection to the propeller from trailing ground handling
31
lines, the use of acoustic liners to reduce external propeller noise and enhanced performance
through guide vanes to reduce swirl in heavily loaded propellers (Khoury and Gillet, 2004,
p 129). All of these advantages are equally relevant to a paramotor. A ducted fan is used in a
hovercraft for similar reasons to an airship, with the primary reason of reducing the risk to
personnel in close vicinity to the propeller. There is one critical area of difference to a
paramotor; both the airship and hovercraft do not have any design requirement to have low
drag in no power situations. For an airship, the propulsor volume is minimal compared to the
overall volume and drag is of minimal importance as it operates as a balloon with loss of
power. Even though there are inherent differences in operations, the design methods to
create hovercraft and airship propulsors should be applicable for the paramotor ducted fan
design.
‘If the duct is at an AoI not normal to the oncoming airflow the thrust generated by the duct
will not be uniform. This asymmetric flow causes greater lift to be generated by the
windward side of the duct than the lee side’ (Weir, 2004, p 421). This is due to the windward
side having a higher effective AoI and as a result creating more lift. A large pitching moment
is created by this asymmetric lift tending to align the duct with the oncoming airflow.
Inlet design will be critical for a ducted fan paramotor as the need for uniform inflow across
the rotor face will be critical to achieving a high propulsive efficiency. Large inefficiencies
exist at the intake position highlighted by the position of the duct in relation to the pilot (fig
28), as can be seen by the position of duct in relation to the pilot. This particular paramotor
only flew a few flights due to the high noise level in operation. This increased noise was
possibly due to a direct drive from the Solo 210 motor which caused high propeller tip
velocities or it could have been due to airflow separation at the inlet. An efficient intake
design for a pusher propeller is shown in figure 28. The Optica pictured was designed for
slow speed flight in place of a helicopter for reduced operating costs. One of its uses was
power line observation for preventative maintenance. Airflow separation can be reduced with
careful design of the intake nacelle. One method to achieve this is by using inlet stator vanes
that can pre-turn the air to remove axial swirl as well as screening out flow disturbances to
the rotor (Worobel and Mayo, 1973, p 14). Also, the use of inlet vane stators in a pusher prop
design can reduce the amount of noise produced over an open propeller with correct size and
spacing (Worobel and Mayo, 1973, p 9). Lost propulsive momentum can be regained by the
32
removal of swirl velocity post rotor. A method of achieving this is by adding inlet and/or
outlet guide vanes to change the airflow direction (Khoury and Gillet, 2004, p 114).
Figure 28. Left. Photograph of C. Bowles flying his ducted fan paramotor. It is the only ducted fan paramotor known by the author; the duct is a variation of the Q-Fan design (Bowles, 2004). Right. Photograph of a low speed observation aircraft the Edgley Optica which utilised a ducted propeller for its innovative design. Figure taken from http://upload.wikimedia.org/wikipedia/en/8/83/G-BGMW.jpg. taken 21 July 06.
It appears that most ducted fan designs for low speed flight utilise a diffuser after the rotor on
the inside of the duct. A reason for this is provided by Raspet, ‘If the velocity energy of the
flow can be recovered as pressure applied to the inclined inner wall of the diffuser, one can
gain in static thrust for the same power expended in the propeller’ (Raspet, 1960, p 8).
Computation fluid dynamic studies have also shown that the compromise of reducing post
rotor velocity to develop higher pressures on the diffuser shroud are worthwhile with ‘every
degree increase [in diffuser angle] is found to give about 1% power saving, and the power
saving comes from increased mass flow into the fan duct’ (Lee, 2004, p 5). However other
researchers have found that theory cannot be always practically applied. ‘Adding the diffuser
extension also slightly degrades the lift performance. This does not agree with linear invisid
flow theory which predicts an increase in lift with increasing exit area and is most likely due
to frictional losses and separation losses associated with an increased duct length’ (Weir,
2004, p 431). However using a diffuser post rotor disk has been identified as a critical
component in many studies, as Black states ‘Results show that the most powerful shrouded
propeller variable is shroud exit area ratio’ (Black et al., 1968, p 1). It would appear that as
long as the size of the duct does not increase to a point where it may affect cruise or glide
performance then a diffuser is essential.
No research has been found relating to the effect of gliding with a ducted fan. It would
appear that the reason for lack of information on glide effects of ducted fans is due to the use
of these devices in vertical lift machines and UAVs where an engine failure is critical and
glide angle is irrelevant. The Optica shown in figure 28 is listed as having a glide ratio of
13:1 (Anonymous, 2006) and therefore the possibility of the duct powered aircraft being
33
capable of glide is achievable, however wind tunnel testing is required to determine the full
effects on a paramotor.
Concept of a ducted fan paramotor
A basic study was conducted into the merits of a ducted fan paramotor. A basic concept was
drawn in AutoCAD as the basis for obtaining a first order approximation of weight, drag and
design of the duct inflow. The basic sketch is shown in figure 29.
Figure 29. Left. Concept sketch of a paramotor optimised for glide using a ducted fan (Author, 2006). Right. Concept sketch of a paramotor shown to scale with standard paramotor frame superimposed for comparison of frontal areas (Author, 2006).
The concept shown has a cutaway cross section for the duct (shown in yellow). It utilised
inlet guide vanes to provide pre-swirl also shown in yellow. The blue components illustrate
the fan from side on, while the red components are the existing power plant with drive shaft
extension. A brief analysis of the concept found the paramotor would weigh significantly
more than the existing paramotor due to the weight of the ducting and fan supports even if
constructed from advanced composites. The highly loaded propeller disk would possibly
consume more power than the existing power plant could supply. There was also high
possibility of inlet airflow separation occurring if a small frontal area was used on the duct. If
a bell mouth duct inlet arrangement was used to allow sufficient inflow to the fan then during
glide this would create excessive drag. At an AoI of 32o parts of the duct would be stalled
during glide creating large drag. As the negatives outweighed the potential benefits the
ducted fan concept was not pursued.
34
5. SCALE MODEL PARAMOTOR
Introduction
For accurate data from the wind tunnel testing the manufacture of a very accurate paraglider
model was required. Images taken during flight, and measurements from the experimental
paramotor were used to develop the model. The PAP 1400AS paramotor was then accurately
rendered in CATIA as it was envisaged that the low drag paramotor would be built in the
future. Plans were printed in 10% scale and the model was built ready for wind tunnel testing
Determination of the scale factor
The scale factor for the wind tunnel model is 10% of the full size paramotor. This was
determined based on ease of construction and the blockage factor in the low turbulence wind
tunnel. With the initial first order approximation that the paramotor is a non porous circular
disk in the y and z axes (where x axis isV∞ ) correlating to the outer diameter of the
paraglider frame, the wind tunnel blockage factor is 8.14%. This is within the recommended
range by (Pankhurst, 1952, p 341) who states ‘Chord should not normally exceed about one
third of tunnel height or about two thirds of the tunnel breadth. Span should not exceed 0.7 of
tunnel breadth’. Pope makes the point that ‘a maximum ratio of model frontal area to test
section cross-sectional area of 7.5% should probably be used, unless errors of several percent
can be accepted’ (Pope et al., 1984, p 371). In this experiment the paramotor cage will be
measured at an angle of inclination, as a result the circular disk will effectively become an
eclipse resulting in a lower frontal area. In addition to this the netting on the frame has a low
solidity ratio therefore an effective test section cross sectional area below 7.5% was obtained.
In order to reduce scale effect errors to a minimum, dynamic flow similarity must occur.
Anderson states ‘the two flows will be dynamically similar if: 1. The bodies and any other
solid boundaries are geometrically similar for both flows, and 2. The similarity parameters
are the same for both flows’ (Anderson, 2001, p 36). Therefore because the wind tunnel has
walls, the wake blockage factor must be determined (Pope et al., 1984, p 355). To fulfil
Pope’s requirements, the individual wake blockage factor was determined for each model
configuration.
Maintaining similarity parameters is more involved, Pope states, ‘If the flow cannot be
considered incompressible, the Mach number must be matched. Usually it is not necessary to
produce the full scale Reynolds number but it must be a reasonable value. …In an
35
unpressurised tunnel using air this means that the Reynolds number ratio of model to full size
is approximately equal to the scale ratio between the scale-model and the aircraft’ (Pope et
al., 1984, p 38). The basic experimental parameters are that the velocity of flight is 10.6m/s at
0m ASL on an ISA day, then the Mach number is 0.031. This is firmly in the realms of
incompressible flow therefore the Mach number does not have to be matched. The Reynolds
number of 980,000 is achieved when the paramotor is at the speed and altitude as stated
previously, while using a 1.5m chord (as measured from the pilot’s toes to the propeller). As
there is a 10% scale factor of the model, this equates to a scale factor of Reynolds number at
98,000 and a final wind speed velocity of 9.6m/s in the low turbulence wind tunnel
accounting for ISA conditions. These calculations are based on Pope’s methods.
Scale model of standard paramotor
During previous experimentation, inflight photography showed the standard paramotor with
manikin had to be mounted on the force balance from 0 to 32o AoI. Figure 18 became the
basis for the model with one minor change. During flight the pilot had to aim an infra red
device at the camera to trigger a shutter release. As a result the left hand forearm was always
moved forward in the photographs. The manufactured manikin had vertical forearms. After
measuring several figurines in toy shops for true life proportions it was decided that none
would be accurate enough for wind tunnel testing. Therefore the manikin selected was an
85% percentile male developed from the CATIA database. This accurately matched the
typical pilot specifications for the experimental paramotor. A screen print from CATIA was
used to manufacture the alloy manikin. This screen print was traced in AutoCAD 2000 then
converted to a MasterCAD file for the SACME wire cutter. The manikin was then cut out on
the x,y,z axes from a solid block of aluminium (fig 30), then manually sculptured using hand
tools to remove excess material for the finished figurine. The final product was sandblasted to
achieve a uniform surface finish.
Figure 30. Wind tunnel manikin at 10% scale after initial cuts on 3 axes by the SACME wirecutter from a solid block of aluminium alloy.
36
The experimental paramotor was disassembled to allow measurement. The bare frame was
placed onto a Cartesian coordinated grid and all frame junctions and bend radii were
measured and photographed. The engine, reduction gearbox, expansion chamber, silencer and
engine mounts were also disassembled and photographed from the x,y,z axes. The
photographs were printed into a booklet, and the measurements of all the components were
recorded on the photographs. This enabled an accurate scale model of the paramotor to be
built in CATIA. The accuracy of this rendering was very important as it is intended to build
and fly a low drag paramotor in the future and these images will form the basis for these
plans. Therefore an extended period of time was devoted to the CATIA model to ensure it
was adequate for post thesis uses.
From the CATIA, model plans at 10% scale were printed and used as the template for the
scale paramotor. The engine, reduction gearbox, inlet silencer, expansion chamber, fuel tank
and reserve were manufactured by hand tools from aluminium blocks. These were then
sandblasted to achieve a uniform surface finish. The frame was manufactured from 1.2mm
diameter hollow stainless tubing that was soldered at the joints. The netting was
manufactured from 0.11mm Dyneema fishing line with 5mm openings. The propeller was a
model aircraft propeller.
The force balance arm (fig 31) was built from 12mm diameter steel that was bent around
behind the model to limit interference effects. The arm was placed in a lathe to accurately
drill the angle pivot along the same axis as the force balance. The angle pivot allowed the
model to be secured at the desired AoI. A locknut was used to adjust the tension on the
propeller to allow it to either windmill or be fixed. During later testing the arm was faired.
Figure 31. Completed 10% scale model mounted to force balance in low turbulence wind tunnel, note during experimentation the propeller was vertical and this harness was a initial prototype, the final product was more accurate.
37
Low turbulence wind tunnel
The wind tunnel used during experimentation was the SACME low turbulence wind tunnel. It
has a range of test velocities from 5 to 35m/s. The velocity of the air in the test section was
measured by a pilot probe forward of the model. The model was mounted on the force
balance arm in the centre of the test section, which was calibrated before experimentation as
detailed in appendix I. An image of the low turbulence wind tunnel is shown in figure 32.
Figure 32. Low turbulence wind tunnel photographed from workstation. Model can be seen through window connected to the force balance. The analogue strain gauge signal is converted to a digital value then sent to the computer for processing by HP-Vee software.
6. WIND TUNNEL TESTING 6.1 CORRECTIONS AND CALCULATIONS
Introduction
The desired result of model wind tunnel experimentation is qualitative data to assess the
impact of configuration changes and the most useful term to express the results is drag area.
‘Flat plate drag area D
D C Sq= is useful in cases where an area of reference is not obvious
(such as, for instance, in the case of a motorcycle) or where several component parts are
combined in some system' (Hoerner , 1965, p 1-8). In order to calculate the flat plate area, S,
the frontal area of the model in m2 had to be found. D is the force recorded in Newtons by the
force balance, q the dynamic pressure of the oncoming airflow and DC the coefficient of
drag.
38
Calculations
Initial method of calculating frontal area
The method of determining frontal areas was initially calculated by using the screen print of
the paramotor model with pilot in CATIA for each attitude which ranged between 0 to 32o
AoI (appendix H). The area calculation tool in CATIA software could not be used because
the manikin could not be dimensioned in a CATIA rendering. Therefore a screen print was
placed into AutoCAD 2000 at the correct scale then redrawn in two dimensions. With this
second drawing the AutoCAD area calculator was used to find the areas of each component.
The tables in appendix H depict the individual breakdown of frontal area for each component
in the different configurations tested at each AoI.
The netting area was calculated by manually measuring each Dyneema line used in the
model. The total line length of 841mm was multiplied by the diameter of 0.11mm to find the
total surface area of the netting at 0o AoI. At 8o AoI it was recalculated at approximately 1%
less overall netting frontal area, therefore at each inclination change the frontal netting area
was reduced by 1%. An error exists where the individual knots used to tie each line were not
included in the frontal area.
Final method of calculating the frontal area.
The drag area results from initial experiments were of concern as the blockage factor was
calculated as if the paramotor maximum frontal area occurred in one plane. At high AoI this
excessive blockage factor was exaggerated. Therefore an alternative method of calculating
the blockage factor was suggested by the thesis supervisor, Mr Fien. This method was to
algebraically find the blockage factor. A sample calculation is shown in appendix H.
Once the drag area for the model was calculated using Excel, the drag area value for the force
balance arm at that velocity was subtracted. Due to the relocation of the SACME barometer
to the supersonic wind tunnel it was difficult to access to obtain the local atmospheric
pressure. During some experiments the local air pressure could not be obtained therefore all
differing configurations were tested against each other in a short period of time. A pressure
altimeter was used to indicate changes in pressure and temperature during each experiment.
However it could not be calibrated, therefore a baseline value could not be found. As a result
comparisons should only be made between results for each experiment, as opposed a
comparison of drag area values between experiments.
39
6.2 COMPONENT BREAKDOWN DUE TO DRAG – EXPERIMENT 1
Aims
This experiment fulfils the second requirement of the primary aims of the thesis project. The
aim was to complete low turbulence wind tunnel testing to determine the major contributors
to drag while in gliding flight of a conventional paramotor.
Introduction
Full scale glide testing was restricted to flying with a safe aircraft configuration. It was an
unacceptable risk to remove components before or during flight in order to determine their
drag contribution. Therefore a scale model in the low turbulence wind tunnel was substituted
for flight data. The scale model build development is shown in the previous chapter. In order
to obtain the drag data, wind tunnel experiments on scale models were undertaken on the
SACME low turbulence wind tunnel. Measurements were recorded using a force balance
with three axis of freedom, these being lift, drag and the pitching moment, with drag being
the area of primary concern.
Procedure
The 10% scale standard paramotor was tested in nine different configurations at 0, 8, 16, 24
and 32o AoI in the SACME low turbulence wind tunnel at velocities between 7 to 19 m/s. The
experiment began with the complete paramotor with force balance arm and pilot. The
configuration changes are shown in appendix J, figures J.2 to J.4.
Results and Calculations
Raw results are shown for each different configuration and AoI in appendix J.
In accordance with the Pope method ‘the Reynolds number ratio of model to full size is
approximately equal to the scale ratio between the scale model and the aircraft’ (Pope et al.,
1984, p 38). This calculation is shown in appendix J.
40
Drag Area Change by Removal of Paramotor Components at 0 Degrees AoI
0.000
0.001
0.002
0.003
0.004
0.005
1
Dra
g A
rea
in m
^2
1 Paramotor with pilot and propeller 2 Minus harness3 Minus propeller 4 Minus fuel tank 5 Minus netting 6 Minus reserve7 Minus cage 8 Minus powerplant
Figure 33. Graph showing the effects of drag area as a result of removal of individual paramotor components in sequence at 0o AoI.
Drag Area Change by Removal of Paramotor Components at 32 Degrees AoI
0.00000.00050.00100.00150.00200.00250.00300.0035
1
Dra
g A
rea
in m
^2
1 Paramotor with pilot and propeller 2 Minus harness3 Minus propeller 4 Minus fuel tank5 Minus netting 6 Minus reserve7 Minus cage 8 Minus powerplant
Figure 34. Graph showing the effects of drag area as a result of removal of individual paramotor components in sequence at 32o AoI.
Discussion
This experiment achieved the aim of determining the contributions of the components to total
drag of a standard paramotor. However, due to Reynolds numbers effects at different
velocities there is a difference in the drag area recorded. An example of this is shown in
appendix J, fig J.15 where the Reynolds numbers are shown along the x axis instead of the 7
to 19m/s velocity.
It can be seen that there is a substantial rise in drag area in the vicinity of Re = 120,000. This
is caused by the variation of cylinder's drag coefficient with Reynolds number (fig 35). As a
result the tables shown in appendix J use an average force balance drag area of 0.003m2
subtracted from the values to remove the effects of the force balance bar. All subsequent
41
wind tunnel testing was completed from the velocity of 5 to 30m/s which is the upper limit of
the wind tunnel.
Figure 35. Variation of drag coefficient for a cylinder at various Reynolds numbers (Anderson, 2001, p. 257). This experiment found a well defined breakdown of drag area for all components. From 0 to
32o AoI there was minimal difference in drag area whether the model was fitted with a
harness or vertical propeller, the result was the same as the full model. This signified that a
feathering, hinged or folding propeller would not increase the glide ratio for a standard
paramotor. The fuel tank which was sourced from a go-kart was not aerodynamically
optimised and resulted in a component of drag that reduced as AoI increased. The netting was
a minor contributor to drag. The reserve parachute container appeared to have a detrimental
effect at 0o AoI but became advantageous at 32o AoI. This could be due to the reserve
parachute container acting as a splitter plate type device and reducing the vortex street off the
pilot’s neck and head. Vortex street which occurs at certain Reynolds numbers (fig 36). The
frame of the paramotor was the largest drag contributor; the round section tubing creates
considerable drag. The power plant created a minimal increase in drag area; this would
possibly be due to the intake silencer and expansion chamber protruding outside the pilot’s
silhouette. This drag area was smaller than expected and could possibly be due to the engine
stopping the vortex street and thus reducing drag.
Figure 36. Theoretical pattern of vortex street behind a circular object with Reynolds numbers from 104 to 105
(Hoerner, 1965, 8-9).
42
Conclusion
This experiment determined the major contributors to drag while in gliding flight of a
conventional paramotor and was performed at a reduced scale in a wind tunnel because of the
unacceptable risk of removing components before or during flight. The experiment found a
well-defined drag area breakdown of components and was able to identify the main drag
contributors. The order of importance in reducing the drag area of a standard paramotor
would be a redesign of the frame, netting and fuel tank. More experimentation is needed to
determine the interaction between the reserve parachute container and the pilot.
6.3 EFFECT OF FUEL TANK PLACEMENT ON TOTAL DRAG AREA
Aims
Investigate the difference on overall drag area at varying angles of attack on a 10% scale
paramotor model when:
(1) Standard 10 litre fuel tank is used.
(2) Streamlined 10 litre fuel tank.
(3) Two 5 litre Jerry can fuel tanks are placed either side of the pilot.
(4) Two 5 litre Jerry can fuel tanks with a basic fairing over pilot and tanks.
