aerospace
Article
Vertical Wind Tunnel for Prediction of Rocket
Flight Dynamics
Hoani Bryson 1 , Hans Philipp Sültrop 1 , George Buchanan 1 , Christopher Hann 1, *,
Malcolm Snowdon 2 , Avinash Rao 2 , Adam Slee 1 , Kieran Fanning 1 , David Wright 1 ,
Jason McVicar 3 , Brett Clark 1 , Graeme Harris 4 and Xiao Qi Chen 5
1
2
3
4
5
*
Department of Electrical and Computer Engineering, University of Canterbury, Private Bag 4800,
Christchurch 8140, New Zealand; hoani.bryson@gmail.com (H.B.);
philipp.sueltrop@pg.canterbury.ac.nz (H.P.S.); georgebuchanannz@gmail.com (G.B.);
a.slee@rocketlab.co.nz (A.S.); kieranfanning@hotmail.co.nz (K.F.); djwnz@hotmail.com (D.W.);
clarkbab@gmail.com (B.C.)
Rocket Lab Ltd., 3A Airpark Drive, Auckland 2022, New Zealand; malcolm.snowdon@gmail.com (M.S.);
avinash.rao43@gmail.com (A.R.)
School of Engineering and Information and Communication Technology (ICT), University of Tasmania,
Private Bag 65, Hobart 7001, Australia; jason.j.mcvicar@gmail.com
Engineering and Architecture Department, Christchurch Polytechnic Institute of Technology (CPIT),
P.O. Box 540, Christchurch Mail Centre, Christchurch 8140, New Zealand; Graeme.Harris@cpit.ac.nz
Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140,
New Zealand; xiaoqi.chen@canterbury.ac.nz
Correspondence: chris.hann@canterbury.ac.nz; Tel.: +64-3-364-2987 (ext. 7242); Fax: +64-3-364-2264
Academic Editor: Raffaello Mariani
Received: 1 February 2016; Accepted: 22 March 2016; Published: 29 March 2016
Abstract: A customized vertical wind tunnel has been built by the University of Canterbury Rocketry
group (UC Rocketry). This wind tunnel has been critical for the success of UC Rocketry as it allows
the optimization of avionics and control systems before flight. This paper outlines the construction
of the wind tunnel and includes an analysis of flow quality including swirl. A minimal modelling
methodology for roll dynamics is developed that can extrapolate wind tunnel behavior at low wind
speeds to much higher velocities encountered during flight. The models were shown to capture
the roll flight dynamics in two rocket launches with mean roll angle errors varying from 0.26˝ to
1.5˝ across the flight data. The identified model parameters showed consistent and predictable
variations over both wind tunnel tests and flight, including canard–fin interaction behavior. These
results demonstrate that the vertical wind tunnel is an important tool for the modelling and control
of sounding rockets.
Keywords: rocketry; canard actuation; vertical wind tunnel; flow quality; minimal modelling; roll
dynamics; PD control; minimal modelling
1. Introduction
A customized vertical wind tunnel has been built by the University of Canterbury (UC) Rocketry
Research group [1] to test advanced control systems for application on small sounding rockets at
subsonic and supersonic speeds. The common approach to designing and analyzing supersonic rockets
is to quantitatively identify aerodynamics in a supersonic wind tunnel. However, these types of wind
tunnels have large power requirements and are thus very costly, and usually have much shorter run
times around 0.1–0.2 s [2].
Another approach to subsonic and supersonic flow analysis is Computational Fluid Dynamics
(CFD). For example, canard–fin interactions have been well studied and modelled with CFD using
Aerospace 2016, 3, 10; doi:10.3390/aerospace3020010
www.mdpi.com/journal/aerospace
Aerospace 2016, 3, 10
2 of 27
wind tunnel data with relatively good predictions for the smaller angle of attacks [3,4]. However, the
available comparisons in the literature are usually for static movements of the canards, so it is not
clear how well the CFD models predict transient response in flight. Only very limited comparisons
between flight and wind tunnel data have been published and are typically old NASA technical
notes (e.g., [5–7]). The results of [6] show a reasonable prediction of pitch flight dynamics in terms of
the frequency and phase responses of the pitching velocity per unit canard-fin-deflection frequency,
however no roll comparisons are given and CFD analysis is not performed. Hence, although CFD
analysis is commonly used for predicting rocket response in a wind tunnel, it has not been fully
validated in flight. For the case of hypersonic flow, no vehicle has been flown long enough to obtain
the data needed to improve the model accuracy and hypersonic wind tunnels only provide very short
durations. Thus, in general, although CFD are useful for gaining trends on the expected flight response,
they are not sufficiently accurate to design robust control systems and hence, extensive flight testing is
usually required.