Introduction
The placement of the standard fuel tank on the PAP1400 paramotor appears to be a major
contributor to drag (appendix J). As a result, 4 differing configurations of fuel tank placement
were tested in order to find the lowest drag. The first was the standard 10 litre tank
commonly used on paramotors. The second tank tested was a NACA0025 aerofoil profile
tank cut off at 40% chord and installed in place of the standard fuel tank. The NACA profile
was set at 30o AoI to vertical to be most efficient at glide AoI. This tank was designed to
have a capacity of 10 litres and the aft of the tank was cut off to shroud the lower blade of the
propeller to possibly reduce drag. The third fuel tank tested was based on a design by G.
Sutherland and involved twin 5 litre fuel tanks one either side of the pilot (fig 37). This
design was tested to determine the effect on drag created by the paramotor. The fourth
configuration tested is similar to the third fuel tank tested, but with a simple fairing made out
of plaster in an attempt to reduce the drag ratio. Photographs of all fuel tank configurations
are shown in appendix K.
43
Figure 37. Twin 5 litre fuel tank set up on paramotor designed by G Sutherland.
Procedure
The experiment was conducted as per chapter 6.2 with the exception that the range of test
velocity was extended from 5 to 30 m/s.
Results and Calculations
Raw data and initial calculations including frontal areas are shown in appendix K. Frontal
area results have been included in the appendix however final calculations were done in
conjunction with appendix H.
Between 15 to 30m/s at varying AoI the results show the standard tank, faired and unfaired
Jerry cans are the worst performers (fig 38) This may be due to the Jerry cans having a
defined sharp edge on the lower surfaces which would increase flow separation at that point.
Rebuilding the model with higher tanks and greater plaster fairing around the lower surfaces
to reduce flow separation was considered, however due to the poor 0o AoI results it was not
pursued in the aim of creating larger drag area reductions elsewhere. The lowest drag area
from this test was the NACA0025 tank cut off at 60% chord.
Drag Area of Different Paramotor Fuel Tanks
0.000
0.001
0.002
0.003
0.004
0.005
0.006
1
Dra
g A
rea
in m
^2
0 Deg AoI, Standard Fuel Tank 0 Deg AoI, Side Jerry Cans0 Deg AoI, Faired Side Jerry Cans 0 Deg AoI, NACA Profile Fuel Tank32 Deg AoI, Standard Fuel Tank 32 Deg AoI, Side Jerry Cans32 Deg AoI, Faired Side Jerry Cans 32 Deg AoI, NACA Profile Fuel Tank
Figure 38. Drag area as a result of fuel tank placement at varying AoI.
Fuel Tanks
44
Discussion
The experiment results show that the fuel tank can be beneficial in lowering the drag area at
both 0 and 32o AoI. At 0o AoI there was a larger spread in results in the area of interest
ranging from 15 to 30m/s. Surprisingly, both the faired and unfaired Jerry cans were the
highest drag areas; this is not due to the propeller becoming unshrouded as the no fuel tank
configuration was one of the lower drag performers in the area of interest. The faired Jerry
can configuration was optimised toward 0o AoI due to the plaster design forming a gentle
transition in frontal area from the knees to tank location. In the area of interest the other three
configurations (standard, NACA0025 cut off at 60% and no tank) are similar in achieving
lower drag area results. Out of these three the NACA profile appears most promising; it may
also be better under power as it could allow more inflow to the propeller disk.
Conclusion
This experiment sought to determine the most efficient position of the fuel tank in terms of
location and shape at varying AoI. Five different configurations were tested including the
option of no fuel tank. This was done to assess the fuel tank propeller interactions. The 5 litre
Jerry can tanks on each side of the pilot was proved to be most inefficient at all angles of
attack tested, however the standard tank recorded the worse result at 32o AoI. The
NACA0025 tank cut off at 60% chord was the most promising with lower drag area results
recorded; this could possibly be further improved by a redesign of the base of the tank.
6.4 DRAG AREA VARIATION CAUSED BY REMOVAL OF PROPELLER AND RESERVE PARACHUTE
Aims
(1) To quantitatively assess the effect on the overall drag area of a paramotor by
removal of the propeller and reserve parachute.
(2) To gain further understanding of the relationship of overall drag reduction caused
by the existing location of the reserve parachute container.
(3) To gain further understanding of propeller drag to determine whether investigation
into feathering or folding propellers is warranted.
45
Introduction
This wind tunnel experimentation was conducted to find the effect of the change in total drag
area by removal of the propeller and reserve parachute. The removal of each item was
assessed separately. The intent was to ascertain whether earlier test results were correct in
that the reserve was a beneficial item as it lowers the drag area at 32o AoI. The tests were
conducted with the paramotor model using two 5 litre fuel tanks and a basic fairing over the
tanks.
Procedure
The experiment was conducted as per chapter 6.2 with the exception that the range of test
velocity was extended from 5 to 30 m/s. The previous experimentation shown in chapter
measured the drag forces of the model at varying velocities and AoI. This was used as the
base line data for comparison for this experiment. The model was then tested at 0 and 32o
AoI with the propeller removed (fig 39). The propeller was then replaced in the fixed vertical
position and the reserve parachute container removed. The model with the reserve container
removed was measured in the wind tunnel at 0 and 32o AoI.
Figure 39. Side view of model mounted on force balance at 0o AoI. The reserve parachute container is indicated by the red arrow.
The model was then reconfigured to the standard paramotor configuration and a solution of
titanium dioxide (TiO2), kerosene and olive oil was applied. The wind tunnel containing the
model was operated at 32o AoI with a velocity of 20m/s. The resulting flow patterns were
analysed in the vicinity of the pilot’s head and reserve parachute container in order to
understand local airflow.
Results and Calculations
Raw wind tunnel data is shown in appendix L. All calculations were done as per chapter 6.2,
final results are displayed in figure 40.
Reserve Parachute container
46
Figure 40. Showing the drag area of the model for various configurations in the wind tunnel.
Discussion
This experiment confirmed the results of the earlier experiment (Chap 6.2) in that the reserve
parachute container is beneficial in reducing the drag area at high AoI. The use of TiO2
solution indicated that further improvement may occur if the reserve container is mounted
vertically rather than the current horizontal location (appendix L). It is possible this may
reattach airflow from the top of the pilot’s head and therefore gain a reduced drag. An
example of this is shown in relation to two circular cylinders (fig 41).
Figure 41. Drag coefficients of two cylinders, one placed behind the other (Hoerner, 1965, p. 8-1).
The propeller was found to create additional drag during this experiment. This is contrary to
earlier experimentation and is due to the change of the fuel tank position to either side of the
pilot. This left the propeller unshrouded, and resulted in the propeller having a greater
contribution to the overall drag area.
Drag Area of Standard Paramotor with Jerry Can Fuel Tanks Covered with Basic Fairing
0.00000.00050.00100.00150.00200.00250.00300.00350.0040
1
Dra
g A
rea
in m
^2
0 Deg AoI, Standard 0 Deg AoI,No Propeller0 Deg AoI, No Reserve Container 32Deg AoI, Standard32 Deg AoI, No Propeller 32 Deg AoI, No Reserve Container
47
Conclusion
This wind tunnel experimentation was conducted to find the effect of the change in total drag
area by removal of the propeller and reserve parachute. The intent was to ascertain whether
earlier test results were correct in proving that the reserve is a beneficial item in lowering the
drag area at 32o AoI. This experiment was successful in proving the reserve container is
mildly beneficial at high AoI, however further experimentation has to occur to determine if a
vertical container would provide greater benefits. Due to fuel tank repositioning, it was found
that unshrouding the propeller created more drag. Potential benefits from fuel tank
positioning may have been reduced by the interaction of the propeller. Further
experimentation is required to prove this.
6.5 COMPONENT BREAKDOWN DUE TO DRAG – EXPERIMENT 2
Aims
To gain a greater understanding of the major drag contributors in a standard paramotor at
10% scale and varying angles of attack by investigating:
(1) The effect of single component removal.
(2) The relations between components as a result of interference drag.
(3) Whether the reserve parachute container turned at 90o to the airflow would reduce
overall flat plate drag area.
Introduction
Component breakdown due to drag in experiment 1 was successful; however it may have
produced misleading results due to the fact that the items were removed in series. This series
could produce dramatically different drag area results if the order was changed. To correct
this potential source of error a further experiment was necessary to individually remove each
item for drag testing, followed by replacement prior to testing of the next item.
Procedure
This experiment was conducted in the same manner as experiment 1, with the following
exceptions: velocity was measured between 5 to 30m/s and only one component was
removed at a time. After data was recorded the component was replaced on the model before
a different component was removed for testing.
48
Results and Calculations
Results are shown in appendix M. All calculations were done as per chapter 6.2. Final results are displayed in figures 42 - 43.
Drag Area of Individual Paramotor Components at 0 Degrees AoI
0.000
0.001
0.002
0.003
0.004
0.005
0.006
1
Dra
g Ar
ea in
m^2
Full Configuration No Reserve No MotorNo Intake No Propeller No TankNo Cage No Net No Net, No Tank
Figure 42. Drag area results for standard paramotor at 0o AoI.
Drag Area of Individual Paramotor Components at 32 Degrees AoI
0.00000.00050.00100.00150.00200.00250.00300.00350.0040
1
Dra
g A
rea
in m
^2
Full Configuration No Reserve No MotorNo Intake No Propeller No TankNo Cage No Net No Net, No Tank
Figure 43. Drag area results for standard paramotor at 32o AoI.
Discussion
With individual components being removed, tested, then refitted there are differences in
results with experiment 1 due to the change in procedure. At 0o AoI there was little difference
in drag area effects of the removal of the reserve, motor or intake silencer. The propeller and
the netting created a larger drag area than shown in experiment 1. However, the most
significant drag contributor was the frame of the paramotor.
The results of the testing at 32o AoI was similar to 0o AoI, however the propeller did not
create any significant extra drag when fixed vertically. The tank created less drag than
recorded in experiment 1 at 32o AoI, therefore there may not be as much emphasis on
49
redesigning as previously concluded. The area of interest in this experiment was with the
frame of the paramotor; when it was removed at 32o AoI, the drag area dropped by 50%.
Conclusion
The experiment sought to gain further understanding of the effects of single component
removal on a paramotor. A greater understanding of the interference drag between
components was also sought. It was found that at varying AoI the reserve parachute
container, motor or propeller individually had little effect on the drag recorded. At varying
angles of attack the netting was a major contributor to drag, however more significant results
were recorded with the paramotor frame. Further design work on the frame would need to be
undertaken to reduce drag.
6.6 TESTING OF ANNULAR AEROFOILS
Aims
The aims of this experiment were:
1. To determine if a lower drag paramotor frame can be designed that provides
equivalent pilot protection as the standard frame.
2. To determine if a twisted annular aerofoil recorded lower drag at both 0 and 320
AoI.
Introduction
From the data obtained from experiments 1 and 2, the component breakdown due to drag
conclude that the paramotor frame was the largest individual drag contributor. In this
experiment the aim was to test the standard cage against two annular aerofoils in search of a
drag reduction. One annular aerofoil had the chord in line with V∞ at the paramotor 0o AoI.
The other has an elliptical profile so that when the paramotor is at 0o AoI the chord of the
aerofoil at top/bottom dead centre is at 30 o AoA. At 32o AoI the chord of the aerofoil is
effectively at 0 o AoA.
Procedure
A lower drag paramotor frame is virtually useless if it does not adequately protect the pilot in
case of a mishap. Therefore, before the frame could be redesigned, a basic understanding of
the design loads encountered have to be clarified (appendix P). The standard paramotor was
50
drawn in CATIA with the frame and fuel tank hidden from view. This provided a scaled
pilot, power plant and propeller that could be utilised for concept sketching. After multiple
ideas were considered, such as using fuel in the frame, streamline grids and other concepts,
an annular aerofoil at 30o AoI was chosen as the most practicable. This was then drawn to
scale in CATIA (appendix P).
A symmetrical NACA0025 aerofoil was chosen with a 150mm chord because it could hold
two chrome molybdenum tubes. A second standard annular aerofoil was made to the same
profile and dimensions for comparison to determine whether the extra effort of the twisted
annular aerofoil was worth while in terms of drag reduction. The annular aerofoils were made
by the author by turning down a mild steel bar to a tube of 138mm ID, 142mm OD. A piece
of 15mm wide tubing was cut off at 90o, with another piece 15mm wide cut off at 30o
(appendix N). A NACA0025 aerofoil template with 15mm chord was made up out of 0.054"
stainless steel sheet and the cut off sections were made into annular aerofoils using hand
tools. Once the approximate shape had been manufactured, spray putty was applied and the
surface built up between sanding to obtain an accurate profile. The frame central members
were soldered in place and the model painted. It was not sandblasted as a high standard of
surface finish was desired to match the polished stainless steel tubing of the standard
paramotor model. The NACA fuel tank from earlier experiments was fitted to the models.
The six model configurations are shown in figures 44 to 46. The models were tested with and
without the fuel tank, standard cage without netting and both types of annular aerofoil at
velocities between 5 to 30m/s. Throughout this thesis the assumption has been made that at 32o AoI a fixed vertical propeller
has the lowest drag. To test this assumption, at the end of the experiment, data was recorded
with the propeller at 45o and horizontal.
Figure 44. Left. Image of standard paramotor, minus netting and NACA0025 fuel tank at 0o AoI. Centre. Image of annular aerofoil, minus netting and NACA0025 fuel tank at 0o AoI. Right. Image of twisted annular aerofoil, minus netting and NACA0025 fuel tank at 0o AoI.
51
Figure 45. Left. Image of standard paramotor, minus netting and NACA0025 fuel tank at 32o AoI. Centre. Image of annular aerofoil, minus netting and NACA0025 fuel tank at 32o AoI. Right. Image of twisted annular aerofoil, minus netting and NACA0025 fuel tank at 32o AoI.
Figure 46. Left. Image of twisted annular aerofoil, with vertical propeller. Centre. Image of twisted annular aerofoil, with 45o propeller. Right. Image of twisted annular aerofoil, with horizontal propeller.
Results and Calculations
Raw results are listed in appendix N. All calculations were done as per chapter 6.2. Final
results are displayed in graphs 47 and 48.
Drag Area for Different Frame Configurations at Various Degrees AoI
0.0000.0010.0020.0030.0040.0050.006
1Differing Configurations
Dra
g A
rea
in m
^2
0 Deg AoI, Standard Paramotor0 Deg AoI,Annular Aerofoil0 Deg AoI, Twisted Annular Airfoil32 Deg AoI, Standard Paramotor32 Deg AoI, Annular Aerofoil32 Deg AoI, Twisted Annular Aerofoil32 Deg AoI, Twisted Annular Aerofoil, with No Fuel Tank
Figure 47. Summary of data of different frames at various degrees AoI. Note netting not fitted to any
configuration.
52
Drag Area for Different Propeller Positions at 32 Degrees AoI
0.000
0.001
0.002
0.003
0.004
1
Differing Configurations
Dra
g A
rea
in m
^2
32 Deg AoI, Twisted Annular Aerofoil, with No Fuel Tank
Twisted Annular Aerofoil, 45 Degree Propeller, with No FuelT k
Figure 48. Drag areas of different propeller positions at 32o AoI. Note netting not fitted to any configuration.
Discussion
If the paramotor was only to fly at 0o then the standard annular aerofoil is clearly the most
efficient. However, this expectation is unrealistic. The 30o (twisted) annular aerofoil obtains
similar figures to the standard paramotor. At 32o AoI the results are more spread however the
twisted annular aerofoil gives an average 13% drag reduction with fuel tank and a 22%
reduction with no fuel tank. This decrease is very significant and also shows that the fuel tank
is still an inefficient design not optimised for the annular aerofoils (fig 49). The experiment
used the same tank between differing configurations to reduce error, therefore on the twisted
annular aerofoil because of the separation distance between the aerofoil and the base of the
tank, potentially greater losses occurred. Also there was an experimental error, as the chord
of the propeller was not accurately 10% of full size; this is significant as the NACA0025 was
created in CATIA to suit the full scale propeller. As such when placed on the model the
chord was wider than the trailing edge of the tank. There is a possibility that if corrected the
NACA tank could provide greater gains at 0 and 32o AoI. The assumption that a vertical
propeller at 32o AoI produced the least drag was correct (fig 49).
Figure 49 Left. The red arrow shows potential loss point on the 30o annular aerofoil at 32o AoI. Right. Frontal view of 30o annular aerofoil at 32o AoI, note aerofoil is efficiently moving through air at approximately 0o AoI. The red arrow shows the site of potential drag losses due to poorly designed tank base.
53
Conclusion
This experiment sought to determine the most efficient type of paramotor frame with respect
to reducing drag area. At 0o AoI it was found that the standard annular aerofoil was most
efficient, with the twisted annular aerofoil producing similar drag to a standard paramotor. At
32o AoI, the twisted annular aerofoil was found to be superior. At 32o AoI, there was an
average 13% on drag reduction with the fuel tank and a 22% reduction with no fuel tank.
This could possibly be improved by a redesign of the base of the tank. After this redesign
further experimentation with the correct scale propeller fitted should be done. The vertical
propeller at 32o AoI creates lower drag than at 45o or horizontal.
6.7 USE OF FAIRED FORCE BALANCE ARM
Aims
The aims of this experiment were:
(1) To determine if the unfaired force balance arm used in previous experiments was
creating error in drag area values.
(2) To determine if the modifications to NACA fuel tank on twisted annular aerofoil
produced less drag.
(3) To determine if propeller at correct chord affects the test results.
Introduction
In an attempt to reduce the Reynolds number effects on the wind tunnel model the force
balance arm was faired. Similar model configurations were tested in chapter 6.6, with the
design differences of the twisted annular aerofoil having a silicone fillet to blend the base of
the tank to the aerofoil. The propeller was also modified to remove the previous experimental
error. The chord of the propeller was reduced to enable dynamic flow similarity to a full scale
paramotor.
Procedure
The procedure was similar to chapter 6.6, with the following differences:
1. A symmetrical aerofoil constructed from balsa wood was bonded to the existing
force balance arm. The profile was based on a NACA0020 aerofoil (fig 50).
54
2. The NACA fuel tank attached to paramotor model was moved 5mm downwards and
rebonded to the frame. The base of the tank was filleted to the annular aerofoil to
approximately 5mm radius by use of silicone. Another test was conducted with a
domed fairing placed on the tank in an attempt to reduce drag.
3. The model’s propeller chord was reduced to 10% scale.
4. Due to the lower drag created by the modified force balance arm the wind tunnel
velocity was able to be increased to 35m/s during testing while still remaining under
the 50 Amp limit imposed on the wind tunnel fan motor.
Figure 50. Left. The NACA0020 fairing fitted to the force balance arm can be seen at the right hand side of the image, with the base of the fuel tank filleted to the annular aerofoil. Right. Same model, with addition of a silicone mound to the top of the fuel tank.
Results and Calculations
Raw results are listed in appendix O. All calculations were done as per chapter 6. Final
results are displayed in figure 51.
Drag Area Comparision with Faired Force Balance Arm
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
1
Dra
g A
rea
in m
^2
0 Deg AoI Standard Paramotor0 Deg AoI, Twisted Annular Aerofoil with NACA Fuel Tank0 Deg AoI, Twisted Annular Aerofoil with No Fuel Tank32 Deg AoI Standard Paramotor32 Deg AoI, Twisted Annular Aerofoil with NACA Fuel Tank32 Deg AoI, Twisted Annular Aerofoil with No Fuel Tank
Figure 51. Drag areas of different paramotor frames at various AoI. Note netting not fitted to any configuration.
55
Discussion
This experiment produced similar results to the experiment in chapter 6.6. The difference
being that during previous experimentation the force balance arm was over accounted for in
drag area. With the faired balance arm drag area values for the paramotor increased. This
meant instead of a 20% reduction in drag obtained in previous experiment, approximately
11% reduction in drag was obtained.
Effectively no difference in drag area was measured between having a fuel tank fitted and
removed. The filleting of the bottom of the tank to the twisted annular aerofoil reduced the
drag area. This was expected as shown in figure 52. No difference in drag area was recorded
with addition of a fairing on top of the fuel tank.
Figure 52. Influence of fairings on interference drag at the junction of two struts (Hoerner, 1965, p. 8-13).
It is difficult to determine if the reduction in propeller chord had any effect. This is due to
three changes being made at the same time (chord reduction, filleting of tank and force
balance arm fairing). It may have had a slight effect on making the fuel tank configuration
more efficient.
The coefficient of drag for all configurations is almost identical at approximately 1.0 between
20 to 35 m/s.
Conclusion
This experiment was successful as it determined that the unfaired force balance arm was
creating an error. The removal of this experimental error showed that overall drag area was
higher than previous calculations. Therefore drag reductions gained were only half the
percentage previously determined. The filleting of the base of the NACA profile fuel tank
56
was successful in the reduction of the drag area, but it is difficult to determine if the reduction
of the chord of the propeller created a lower drag area.
7. REDUCTION IN DRAG AREA BY CHANGE OF NETTING CONFIGURATION
Aims
(1) To determine the contribution to drag caused by the netting in a standard paramotor.
(2) To evaluate other forms of protection from the propeller.
(3) To determine if design change is worthwhile.
Introduction
The conventional paramotor has shortcomings relating to drag and this may be overcome by
alternative designs. This chapter will explore the drag currently produced by the netting and
evaluate alternatives.
The netting on a paramotor cage performs a critical safety task, which is the separation of the
pilot from the propeller. A paramotor is started by the pilot facing the motor, bracing
themselves against the frame with the throttle and recoil starter in either hand. According to
incident reports (USPPG, 2006), a significant number of accidents occur at this stage. A
starting incident may occur when the pilot inadvertently places their hand against the mesh to
hold the propeller away from the body, perhaps in response to the motor being at full throttle
or the pilot’s hand being in a position where the thrust of the paramotor results in an
increased application of the throttle. There are several instances where the netting and/or
frame have deformed to the point where the hand was struck by the propeller causing injury.
Background
Netting Drag on Standard Paramotor
The initial stage of this task was to measure the drag of the netting on a standard paramotor.
This was achieved using a scaled model of a paramotor in the wind tunnel and adopting the
same procedure as chapter 6.2. Refer to this chapter for the method and calculations (Table
53).
57
Table 53. The drag area effects of removal of netting at 0o and 32o AoI of a standard paramotor. Effect of Netting Removal on Drag Area of a Standard Paramotor at varying AoI
Average drag area value for 15 to 30m/s in m^2
Percent difference as a result of netting removal
32o AoI, Standard Paramotor 0.0037
32o AoI, No Netting 0.0032 13.9%
0o AoI, Standard Paramotor 0.0054
0o AoI, No Netting 0.0044 17.6%
At the velocity of 15 to 30m/s when Reynolds numbers effects have been minimalised, at 0o
AoI the removal of netting causes a significant reduction in the drag area of a standard
paramotor. At 32o AoI the reduction in drag area is also considerable.
Calculations
Theoretical Drag
The Borda equations (Hoerner, 1965, p. 3-24), used to calculate the drag of permeable
surfaces, were used for the calculations of drag on the netting of the full scale paramotor. The
final drag value was unrealistically low at 0.26 N, due to the low solidity ratio of 0.048 using
a 1.2mm diameter line with 50mm square spacing. To obtain a realistic figure, the drag
equation DD C qS= was used. The flight velocity of the paramotor at half accelerated flight
is approximately 12.5m/s. At this speed the Reynolds number for 1.2mm diameter line is
1027. The variation of cylinder drag coefficient with Reynolds number is shown in figure 54.
At this Reynolds number the coefficient of drag is approximately 1.0. Assuming a 21.1m net
the drag force created is 5.06 N.
Figure 54. Variation of cylinder drag coefficient with Reynolds number (Anderson, 2001, p. 257).
58
Discussion
Alternatives to existing netting
Some alternatives to the netting used in the standard paramotor have been based on the use of
a streamline grid or low drag netting. At present an alternative design that doesn’t use netting
or structural elements to prevent contact with the propeller is unknown. An example of a
cageless paramotor for soaring and a design without netting are shown (fig 55). Both designs
compromise safety for a potentially better glide ratio. The larger openings in the no-netting
design have caused problems during hands-free flight when the paraglider brake toggles
come in contact with the propeller during turbulent air (Parajet, 2006), resulting in a higher
possibility of the brake toggles becoming wrapped around rotating components causing
paraglider collapse. Therefore, designs that do not offer equivalent protection to the standard
paramotor have been rejected.
Figure 55. Left. Example of cageless paramotor with folding propeller, weighing a total of 12 kg (Deplanche, 2004). Right. Example of a no-netting frame (Parajet, 2006). Streamline grids have a much smaller loss coefficient than a round wire grid (or netting) up
to a solidity ratio of 0.5 (Hoerner, 1965, p. 3-23), resulting in the reduction of drag. The use
of vertical streamline members in the frame construction of a paramotor to prevent contact
with the propeller has the potential to reduce drag over the 0o to 30o AoI. This method has not
been explored due the potential cost of making high strength low weight streamline sections.
A powered paraglider is a cost sensitive aircraft; one of the appeals of it is the low entry cost
to flying. If the price increased significantly this form of recreational aviation would become
less attractive to the potential pilot.
The cheapest method of obtaining low drag netting is by using advanced materials with
superior tensile strength enabling a smaller diameter netting to be used with no loss in
59
strength. Dyneema (Ultra High Molecular Weight Polyethylene) is a prime example of such a
material (fig 56). It has been used for trawling as it ‘is much stronger than nylon (the more
conventional material for trawling nets) and the twines only need to be 55% of the diameter.
This reduces the drag on the net by about 40%, resulting in a substantial increase in
efficiency’ (Onbekend, 2005, p. 1). It is also becoming widely used for recreational fishing
due to the low density (0.97g/cm3) and minimal elongation of 5% for braided fishing line
(DSM Dyneema, 2006). Early braided lines were made from Kevlar (which breaks down
under UV light), whereas current braided lines made of Dyneema are unaffected by UV light
(Australian Monofil Co Pty Ltd, 2006, pers. comm., 25 Aug.). Due to the reduction in
diameter and the lack of stretch, the potential of Dyneema to lacerate the pilot upon impact is
greater, but this must be determined by further experimentation.
Figure 56. High level strength to tensile modulus against other materials. The existing polyester nylon netting
material can be seen in the lower left corner (DSM Dyneema, 2006).
The current netting material on the standard paramotor is unknown. Assuming that the
material is braided nylon, for high quality 1.2mm diameter twine of Du Pont type 66-728, the
breaking strain is 119lbs (Duratech netting, 2006, p.1). An equivalent breaking strain in
braided Dyneema fishing line is approximately 0.5mm diameter (DSM Dyneema, 2006). A
sample calculation for calculating the drag on a 0.5mm diameter Dyneema netting is in
appendix N. This shows for a reduction in line diameter by approximately half, there is a
60% reduction in drag at accelerated glide velocity.
In the current paramotor, the elongation of the nylon twine is approximately 30% (DuPont,
2006); the netting is prestretched on the frame by an undetermined amount. As Dyneema has
5% elongation before yield (DSM Dyneema, 2006), this could possibly enhance the safety
60
level by increasing the distance between the netting and propeller under applied load due to
the lack of stretch.
Method of netting attachment
The standard paramotor has the netting attached to the frame by means of zip ties at
approximately 50mm intervals. These zip ties increase interference drag and have a higher
possibility of snagging suspension lines during launch. An alternative method of fastening the
netting is to drill small diameter holes in the forward face of the main frame hoop. Lengths of
Dyneema line could then be threaded through the holes with a soft ferrule to protect against
abrasion. The lines are then knotted by hand with the use of a wooden block to ensure
consistency in the size and quality control of the netting, and joined to the centre of the frame
by a tensioning device. This method of netting construction could be used to increase the
torsional rigidity of the outer frame due to the minimal elongation of the Dyneema. This has
not yet been tested by analysis.
Conclusion
With a standard paramotor the netting drag is a major contributor to a reduction in glide ratio;
therefore design improvements are worth pursuing. Alternative designs may be
advantageous because they have reduced drag area, but because pilot protection from the
propeller is compromised these designs were not considered. The streamline grid design has
potential but present cost considerations rule it out. The use of an advanced material in the
netting such as Dyneema, which offers reduced weight, a potential reduction in drag of 60%
and reduced elongation under load, safety is improved and the netting contributes to the
overall structural integrity. The disadvantage of this design is the potential to cause injury
during impact due to the small diameter and lack of elongation of the netting. Further
experimentation on a full scale frame needs to occur with impact testing, to ensure safety of
proposed Dyneema netting, before a design change can be recommended.
61
8. CONCLUSION There were four basic aims to investigate the feasibility of the reduction of drag of a
paramotor to increase the lift to drag (L/D) ratio in gliding flight.
The first aim of the thesis was to obtain experimental results of lift to drag ratio and surface
airflow visualisation of a typical paramotor while gliding. This aim was successfully
executed, with the design and construction of camera mounts and propeller brake, to facilitate
the collection of lift to drag ratios when gliding at trim and accelerated velocities, and with
the propeller windmilling and vertically braked. Previously published glide ratio results with
a windmilling propeller were found to be incorrect, with no change in a windmilling and 120
rpm propeller found on glide angle when at 32o AoI. Surface airflow visualisation was also
conducted to obtain a greater understanding of airflow over the paramotor and pilot.
The subsequent aim of the wind tunnel testing was completed to determine the major drag
contributors to drag of a standard paramotor while in gliding flight. Measurements taken at 0,
8, 16, 24 and 32o AoI would be of benefit to high and low hook-in paramotors. Experiments
showed that there is a 27% reduction in drag area when a low hook-in paramotor’s AoI
changes from 0 to 32o during accelerated glide. At various AoI, the most significant
individual contributors to drag area were the frame and netting. The reserve parachute
container, motor and propeller individually had little effect on the drag recorded. A folding
propeller would have no benefit if the standard frame and netting was retained.
The third aim involved the further wind tunnel testing and redesigning of high drag area
components. This was conducted with the majority of effort placed on the paramotor, frame,
netting, fuel tank and reserve. Each of the components was replaced with alternatives which
produced less drag, but retained full functionality.
The final aim was the testing for reduction of drag of the revised paramotor design.
Repeatable experiments found over 10% reduction in drag area at 32o AoI, the glide ratio
would therefore improve (fig 57). These results do not include the 60% reduction in drag
obtained by use of advanced netting materials. There is a calculated reduction in drag area
from 0.0040m2 for a 32o AoI standard paramotor to0.0033m2 for a 32o AoI twisted annular
aerofoil paramotor when netting is included, effectively a 17% reduction in drag area. At 0o
AoI the paramotor would be creating thrust therefore drag at this AoI is less relevant.
62
Drag Area Comparison at Varying Degrees AoI
0.00000.00100.00200.00300.00400.00500.0060
1
Ave
rage
Dra
g A
rea
in m
^2
0 Deg AoI Standard Paramotor0 Deg AoI,Twisted Annular Aerofoil with NACA Fuel Tank32 Deg AoI Standard Paramotor32 Deg AoI,Twisted Annular Aerofoil with NACA Fuel Tank32 Deg AoI Standard Paramotor with netting32 Deg AoI, Twisted Annular Aerofoil with Dyneema Netting
Figure 57. Comparison of drag area results, experimental error is shown at top of column.
The drag reduction obtained is less than desired. The proposed design is shown in appendix
P, however unless the current paramotor frame is destroyed it will not be built in the near
future. It is more cost effective to remove the existing netting, replace it with smaller
diameter Dyneema netting and create a small but worthwhile reduction in drag with potential
thrust gains.
63
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Weir, R. J. (Unknown). Aerodynamic Design Considerations for a Free-Flying Ducted Propellor. Albuquerque, Sandia National Laboratories.
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DSM Dyneema (2006). Dyneema netting, retrieved 24 August 2006 at http://www.dsm.com/en_US/html/hpf/nets.htm
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Gleitschirm (2006), Leistungsme - schwierig, fehleranfallig, aufwendig - aber machbar, retrieved 20 February 2006 at http://www.gleitschirm-magazin.com/pdf/neues-testverfahren-GLEITSCHIRM.pdf
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Caldara, O. (personal communication, December 10, 2005). Translation of key points of Dr Herve Belloc study.
Appendix B
65
APPENDIX A - CLIENT BRIEF Removed for online version
APPENDIX B - PROJECT SPECIFICATION Removed for online version
Appendix C
66
APPENDIX C- EXAMPLE OF A STANDARD PARAMOTOR Table C.1. Specifications of paramotor used during experimentation. PAP 1400AS, POWERED BY TOP 80 Motor Type TOP 80 single cylinder, 2-stroke, forced air cooled Cylinder 78,63 cc (47,7x44mm) Carburettor Walbro 24 mm. Optional DellOrto 17,5 mm Power & Ignition 15 HP at 9200 R.P.M., Electronic Reduction gear Mechanical in oil bath, inclined teeth Reduction ratio 1/3.84 Transmission Centrifugal clutch Start Manual (pull) with foot extension (kick start in flight) *Thrust (kg) +/- 50
Fuel Leaded or unleaded Super grade + synthetic oil 2% (we recommend Castrol)
Fuel tank 13,5 L *Autonomy hours +/-4h Cage Round pipes in stainless steel , T.I.G. welding Cage in 2 parts yes Wood propeller (cm) 2 blades 125 Metal reinforced Wood propeller Optional Carbon fibre propeller Optional Paramotor weight including harness 25,5 kg. Max. Pilot weight 100 kg. Recommended Pilot weight 80 kg.
Harness Sup'Air Special PAP, with automatic buckles + neoprene pockets.
Size (cm) 140 x 140 x 40 Propeller case yes Head rescue system yes RPM counter optional / yes * Thrust, autonomy and general performance depend greatly on the glider, the altitude and the pilot, so the data offered here must be taken only as reference data. ** The best thrust we have obtained with carbon prop
Figure C.2. Rear view of paramotor used during experimentation.
Appendix D
67
APPENDIX D – SURFACE AIRFLOW VISUALISATION EXPERIMENTS
Figure D.1. Image of camera mount components in MasterCAM as drawn to be cut out in the SACME wire
cutter.
Eccentric cam lever
Boom clamps
Camera mount
Appendix D
68
Figure D.2. Technical drawing of camera mount (overview).
Appendix D
69
Figure D.3. Technical drawing of camera mount (detail).
Appendix D
70
Figure D.4. Frontal image of paraglider climbing under full throttle. Note direction of wool tufts around the
cage signifying inflow to the propeller.
Appendix D
71
Figure D.5. Image of paramotor in full climb from a lower 45o angle. Greater inflow to propeller disk during
climb creates attached airflow over pilot’s body.
Appendix D
72
Figure D.6. Image of paramotor gliding from a 45o perspective. Note turbulence in upper half of paramotor cage. Differing AoI of wool in proximity of pilot signifies an increased local wind velocity. Increased AoI away from interference of pilot shows more accurate indication of glide ratio. At rear of tank is either minimal airflow or a downwards air stream.
Figure D.7. Image of half accelerated glide.
Appendix D
73
Figure D.8. Image of half accelerated glide, braked propeller.
Figure D.9. Image of unaccelerated glide.
Appendix E
74
APPENDIX E – PROPELLER BRAKE DESIGN AND MANUFACTURE
Figure E.1. Image of propeller brake components in MasterCAM as drawn to be cut out in the SACME
wirecutter as delivered by author to workshop.
Appendix F
75
APPENDIX F – GLIDING FLIGHT EXPERIMENTATION Table F.1. Flight path data recorded 5/5/06 on Top Navigator converted to a glide ratio. Sample calculations for glide ratio Windmilling Propeller
Date Marker TAS (km/hr)
Distance (m)
Alt Start (m)
Alt Finish (m)
Altitude loss Glide ratio :1
06.05.05 M1-M2 38 1747.64 1785 1513 272 6.43 Braked Propeller
Date Marker TAS (km/hr)
Distance (m)
Alt Start (m)
Alt Finish (m)
Altitude loss Glide ratio :1
06.05.06 M3-M4 38 1201.537 1462 1277 185 6.49 The calculations are performed using GRS80 ellipsoid values which is used for Australia's
new coordinate system (The Geocentric Datum of Australia - GDA). http://www.ga.gov.au/geodesy/datums/vincenty_inverse.jsp
Appendix F
76
Figure F.1 Flight path data recorded 5/5/06 on Top Navigator.Figure F.2. Flight path data recorded 5/5/06 on Top Navigator. Detail of flight path between milestones with propeller windmilling.
Appendix F
77
Figure F.3. Flight path data recorded 5/5/06 on Top Navigator. Detail of flight path between milestones with propeller windmilling.
Appendix F
78
Figure F.4. Flight path data recorded 5/5/06 on Top Navigator. Detail of flight path between milestones with propeller braked.
Appendix F
79
Figure F.5. Flight path data recorded 5/5/06 on Top Navigator. Detail of flight path between milestones with propeller braked.
Appendix G
80
APPENDIX G – SCALE WIND TUNNEL MODEL DEVELOPMENT
Figure G.1. CATIA rendering of experimental paramotor.
Appendix G
81
Figure G.2. CATIA rendering of experimental paramotor.
Appendix G
82
Figure G.3. CATIA rendering of experimental paramotor.
Appendix G
83
Figure G.4. CATIA rendering of experimental paramotor.
Appendix H
84
APPENDIX H – CORRECTION FACTORS AND CALCULATIONS
Model at 0o AoI
Figure H.1. (left) CATIA rendering at 0o AoI used to create the low turbulence wind tunnel model for frontal area calculations. H.2. (right) The model in the wind tunnel at 0o AoI minus the harness. Table H.3. Frontal area figures at 0o AoI
Standard Paramotor 0o AoI
Components Area (m2) Pilot 0.004503 Tank 0.000111 Propeller 0.000060 Engine 0.000370 Netting 0.000464 Reserve Parachute 0.000161 Frame 0.001325 Total Frontal Area is 0.006994m2
Appendix H
85
Model at 8o AoI
Figure H.4. (left) CATIA rendering at 8o AoI used to create the wind tunnel model and for frontal area calculations. H.5. (right) The model in the low turbulence wind tunnel at 8o AoI. Note the force balance arm is pivoted along the axis of the force balance. Table H.6. Frontal area figures at 8o AoI
Standard Paramotor 8o AoI
Components Area (m2) Pilot 0.004244 Tank 0.000264 Propeller 0.000060 Engine 0.000377 Netting 0.000459 Reserve Parachute 0.000128 Frame 0.001311 Total Frontal Area is 0.006843m2
Appendix H
86
Model at 16o AoI
Figure H.7. (left) CATIA rendering at 16o AoI used to create the wind tunnel model and for frontal area calculations. H.8. (right) The model in the low turbulence wind tunnel at 16o AoI. Table H.9. Frontal area figures at 16o AoI
Standard Paramotor 16o AoI
Components Area (m2) Pilot 0.003985 Tank 0.000495 Propeller 0.000000 Engine 0.000485 Netting 0.000454 Reserve Parachute 0.000075 Frame 0.001298 Total Frontal Area is 0.006792m2
Appendix H
87
Model at 24o AoI
Figure H.10. (left) CATIA rendering at 24o AoI used to create the wind tunnel model and for frontal area calculations. H.11. (right) The model in the low turbulence wind tunnel at 24o AoI. Table H.12. Frontal area figures at 24o AoI
Standard Paramotor 24o AoI
Components Area (m2) Pilot 0.003707 Tank 0.000533 Propeller 0.000060 Engine 0.000464 Netting 0.000449 Reserve Parachute 0.000000 Frame 0.001285 Total Frontal Area is 0.006498m2
Appendix H
88
Model at 32o AoI
Figure H.13. (left) CATIA rendering at 32o AoI used to create the wind tunnel model and for frontal area calculations. H.14. (right) The model in the low turbulence wind tunnel at 32o AoI. The complete shape of the force balance arm is easily seen. The reason for the shape was to minimise the wake turbulence on the model. Table H.15. Frontal area figures at 32o AoI
Standard Paramotor 32o AoI
Components Area (m2) Pilot 0.003660 Tank 0.000586 Propeller 0.000090 Engine 0.000571 Netting 0.000444 Reserve Parachute 0.000000 Frame 0.001285 Total Frontal Area is 0.006636m2
Appendix H
89
Algebraic Method of Finding the Blockage Factor
( )
212
C
C
212
tep 1. Local Density
Step 2. Blockage Factor
TSAWhere:
blockage factorD=drag recorded in NTSA=test section areaV corrected velocity
1
Step 3. Sub V into
( (1 ))TSA
Step 4
C
C M
M
SP
RT
DV
V V
DV
ρ
ρε
ε
ε
ε
ρ εε
=
=
=
=
= +
+=
( )
2
2
. Solve for , as all other values are constants.