In addition to CFD, there are a number of empirical approaches to modelling subsonic and
supersonic rocket steady state aerodynamics. These methods are primarily based on NASA wind
tunnel data and have been developed into engineering-level and intermediate-level aerodynamic
prediction codes [7–9]. The models have also been extended to include canard interaction [10,11] but
the experimental work is restricted to wind tunnels, so only considers steady state responses to fixed
canard angles. Therefore, these methods are primarily for designing responsive canards in missiles
and have not been used to understand actual rocket flight, where there are very fast movements and
transient effects that often behave very differently to steady state response in a wind tunnel.
This paper develops models of rocket roll dynamics that are first identified in the wind tunnel
at low speeds and then validated on actual rocket launches at much higher speeds. This type
of validation is unique in the literature as most other approaches do not go any further than
wind tunnel evaluation [10,11]. The UC rocketry modelling and control methodology is to use
a combination of dynamic subsonic wind tunnel testing and sounding rocket launches, to test
qualitatively methodologies that have the ability to account for new dynamics in real-time. In other
words, the approach is to model the rocket response in the wind tunnel during a control actuation
that will be implemented in a flight. In addition, the damping or lift coefficients are not needed to
be precisely known before launch, as any uncertainty from the wind tunnel tests, can be accounted
for “on-the-fly” during the rocket flight. This UC rocketry control methodology has been successfully
validated on several subsonic launches including an unstable rocket. For more details and results
see [1].
The vertical wind tunnel has been a critical component to the success of UC Rocketry. In particular,
it is important for obtaining quantitative information on the first few seconds of flight and can be used
to estimate a full subsonic flight response using minimal modelling and parameter identification [12].
In addition, the vertical test section allows a much simpler and more accurate way of testing roll
dynamics since the rocket can be suspended from a string. In a standard horizontal wind tunnel there
is extra friction since an additional moving surface, like a bearing is required, so roll response is less
realistic. For pitch and yaw dynamics, a gimbal frame [13] is used to allow three˝ of freedom control.
This gimbal frame set up is important for debugging the avionics control hardware and software before
flight. To test the stability of a fully fueled rocket, two sets of strings are horizontally attached from
one edge of the wind tunnel to the center of mass of the rocket, which allows movement in one axis.
Hence this vertical wind tunnel has a number of unique features tailored for rocket flight analysis.
A typical closed-circuit subsonic horizontal wind tunnel has a motor powered fan which blows
air around a looping tube [14]. The settling chamber usually contains a honeycomb flow straightener
followed by several wire mesh screens to reduce turbulence [15]. Following the settling chamber, and
just prior to the test section, is a contraction in the tube, which increases air speed. The test section is
where the test article is placed and data is collected. A diffuser, which is a gradually diverging section
of tube, is placed after the test section to decrease the velocity and thus decrease power requirements.
Aerospace 2016, 3, 10
3 of 27
Curved vanes guide air around corners [16]. The disadvantage of using a closed-circuit is that more
space and materials are required to construct the back loop of the circuit. The curved vanes are complex
features and an additional expense in the construction. Heat exchangers are often needed to keep the
Aerospace 2016, 3, 10
3 of 27
tunnel at the desired temperature, since the same air is being re-circulated through the circuit many
times exchangers
and may deviate
significantly
fromthe
thetunnel
ambient
airdesired
temperature
[16]. since the same air is
are often
needed to keep
at the
temperature,
re-circulated
through
the circuit
many
times
and may
deviate
significantly
from the[17]
ambient
Abeing
key part
of the UC
Rocketry
wind
tunnel
design
is the
use of
bendy plywood
due to its
air temperature
low cost,
light weight[16].
and ease of constructing a circular cross section. Another advantage is that with
A key part
the UC Rocketry
windto
tunnel
is the
use of bendy plywood
[17] is,
dueifto
its shape
a circular shape
lessof
material
can be used
give design
the same
cross-sectional
area. That
the
low cost, light weight and ease of constructing a circular cross section. Another advantage is that
was changed to a square with side length equal to the circle’s diameter, the volume of space would be
with a circular shape less material can be used to give the same cross-sectional area. That is, if the
greatershape
and was
manufacturing
simpler, but the maximum displacement of the rocket that can be achieved
changed to a square with side length equal to the circle’s diameter, the volume of space
in anywould
direction,
would
be the samesimpler,
as for the
circle.
Thus the
extra power
required
in the
be greater
andstill
manufacturing
but the
maximum
displacement
of the
rocket that
can fan to
maintain
a given flow
inwould
the square
configuration
is the
effectively
wasted.