Step 5. Find corrected velocity1
Step 6. Calculate drag area in m
12
C M
DC
V V
DC AV
ε
ε
ρ
= +
=
Appendix J
90
APPENDIX I – WIND TUNNEL CALIBRATION Removed for online version
APPENDIX J – COMPONENT BREAKDOWN DUE TO DRAG - EXPERIMENT 1
Sample Calculations
In accordance with the Pope method ‘the Reynolds number ratio of model to full size
is approximately equal to the scale ratio between the scale model and the aircraft’
(Pope et al., 1984, p 38). This calculation is shown below.
Re
12.5 1.5 1.225Re1.789 5
Re 1.284 6
Re
0.15 1.2251.284 61.789 5
12.5 /
FS FSFS
E
E
SM SMSM
SME
E
SM
V L
V L
V
V m s
ρμ
ρμ
=
× ×=
−=
=
× ×=
−=
Figure J.1. Configuration 1- Paramotor with pilot and propeller. Image shows model in wind tunnel mounted to force balance. Note that during testing the model and propeller were vertical.
Appendix J
91
Figure J.2 Left. Configuration 2 – Harness was removed from the model. Image shows model in wind tunnel. Centre. Configuration 3 - Propeller was removed from the model. Right. Configuration 4 - Fuel tank was removed from the model.
Figure J.3 Left. Configuration 5 - Netting was removed from the paramotor frame.Centre. Configuration 6 - Reserve was removed from the paramotor frame. Right. Configuration 7 - Frame was removed from the model.
Figure J.4 Left. Configuration 8 - Power plant was removed from the model. Right. Configuration 9 - Force balance arm.
Appendix J
92
Results Table J.5. Calculated drag area values in m2 of differing configurations of standard paramotor at 0o AoI.
Drag Area of Standard Paramotor at 0o AoI in Varying Configurations
Indicated velocity m/s1 Paramotor
with pilot and propeller
2 Minus harness
3 Minus propeller
4 Minus fuel tank
5 Minus netting
6 Minus reserve
7 Minus cage
8 Minus powerplant
7 0.0044 0.0044 0.0045 0.0041 0.0032 0.0033 0.0025 0.0024 9 0.0044 0.0044 0.0044 0.0035 0.0033 0.0034 0.0022 0.0022 11 0.0044 0.0044 0.0045 0.0037 0.0034 0.0034 0.0025 0.0022 13 0.0044 0.0044 0.0043 0.0037 0.0034 0.0033 0.0022 0.0021 15 0.0044 0.0044 0.0044 0.0037 0.0033 0.0031 0.0023 0.0021 17 0.0043 0.0043 0.0042 0.0034 0.0034 0.0032 0.0022 0.0021 19 0.0044 0.0045 0.0042 0.0036 0.0034 0.0031 0.0021
Average 15 to 30m/s 0.0044 0.0044 0.0043 0.0036 0.0033 0.0031 0.0022 0.0021 Percent Difference
From Full Configuration
0.00 2.24 18.03 23.78 28.05 48.94 51.47
Appendix J
93
Drag Area of a Standard Param otor at 0 Degrees Angle of Attack In Varying Configurations .
0.0010
0.0020
0.0030
0.0040
0.0050
7 9 11 13 15 17 19
Velocity of Wind Tunnel in m /s
Dra
g A
rea
of M
odel
in m
^2
1 Paramotor w ith pilot and propeller 2 Minus harness 3 Minus propeller
4 Minus fuel tank 5 Minus netting 6 Minus reserve
7 Minus cage 8 Minus pow erplant
Figure J.6. Calculated drag area values in m2 of differing configurations of standard paramotor at 0o AoI.
Appendix J
94
Table J.7. Calculated drag area values in m2 of differing configurations of standard paramotor at 8o AoI. Drag Area of Standard Paramotor at 8o AoI in Varying Configurations
Indicated velocity m/s1 Paramotor
with pilot and propeller
2 Minus harness
3 Minus propeller
4 Minus fuel tank
5 Minus netting
6 Minus reserve
7 Minus cage
8 Minus powerplant
7 0.0042 0.0042 0.0041 0.0037 0.0029 0.0030 0.0021 9 0.0039 0.0039 0.0039 0.0035 0.0030 0.0031 0.0018 11 0.0039 0.0039 0.0039 0.0035 0.0031 0.0030 0.0019 13 0.0039 0.0039 0.0039 0.0034 0.0028 0.0030 0.0017 15 0.0039 0.0039 0.0039 0.0033 0.0028 0.0028 0.0019 17 0.0040 0.0040 0.0039 0.0033 0.0029 0.0029 0.0018 19 0.0040 0.0040 0.0038 0.0034 0.0031 0.0028 0.0018
Average 15 to 30m/s 0.0040 0.0040 0.0039 0.0034 0.0029 0.0028 0.0018 Percent Difference
From Full Configuration
0.00 2.26 15.59 25.96 28.88 54.46
Appendix J
95
Drag Area of a Standard Param otor at 8 Degrees Angle of Attack In Varying Configurations .
0.0010
0.0020
0.0030
0.0040
0.0050
7 9 11 13 15 17 19
Velocity of Wind Tunnel in m /s
Dra
g A
rea
of M
odel
in m
^2
1 Paramotor w ith pilot and propeller 2 Minus harness 3 Minus propeller
4 Minus fuel tank 5 Minus netting 6 Minus reserve
7 Minus cage
Figure J.8. Calculated drag area values in m2 of differing configurations of standard paramotor at 8o AoI.
Appendix J
96
Table J.9. Calculated drag Area Values in m2 of differing configurations of standard paramotor at 16o AoI. Drag Area of Standard Paramotor at 16o AoI in Varying Configurations
Indicated velocity m/s1 Paramotor
with pilot and propeller
2 Minus harness
3 Minus propeller
4 Minus fuel tank
5 Minus netting
6 Minus reserve
7 Minus cage
8 Minus powerplant
7 0.0034 0.0034 0.0038 0.0035 0.0024 0.0029 0.0017 9 0.0035 0.0035 0.0037 0.0028 0.0027 0.0027 0.0017 11 0.0038 0.0038 0.0036 0.0029 0.0026 0.0026 0.0016 13 0.0037 0.0037 0.0036 0.0030 0.0025 0.0026 0.0016 15 0.0035 0.0035 0.0035 0.0030 0.0023 0.0026 0.0015 17 0.0036 0.0036 0.0029 0.0025 0.0026 0.0016 19 0.0035 0.0035 0.0034 0.0030 0.0025 0.0025 0.0015
Average 15 to 30m/s 0.0035 0.0035 0.0035 0.0030 0.0024 0.0026 0.0015 Percent Difference
From Full Configuration
0.00 2.16 16.55 31.34 27.96 56.56
Appendix J
97
Drag Area of a Standard Param otor at 16 Degrees Angle of Attack In Varying Configurations.
0.0010
0.0020
0.0030
0.0040
0.0050
7 9 11 13 15 17 19
Velocity of Wind Tunnel in m /s
Dra
g A
rea
of M
odel
in m
^2
1 Paramotor w ith pilot and propeller 2 Minus harness 3 Minus propeller
4 Minus fuel tank 5 Minus netting 6 Minus reserve
7 Minus cage
Figure J.10. Calculated drag area values in m2 of differing configurations of standard paramotor at 16o AoI.
Appendix J
98
Table J.11. Calculated drag area values in m2 of differing configurations of standard paramotor at 24o AoI. Drag Area of Standard Paramotor at 24o AoI in Varying Configurations
Indicated velocity m/s1 Paramotor
with pilot and propeller
2 Minus harness
3 Minus propeller
4 Minus fuel tank
5 Minus netting
6 Minus reserve
7 Minus cage
8 Minus powerplant
7 0.0032 0.0032 0.0032 0.0029 0.0022 0.0025 0.0017 9 0.0035 0.0035 0.0035 0.0027 0.0020 0.0024 0.0015 11 0.0034 0.0034 0.0034 0.0027 0.0023 0.0024 0.0015 13 0.0033 0.0033 0.0033 0.0027 0.0022 0.0024 0.0014 15 0.0033 0.0033 0.0033 0.0026 0.0022 0.0023 0.0015 17 0.0032 0.0032 0.0032 0.0027 0.0022 0.0023 0.0014 19 0.0032 0.0032 0.0032 0.0026 0.0022 0.0022 0.0014
Average 15 to 30m/s 0.0032 0.0032 0.0032 0.0026 0.0022 0.0023 0.0014 Percent Difference
From Full Configuration
0.00 -0.14 18.73 31.70 30.00 55.38
Appendix J
99
Drag Area of a Standard Param otor at 24 Degrees Angle of Attack In Varying Configurations.
0.0010
0.0020
0.0030
0.0040
0.0050
7 9 11 13 15 17 19
Velocity of Wind Tunnel in m /s
Dra
g A
rea
of M
odel
in m
^2
1 Paramotor w ith pilot and propeller 2 Minus harness 3 Minus propeller
4 Minus fuel tank 5 Minus netting 6 Minus reserve
7 Minus cage
Figure J.12. Calculated drag area values in m2 of differing configurations of standard paramotor at 24o AoI.
Appendix J
100
Table J.13. Calculated drag area values in m2 of differing configurations of standard paramotor at 32o AoI. Drag Area of Standard Paramotor at 32o AoI in Varying Configurations
Indicated velocity m/s1 Paramotor
with pilot and propeller
2 Minus harness
3 Minus propeller
4 Minus fuel tank
5 Minus netting
6 Minus reserve
7 Minus cage
8 Minus powerplant
7 0.0029 0.0029 0.0030 0.0025 0.0020 0.0025 0.0016 0.0013 9 0.0029 0.0029 0.0030 0.0024 0.0020 0.0023 0.0013 0.0012 11 0.0030 0.0030 0.0029 0.0023 0.0020 0.0022 0.0013 0.0011 13 0.0028 0.0028 0.0030 0.0023 0.0020 0.0021 0.0012 0.0011 15 0.0029 0.0029 0.0029 0.0023 0.0019 0.0020 0.0012 0.0011 17 0.0028 0.0028 0.0030 0.0022 0.0020 0.0020 0.0012 0.0010 19 0.0028 0.0028 0.0029 0.0022 0.0019 0.0020 0.0012 0.0011
Average 15 to 30m/s 0.0029 0.0029 0.0029 0.0022 0.0019 0.0020 0.0012 0.0011 Percent Difference
From Full Configuration
0.00 -2.11 22.66 32.79 28.99 57.24 61.94
Appendix J
101
Drag Area of a Standard Param otor at 32 Degrees Angle of Attack In Varying Configurations.
0.0010
0.0020
0.0030
0.0040
0.0050
7 9 11 13 15 17 19
Velocity of Wind Tunnel in m /s
Dra
g A
rea
of M
odel
in m
^2
1 Paramotor w ith pilot and propeller 2 Minus harness 3 Minus propeller
4 Minus fuel tank 5 Minus netting 6 Minus reserve
7 Minus cage 8 Minus pow erplant
Figure J.14. Calculated drag area values in m2 of differing configurations of standard paramotor at 32o AoI.
Appendix J
102
Table J.15. Raw data of differing configurations of standard paramotor at 0o AoI. Summary of Raw Data for Standard Paramotor At 0o AoI
Average Drag Force Recorded in N
Indicated velocity m/s1 Paramotor
with pilot and propeller
2 Minus harness
3 Minus propeller
4 Minus fuel tank
5 Minus netting
6 Minus reserve
7 Minus cage
8 Minus powerplant
7 0.222 0.222 0.224 0.209 0.183 0.185 0.160 0.1599 0.364 0.364 0.363 0.318 0.307 0.310 0.251 0.25211 0.541 0.541 0.548 0.488 0.464 0.462 0.392 0.37413 0.758 0.758 0.747 0.688 0.648 0.637 0.519 0.51615 1.009 1.009 1.012 0.906 0.849 0.823 0.707 0.68617 1.276 1.276 1.261 1.120 1.105 1.077 0.888 0.87219 1.633 1.633 1.575 1.443 1.379 1.323 1.102
Table J.16. Blockage factors of differing configurations of standard paramotor at 0o AoI. Summary of Blockage Factors for Standard Paramotor at 0o AoI
Indicated velocity m/s1 Paramotor
with pilot and propeller
2 Minus harness
3 Minus propeller
4 Minus fuel tank
5 Minus netting
6 Minus reserve
7 Minus cage
8 Minus powerplant
7 0.0355 0.0355 0.0343 0.0316 0.0303 0.0291 0.0246 0.0244 9 0.0355 0.0355 0.0343 0.0316 0.0303 0.0291 0.0246 0.0244 11 0.0355 0.0355 0.0343 0.0316 0.0303 0.0291 0.0246 0.0244 13 0.0355 0.0355 0.0343 0.0316 0.0303 0.0291 0.0246 0.0244 15 0.0355 0.0355 0.0343 0.0316 0.0303 0.0291 0.0246 0.0244 17 0.0355 0.0355 0.0343 0.0316 0.0303 0.0291 0.0246 0.0244 19 0.0355 0.0355 0.0343 0.0316 0.0303 0.0291 0.0246 0.0244
Appendix J
103
Table J.17. Corrected velocity of differing configurations of standard paramotor at 0o AoI. Summary of Corrected Velocity for Standard Paramotor at 0o AoI.
Indicated velocity m/s1 Paramotor
with pilot and propeller
2 Minus harness
3 Minus propeller
4 Minus fuel tank
5 Minus netting
6 Minus reserve
7 Minus cage
8 Minus powerplant
7 7.249 7.249 7.240 7.221 7.212 7.204 7.172 7.171 9 9.320 9.320 9.309 9.284 9.273 9.262 9.221 9.220 11 11.391 11.391 11.377 11.348 11.333 11.320 11.271 11.268 13 13.462 13.462 13.446 13.411 13.394 13.378 13.320 13.317 15 15.533 15.533 15.515 15.474 15.455 15.437 15.369 15.366 17 17.604 17.604 17.583 17.537 17.515 17.495 17.418 17.415 19 19.675 19.652 19.652 19.600 19.576 19.553 19.467 19.464
Table J.18. Dynamic pressure of differing configurations of standard paramotor at 0o AoI. Summary of Dynamic Pressure on Standard Paramotor at 0o AoI
Indicated velocity m/s1 Paramotor
with pilot and propeller
2 Minus harness
3 Minus propeller
4 Minus fuel tank
5 Minus netting
6 Minus reserve
7 Minus cage
8 Minus powerplant
7 29.937 29.937 29.867 29.712 29.637 29.568 29.310 29.298 9 49.487 49.487 49.373 49.115 48.991 48.877 48.451 48.432 11 73.925 73.925 73.754 73.369 73.185 73.014 72.377 72.349 13 103.251 103.251 103.012 102.475 102.217 101.979 101.089 101.049 15 137.464 137.464 137.146 136.431 136.087 135.770 134.586 134.533 17 176.565 176.565 176.156 175.238 174.796 174.389 172.868 172.800 19 220.554 220.043 220.043 218.896 218.344 217.836 215.935 215.851
Appendix J
104
Drag Area of Force Balance Bar With No Model.
0.0010
0.0020
0.0030
0.0040
0.0050
50,000 70,000 90,000 110,000 130,000 150,000Reynolds Number
Dra
g Are
a of
For
ce B
alan
ce B
ar in
m̂2
Bare Force Bar
Figure J.19. Calculated drag area values in m2 vs. Reynolds number of the force balance bar with no model fitted.
Appendix K
105
APPENDIX K – EFFECT OF FUEL TANK PLACEMENT ON DRAG AREA
Results Table K.1. Summary of Raw Data for Paramotor with Standard Fuel Tank
Raw Data for Paramotor with Standard Fuel Tank Average Drag Force Recorded in N
Indicated velocity m/s 0o AoI 8o AoI 16o AoI 24o AoI 32o AoI 5 0.130 0.120 0.106 0.103 0.094
10 0.480 0.454 0.415 0.395 0.379 15 1.082 1.015 0.936 0.932 0.864 20 1.897 1.834 1.725 1.696 1.599 25 2.964 2.871 2.716 2.601 2.453 30 4.297 4.169 3.827 3.812 3.584
Table K.2. Summary of Raw Data for Paramotor with Side Jerry Cans
Raw Data for Paramotor with Side Jerry Cans Average Drag Force Recorded in N
Indicated velocity m/s 0o AoI 8o AoI 16o AoI 24o AoI 32o AoI 5 0.136 0.117 0.093 0.121 0.096
10 0.465 0.438 0.413 0.398 0.387 15 1.077 1.018 0.936 0.887 0.846 20 1.973 1.861 1.733 1.622 1.531 25 3.000 2.883 2.729 2.489 2.427 30 4.420 4.122 3.918 3.686 3.391
Table K.3. Summary of Raw Data for Paramotor with Faired Side Jerry Cans
Raw Data for Paramotor with Faired Side Jerry Cans Average Drag Force Recorded in N
Indicated velocity m/s 0o AoI 8o AoI 16o AoI 24o AoI 32o AoI 5 0.131 0.107 0.108 0.106 0.099
10 0.493 0.450 0.416 0.405 0.360 15 1.127 1.014 0.974 0.929 0.867 20 1.994 1.846 1.732 1.657 1.536 25 3.091 2.931 2.737 2.637 2.440 30 4.403 4.221 3.951 3.820 3.501
Table K.4. Summary of Raw Data for Paramotor with Streamlined Fuel Tank
Raw Data for Paramotor with Streamlined Fuel Tank Average Drag Force Recorded in N
Indicated velocity m/s 0o AoI 8o AoI 16o AoI 24o AoI 32o AoI 5 0.114 0.117 0.102 0.096 0.090
10 0.462 0.439 0.415 0.361 0.349 15 1.047 0.996 0.871 0.820 20 1.884 1.795 1.662 1.574 1.511 25 2.943 2.732 2.564 2.495 2.324 30 4.115 4.001 3.771 3.628 3.373
Appendix K
106
Difference in Raw Force Balance Readings As A Result Of Fuel Tank Placement On A Paramotor At 0 Degrees AoI.
0.00.51.01.52.02.53.03.54.04.55.0
5 10 15 20 25 30
Indicated Wind Velocity (uncorrected) m/s
Forc
e R
ecor
ded
in N
Standard Fuel TankNACA 0025 Profile Tank Cut Off at 40% ChordUnfaired Jerry CansFaired Jerry Cans
Figure K.5. Difference in Raw Force Balance Readings as a result of fuel tank placement on a paramotor at 0o AoI.
Difference in Raw Force Balance Readings As A Result Of Fuel Tank Placement On A Paramotor At 32 Degrees AoI.
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
5 10 15 20 25 30
Indicated Wind Velocity (uncorrected) m/s
Forc
e R
ecor
ded
in N
Standard Fuel TankNACA 0025 Profile Tank Cut Off at 40% ChordUnfaired Jerry CansFaired Jerry Cans
Figure K.6. Difference in Raw Force Balance Readings as a result of fuel tank placement on a paramotor at 32o AoI.
Appendix K
107
Paramotor with Streamlined Fuel Tank at 0o AoI
Components Area (m2) Pilot 0.004503Tank 0.000000Propeller 0.000060Engine 0.000370Netting 0.000464Reserve Parachute 0.000161Frame 0.001325Total Frontal Area is 0.006883m2
Paramotor with Streamlined Fuel Tank at 8o AoI
Components Area (m2) Pilot 0.004244Tank 0.000119Propeller 0.000060Engine 0.000377Netting 0.000459Reserve Parachute 0.000128Frame 0.001311Total Frontal Area is 0.006698m2
Paramotor with Streamlined Fuel Tank at 16o AoI
Components Area (m2) Pilot 0.003985Tank 0.000325Propeller 0.000000Engine 0.000485Netting 0.000454Reserve Parachute 0.000075Frame 0.001298Total Frontal Area is 0.006622m2
Calculations
Frontal areas for standard paramotor are shown in Appendix G. Other configurations are shown below.
Figure K.7. Paramotor with Streamlined Fuel Tank at 0, 8, 16, 32o AoI
Appendix K
108
Paramotor with Streamlined Fuel Tank at 24o AoI
Components Area (m2) Pilot 0.003707Tank 0.000433Propeller 0.000060Engine 0.000464Netting 0.000449Reserve Parachute 0.000000Frame 0.001285Total Frontal Area is 0.006398m2
Paramotor with Streamlined Fuel Tank at 32o AoI
Components Area (m2) Pilot 0.003660Tank 0.000469Propeller 0.000090Engine 0.000571Netting 0.000444Reserve Parachute 0.000000Frame 0.001285Total Frontal Area is 0.006519m2
Paramotor with Jerry Fuel Tanks at 0o AoI
Components Area (m2) Pilot 0.004503Tank 0.000634Propeller 0.000178Engine 0.000168Netting 0.000450Reserve Parachute 0.000161Frame 0.001300Total Frontal Area is 0.007394m2
Figure K.8. Paramotor with Jerry Fuel Tanks at 0, 8, 16, 32o AoI
Appendix K
109
Paramotor with Jerry Fuel Tanks at 8o AoI
Components Area (m2) Pilot 0.004244Tank 0.000689Propeller 0.000130Engine 0.000197Netting 0.000440Reserve Parachute 0.000160Frame 0.001300Total Frontal Area is 0.007160m2
Paramotor with Jerry Fuel Tanks at 16o AoI
Components Area (m2) Pilot 0.003985Tank 0.000743Propeller 0.000248Engine 0.000170Netting 0.000440Reserve Parachute 0.000128Frame 0.001298Total Frontal Area is 0.007012m2
Paramotor with Jerry Fuel Tanks at 24o AoI
Components Area (m2) Pilot 0.003707Tank 0.000820Propeller 0.000420Engine 0.000095Netting 0.000430Reserve Parachute 0.000161Frame 0.001265Total Frontal Area is 0.006478m2
Appendix K
110
Paramotor with Jerry Fuel Tanks at 32o AoI
Components Area (m2) Pilot 0.003660Tank 0.000828Propeller 0.000510Engine 0.000104Netting 0.000420Reserve Parachute 0.000100Frame 0.001265Total Frontal Area is 0.006467m2
Figure K.9. Paramotor with Basic Fairing over Jerry Fuel Tanks at 0, 8, 16, 32o AoI Paramotor with Basic Fairing over Jerry Fuel Tanks at 0o AoI.
Paramotor with Basic Fairing Over Jerry Fuel Tanks at 8o AoI.
Appendix K
111
Paramotor with Basic Fairing Over Jerry Fuel Tanks at 16o AoI.
Paramotor with Basic Fairing Over Jerry Fuel Tanks at 24o AoI.
Paramotor with Basic Fairing Over Jerry Fuel Tanks at 32o AoI.
Appendix K
112
Figure K.10. Technical drawing of NACA0025 cut off at 60% chord fuel tank for wind tunnel model.
Appendix K
113
Table K.11. Summary of Drag Area of Paramotor with Standard Fuel Tank. Drag Area of Paramotor with Standard Fuel Tank.
Indicated velocity m/s 0o AoI 8o AoI 16o AoI 24o AoI 32o AoI 5 0.0057 0.0051 0.0042 0.0040 0.0035
10 0.0051 0.0047 0.0041 0.0037 0.0035 15 0.0052 0.0047 0.0042 0.0041 0.0037 20 0.0051 0.0048 0.0044 0.0043 0.0039 25 0.0051 0.0049 0.0045 0.0042 0.0039 30 0.0051 0.0049 0.0043 0.0043 0.0039
Table K.12. Summary of Drag Area of Paramotor with Side Jerry Cans.
Drag Area of Model Paramotor with Side Jerry Cans. Indicated velocity m/s 0o AoI 8o AoI 16o AoI 24o AoI 32o AoI
5 0.0061 0.0049 0.0034 0.0052 0.0036 10 0.0048 0.0044 0.0040 0.0038 0.0036 15 0.0051 0.0047 0.0042 0.0038 0.0035 20 0.0054 0.0050 0.0045 0.0040 0.0037 25 0.0052 0.0049 0.0045 0.0039 0.0038 30 0.0054 0.0049 0.0045 0.0041 0.0036
Table K.13. Summary of Drag Area of Paramotor with Streamlined Fuel Tank.
Drag Area of Paramotor with Streamlined Fuel Tank. Indicated velocity m/s 0o AoI 8o AoI 16o AoI 24o AoI 32o AoI
5 0.0047 0.0049 0.0040 0.0036 0.0032 10 0.0048 0.0044 0.0041 0.0032 0.0030 15 0.0049 0.0046 0.0037 0.0034 20 0.0050 0.0047 0.0042 0.0038 0.0036 25 0.0051 0.0045 0.0041 0.0040 0.0035 30 0.0048 0.0047 0.0043 0.0040 0.0036
Table K.14. Summary of Drag Area of Paramotor with Faired Jerry Cans.
Drag Area of Paramotor with Faired Side Jerry Cans. Indicated velocity m/s 0o AoI 8o AoI 16o AoI 24o AoI 32o AoI
5 0.0058 0.0043 0.0043 0.0042 0.0038 10 0.0053 0.0046 0.0041 0.0039 0.0032 15 0.0055 0.0047 0.0044 0.0041 0.0037 20 0.0055 0.0049 0.0045 0.0042 0.0037 25 0.0054 0.0050 0.0046 0.0043 0.0038 30 0.0053 0.0050 0.0046 0.0043 0.0038
Appendix K
114
Difference in Drag Area As a Result of Fuel Tank Placement On Paramotor At 0 Degrees AoI.
0.002
0.003
0.004
0.005
0.006
0.007
5 10 15 20 25 30Local Air Velocity in m/s
Dra
g A
rea
(D/q
) in
m^2
Standard Fuel TankNACA0025 Profile Tank Cut Off, 60% ChordUnfaired Jerry CansFaired Jerry CansNo Tank
Figure K.15. Drag area as a result of fuel tank placement at 0o AoI.
Difference in Drag Area As a Result of Fuel Tank Placement On Paramotor At 32 Degrees AoI.
0.002
0.003
0.004
0.005
0.006
0.007
5 10 15 20 25 30Local Air Velocity in m/s
Dra
g A
rea
(D/q
) in
m^2
Standard Fuel TankNACA0025 Profile Tank Cut Off, 60% ChordUnfaired Jerry CansFaired Jerry CansNo Tank
Figure K.16. Drag area as a result of fuel tank placement at 32o AoI.
Appendix L
115
APPENDIX L - DRAG AREA VARIATION CAUSED BY REMOVAL OF PROPELLER AND RESERVE PARACHUTE
0o AoI
Figure L.1. Complete model in wind tunnel at 0o AoI. Table L.2. Table showing the raw data for the complete paramotor at 0o AoI.
Average Values for 0o AoI Indicated velocity m/s Pitch Lift Drag
5 0.00 -0.03 0.13 10 0.01 -0.10 0.49 15 0.03 -0.24 1.13 20 0.05 -0.39 1.99 25 0.08 -0.67 3.09 30 0.12 -0.97 4.40
Paramotor At 0 Degrees AoI With Full Configuration, Streamlined Fairing Over Jerrycans and Fixed Vertical Propeller
-2-1012345
5 10 15 20 25 30
Indicated Velocity of Wind Tunnel in m/s
Rec
orde
d Fo
rce
in
New
tons
PitchLiftDrag
Figure L.3. Graph shows averaged data plotted complete paramotor at 0o AoI to confirm force balance was operating correctly.
Appendix L
116
0o AoI Minus Propeller
Figure L.4. Complete model in wind tunnel at 0o AoI with no propeller fitted. Table L.5. Table showing the raw data for the complete paramotor at 0o AoI with no propeller fitted.
Average Values for 0o AoI, No Propeller Indicated velocity m/s Pitch Lift Drag
5 0.003 -0.022 0.105 10 0.013 -0.098 0.444 15 0.030 -0.222 0.997 20 0.053 -0.411 1.799 25 0.083 -0.643 2.816 30 0.120 -0.946 4.007
Paramotor At 0 Degrees AoI With Full Configuration, Streamlined Fairing Over Jerrycans and No Propeller
-1012345
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Forc
e M
easu
red
in
New
tons Pitch
LiftDrag
Figure L.6. Graph shows averaged data plotted complete paramotor at 0o AoI with no propeller fitted to confirm force balance was operating correctly.
Appendix L
117
0o AoI Minus Reserve Parachute
Figure L.7. Complete model in wind tunnel at 0o AoI with no reserve parachute container fitted. Table L.8. Table showing the raw data for the complete paramotor at 0o AoI with no reserve parachute container fitted.
Average Values for 0o AoI, No Reserve Indicated velocity m/s Pitch Lift Drag
5 0.004 -0.032 0.132 10 0.013 -0.097 0.484 15 0.028 -0.215 1.098 20 0.052 -0.397 1.950 25 0.080 -0.602 3.008 30 0.115 -0.866 4.426
Paramotor At 0 Degrees AoI With Full Configuration, Streamlined Fairing Over Jerrycans,
No Reserve and Fixed Vertical Propeller
-2-1012345
5 10 15 20 25 30
Indicated Wind Tunnel Velocity m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure L.9. Graph shows averaged data plotted complete paramotor at 0o AoI with no reserve parachute container fitted to confirm force balance was operating correctly.
Appendix L
118
32o AoI
Figure L.10. Complete model in wind tunnel at 32o AoI with no propeller fitted. Table L.11. Table showing the raw data for the complete paramotor at 32o AoI with no propeller fitted.
Average Values for 32o AoI Indicated velocity m/s Pitch Lift Drag
5 0.000 -0.014 0.099 10 -0.002 -0.054 0.360 15 -0.007 -0.117 0.867 20 -0.014 -0.251 1.536 25 -0.020 -0.342 2.440 30 -0.028 -0.545 3.501
Paramotor At 32 Degrees AoI With Full Configuration, Streamlined Fairing Over Jerrycans
and Vertical Fixed Propeller
-1012345
0 5 10 15 20 25 30
Indicated Wind tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure L.12. Graph shows averaged data plotted complete paramotor at 32o AoI with no propeller fitted to confirm force balance was operating correctly.
Appendix L
119
32o AoI Minus Propeller
Figure L.13. Complete model in wind tunnel at 32o AoI with no propeller fitted. Table L.14. Table showing the raw data for the complete paramotor at 32o AoI with no propeller fitted.
Average Values for 32o AoI Indicated velocity m/s Pitch Lift Drag
5 -0.001 -0.012 0.082 10 -0.004 -0.043 0.336 15 -0.008 -0.096 0.781 20 -0.014 -0.167 1.402 25 -0.022 -0.234 2.227 30 -0.030 -0.380 3.213
Paramotor At 32 Degrees AoI With Full Configuration, Streamlined Fairing Over Jerrycans
and No Propeller
-1
0
1
2
3
4
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure L.15. Graph shows averaged data plotted complete paramotor at 32o AoI with no propeller fitted to confirm force balance was operating correctly.
Appendix L
120
32o AoI Minus Reserve Parachute.
Figure L.16. Complete model in wind tunnel at 32o AoI with no reserve parachute container fitted. Table L.17. Table showing the raw data for the complete paramotor at 32o AoI with no reserve parachute container fitted.
Average Values for 32o AoI, No Reserve Indicated velocity m/s Pitch Lift Drag
5 -0.001 -0.001 0.114 10 -0.003 -0.050 0.383 15 -0.007 -0.127 0.880 20 -0.013 -0.230 1.563 25 -0.019 -0.372 2.480 30 -0.029 -0.557 3.578
Paramotor At 32 Degrees AoI With Full Configuration, Streamlined Fairing Over Jerrycans,
No Reserve and Vertical Fixed Propeller
-1
0
1
2
3
4
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure L.18. Graph shows averaged data plotted complete paramotor at 32o AoI with no reserve parachute container fitted to confirm force balance was operating correctly.
Table L.19. Table showing the drag area of the model for various configurations in the wind tunnel. Summary of Drag Area in m2 for Standard Paramotor With Jerry can Fuel Tanks and Basic Fairing
Indicated velocity m/s 0 AoI No Propeller No Reserve No Prop 32 AoI No Reserve
5 0.0039 0.0027 0.0039 0.0018 0.0026 0.0034 10 0.0035 0.0030 0.0034 0.0019 0.0021 0.0024 15 0.0036 0.0030 0.0034 0.0021 0.0024 0.0025 20 0.0036 0.0031 0.0034 0.0021 0.0024 0.0025 25 0.0035 0.0031 0.0034 0.0022 0.0025 0.0026 30 0.0035 0.0031 0.0035 0.0022 0.0025 0.0026
Appendix L
121
Drag Area of a Complete Paramotor With Faired Jerry Fuel Tank, Showing The Effect of Propeller and Reserve Removal At
0 Degrees AoI.
0.0025
0.0028
0.0030
0.0033
0.0035
0.0038
0.0040
5 10 15 20 25 30
Velocity of Wind Tunnel in m/s
Dra
g A
rea
in m
^2
0 AoA No Propeller No Reserve
Figure L.20. A graph of the drag area of the model at 0o AoI.
Drag Area of a Com plete Param otor With Faired Jerry Fuel Tank , Show ing The Effect of Propelle r and Reserve Rem oval At
32 Degrees AoI.
0.00150.00180.00200.00230.00250.00280.00300.00330.00350.00380.0040
5 10 15 20 25 30
Velocity of Wind Tunnel in m/s
Dra
g A
rea
in m
^2
32 AoA No Prop No Reserve
Figure L.21. A graph of the drag area of the model at 32o AoI.
Appendix L
122
Figure L.22. Close up detail of TiO2 solution on model at pilot’s head to reserve parachute container. Separation point to side and top of pilot’s head is shown by the red arrows.
Figure L.23. Top down detail of TiO2 solution on the model, note the model was only partially painted. Remnants of an airflow separation bubble at top of pilots head is indicated by green arrow. The point of reattachment on the reserve container can be seen as well as the aft separation point indicated by the red arrow.
Figure L.24. Detail of the reserve container removed from the model. This view is taken from the ¾ left hand view with the red line indicating the position of the pilot’s neck. The turbulence due to airflow separation can be seen at the aft side of the reserve container.
Appendix M
123
APPENDIX M – COMPONENT BREAKDOWN DUE TO DRAG AS A RESULT OF WIND TUNNEL TESTING EXPERIMENT 2
Raw results for 0o AoI
Force Balance Arm
Figure M.1. Force balance arm.
Table M.2. Force balance arm values Average Values for Force Balance Arm in N
Indicated velocity m/s Pitch Lift Drag
5 0.000 0.002 0.040
10 0.000 -0.004 0.161
15 0.000 -0.005 0.352
20 -0.001 -0.009 0.620
25 -0.001 -0.010 0.958
30 -0.002 0.007 1.388
Force Balance Arm Values
-0.5
0.0
0.5
1.0
1.5
5 10 15 20 25 30
Indicated Velocity of Wind Tunnel in m/s
Rec
orde
d Fo
rce
in
New
tons Pitch
LiftDrag
Figure M.3. Graph shows force balance arm values
Appendix M
124
Complete Paramotor at 0o AoI
The data was corrupted for the complete paramotor at 0o AoI so no useable data exists. For calculations the equivalent data from Appendix I was substituted.