Thepower
vertical
orientation
be achieved
in anyvelocity
direction,
still be
the same as for
circle. Thus
the extra
required
in the the
fan to
maintain
a given
flow velocity
in the square configuration
is effectivelywind
wasted.
The and
also avoids
large
floor and
building
space requirements
needed for horizontal
tunnels,
vertical
orientation
also
avoids
the
large
floor
and
building
space
requirements
needed
was assembled outdoors in a fenced enclosure further simplifying space allocation. A 15 kWfor
fan was
horizontal
wind in
tunnels,
and was assembled
outdoors
a fenced enclosure
further
simplifying
already
in existence
the Department
of Electrical
and in
Computer
Engineering
at UC,
so the wind
space allocation. A 15 kW fan was already in existence in the Department of Electrical and Computer
tunnel was essentially built around this fan which was at the base and sitting on the ground.
Engineering at UC, so the wind tunnel was essentially built around this fan which was at the base
This paper details some of the design and construction of the wind tunnel, methods for
and sitting on the ground.
overcoming
swirl
induced
fan,design
and presents
a number
of wind
flightforresults.
This
paper
details from
some the
of the
and construction
of the
wind tunnel
tunnel, and
methods
A key overcoming
finding is that
the
verticalfrom
wind
canpresents
provide
realisticof
roll
predictions
of flight
rocketresults.
flights well
swirl
induced
thetunnel
fan, and
a number
wind
tunnel and
beyond
the finding
wind speeds
that
can be
generated
by provide
the current
fan,
and
it provides
an excellent
A key
is that the
vertical
wind
tunnel can
realistic
roll
predictions
of rocket
flights test
wellfor
beyond
the wind
speeds
that can
be generated
the currentidentification
fan, and it provides
an excellent
platform
modelling
rocket
behavior
and
validatingbyparameter
methods
prior to flight.
test
platform
for
modelling
rocket
behavior
and
validating
parameter
identification
methods
For example, similar canard–fin interaction roll dynamics observed and identified in the prior
windtotunnel
flight. For example, similar canard–fin interaction roll dynamics observed and identified in the wind
were also seen in the subsequent rocket flight. The results show that it is possible to create a low-cost
tunnel were also seen in the subsequent rocket flight. The results show that it is possible to create a
wind tunnel with excellent flow characteristics, and thus provides a very valuable research tool for
low-cost wind tunnel with excellent flow characteristics, and thus provides a very valuable research
modelling
and
control and
of sounding
rockets. rockets.
tool for
modelling
control of sounding
2. Methodology—Wind
Tunnel
2. Methodology—Wind
Tunnel
This section
outlines
the design
and and
manufacture
processes
of the
customized
This section
outlines
the design
manufacture
processes
of the
customizedvertical
verticalwind
windtunnel
tunnel
by UCasRocketry
used by
UC used
Rocketry
shown as
in shown
Figurein1.Figure 1.
Figure
1. Customized
tunnelfor
for
Sounding
Rockets.
Figure
1. Customizedvertical
vertical wind
wind tunnel
Sounding
Rockets.
Aerospace 2016, 3, 10
4 of 27
2.1. Concept and Design
To simplify the mounting of the rocket and to provide realistic roll response testing, the key design
specification was to allow the mounting of the rocket vertically by suspending from the nose cone.
Therefore a vertical suck-down wind tunnel was designed.
Due to the significant vertical height requirement, the structure was stored outside in a caged
enclosure adjacent to the High Voltage Lab, which meant that it needed to be weather resistant.
The wind tunnel was designed in individual sections with bolted joints between each section.
This approach simplifies fabrication and assembly as the components could be added to or taken from
the wind tunnel as required. To create a sufficient quality of flow in the wind tunnel, aluminium
honeycomb was used as a flow conditioner. This flow straightener was critical, particularly since
winds affect the flow.
Another important part of the design was utilizing an existing 1 m diameter, 15 kW fan and speed
controller. Thus, the wind tunnel structure was effectively built around the fan. Since the test section
was chosen to have a diameter of 0.6 m, wide angle diffusers were necessary to reduce the height of
the wind tunnel. Bendy plywood was chosen for the structure as it was easy to form into the required
shapes and significantly reduces manufacturing complexity and time, as compared to sheet-metal
or fiberglass.
The overall rocket wind tunnel design consisted of five main components: the flow conditioner,
reducer, test section, diffuser and fan. These components are summarized as follows:
‚
‚
‚
‚
‚
The flow conditioner was a cylindrical section at the inlet of the tunnel with an internal diameter
of 1.4 m and a 9 mm wall thickness. The flow conditioner holds the honeycomb and a mesh screen.
The reducer took the flow from the 1.4 m internal diameter flow conditioner to the 0.6 m internal
diameter test section. This contraction before the test section can also reduce velocity fluctuations
and form a more uniform flow. The reducer walls were fabricated from 6 mm bendy ply so that it
would fit into the smaller internal diameter of the test section.
The test section was 2 m long, had an internal diameter of 0.6 m and was formed with 6 mm
bendy ply. Due to the length and thin walls of the test section a 77 ˆ 38 mm length of pine was run
down each side. The door for the test section was then framed using 75 ˆ 38 mm pine and 17 mm
plywood. The frame was then removed and the door cut from the test section. At the bottom of
the test section, a metal grille recessed into a plywood ring was placed to protect the fan.
The diffuser transitioned the flow from the 0.6 m internal diameter test section to the 1 m internal
diameter fan housing. The diffuser was also made from 6 mm bendy ply.
The fan was 1 m diameter and had up to 15 kW available in power. The blade angle was at 23˝ so
was left unchanged. The fan was on wheels, and could be adjusted to meet flush with the diffuser.
In addition, the wind tunnel was secured to the wall of the High Voltage (HV) lab by a permanent
scaffold and a winch was used to open a lid on the wind tunnel during operation and closed after
testing to ensure no rain came into the wind tunnel and fan.
2.2. Construction
2.2.1. General Methods
Bendy ply was used for the outer skin of the wind tunnel. Bendy ply is plywood with the
two outer lamination grains aligned, and forming most of the thickness of the sheet. A thin central
lamination bonded the two outer laminations together with the grain running perpendicular to the
outer laminations. This property allows the plywood to be bent down to tight radii without the need
for steam/heat, see Figure 2.
Aerospace 2016, 3, 10
5 of 27
Aerospace 2016, 3, 10
Aerospace 2016, 3, 10
5 of 27
5 of 27
Aerospace 2016, 3, 10
5 of 27
Figure 2. A sheet of 6 mm bendy ply.
Figure
of 66 mm
mm bendy
bendyply.
ply.
Figure2.
2. A
A sheet
sheet of
The rest of the tunnel structure was constructed from standard 17 mm plywood and 75 × 38 mm
Figure 2. A sheet of 6 mm bendy ply.
The
the
tunnelstructure
structure
was
constructed
from on
standard
17
plywood
and
7575reduce
׈
3838
mm
pine.The
The
17rest
mm
plywood
was
usedwas
to form
the flanges
the ends
of each
section.
To
the
rest
ofof
the
tunnel
constructed
from
standard
17 mm
mm
plywood
and
mm
pine.
The
17
mm
plywood
was
used
to
form
the
flanges
on
the
ends
of
each
section.
To
reduce
thethe
amount
ofThe
material
wastage,
each
flange
was
made
up
from
four
quarter
flanges.
The
parts
were
pine.
The
17
mm
plywood
was
used
to
form
the
flanges
on
the
ends
of
each
section.
To
reduce
rest of the tunnel structure was constructed from standard 17 mm plywood and 75 × 38 mm cut
amount
of
material
wastage,
each
flange
was
made
up from
quarter
flanges.
TheTo
parts
were
using
a
jigsaw.
sections
of
the
wind
tunnel
fabricated
byofforming
individual
outer
skin
pine.
17The
mm
plywoodeach
was
used
towas
form
thewere
flanges
on four
the
each
section.
reduce
thecut
amount
of The
material
wastage,
flange
made
up from
fourends
quarter
flanges.
The parts
were
cut
using
a
jigsaw.
The
sections
of
the
wind
tunnel
were
fabricated
by
forming
individual
outer
skin
material
wastage,
each
flange
was
made
up from
The
parts
cut
pieces
theofflanges,
and
securing
with
wood
screws,
as four
shown
in flanges.
Figure
3a. Once
askin
complete
using amount
ato
jigsaw.
The
sections
of
the
wind
tunnel
were
fabricated
by quarter
forming
individual
outerwere
pieces
pieces toathe
flanges,
and securing
with
wood
screws,
as shown
in
Figureindividual
Once outer
a complete
jigsaw.
The sections
ofwood
the were
wind
tunnel
fabricated
by with
forming
skin had
section
had been
the
screws
backed
off, epoxy
resin
Westa3a.
Systems
403
modifier
to theusing
flanges,
andsecured,
securing
with
screws,
as were
shown
in Figure
3a.