Figure M.4. Complete paramotor at 0o AoI
Paramotor at 0o AoI with No Reserve
Figure M.5. Paramotor at 0o AoI with No Reserve
Table M.6. Paramotor at 0o AoI with No Reserve
Average Values for 0o AoI, No Reserve Fitted Indicated velocity m/s Pitch Lift Drag
5 0.002 -0.007 0.131
10 0.009 -0.079 0.501
15 0.019 -0.158 1.103
20 0.035 -0.320 1.953
25 0.058 -0.556 3.026
30 0.076 -0.536 4.373
Paramotor At 0o AoI With No Reserve Fitted
-1
0
1
2
3
4
5
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
Pitch
Lift
Drag
Figure M.7. Graph of paramotor at 0o AoI with No Reserve
Appendix M
125
Paramotor at 0o AoI with Reserve at 90o
Figure M.8. Paramotor at 0o AoI with Reserve at 90o
Table M.9. Paramotor at 0o AoI with Reserve at 90o
Average Values for 0o AoI, 90o Reserve Fitted
Indicated velocity m/s Pitch Lift Drag
5 0.003 -0.027 0.126
10 0.010 -0.037 0.502
15 0.023 -0.173 1.081
20 0.038 -0.312 1.946
25 0.064 -0.542 2.951
30 0.086 -0.936 4.283
Paramotor At 0o AoI With 90o Reserve Fitted
-2-1012345
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure M.10. Graph of pParamotor at 0o AoI with Reserve at 90o
Appendix M
126
Paramotor at 0o AoI with No Motor Fitted
Figure M.11. Paramotor at 0o AoI with No Motor Fitted
Table M.12. Paramotor at 0o AoI with No Motor Fitted Average Values for 0o AoI, No Motor Fitted
Indicated velocity m/s Pitch Lift Drag
5 0.002 -0.024 0.130
10 0.009 -0.082 0.488
15 0.020 -0.178 1.088
20 0.036 -0.290 1.957
25 0.057 -0.486 3.073
30 0.083 -0.692 4.378
Paramotor At 0o AoI With No Motor Fitted
-1
0
1
2
3
4
5
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure M.13. Graph of paramotor at 0o AoI with No Motor Fitted
Appendix M
127
Paramotor at 0o AoI with No Intake Silencer Fitted
Figure M.14. Paramotor at 0o AoI with No Intake Silencer Fitted
Table M.15. Paramotor at 0o AoI with No Intake Silencer Fitted
Average Values for 0o AoI, No Intake Silencer Fitted
Indicated velocity m/s Pitch Lift Drag
5 0.001 -0.009 0.141
10 0.008 -0.080 0.502
15 0.021 -0.116 1.114
20 0.040 -0.313 1.957
25 0.062 -0.489 3.005
30 0.085 -0.780 4.348
Paramotor At 0o AoI With No Intake Silencer Fitted
-2-1012345
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure M.16. Graph of paramotor at 0o AoI with No Intake Silencer Fitted
Appendix M
128
Paramotor at 0o AoI with No Propeller Fitted
Figure M.17. Paramotor at 0o AoI with No Propeller Fitted
Table M.18. Paramotor at 0o AoI with No Propeller Fitted Average Values for 0o AoI, With No Propeller
Indicated velocity m/s Pitch Lift Drag
5 0.004 -0.003 0.128
10 0.010 -0.092 0.451
15 0.020 -0.151 1.054
20 0.035 -0.261 1.841
25 0.055 -0.398 2.830
30 0.082 -0.568 4.097
Param otor At 0o AoI With No Propeller
-1012345
0 5 10 15 20 25 30
Indicated Wind tunnel Velocity in m /s
Rea
ctio
n Fo
rce
in
New
tons Pitch
Lif t
Drag
Figure M.19. Graph of paramotor at 0o AoI with No Propeller Fitted
Appendix M
129
Paramotor at 0o AoI with No Tank Fitted
Figure M.20. Paramotor at 0o AoI with No Tank Fitted
Table M.21. Paramotor at 0o AoI with No Tank Fitted Average Values for 0o AoI, With No Tank
Indicated velocity m/s Pitch Lift Drag
5 0.002 -0.024 0.119
10 0.007 -0.075 0.490
15 0.020 -0.165 1.082
20 0.038 -0.331 1.886
25 0.060 -0.490 2.957
30 0.083 -0.759 4.406
Paramotor At 0o AoI With No Tank
-1012345
0 5 10 15 20 25 30
Indicated Wind tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure M.22. Graph of paramotor at 0o AoI with No Tank Fitted
Appendix M
130
Paramotor at 0o AoI with No Cage Fitted
Figure M.23. Paramotor at 0o AoI with No Cage Fitted
Table M.24. Paramotor at 0o AoI with No Cage Fitted Average Values for 0o AoI, With No Cage
Indicated velocity m/s Pitch Lift Drag
5 0.002 -0.007 0.096
10 0.007 -0.058 0.366
15 0.015 -0.127 0.846
20 0.027 -0.214 1.508
25 0.044 -0.349 2.334
30 0.064 -0.503 3.364
Paramotor At 0o AoI With No Cage
-1
0
1
2
3
4
5
0 5 10 15 20 25 30
Indicated Wind tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
PitchLiftDrag
Figure M.25. Graph of paramotor at 0o AoI with No Cage Fitted
Appendix M
131
Paramotor at 0o AoI with No Netting Fitted
Figure M.26. Paramotor at 0o AoI with No Netting Fitted
Table M.27. Paramotor at 0o AoI with No Netting Fitted Average Values for 0o AoI, With No Netting
Indicated velocity m/s Pitch Lift Drag
5 0.003 -0.026 0.117
10 0.008 -0.072 0.432
15 0.019 -0.138 0.978
20 0.034 -0.275 1.712
25 0.054 -0.354 2.690
30 0.079 -0.627 3.838
Paramotor At 0o AoI With No Netting or Tank
-1
0
1
2
3
4
5
0 5 10 15 20 25 30
Indicated Wind tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
Pitch
Lift
Drag
Figure M.28. Graph of paramotor at 0o AoI with No Netting Fitted
Appendix M
132
Paramotor at 0o AoI with No Netting or Tank Fitted
Figure M.29. Paramotor at 0o AoI with No Netting or Tank Fitted
Table M.30 Paramotor at 0o AoI with No Netting or Tank Fitted Average Values for 0o AoI, With No Netting or Tank
Indicated velocity m/s Pitch Lift Drag
5 0.002 -0.020 0.114
10 0.010 -0.070 0.442
15 0.020 -0.141 0.999
20 0.037 -0.253 1.724
25 0.058 -0.428 2.712
30 0.083 -0.622 3.899
Paramotor At 0o AoI With No Netting or Tank
-10
12
345
0 5 10 15 20 25 30
Indicated Wind tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure M.31. Graph of paramotor at 0o AoI with No Netting or Tank Fitted
Appendix M
133
Raw results for 32o AoI
Complete Paramotor at 32o AoI
Figure M.32. Complete Paramotor at 32o AoI
Table M.33. Complete Paramotor at 32o AoI Average Values for Complete Paramotor at 32o AoI
Indicated velocity m/s Pitch Lift Drag
5 -0.002 -0.065 0.094
10 -0.003 -0.057 0.388
15 -0.005 -0.043 0.879
20 -0.014 -0.286 1.520
25 -0.017 -0.491 2.408
30 -0.011 -0.346 3.444
Complete Paramotor At 32o AoI
-1
0
1
2
3
4
5
5 10 15 20 25 30
Indicated Wind Tunnel Velocity m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
Pitch
Lift
Drag
Figure M.34. Complete Paramotor at 32o AoI
Appendix M
134
Paramotor at 32o AoI with No Reserve Fitted
Figure M.35. Paramotor at 32o AoI with No Reserve Fitted
Table M.36. Paramotor at 32o AoI with No Reserve Fitted Average Values for 32o AoI, No Reserve Fitted
Indicated velocity m/s Pitch Lift Drag
5 0.000 -0.027 0.094
10 -0.002 -0.034 0.388
15 -0.005 -0.150 0.857
20 -0.007 -0.271 1.559
25 -0.010 -0.358 2.388
30 -0.012 -0.733 3.386
Paramotor At 32o AoI With No Reserve Fitted
-1
0
1
2
3
4
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure M.37. Paramotor at 32o AoI with No Reserve Fitted
Appendix M
135
Paramotor at 32o AoI with Reserve Fitted at 90o
Figure M.38. Paramotor at 32o AoI with Reserve at 90o
Table M.39. Paramotor at 32o AoI with Reserve at 90o
Average Values for 32o AoI, 90o Reserve Fitted
Indicated velocity m/s Pitch Lift Drag
5 -0.001 -0.063 0.094
10 0.000 -0.045 0.389
15 -0.007 -0.106 0.880
20 -0.009 -0.248 1.539
25 -0.012 -0.418 2.394
30 -0.010 -0.406 3.430
Paramotor At 32o AoI with Reserve Fitted at 90o
-1
0
1
2
3
4
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure M.40. Graph of paramotor at 32o AoI with Reserve at 90o
Appendix M
136
Paramotor at 32o AoI with No Motor Fitted
Figure M.41. Paramotor at 32o AoI with No Motor Fitted
Table M.42. Paramotor at 32o AoI with No Motor Fitted
Average Values for 32o AoI, No Motor Fitted
Indicated velocity m/s Pitch Lift Drag
5 -0.001 -0.018 0.097
10 -0.002 -0.048 0.377
15 -0.005 -0.108 0.862
20 -0.008 -0.241 1.496
25 -0.011 -0.317 2.370
30 -0.019 -0.538 3.474
Paramotor At 32o AoI with No Motor Fitted
-1
0
1
2
3
4
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure M.43. Graph of paramotor at 32o AoI with No Motor Fitted
Appendix M
137
Paramotor at 32o AoI with No Intake Silencer Fitted
Figure M.44 Paramotor at 32o AoI with No Intake Silencer Fitted
Table M.45. Paramotor at 32o AoI with No Intake Silencer Fitted Average Values for 32o AoI, No Intake Silencer Fitted
Indicated velocity m/s Pitch Lift Drag
5 0.000 -0.049 0.090
10 -0.002 -0.044 0.381
15 -0.004 -0.087 0.861
20 -0.009 -0.190 1.489
25 -0.013 -0.310 2.366
30 -0.018 -0.607 3.392
Paramotor At 32o AoA with No Intake Silencer Fitted
-1-1011223344
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
Pitch
Lift
Drag
Figure M.46. Paramotor at 32o AoI with No Intake Silencer Fitted
Appendix M
138
Paramotor at 32o AoI with No Intake Propeller Fitted
Figure M.47. Paramotor at 32o AoI with No Intake Propeller Fitted
Table M.48. Paramotor at 32o AoI with No Intake Propeller Fitted
Average Values for 32o AoI, With No Propeller
Indicated velocity m/s Pitch Lift Drag
5 -0.002 -0.027 0.097
10 -0.003 -0.019 0.382
15 -0.006 -0.135 0.823
20 -0.009 -0.178 1.475
25 -0.018 -0.267 2.314
30 -0.025 -0.410 3.340
Paramotor At 32o AoI with No Propeller
-1
0
1
2
3
4
5
0 5 10 15 20 25 30
Indicated Wind tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
Pitch
Lift
Drag
Figure M.49. Graph of paramotor at 32o AoI with No Intake Propeller Fitted
Appendix M
139
Paramotor at 32o AoI with No Tank Fitted
Figure M.50. Paramotor at 32o AoI with No Tank Fitted
Table M.51. Paramotor at 32o AoI with No Tank Fitted
Average Values for 32o AoI, With No Tank
Indicated velocity m/s Pitch Lift Drag
5 0.001 0.024 0.106
10 -0.004 -0.058 0.385
15 -0.005 -0.106 0.859
20 -0.003 -0.125 1.546
25 -0.011 -0.378 2.395
30 -0.014 -0.485 3.452
Paramotor At 32o AoI With No Tank
-1
0
1
2
3
4
5
0 5 10 15 20 25 30
Indicated Wind tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
Pitch
Lift
Drag
Figure M.52. Graph of paramotor at 32o AoI with No Tank Fitted
Appendix M
140
Paramotor at 32o AoI with No Cage Fitted
Figure M.53. Paramotor at 32o AoI with No Cage Fitted
Table M.54. Paramotor at 32o AoI with No Tank Fitted
Average Values for 32o AoI, With No Cage
Indicated velocity m/s Pitch Lift Drag
5 -0.001 -0.007 0.072
10 -0.001 -0.043 0.295
15 -0.003 -0.082 0.678
20 -0.005 -0.199 1.210
25 -0.006 -0.257 1.899
30 -0.010 -0.417 2.717
Paramotor At 32o AoI With No Cage
-1
0
1
2
3
4
5
0 5 10 15 20 25 30
Indicated Wind tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
Pitch
Lift
Drag
Figure M.55. Paramotor at 32o AoI with No Tank Fitted
Appendix M
141
Paramotor at 32o AoI with No Netting Fitted
Figure M.56. Paramotor at 32o AoI with No Netting Fitted
Table M.57. Paramotor at 32o AoI with No Netting Fitted
Average Values for 32o AoI, With No Netting
Indicated velocity m/s Pitch Lift Drag
5 0.000 -0.016 0.089
10 -0.002 -0.049 0.361
15 -0.002 -0.067 0.804
20 -0.006 -0.201 1.401
25 -0.012 -0.369 2.177
30 -0.013 -0.406 3.162
Paramotor At 32o AoI With No Netting
-1012345
0 5 10 15 20 25 30
Indicated Wind tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure M.58. Paramotor at 32o AoI with No Netting Fitted
Appendix M
142
Paramotor at 32o AoI with No Netting or Tank Fitted
Figure M.59. Paramotor at 32o AoI with No Netting or Tank Fitted
Table M.60. Paramotor at 32o AoI with No Netting or Tank Fitted
Average Values for 32o AoI, With No Netting or Tank
Indicated velocity m/s Pitch Lift Drag
5 -0.001 -0.016 0.089
10 -0.002 -0.048 0.343
15 -0.004 -0.113 0.783
20 -0.006 -0.192 1.404
25 -0.009 -0.285 2.166
30 -0.014 -0.444 3.125
Paramotor At 32o AoI with No Netting or Tank
-1012345
0 5 10 15 20 25 30
Indicated Wind tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure M.61. Paramotor at 32o AoI with No Netting or Tank Fitted
Appendix M
143
CALCULATIONS
Table M.62. Summary of Blockage Factors for Standard Paramotor at 0o AoI. Summary of Blockage Factors For Standard Paramotor at 0o AoI
Indicated velocity m/s Force Balance Arm
Full Configuration No Reserve 90o Reserve No Motor No Intake No
Propeller No Tank No Cage (includes no tank)
No Net No Net, No Tank
5 0.0126 0.0372 0.0378 0.0370 0.0381 0.0376 0.0356 0.0376 0.0296 0.0337 0.0341 10 0.0126 0.0372 0.0378 0.0370 0.0381 0.0376 0.0356 0.0376 0.0296 0.0337 0.0341 15 0.0126 0.0372 0.0378 0.0370 0.0381 0.0376 0.0356 0.0376 0.0296 0.0337 0.0341 20 0.0126 0.0372 0.0378 0.0370 0.0381 0.0376 0.0356 0.0376 0.0296 0.0337 0.0341 25 0.0126 0.0372 0.0378 0.0370 0.0381 0.0376 0.0356 0.0376 0.0296 0.0337 0.0341 30 0.0126 0.0372 0.0378 0.0370 0.0381 0.0376 0.0356 0.0376 0.0296 0.0337 0.0341
Table M.63. Drag Area On Standard Paramotor at 0o AoI.
Drag Area On Standard Paramotor at 0o AoI
Indicated velocity m/s Force Balance Arm
Full Configuration No Reserve 90o Reserve No Motor No Intake No
Propeller No Tank No Cage (includes no tank)
No Net No Net, No Tank
5 0.0028 0.005247 0.0058 0.0055 0.0057 0.0064 0.0056 0.0050 0.0036 0.0049 0.0047 10 0.0028 0.005241 0.0054 0.0054 0.0052 0.0054 0.0046 0.0052 0.0033 0.0043 0.0045 15 0.0027 0.005324 0.0053 0.0052 0.0052 0.0054 0.0050 0.0052 0.0036 0.0045 0.0046 20 0.0027 0.005347 0.0053 0.0053 0.0053 0.0053 0.0049 0.0050 0.0036 0.0044 0.0044 25 0.0026 0.005375 0.0053 0.0051 0.0054 0.0052 0.0048 0.0051 0.0036 0.0044 0.0045 30 0.0026 0.005360 0.0053 0.0051 0.0053 0.0052 0.0048 0.0053 0.0035 0.0044 0.0045
Average 15 to 30m/s 0.0026 0.005352 0.005289 0.005165 0.005295 0.005291 0.004866 0.005157 0.003562 0.004411 0.004500 Percent Difference From Full Configuration 1.2 3.5 1.1 1.1 9.1 3.6 33.4 17.6 15.9
Appendix M
144
Drag Area of a Standard Paramotor at 0 Degrees Angle of Attack.
0.0040
0.0042
0.0044
0.0046
0.0048
0.0050
0.0052
0.0054
0.0056
0.0058
0.0060
5 10 15 20 25 30
Velocity of Wind Tunnel in m/s
Dra
g A
rea
of M
odel
in m
^2
Full Configuration No Reserve 90 Degree Reserve No Motor No Intake
No Propeller No Tank No Cage (includes no tank) No Net No Net, No Tank
Figure M.64 Graph of drag area results for standard paramotor at 0o AoI.
Appendix M
145
Table M.65. Summary of Blockage Factors For Standard Paramotor at 32o AoI. Summary of Blockage Factors For Standard Paramotor at 32o AoI.
Indicated velocity m/s Force Balance Arm
Full Configuration No Reserve 90 Degree
Reserve No Motor No Intake No Propeller No Tank
No Cage (includes no tank)
No Net No Net, No Tank
5 0.0128 0.0303 0.0300 0.0303 0.0302 0.0299 0.0294 0.0304 0.0242 0.0279 0.0276 10 0.0128 0.0303 0.0300 0.0303 0.0302 0.0299 0.0294 0.0304 0.0242 0.0279 0.0276 15 0.0128 0.0303 0.0300 0.0303 0.0302 0.0299 0.0294 0.0304 0.0242 0.0279 0.0276 20 0.0128 0.0303 0.0300 0.0303 0.0302 0.0299 0.0294 0.0304 0.0242 0.0279 0.0276 25 0.0128 0.0303 0.0300 0.0303 0.0302 0.0299 0.0294 0.0304 0.0242 0.0279 0.0276 30 0.0128 0.0303 0.0300 0.0303 0.0302 0.0299 0.0294 0.0304 0.0242 0.0279 0.0276
Table M.66. Drag Area On Standard Paramotor at 32o AoI.
Drag Area On Standard Paramotor at 32o AoI.
Indicated velocity m/s Force Balance Arm
Full Configuration No Reserve 90 Degree
Reserve No Motor No Intake No Propeller No Tank
No Cage (includes no tank)
No Net No Net, No Tank
5 0.0028 0.0034 0.0035 0.0035 0.0036 0.0032 0.0037 0.0043 0.0021 0.0032 0.0032 10 0.0028 0.0037 0.0037 0.0037 0.0035 0.0035 0.0036 0.0036 0.0022 0.0032 0.0029 15 0.0027 0.0038 0.0036 0.0038 0.0037 0.0037 0.0034 0.0036 0.0024 0.0033 0.0031 20 0.0027 0.0036 0.0038 0.0037 0.0035 0.0035 0.0035 0.0037 0.0024 0.0032 0.0032 25 0.0026 0.0037 0.0037 0.0037 0.0036 0.0036 0.0035 0.0037 0.0025 0.0032 0.0031 30 0.0026 0.0037 0.0036 0.0037 0.0037 0.0036 0.0035 0.0037 0.0024 0.0032 0.0031
Average 15 to 30m/s 0.0026 0.0037 0.0037 0.0037 0.0036 0.0036 0.0035 0.0037 0.0024 0.0032 0.0031 Percent Difference From Full Configuration 0.99 -0.17 1.76 3.01 6.69 0.42 35.00 13.90 15.39
Appendix M
146
Drag Area of a Standard Paramotor at 32 Degrees Angle of Attack.
0.0020
0.0022
0.0024
0.0026
0.0028
0.0030
0.0032
0.0034
0.0036
0.0038
0.0040
0.0042
0.0044
5 10 15 20 25 30
Velocity of Wind Tunnel in m/s
Dra
g A
rea
of M
odel
in m
^2
Full Configuration No Reserve 90 Degree Reserve No Motor No Intake
No Propeller No Tank No Cage (includes no tank) No Net No Net, No Tank
Figure M.67. Graph of drag area results for standard paramotor at 32o AoI.
Appendix N
147
APPENDIX N - WIND TUNNEL TESTING OF ANNULAR AEROFOILS Construction of Annular Aerofoils
Figure N.1. Construction process – annual aerofoils
Image of bar stock of mild steel turned down to 140mm diameter with 4mm wall thickness; cut off at 30o.
Image of bar stock from different angle, showing annular airfoil centre.
Image of annular airfoils, one cut off at 90o to axial; the other cut off at 30o.
Appendix N
148
Initial Results
Standard Paramotor at 0o AoI
Figure N.2. Model at 0o AoI Table N.3. Average values for standard paramotor at 0o AoI
Average Values for Standard Paramotor at 0o AoI
Indicated velocity m/s Pitch Lift Drag
5 0.002 -0.009 0.107 10 0.007 -0.052 0.427 15 0.017 -0.106 0.968 20 0.031 -0.241 1.702 25 0.049 -0.373 2.661 30 0.068 -0.473 3.877
Standard Paramotor At 0 Degrees AoI
-1
0
1
2
3
4
5
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Forc
e M
easu
red
in
New
tons Pitch
LiftDrag
Figure N.4. Graph of standard paramotor at 0o AoI
Appendix N
149
Standard Paramotor at 32o AoI
Figure N.5. Model at 32o AoI Table N.6. Average values for standard paramotor at 32o AoI
Average Values for Standard Paramotor at 32o AoI Indicated velocity m/s Pitch Lift Drag
5 0.000 -0.049 0.088 10 -0.002 -0.054 0.348 15 -0.003 -0.081 0.784 20 -0.007 -0.304 1.381 25 -0.010 -0.448 2.165 30 -0.022 -0.433 3.103
Standard Paramotor At 32 Degrees AoI
-1
0
1
2
3
4
5
5 10 15 20 25 30
Indicated Wind Tunnel Velocity m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure N.7. Graph of standard paramotor at 32o AoI
Appendix N
150
Standard Paramotor at 0o AoI, no fuel tank
Figure N.6. Model at 0o AoI Table N.7. Average values for standard paramotor at 0o AoI Figure N.8. Graph of standard paramotor at 0o AoI
Appendix N
151
Paramotor at 32o AoI, no fuel tank
Figure N.9. Model at 32o AoI with no fuel tank Table N.10. Average values for standard paramotor at 32o AoI with no fuel tank
Average Values for Standard Paramotor at 32o AoI, With No Netting or Fuel Tank Fitted
Indicated velocity m/s Pitch Lift Drag
5 0.000 -0.004 0.090 10 -0.004 -0.031 0.354 15 -0.003 -0.067 0.782 20 -0.006 -0.188 1.418 25 -0.010 -0.366 2.142 30 -0.018 -0.532 3.124
Standard Paramotor At 32 Degrees AoI With No Netting or Fuel Tank
-1-101122334
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
PitchLiftDrag
Figure N.11. Graph of standard paramotor at 32o AoI with no fuel tank.
Appendix N
152
Paramotor at 0o AoI, Annular Aerofoil with NACA fuel tank
Figure N.12. Model at 0o AoI fitted with annular aerofoil. Table N.13. Average values for paramotor at 0o AoI with annular aerofoil.
Average Values for 0o AoI, Annular Aerofoil with NACA0025 Tank
Indicated velocity m/s Pitch Lift Drag
5 0.002 -0.008 0.130 10 0.007 -0.048 0.437 15 0.018 -0.140 0.932 20 0.034 -0.233 1.604 25 0.053 -0.462 2.480 30 0.079 -0.634 3.544
Paramotor At 0 Degrees AoI With Annular Airfoil with NACA0025 Fuel Tank
-1
0
1
2
3
4
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
PitchLiftDrag
Figure N.14. Graph of paramotor at 0o AoI with annular aerofoil.
Appendix N
153
Paramotor at 32o AoI, Annular Aerofoil with NACA fuel tank
Figure N.15. Model at 32o AoI with annular aerofoil. Table N.16. Average values for paramotor at 32o AoI with annular aerofoil.