Once
complete
section
section
had
been
secured,
the
screws
were
backed
off,
epoxy
resin
with
West
Systems
403
modifier
pieces to into
the flanges,
andand
securing
with wood
screws,
astightened.
shown in Figure
3a. Once
a complete
was
worked
the
gap,
the
screws
were
again
The
flange
joints
were
then
been secured, the screws were backed off, epoxy resin with West Systems 403 modifier was worked
wassection
worked
gap, the
andscrews
the screws
were off,
again
tightened.
flange
joints
then
had into
been the
secured,
were backed
epoxy
resin withThe
West
Systems
403 were
modifier
reinforced
with
wovenwere
fiberglass
see Figure
3b. The
75 were
× 38 mm
pine
was used
add
into
the gap,
and200
thegscrews
again cloth,
tightened.
The flange
joints
then
reinforced
withto
200
g
reinforced
with 200
woven
cloth, see
Figure
The 75 × The
38 mm
pinejoints
was were
used to
add
was worked
into gthe
gap, fiberglass
and the screws
were
again3b.
tightened.
flange
then
strength
to
the
openings
in
the
tunnel
and
provide
mounting
points
for
fixtures,
see
Figure
4.
woven
fiberglass
cloth,
Figure
3b. The
75provide
ˆ 38
pine
used
tofixtures,
add
strength
to the4.
strength
to thewith
openings
in
the tunnel
andcloth,
mounting
points
see
Figure
reinforced
200see
g woven
fiberglass
seemm
Figure
3b.was
The
75 ×for
38
mm pine
was
used
toopenings
add
in thestrength
tunnel and
provide
mounting
points
for
fixtures,
see
Figure
4.
to the openings in the tunnel and provide mounting points for fixtures, see Figure 4.
(a)
(a)
(a)
(b)
(b)
(b)
Figure
3. (a)
A sheet
ofof
6 mm
200 ggwoven
wovencloth
clothreinforcement.
reinforcement.
Figure
3. (a)
A sheet
6 mmbendy
bendyply;
ply;(b)
(b)Flange
Flange joint
joint with
with 200
Figure
Figure 3.
3. (a)
(a) A
A sheet
sheet of
of 66 mm
mm bendy
bendy ply;
ply; (b)
(b) Flange
Flange joint
joint with
with 200
200 g
g woven
woven cloth
cloth reinforcement.
reinforcement.
Figure 4. 75 × 38 mm pine lengths used for reinforcement and framing.
Figure 4. 75 × 38 mm pine lengths used for reinforcement and framing.
Figure
38mm
mmpine
pinelengths
lengths used
used for
for reinforcement
reinforcement and
and framing.
framing.
Figure 4.
4. 75
75 ˆ
× 38
Aerospace
2016,
3, 10
Aerospace
2016,
3, 10
Aerospace 2016, 3, 10
Aerospace 2016, 3, 10
6 of
6 of
27 27
6 of 27
6 of 27
The internal surface of the tunnel was not perfectly smooth due to the outer skin joints,
Theinternal
internalsurface
surfaceofof the
the tunnel
tunnel was not
not perfectly
smooth
due
totothe
outer
skin
joints,
The
perfectly
smooth
due
the
outer
skin
joints,
The internal
surface
of manufacturing
the tunnel was
wasimperfections
not perfectly
due
to the
outer
skin
joints,
screw-heads,
excess
glue and
onsmooth
the inner
plywood
face.
Therefore,
all
screw-heads,
excess
glue
and
manufacturing
imperfections
on
the
inner
plywood
face.
Therefore,
allall
screw-heads,
excess
glue
and
manufacturing
imperfections
on
the
inner
plywood
face.
Therefore,
screw-heads,
excess
and faces
manufacturing
imperfections
thealso
inner
plywoodtoface.
all
internal
surfaces
andglue
flange
were sanded
smooth. Iton
was
necessary
fill Therefore,
voids on the
internal
surfaces
and
flange
faces
were
sanded
smooth.
It was
also
necessary
to fill
voids
on the
internal
surfaces
and
flange
faces
were
sanded
smooth.
It
was
also
necessary
to
fill
voids
on
the
inner
internal
surfaces
and
flange
faces
were
sanded
smooth.
It
was
also
necessary
to
fill
voids
on
the
inner side of the skin; both along the seams and behind the screw heads. Poly-filler was applied to
inner side of the skin; both along the seams and behind the screw heads. Poly-filler was applied to
side
of the
both
along
the
seams
and
behind
the tunnel
screw
heads.
Poly-filler
was was
applied
to these
inner
sideskin;
ofand
the
skin;
both
along
the seams
andinbehind
the screw
to
these
areas
sanded
back,
so
that
the flow
the
wouldheads.
not
bePoly-filler
disrupted,
as applied
shown
in
these areas and sanded back, so that the flow in the tunnel would not be disrupted, as shown in
areas
and
sanded
back,
so
that
the
flow
in
the
tunnel
would
not
be
disrupted,
as
shown
in
Figure
these areas
Figure
5. and sanded back, so that the flow in the tunnel would not be disrupted, as shown in5.
Figure 5.
Figure 5.
(a)
(a)
(a)
(b)
(b)
(b)
Figure 5. Poly filler (a) before sanding; (b) after sanding.
Figure
sanding;(b)
(b)after
aftersanding.
sanding.
Figure5.5.Poly
Polyfiller
filler (a)
(a) before sanding;
Figure 5. Poly filler (a) before sanding; (b) after sanding.
2.2.2. Flow Conditioner and Fan Grille
2.2.2.
Flow
Conditionerand
and FanGrille
Grille
2.2.2.
Flow
Conditioner
2.2.2.
Flow
Conditioner andFan
Fan Grille
The flow conditioner was constructed similarly to the rest of the tunnel but required some
The
flowconditioner
conditionerwas
wasconstructed
constructed similarly
similarly to
the
rest
tunnel
but
some
The
flow
to
theledge
restof
ofthe
the
tunnel
butrequired
required
some
The
flow
conditioner
was constructed
similarly
the
rest
of
the
tunnel
some
additional
features.
To support
the honey comb,
a 9 to
mm
was
built
for but
it torequired
rest upon.
In
additional
features.
To
support
the
honey
comb,
a
9
mm
ledge
was
built
for
it
to
rest
upon.
In
additional
features.
To
support
the
honey
comb,
a
9
mm
ledge
was
built
for
it
to
rest
upon.
In
addition,
additionalafeatures.
To support
the honey
comb,
a 9 the
mmflow
ledgeconditioner.
was built for
to rest upon.
addition,
galvanized
wire mesh
was put
across
Theit square
sheet In
of
addition, awire
galvanized
wire
mesh
was
put across
the flow
conditioner.
The
square sheet
ofcut
a galvanized
mesh
was
put
across
the
flow
conditioner.
The
square
sheet
of
honeycomb
was
addition,
a
galvanized
wire
mesh
was
put
across
the
flow
conditioner.
The
square
sheet
of
honeycomb was cut to fit the circular flow conditioner, see Figure 6.
wasflow
cut to
fit the circular
flow conditioner,
see Figure 6.
to honeycomb
fit
the circular
conditioner,
see Figure
6.
honeycomb
was cut to
fit the circular
flow conditioner,
see Figure 6.
Figure 6. Honeycombedge
edge cut to
to match internal
diameter
ofofflow
conditioner.
Figure
internaldiameter
diameterof
flowconditioner.
conditioner.
Figure6.6.Honeycomb
Honeycomb edge cut
cut to match
match internal
flow
Figure 6. Honeycomb edge cut to match internal diameter of flow conditioner.
To prevent damage to the fan due to falling objects, a simple grille was fabricated. A plywood
prevent
damagetotothe
thefan
fandue
dueto
tofalling
falling objects,
objects, aa simple
plywood
ToTo
prevent
damage
simple grille
grillewas
wasfabricated.
fabricated.A
plywood
To
prevent
to the
fan duematching
to fallingthe
objects,
a simple
grille
was
fabricated.
AA
plywood
ring was
cut withdamage
an internal
diameter
internal
diameter
of the
test
section, and
outside
ring
was
cut
with
an
internal
diameter
matching
the
internal
diameter
of
the
test
section,
and
outside
ring
was
cut
with
an
internal
diameter
matching
the
internal
diameter
of
the
test
section,
and
outside
ring was cut
with anthe
internal
the internal
diameter
the test
diameter
matching
outer diameter
diameter matching
of the flanges.
A recess
was cutofalong
thesection,
inside and
edgeoutside
of the
diameter
matchingthe
theouter
outerdiameter
diameter of
of the
the flanges.
flanges. A
recess
was
cut
along
the
inside
edge
of of
the
diameter
matching
A
recess
was
cut
along
the
inside
edge
diameter
matching
thegrille
flanges.
A recess
was cutinalong
the
flange
using
a routerthe
to outer
form adiameter
ledge forofthe
to rest
on, as shown
Figure
7. inside edge of thethe
flange
using
a
router
to
form
a
ledge
for
the
grille
to
rest
on,
as
shown
in
Figure
7.
flange
using
a router
totoform
as shown
shownin
inFigure
Figure7.7.
flange
using
a router
forma aledge
ledgefor
forthe
thegrille
grille to
to rest
rest on,
on, as
Figure 7. Wind tunnel grille to protect fan.
Figure 7. Wind tunnel grille to protect fan.