Average Values for 32o AoI, Annular Aerofoil with NACA0025 Fuel Tank
Indicated velocity m/s Pitch Lift Drag
5 -0.002 0.009 0.075 10 -0.006 0.061 0.378 15 -0.005 -0.076 0.891 20 -0.027 0.287 1.551 25 -0.044 0.474 2.436 30 -0.064 0.649 3.505
Paramotor At 32 Degrees AoI, Annular Airfoil with NACA0025 Fuel Tank
-1011223344
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
PitchLiftDrag
Figure N.17. Graph of paramotor at 32o AoI with annular aerofoil.
Appendix N
154
Paramotor at 0o AoI, Annular Aerofoil with no fuel tank
Figure N.18. Model at 0o AoI with annular aerofoil and no fuel tank. Table N.19. Average values for paramotor at 0o AoI with annular aerofoil and no fuel tank.
Average Values for 0o AoI, Annular Aerofoil With No Fuel Tank
Indicated velocity m/s Pitch Lift Drag
5 0.002 -0.010 0.109 10 0.008 -0.070 0.421 15 0.018 -0.142 0.917 20 0.039 -0.268 1.675 25 0.060 -0.428 2.567 30 0.088 -0.797 3.660
Paramotor At 0 Degrees AoI, Annular Airfoil With No Fuel Tank
-2-1-1011223344
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
PitchLiftDrag
Figure N.20. Graph of paramotor at 0o AoI with annular aerofoil and no fuel tank.
Appendix N
155
Paramotor at 32o AoI, Annular Aerofoil with no fuel tank
Figure N.21. Model at 32o AoI with annular aerofoil and no fuel tank. Table N.22. Average values for paramotor at 32o AoI with annular aerofoil and no fuel tank. Average Values for 32o AoI, Annular Aerofoil with No
Fuel Tank
Indicated velocity m/s Pitch Lift Drag
5 -0.002 -0.002 0.106 10 -0.006 0.062 0.379 15 -0.013 0.131 0.869 20 -0.027 0.282 1.619 25 -0.041 0.402 2.432 30 -0.056 0.646 3.578
Paramotor At 32 Degrees AoI, Annular Airfoil with No Fuel Tank
-1011223344
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
PitchLiftDrag
Figure N.23. Graph of paramotor at 32o AoI with annular aerofoil and no fuel tank.
Appendix N
156
Paramotor at 0o AoI, Twisted Annular Aerofoil with NACA fuel tank
Figure N.24. Paramotor at 0o AoI, twisted annular aerofoil with NACA fuel tank Table N.25. Average values for standard paramotor at 0o AoI twisted annular aerofoil with NACA fuel tank
Average Values for 0O AoI, 30o Annular Aerofoil with Fuel Tank
Indicated velocity m/s Pitch Lift Drag
5 0.001 -0.050 0.103 10 0.010 -0.155 0.488 15 0.024 -0.345 1.113 20 0.047 -0.638 1.973 25 0.071 -0.947 3.133 30 0.102 -1.393 4.478
Paramotor At 0 Degrees AoI, 30 Degree Annular Airfoil With Fuel Tank
-2
-1
0
1
2
3
4
5
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
PitchLiftDrag
Figure N.26. Graph of standard paramotor at 0o AoI twisted annular aerofoil with NACA fuel tank
Appendix N
157
Paramotor at 32o AoI, Twisted Annular Aerofoil with NACA fuel tank
Figure N.27. Model at 32o AoI twisted annular aerofoil with NACA fuel tank Table N.28. Average values for paramotor at 32o AoI twisted annular aerofoil with NACA fuel tank
Average Values for 32o AoI, 30o Annular Aerofoil With Fuel Tank
Indicated velocity m/s Pitch Lift Drag
5 -0.001 -0.022 0.078 10 -0.001 -0.068 0.315 15 -0.002 -0.132 0.706 20 -0.006 -0.167 1.277 25 -0.012 -0.242 2.026 30 -0.017 -0.254 2.902
Paramotor At 32 Degrees AoI, 30 Deg Annular Airfoil With Fuel Tank
-1
0
1
1
2
2
3
3
4
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
PitchLiftDrag
Figure N.29. Graph of paramotor at 32o AoI twisted annular aerofoil with NACA fuel tank
Appendix N
158
Paramotor at 0o AoI, Twisted Annular Aerofoil with no fuel tank
Figure N.30. Model at 0o AoI twisted annular aerofoil with no fuel tank Table N.31. Average values for paramotor at 0o AoI twisted annular aerofoil with no fuel tank
Average Values for 0o AoI, 30o Annular Aerofoil With No Fuel Tank
Indicated velocity m/s Pitch Lift Drag
5 0.004 -0.003 0.128
10 0.010 -0.092 0.451
15 0.020 -0.151 1.054
20 0.035 -0.261 1.841
25 0.055 -0.398 2.830
30 0.082 -0.568 4.097
Paramotor At 0 Degrees AoI With 30 Degree Annular Propeller With No Fuel Tank
-1
0
1
2
3
4
5
0 5 10 15 20 25 30
Indicated Wind tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
PitchLiftDrag
Figure N.32. Graph of paramotor at 0o AoI twisted annular aerofoil with no fuel tank
Appendix N
159
Paramotor at 32o AoI, Twisted Annular Aerofoil with no fuel tank
Figure N.33. Model at 32o AoI twisted annular aerofoil with no fuel tank Table N.34. Average values for paramotor at 32o AoI twisted annular aerofoil with no fuel tank
Average Values for 32o AoI, 30o Annular Aerofoil With No Fuel Tank
Indicated velocity m/s Pitch Lift Drag
5 -0.001 -0.032 0.072 10 -0.002 -0.052 0.319 15 -0.004 -0.130 0.736 20 -0.005 -0.160 1.312 25 -0.010 -0.202 2.056 30 -0.017 -0.400 2.877
Paramotor At 32 Degrees AoI, 30 Deg Annular Airfoil With No Fuel Tank
-1
0
1
2
3
4
5
0 5 10 15 20 25 30
Indicated Wind tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure N.35. Graph of paramotor at 32o AoI twisted annular aerofoil with no fuel tank
Appendix N
160
Paramotor at 32o AoI, Twisted Annular Aerofoil with No Fuel Tank and 45o Propeller Angle
Figure N.36. Model at 32o AoI, twisted annular aerofoil with no fuel tank and 45o propeller angle. Table N.37. Average values for standard paramotor at 32o AoI, twisted annular aerofoil with no fuel tank and 45o propeller angle.
Average Values for 32o AoI, 30o Annular Aerofoil, 45o Prop, With No Fuel Tank
Indicated velocity m/s Pitch Lift Drag
5 -0.001 -0.026 0.071 10 -0.002 -0.049 0.334 15 -0.004 -0.079 0.788 20 -0.006 -0.084 1.386 25 -0.014 -0.178 2.196 30 -0.021 -0.264 3.097
Paramotor At 32 Degrees AoI, 30 Degree Annular Airfoil, 45 Degree Propeller With No Fuel Tank
-1
0
1
2
3
4
5
0 5 10 15 20 25 30
Indicated Wind tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure N.38. Graph of standard paramotor at 32o AoI, twisted annular aerofoil with no fuel tank and 45o propeller angle.
Appendix N
161
Paramotor at 32o AoI, Twisted Annular Aerofoil with No Fuel Tank and Horizontal Propeller
Figure N.39. Model at 32o AoI, twisted annular aerofoil with no fuel tank and horizontal propeller. Table N.40. Average values for standard paramotor at 32o AoI, twisted annular aerofoil with no fuel tank and horizontal propeller.
Average Values for 32o AoI, 30o Annular Aerofoil, Horizontal Propeller, With No Fuel Tank
Indicated velocity m/s Pitch Lift Drag
5 0.000 -0.019 0.098 10 -0.001 -0.057 0.368 15 -0.004 -0.142 0.814 20 -0.009 -0.178 1.448 25 -0.019 -0.211 2.191 30 -0.031 -0.261 3.155
Paramotor At 32 Degrees AoI, 30 Degree Annular Airfoil, Horizontal Propeller, With No Fuel
Tank
-1012345
0 5 10 15 20 25 30Indicated Wind tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in
New
tons Pitch
LiftDrag
Figure N.41. Graph of standard paramotor at 32o AoI, twisted annular aerofoil with no fuel tank and horizontal propeller.
Appendix N
162
Calculations Table N.42. Summary of raw data at 0o AoI.
Summary of Raw Data For Different Frame and Propeller Configurations At 0o AoI Average Drag Force Recorded in N
Indicated velocity
m/s
Force Balance Arm
Standard Paramotor With Fuel Tank
Standard Paramotor, With No Fuel Tank
Fitted
Annular Aerofoil with Fuel Tank
Annular Aerofoil With No Fuel Tank
30o Annular Aerofoilwith Fuel Tank
5 0.040 0.107 0.131 0.130 0.109 0.103 10 0.161 0.427 0.501 0.437 0.421 0.488 15 0.352 0.968 1.103 0.932 0.917 1.113 20 0.620 1.702 1.953 1.604 1.675 1.973 25 0.958 2.661 3.026 2.480 2.567 3.133 30 1.388 3.877 4.373 3.544 3.660 4.478
NOTE: netting not fitted to any configuration
Table N.43. Summary of raw data at 32o AoI.
Summary of Raw Data For Different Frame and Propeller Configurations At 32o AoI Average Drag Force Recorded in N
Indicated velocity
m/s
Force Balance Arm
Standard Paramotor With Fuel Tank
Standard Paramotor, With No Fuel Tank
Annular Aerofoil with Fuel Tank
Annular Aerofoil with No Fuel Tank
30o Annular AerofoilWith Fuel Tank
30o Annular Aerofoil, Vertical Propeller
With No Fuel Tank
30o Annular Aerofoil, 45o Prop,
With No Fuel Tank
30o Annular Aerofoil, Horizontal Propeller, With No Fuel Tank
5 0.040 0.088 0.090 0.075 0.106 0.078 0.072 0.071 0.098 10 0.161 0.348 0.354 0.378 0.379 0.315 0.295 0.334 0.368 15 0.352 0.784 0.782 0.891 0.869 0.706 0.678 0.788 0.814 20 0.620 1.381 1.418 1.551 1.619 1.277 1.210 1.386 1.448 25 0.958 2.165 2.142 2.436 2.432 2.026 1.899 2.196 2.191 30 1.388 3.103 3.124 3.505 3.578 2.902 2.717 3.097 3.155
NOTE: netting not fitted to any configuration
Appendix N
163
Table N.44. Summary of blockage factors at 0o AoI. Summary of Blockage Factors For Different Frame and Propeller Configurations At 0o AoI
Indicated velocity
m/s
Force Balance Arm
Standard Paramotor With Fuel Tank
Standard Paramotor, With No Fuel Tank
Fitted
Annular Aerofoil with Fuel Tank
Annular Aerofoil With No Fuel Tank
30o Annular Aerofoilwith Fuel Tank
5 0.0126 0.0337 0.0379 0.0313 0.0323 0.0389 10 0.0126 0.0337 0.0379 0.0313 0.0323 0.0389 15 0.0126 0.0337 0.0379 0.0313 0.0323 0.0389 20 0.0126 0.0337 0.0379 0.0313 0.0323 0.0389 25 0.0126 0.0337 0.0379 0.0313 0.0323 0.0389 30 0.0126 0.0337 0.0379 0.0313 0.0323 0.0389
Table N.45. Summary of blockage factors at 32o AoI.
Summary of Blockage Factors For Different Frame and Propeller Configurations At 32o AoI
Indicated velocity
m/s
Force Balance Arm
Standard Paramotor With Fuel Tank
Standard Paramotor, With No Fuel Tank
Annular Aerofoil with Fuel Tank
Annular Aerofoil with No Fuel Tank
30o Annular AerofoilWith Fuel Tank
30o Annular Aerofoil, Vertical Propeller, With No Fuel Tank
30o Annular Aerofoil, 45o Prop,
With No Fuel Tank
30o Annular Aerofoil, Horizontal Propeller, With No Fuel Tank
5 0.0128 0.0275 0.0274 0.0308 0.0304 0.0259 0.0243 0.0277 0.0279 10 0.0128 0.0275 0.0274 0.0308 0.0304 0.0259 0.0243 0.0277 0.0279 15 0.0128 0.0275 0.0274 0.0308 0.0304 0.0259 0.0243 0.0277 0.0279 20 0.0128 0.0275 0.0274 0.0308 0.0304 0.0259 0.0243 0.0277 0.0279 25 0.0128 0.0275 0.0274 0.0308 0.0304 0.0259 0.0243 0.0277 0.0279 30 0.0128 0.0275 0.0274 0.0308 0.0304 0.0259 0.0243 0.0277 0.0279
NOTE: netting not fitted to any configuration
Appendix N
164
Table N.45. Summary of drag area at 0o AoI. Summary of Drag Area For Different Frame and Propeller Configurations At 0o AoI in m2
Indicated velocity
m/s
Force Balance Arm
Standard Paramotor With Fuel Tank
Standard Paramotor, With No Fuel Tank
Fitted
Annular Aerofoil with Fuel Tank
Annular Aerofoil With No Fuel Tank
30o Annular Aerofoilwith Fuel Tank
5 0.0028 0.005247 0.0058 0.0058 0.0044 0.0039 10 0.0028 0.005241 0.0054 0.0045 0.0042 0.0052 15 0.0027 0.005324 0.0053 0.0042 0.0040 0.0054 20 0.0027 0.005347 0.0053 0.0040 0.0042 0.0054 25 0.0026 0.005375 0.0053 0.0039 0.0041 0.0055 30 0.0026 0.005360 0.0053 0.0039 0.0041 0.0055
Average 15 to 30m/s
0.0026 0.005352 0.005288 0.003977 0.004120 0.005428
Percent Difference From Full Configuration 1.2 25.7 23.0 -1.4
NOTE: netting not fitted to any configuration
Table N.46. Summary of drag area at 32o AoI.
Summary of Drag Area For Different Frame and Propeller Configurations At 32o AoI in m2
Indicated velocity
m/s
Force Balance Arm
Standard Paramotor With Fuel Tank
Standard Paramotor, With No Fuel Tank
Annular Aerofoil with Fuel Tank
Annular Aerofoil with No Fuel Tank
30o Annular Aerofoil With Fuel Tank
30o Annular Aerofoil, Vertical Propeller, With No Fuel Tank
30o Annular Aerofoil, 45o Prop,
With No Fuel Tank
30o Annular Aerofoil, Horizontal Propeller, With No Fuel Tank
5 0.0028 0.0031 0.0032 0.0022 0.0043 0.0025 0.0021 0.0019 0.0037 10 0.0028 0.0030 0.0031 0.0035 0.0035 0.0025 0.0022 0.0028 0.0034 15 0.0027 0.0031 0.0031 0.0039 0.0037 0.0026 0.0024 0.0031 0.0033 20 0.0027 0.0031 0.0032 0.0038 0.0040 0.0027 0.0024 0.0031 0.0034 25 0.0026 0.0031 0.0031 0.0038 0.0038 0.0028 0.0025 0.0032 0.0032 30 0.0026 0.0031 0.0031 0.0038 0.0039 0.0027 0.0024 0.0031 0.0032
Average 15 to 30m/s
0.0026 0.0031 0.0031 0.0038 0.0039 0.0027 0.0024 0.0031 0.0033
Percent Difference From Full Configuration -0.95 -22.46 -24.60 13.51 22.41 -0.90 -5.18
NOTE: netting not fitted to any configuration
Appendix N
165
Table N.47. Summary of data at 32o AoI. Summary of Drag Area For Different Frame and Propeller Configurations At 32o AoI in m2
Indicated velocity
m/s
Standard Paramotor with Fuel
Tank
Standard Paramotor,
with No Fuel Tank Fitted
Annular Aerofoil with Fuel
Tank
Annular Aerofoil
with No Fuel Tank
30o Annular Aerofoil with Fuel
Tank
30o Annular Aerofoil, Vertical
Propeller with No Fuel Tank
30o Annular Aerofoil, 45o Prop,
with No Fuel Tank
30o Annular Aerofoil,
Horizontal Propeller, with No Fuel Tank
5 0.0031 0.0032 0.0022 0.0043 0.0025 0.0021 0.0019 0.0037 10 0.0030 0.0031 0.0035 0.0035 0.0025 0.0022 0.0028 0.0034 15 0.0031 0.0031 0.0039 0.0037 0.0026 0.0024 0.0031 0.0033 20 0.0031 0.0032 0.0038 0.0040 0.0027 0.0024 0.0031 0.0034 25 0.0031 0.0031 0.0038 0.0038 0.0028 0.0025 0.0032 0.0032 30 0.0031 0.0031 0.0038 0.0039 0.0027 0.0024 0.0031 0.0032
Average 15 to 30m/s
0.0031 0.0031 0.0038 0.0039 0.0027 0.0024 0.0031 0.0033
Percent Difference From Full
Configuration -0.95 -22.46 -24.60 13.51 22.41 -0.90 -5.18
NOTE: netting not fitted to any configuration
Drag Area of Different Paramotor Frames at 0 Degrees AoI.
0.0040
0.0045
0.0050
0.0055
5 10 15 20 25 30Velocity of Wind Tunnel in m/s
Dra
g A
rea
of M
odel
in m
^2
Standard Paramotor With Fuel Tank Annular Airfoil with Fuel Tank30 Deg Annular Airfoil with Fuel Tank
Figure N.48. Drag areas of different paramotor frames at 0o AoI.
Drag Area of Diffe rent Param otor Fram es at 32 Degrees AoI.
0.0020
0.0025
0.0030
0.0035
0.0040
5 10 15 20 25 30
Velocity of Wind Tunnel in m /s
Dra
g A
rea
of M
odel
in
m^2
Standard Paramotor With Fuel Tank Annular Airfoil w ith Fuel Tank
30 Deg Annular Airfoil With Fuel Tank
Figure N.49. Drag areas of different paramotor frames at 32o AoI.
Appendix N
166
Drag Area of Different Propeller Positions at 32 Degrees Angle of Attack.
0.0020
0.0025
0.0030
0.0035
0.0040
5 10 15 20 25 30
Velocity of Wind Tunnel in m/s
Dra
g A
rea
of M
odel
in
m^2
30 Deg Annular Airfoil, With No Fuel Tank30 Deg Annular Airfoil, 45 Degree Prop, With No Fuel Tank30 Deg Annular Airfoil, Horizontal Propeller, With No Fuel Tank
Figure N.50. Drag areas of different propeller positions at 32o AoI. Sample calculation to determine netting drag
2
2
2
D
D
Solidity Ratio= =
For 1m area with 50x50mm netting.2 (20 1 0.0012)
0.02
0.02
Re
12.5 0.0012 1.225Re1.789 5
Re 214
From Anderson, pg 257, 2001C 1.05
C2.00
Standard paramotor h
o
o
o
E
SS
S
S m
mVd
D qSD N
σ
σρ
μ
= × × ×
=
=
=
× ×=
−=
===
2
T
as approximately 1.1m of netting.D 1.1 2.2D N= × =
Appendix O
167
APPENDIX O - FAIRED FORCE BALANCE ARM Initial Results Standard Paramotor at 0o AoI
Figure O.1. Standard paramotor model in wind tunnel at 00 AoI.
Standard Paramotor At 0 Degrees AoI
-1
0
1
2
3
4
5
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Forc
e M
easu
red
in
New
tons Pitch
Lift
Drag
Figure O.2. Graph of standard paramotor model at 00 AoI force balance. Table O.3. Standard paramotor model at 00 AoI summary data .
Average Values for Standard Paramotor at 0o AoI
Indicated velocity m/s Pitch Lift Drag
5 0.000 -0.033 0.075 10 0.006 -0.079 0.317 15 0.020 -0.067 0.723 20 0.038 -0.106 1.247 25 0.066 -0.024 1.969 30 0.092 -0.172 2.855
Appendix O
168
Standard Paramotor at 32o AoI.
Figure O.4. Standard paramotor model in wind tunnel at 320 AoI.