Figure 7. Wind tunnel grille to protect fan.
Figure 7. Wind tunnel grille to protect fan.
Aerospace 2016, 3, 10
Aerospace 2016, 3, 10
7 of 27
7 of 27
3. Methodology—Rocket
3.
Methodology—RocketSystems
Systemsand
andModelling
Modelling
3.1. Improvements to Airframe and Avionics Stack
Since the launch of Smokey at the end of 2014 [12], there have been a number of improvements
improvements
can
be be
seen
in Figure
8, which
shows
the
implemented to
to the
the rocket
rocketsystems.
systems.These
These
improvements
can
seen
in Figure
8, which
shows
three
launch
configurations
of the
Smokey
and
Tasha
the
three
launch
configurations
of the
Smokey
and
TashaIIIIIIairframes.
airframes.The
TheSmokey
Smokeyand
and Tasha
Tasha III
airframe designs
designsare
areaerodynamically
aerodynamically
equivalent.
Both
designs
identical
canard,
fin,length,
tube
equivalent.
Both
designs
havehave
identical
canard,
fin, tube
length,
tube diameter
andcone
nosegeometry.
cone geometry.
The main
difference
between
the two
airframes
tube
diameter
and nose
The main
difference
between
the two
airframes
waswas
the
the
manufacturing
process
for
attaching
the
back
fins.
manufacturing process for attaching the back fins.
Figure 8. Improvements
(b)(b)
Tasha
III,III,
launch
1; (c)
Tasha
III,
Improvementsto
toairframe
airframeand
andavionics
avionicsstack.
stack.(a)(a)Smokey;
Smokey;
Tasha
launch
1; (c)
Tasha
launch
2. 2.
III, launch
Smokey used
used Acrylonitrile
Acrylonitrilebutadiene
butadienestyrene
styrene(ABS)
(ABS)3D
3Dprinted
printedfins
fins
and
canards.
The
strength
Smokey
and
canards.
The
strength
of
of
these
parts
were
appropriate
for
subsonic
flight;
however,
they
can
be
damaged
on
landing
these parts were appropriate for subsonic flight; however, they can be damaged on landing resulting
resulting
in more
spent the
repairing
the To
airframe.
To this
overcome
thisTasha
problem,
Tasha
also
used
in
more time
spenttime
repairing
airframe.
overcome
problem,
III also
usedIII3D
printed
3D printed
but
they were
towith
the airframe
Two
of3D
theprinted
Tasha canards
III’s 3D
fins,
but theyfins,
were
laminated
to laminated
the airframe
fiberglass.with
Twofiberglass.
of the Tasha
III’s
printed
canards
were
damaged
after
its
first
flight,
so
on
its
second
flight
we
used
our
supersonic
were damaged after its first flight, so on its second flight we used our supersonic capable stack, which
capable
stack, canards.
which has fiberglass canards.
has
fiberglass
Cameras were
were placed
placed in
in Tasha
III allowing
allowing the
the recording
recording of
of flights
flights to
to provide
provide an
an insight
Cameras
Tasha III
insight on
on how
how
the
on-board
avionics
were
performing.
Some
holes
were
cut
in
the
airframe,
with
one
of the
the on-board avionics were performing. Some holes were cut in the airframe, with one of the cameras
camerasout
placed
out one
side
of the airframe
by Smokey
10 mm. Smokey
did an
noton-board
use an on-board
it
placed
one side
of the
airframe
by 10 mm.
did not use
camera,camera,
so it hadsono
had
no
camera
holes.
camera holes.
UC Rocketry’s
Rocketry’ssupersonic
supersoniclaunches
launchesrequire
require
a device
to report
where
the rocket
Both
UC
a device
to report
where
the rocket
lands.lands.
Both Tasha
Tasha
III flights
included
the
Spot Tracker
to capability
test its capability
report landing
locations.
Spot
III
flights
included
the Spot
Tracker
to test its
to reporttolanding
locations.
The SpotThe
Tracker
Tracker
and
cameras
are
the
main
reason
the
Tasha
III
vehicle
was
heavier
than
Smokey.
The
second
and cameras are the main reason the Tasha III vehicle was heavier than Smokey. The second Tasha III
Tasha III
launch
wasthan
heavier
thanTasha
the first
Tasha IIIbecause
launch,the
because
thewere
avionics
were exchanged
to
launch
was
heavier
the first
III launch,
avionics
exchanged
to the more
the more
robust supersonic
capable avionics.
robust
supersonic
capable avionics.
Each
launch
of
the
Smokey
Tasha
III airframes
had different
properties.
Between
each
Each launch of the Smokey andand
Tasha
III airframes
had different
properties.