Standard Paramotor At 32 Degrees AoI
-1
0
1
2
3
4
5
5 10 15 20 25 30 35
Indicated Wind Tunnel Velocity m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
PitchLiftDrag
Figure O.5. Graph of standard paramotor model at 320 AoI force balance. Table O.6. Standard paramotor model at 320 AoI summary data
Average Values for Standard Paramotor at 32o AoI
Indicated velocity m/s Pitch Lift Drag
5 -0.002 -0.031 0.076 10 -0.004 -0.053 0.268 15 -0.001 -0.064 0.557 20 -0.001 -0.065 0.936 25 -0.005 -0.117 1.462 30 -0.003 -0.140 2.095 35 -0.005 -0.117 2.852
Appendix O
169
Twisted Annular Aerofoil with Filleted Fuel Tank Paramotor at 0o AoI
Figure O.7. Twisted annular airfoil paramotor with faired fuel tank model in wind tunnel at 00 AoI.
Paramotor At 0 Degrees AoI With Twisted Annular Aerofoil with NACA0025 Fuel Tank
-2
-1
0
1
2
3
4
5 10 15 20 25 30
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
PitchLiftDrag
Figure O.8. Graph of twisted annular airfoil paramotor with faired fuel tank model in wind tunnel at 00 AoI force balance. Table O.9. Twisted annular airfoil paramotor with faired fuel tank model in wind tunnel at 00 AoI summary data
Average Values for 0o AoI, Twisted Annular Aerofoil with NACA0025 Tank
Indicated velocity m/s Pitch Lift Drag
5 0.001 -0.038 0.102 10 0.009 -0.106 0.414 15 0.028 -0.225 0.880 20 0.056 -0.371 1.546 25 0.083 -0.655 2.428 30 0.125 -0.797 3.503
Appendix O
170
Twisted Annular Aerofoil with Filleted Fuel Tank Paramotor at 32o AoI
Figure O.10. Twisted annular aerofoil paramotor with faired fuel tank model in wind tunnel at 320 AoI.
Paramotor At 32 Degrees AoI, Twisted Annular Aerofoil with NACA Fuel Tank
-1-10112233
5 10 15 20 25 30 35
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
PitchLiftDrag
Figure O.11 Twisted annular aerofoil paramotor with faired fuel tank model in wind tunnel at 320 AoI force balance graph. Table O.12 Twisted annular aerofoil paramotor with faired fuel tank model in wind tunnel at 320 AoI summary data Average Values for 32o AoI, Twisted Annular Aerofoil
with NACA Fuel Tank
Indicated velocity m/s Pitch Lift Drag
5 -0.001 -0.028 0.068 10 -0.003 -0.080 0.237 15 0.004 -0.095 0.489 20 0.014 -0.081 0.842 25 0.023 -0.073 1.280 30 0.014 -0.425 1.920 35 0.022 -0.360 2.564
Appendix O
171
Twisted Annular Aerofoil with no Fuel Tank Paramotor at 0o AoI
Figure O.13 Twisted annular airfoil paramotor with no fuel tank model in wind tunnel at 00 AoI.
Paramotor At 0 Degrees AoI, Twisted Annular Aerofoil With No Fuel Tank
-2-10123456
5 10 15 20 25 30 35
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
PitchLiftDrag
Figure O.14. Twisted annular aerofoil paramotor with no fuel tank model in wind tunnel at 00 AoI force balance graph. Table O.15. Twisted annular aerofoil paramotor with no fuel tank model in wind tunnel at 00 AoI summary data
Average Values for 0o AoI, Twisted Annular Aerofoil With No Fuel Tank
Indicated velocity m/s Pitch Lift Drag
5 0.002 -0.045 0.113 10 0.010 -0.178 0.397 15 0.033 -0.289 0.924 20 0.062 -0.467 1.577 25 0.096 -0.875 2.494 30 0.139 -1.153 3.566 35 0.185 -1.676 4.726
Appendix O
172
Twisted Annular Aerofoil with no Fuel Tank Paramotor at 32o AoI
Figure O.16. Twisted annular airfoil paramotor with no fuel tank model in wind tunnel at 320 AoI.
Paramotor At 32 Degrees AoI, Twisted Annular Aerofoil with No Fuel Tank
-1
0
1
1
2
2
3
3
5 10 15 20 25 30 35
Indicated Wind Tunnel Velocity in m/s
Rea
ctio
n Fo
rce
in N
ewto
ns
PitchLiftDrag
Figure O.17. Twisted annular aerofoil paramotor with no fuel tank model in wind tunnel at 320 AoI force balance graph. Table O.18. Twisted annular aerofoil paramotor with no fuel tank model in wind tunnel at 320 AoI summary data Average Values for 32o AoI, Twisted Annular Aerofoil
with No Fuel Tank
Indicated velocity m/s Pitch Lift Drag
5 -0.001 -0.011 0.060 10 -0.003 0.010 0.226 15 0.000 0.074 0.490 20 0.000 0.085 0.841 25 0.000 0.330 1.308 30 -0.005 0.687 1.868 35 -0.010 0.638 2.459
Appendix O
173
Faired force balance arm values
Faired Force Balance Arm Values
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
5 10 15 20 25 30 35
Indicated Velocity of Wind Tunnel in m/s
Rec
orde
d Fo
rce
in N
ewto
ns
PitchLiftDrag
Figure O.19. Graph of faired force balance. Table O.20. Faired force balance summary.
Average Values for Force Balance Arm in N Indicated velocity m/s Pitch Lift Drag
5 0.000 -0.005 0.006 10 0.001 -0.013 0.029 15 0.006 0.068 0.062 20 0.016 0.133 0.109 25 0.026 0.207 0.174 30 0.036 0.423 0.286 35 0.050 0.325
Appendix O
174
Calculations Table O.21. Summary of drag area.
Drag Area For Different Frame and Propeller Configurations in m2
Indicated velocity m/s
Force Balance Arm
0o AoI Standard
Paramotor
0o AoI, Twisted Annular
Aerofoil with NACA Fuel
Tank
0o AoI, Twisted Annular Aerofoil
with No Fuel Tank
32o AoI Standard
Paramotor
32o AoI, Twisted Annular
Aerofoil with NACA Fuel
Tank
32o AoI, Twisted Annular
Aerofoil with No Fuel Tank
5 0.0004 0.0046 0.0063 0.0070 0.0047 0.0042 0.0037 10 0.0005 0.0048 0.0063 0.0061 0.0040 0.0035 0.0034 15 0.0005 0.0049 0.0060 0.0063 0.0037 0.0032 0.0032 20 0.0005 0.0047 0.0059 0.0060 0.0035 0.0031 0.0031 25 0.0005 0.0048 0.0059 0.0061 0.0035 0.0030 0.0031 30 0.0005 0.0048 0.0059 0.0060 0.0034 0.0031 0.0030 35 0.0005 0.0059 0.0035 0.0031 0.0030
Average 20 to 35m/s 0.0005 0.0048 0.0059 0.0060 0.0035 0.0031 0.0030
Percent Difference From Full Configuration 0.00 11.30 12.51 NOTE: netting not fitted to any configuration
Table O.22. Summary of coefficient of drag.
Coefficient Of Drag For Different Frame and Propeller Configurations in m2
Indicated velocity m/s
Force Balance Arm
0o AoI Standard
Paramotor
0o AoI, Twisted Annular
Aerofoil with NACA Fuel
Tank
0o AoI, Twisted Annular Aerofoil
with No Fuel Tank
32o AoI Standard
Paramotor
32o AoI, Twisted Annular
Aerofoil with NACA Fuel
Tank
32o AoI, Twisted Annular
Aerofoil with No Fuel Tank
5 0.155 0.959 1.040 1.148 1.294 1.295 1.154 10 0.184 1.015 1.056 1.013 1.141 1.134 1.083 15 0.176 1.028 0.998 1.047 1.055 1.038 1.041 20 0.175 0.997 0.986 1.006 0.997 1.006 1.005 25 0.178 1.008 0.991 1.018 0.997 0.979 1.001 30 0.203 1.015 0.993 1.011 0.992 1.020 0.992 35 0.170 0.984 0.992 1.001 0.959
Average 20 to 35m/s 0.1814 1.0070 0.9899 1.0046 0.9944 1.0012 0.9895
NOTE: netting not fitted to any configuration
Appendix O
175
Drag Area of Diffe rent Param otor Fram es at 0 Degrees AoI.
0.0030
0.0040
0.0050
0.0060
0.0070
5 10 15 20 25 30 35
Velocity of Wind Tunnel in m /s
Dra
g A
rea
of
Mod
el in
m^2
0 Deg AoI Standard Paramotor
0 Deg AoI,Tw isted Annular Aerofoil w ith NACA Fuel Tank
0 Deg AoI, Tw isted Annular Aerofoil w ith No Fuel Tank
Figure O.23. Drag areas of different paramotor frames at 0o AoI.
Drag Area of Different Param otor Fram es at 32 Degrees AoI.
0.0025
0.0030
0.0035
0.0040
0.0045
5 10 15 20 25 30 35
Velocity of Wind Tunnel in m /s
Dra
g A
rea
of M
odel
in
m^2
32 Deg AoI Standard Paramotor32 Deg AoI,Tw isted Annular Aerofoil w ith NACA Fuel Tank
32 Deg AoI, Tw isted Annular Aerofoil w ith No Fuel Tank
Figure O.24. Drag areas of different paramotor frames at 32o AoI.
Coefficient of Drag of a Paramotor at 32 Degrees AoI (including force balance arm).
0.00
0.40
0.80
1.20
5 10 15 20 25 30 35
Velocity of Wind Tunnel in m/s
Coe
ffici
ent o
f Dra
g
Force Balance Arm0 Deg AoI Standard Paramotor0 Deg AoI,Twisted Annular Aerofoil with NACA Fuel Tank32 Deg AoI Standard Paramotor32 Deg AoI,Twisted Annular Aerofoil with NACA Fuel Tank
Figure O.25. Drag areas of different paramotor frames at 32o AoI.
Appendix P
176
APPENDIX P – PROPOSED DESIGN
10 STEP DESIGN PROCESS
1. Identification of a need.
As stated in Client Brief description.
2. Problem Definition.
As stated in Client Brief aim.
3. Search.
Experimentation has provided sound background knowledge of the drag contributors
in a paramotor.
4. Constraints.
Constraints imposed on the future design are:
i. Forces the paramotor has to withstand (first order approximations):
a. Resistant to damage from a hard landing. Assume 2G tolerance.
b. An asymmetric collapse of paraglider wing during flight with a
resulting spin, creates total lift loading on one underarm bar at 4G.
c. Engine mounts must withstand thrust developed by power plant (50kg
static thrust).
d. Method of stopping pilot’s body from entering propeller arc. Worst
case scenario is for a jammed throttle on start up. Pilot places fingers
into mesh fingers to keep paramotor away from body, with engine
producing 50kg of opposing thrust.
e. Fuel tank to retain structural integrity on hard landing. Assume 4G
landing.
f. Limiting travel of engine mounts as a result of hard landing to reduce
the possibility of the propeller arc impacting with a structural member.
Assume 2G landing.
Appendix P
177
g. Incorrect forward launch in moderate wind causes paraglider wing to
pull the paraglider pilot onto their back. Results in paramotor and pilot
placing full weight on cage with propeller possibly at maximum rpm.
Assume 2G load.
h. Forces exerted on top hoop of paramotor frame by paraglider
suspension lines during forward launch.
ii. Use existing Top 80 powerplant and propeller in future design.
iii. Use existing harness and reserve parachute in future design, therefore pilots
positioning will remain the same.
iv. Create a design that can be homebuilt by amateur builders.
5. Criteria.
The criterion that the future design will be assessed against is shown below.
i. Increase in glide ratio.
ii. Feasibility.
iii. Safety
iv. Weight
v. Reduction in moment of inertia in Z axis
vi. Cost.
6. Alternative solutions.
i. Ducted fan
ii. Folding propeller
a. Folding along driveshaft axis.
b. Folding along rotation plane.
c. Feathering.
iii. Cage
a. Umbrella cage
b. Streamlined cage
c. No cage
iv. Mesh
a. Folding mesh barrier
Appendix P
178
b. Curtain type mesh barrier
7. Analysis.
As shown in chapters 4 to 7.
8. Decision.
As shown in chapters 6, 7, 8 and 9.
9. Specification.
To be detailed in this appendix.
10. Communication.
As per chapter 8, decision not to proceed to build stage.
Appendix P
179
PROPOSED DESIGN
Introduction
The paramotor currently has a 6.5:1 glide ratio with the same wing in paragliding having a
8.2:1 glide ratio. The design aim was to achieve a glide ratio of 7.35:1, halfway between these
points. Therefore the design principal was minimal drag at 30o AoI (23o recline plus 7o glide
slope). Wind tunnel testing determined that a twisted annular aerofoil recorded the lowest
drag of any configuration tested. A lower drag paramotor frame is virtually useless if it does
not adequately protect the pilot in case of a mishap. Before the frame could be redesigned, a
basic understanding of the design loads encountered had to be clarified. This was done in the
10 step design process shown previously.
Construction
Weight of the replacement frame was desired to be lighter than the existing frame, however
through calculations performed in CATIA and by direct measurement, the outcome of the
proposed frame was heavier (table P.1). The increase in weight of 0.3 kg could possibly be
reduced with further structural analysis. The fuel system was not weighed separately,
therefore a conservative weight of 1 kg has been given for the plastic tank and lines. The
proposed paramotor design is shown in figures P.2. to P.9.
A symmetrical NACA0025 aerofoil was chosen with a 150mm chord because it could hold
two hoops of 1.4m diameter. These hoops were constructed from 12.7mm diameter, 0.9mm
wall thickness, chrome molybdenum tubing. The centre of the frame was constructed from
25.4mm diameter chrome molybdenum tubing. This tubing was to have been TIG welded.
The non structural aerofoil section is created from 2 plies of pre-impregnated bidirectional
carbon fibre cloth. The plies were to have 0 the 45o orientation. The aerofoils would be
created in two halves in 1 metre long sections in a straight mould (fig. P.10). Once
manufactured the fairing half would be joined to balsa wood ribs bonded at 0.5m intervals and
at the ends. Two halve fairings would be placed over the hoops of the frame with cold cure
adhesive applied to contact points. A vacuum bag would then be placed over the fairings and
vacuum applied. The anticipated result would be the composite fairing twisting to follow the
outer hoops of the frame to create a twisted annular aerofoil. Trial and error would have to
occur to obtain correct balsa wood spacing to obtain the optimal result.
Appendix P
180
Table P.1 Table of mass build up of proposed design as a comparison with existing paramotor.
Mass of proposed design
Quantity Volume (m3)
Density (kg/m3) Description
Weight per component
(kg)
Sub total (kg)
2 4.4 0.262 * Outer hoops, 12.7mm dia, 0.9mm wall thickness, chrome moly tubing. 1.153 2.306
1 2.2 0.544 * Inner frame, 25.4mm dia, 1.2mm wall thickness, chrome moly tubing. 1.197 1.197
2 0.00002011 7850 Underarm mounting brackets 0.158 0.316 35 0.00000003 7850 TIG weld 0.00025 0.009
1 0.00084 1740 # Fairing, 2 ply hot bonded bidirectional graphite pre preg 1.462 1.462
16 0.000004 140 ~ Balsa wood ribs 0.001 0.009 281 0.000001 970 Dyneema netting 0.001 0.214
4 1430 ~ Delran wheels 0.024 0.096 7850 Wheel mounts 0.000 0.000 3 0.000002 7850 Axles 0.016 0.047 1 7850 ~ RH underarm bar 0.115 0.115 1 7850 " LH underarm bar 0.285 0.285 Fuel system(empty) 1.000
TOTAL WEIGHT (kg) 7.055 Weight of PAP1400AS frame, minus harness (kg) 6.726
* As per Performance Metals specifications, specifications are length and density per metre. # As per Shackelford, J.F. (2000). Materials science for engineers, New Jersey, Prentice-Hall
~ As per CATIA calculations " Approximation
The netting would be made to the frame as mentioned in chapter 7. Holes would be drilled at
intervals around the outer hoop. Lengths of Dyneema line would be knotted and a protective
ferrule would be made to cover it. The lines would be placed into the frame by use of a
vacuum cleaner over the desired hole to draw the Dyneema line through the frame. This line
would then be pulled out with the ferrule preventing abrasion of the Dyneema on the tubing.
A 50mm cube of wood would be used to maintain hole spacing when making the net. If
desired the hole size could be reduced at points of likely contact. Using net making
techniques the net would be tied working towards the centre of the frame. The two sides
would be secured by a modified tie down strap ratchet mechanism. This would enable quick
disassembly of outer hoops for transport and could control netting tension.
Appendix P
181
Finite Element Analysis (FEA)
The CATIA model was constructed to enable FEA, which allows point of high stress or strain
to be identified when the model is placed under load and allows any structural shortcomings
in the design to be identified the design revised.
As a result of the decision not to proceed with the building of the proposed design, FEA was
not completed.
Moment of inertia calculations
These were not completed beyond first approximations due to the decision not to proceed
with building the proposed design. An indication of the C of G of both the pilot and
paramotor can be seen in figure P.7.
Appendix P
182
Figure P.2. CATIA Images of the proposed low drag design are shown below with non structural composite fairing fitted.
Appendix P
183
Figure P.3. CATIA Images of the proposed low drag design are shown below with non structural composite fairing removed showing the 12.5mm OD, 0.9mm wall thickness chrome-moly double hoop frame. The centre frame is constructed from 25.4mm OD, 0.9mm wall thickness chrome-moly tubing.
Appendix P
184
Figure P.4. CATIA Images of the proposed low drag design are shown below with non structural composite fairing removed as well as the hoop arcs to the sides. This configuration was for transport.
Appendix P
185
Figure P.5. Isometric view of the proposed low drag design.
Appendix P
186
Figure P.6. Isometric view of the proposed low drag design with non structural fairing removed.
Appendix P
187
Figure P.7. Isometric view of the proposed low drag design, pink dot signifies C of G of pilot, cross is overall C of G with proposed paramotor weight and full tank of fuel.
Centre of Gravity
Overall Centre of Gravity with proposed paramotor weight and full tank of fuel.
Appendix P
188
Figure P.8. Isometric view of the proposed low drag design with side hoops to showing mounting dowels.
Figure P.9. Emphasis on hard landing wheels fitted to proposed low drag design.
Appendix P
189
Figure P.10. Preliminary plans created by author for SACME workshop. Used to discuss how mould would be created, to manufacture fairing for proposed low drag design. Insert. Image of bonded balsa wood ribs to composite skin.
Appendix R
190
APPENDIX R – PARAMOTOR CROSS SECTION VISUALISATION
Figure R. 1. Slice taken at 32o AoI, in an attempt to visualise profile of paraglider and paramotor to oncoming airflow.
Figure R. 2. Slice taken at 32o AoI, in an attempt to visualise profile of paraglider and paramotor to oncoming airflow.
Appendix R
191
Figure R. 3. Slice taken at 32o AoI, in an attempt to visualise profile of paraglider and paramotor to oncoming airflow.
Figure R. 4. Slice taken at 32o AoI, in an attempt to visualise profile of paraglider and paramotor to oncoming airflow.
Appendix R
192
Figure R. 5. Slice taken at 32o AoI, in an attempt to visualise profile of paraglider and paramotor to oncoming airflow.
Figure R. 6. Slice taken at 32o AoI, in an attempt to visualise profile of paraglider and paramotor to oncoming airflow.
Appendix R
193
Figure R. 7. Slice taken at 32o AoI, in an attempt to visualise profile of paraglider and paramotor to oncoming airflow.
Figure R. 8. Slice taken at 32o AoI, in an attempt to visualise profile of paraglider and paramotor to oncoming airflow.
Appendix R
194
Figure R. 9. Slice taken at 32o AoI, in an attempt to visualise profile of paraglider and paramotor to oncoming airflow.
Figure R. 10. Slice taken at 32o AoI, in an attempt to visualise profile of paraglider and paramotor to oncoming airflow.
Appendix R
195
Figure R. 11. Slice taken at 32o AoI, in an attempt to visualise profile of paraglider and paramotor to oncoming airflow.
Figure R. 12. Slice taken at 32o AoI, in an attempt to visualise profile of paraglider and paramotor to oncoming airflow.
Appendix W
196
APPENDIX S - PROJECT TASK OUTLINE Removed for online version
APPENDIX T – TASK BREAK DOWN STRUCTURE Removed for online version
APPENDIX U – PROJECT GANTT CHART Removed for online version
APPENDIX V – PROJECT MILESTONE CHART Removed for online version
APPENDIX W – RISK ASSESSMENT Removed for online version
End