Between
each launch,
launch, changes
weretomade
to the internal
avionics
which affects
theofmass
of the vehicle.
Changes
in
changes
were made
the internal
avionics
which affects
the mass
the vehicle.
Changes
in mass
mass
affect
the
torques
and
airspeeds
experienced
during
flight.
Table
1
summarizes
the
key
affect the torques and airspeeds experienced during flight. Table 1 summarizes the key differences
differences
for each launch.
between
thebetween
vehiclesthe
for vehicles
each launch.
Aerospace 2016, 3, 10
8 of 27
Table 1. Vehicle comparisons between Smokey and Tasha III.
Property
Aerospace
2016, 3, 10
Mass
Length
Z-axis
Property
Inertia
Smokey
Tasha III Launch 1
Tasha III Launch 2
3.0 kg
1.52 m
3.47 kg
1.51 m
3.99 kg
1.51 m
0.00361 kg·m2
0.00393 kg·m2
Table 1. Vehicle comparisons between Smokey and Tasha III.
0.00311 kg·m2
Smokey
Tasha III Launch 1
Tasha III Launch 2
Mass
3.0 kg
kg
3D3.47
printed
PLA with
Fin material 1.52
3D
Length
m printed ABS
1.51 m
2
fibreglass
Z-axis Inertia
0.00311 kg¨ m2
0.00361
kg¨ mlamination
Fin material
3D
printed
ABS
3D
printed
PLA
with
fibreglass
Canards
3D printed ABS
3D printedlamination
ABS
Canards
3D printed ABS
3D printed ABS
with
Avionics
Subsonic capable
Subsonic Subsonic
capable withcapable
spot tracker
Avionics
8 of 27
Subsonic capable
spot tracker
kg with
3D printed3.99
PLA
1.51 m
fibre glass
lamination
0.00393
kg¨ m2
3D printed
PLA
with
fibre
glass lamination
Fibre glass moulded
Fibre glass moulded
Supersonic
capable
with
Supersonic capable
with spot
tracker
spot tracker
3.2. Testing Rocket Stability
3.2. Testing Rocket Stability
A major advantage of the vertical wind tunnel is that it is a straightforward way to test rocket
A major
advantage
of Rocketry
the vertical
tunnelthe
is that
it is a procedure
straightforward
way stability:
to test rocket
stability
before
flight. UC
haswind
developed
following
for testing
stability before flight. UC Rocketry has developed the following procedure for testing stability:
‚
Assemble the rocket with a dummy mass motor.
•‚ Assemble
the center
rocket of
with
a dummy
mass motor.
Measure the
mass
by balancing
the rocket on a beam less than 20 mm wide. Mark the
•
Measure
the
center
of
mass
by
balancing
the
rocket on a beam less than 20 mm wide. Mark the
center of mass.
center of mass.
‚
Fix a pipe clamp, with string tied securely to both ends of the pipe clamp to the rocket, at the
•
Fix a pipe clamp, with string tied securely to both ends of the pipe clamp to the rocket, at the
measured center of mass.
measured center of mass.
Feed the string from both sides of the clamp through the two 4 mm holes on the sides of the wind
‚
•
Feed the string from both sides of the clamp through the two 4 mm holes on the sides of the
tunnel. Tie the string around the back of the wind tunnel, and tension the ropes to lift the center
wind tunnel. Tie the string around the back of the wind tunnel, and tension the ropes to lift the
of mass of the rocket as close as possible to the holes in the side of the wind tunnel.
center of mass of the rocket as close as possible to the holes in the side of the wind tunnel.
‚
Attach the nose tip of the rocket to the vertical string. The purpose of this string is to prevent
•
Attach the nose tip of the rocket to the vertical string. The purpose of this string is to prevent an
an unstable rocket from damaging the walls, or prevent the rocket from falling should the clamps
unstable rocket from damaging the walls, or prevent the rocket from falling should the clamps
slip. The vertical string should be taut only when the nose of the rocket is close to the wind
slip. The vertical string should be taut only when the nose of the rocket is close to the wind
tunnel walls.
tunnel walls.
‚
Startthe
thewind
windtunnel,
tunnel,and
andcheck
checkthe
therocket
rocketstraightens
straightensat
at15,
15,20
20and
and30
30m/s.
m/s.
•
Start
Figure99gives
givesaapicture
pictureof
ofaastability
stabilitytest
testset
setup.
up.
Figure
(a)
(b)
Figure
9. Stability set up (a) connection to string; (b) connection to center of mass of rocket.
Figure 9. Stability set up (a) connection to string; (b) connection to center of mass of rocket.
Since these tests were for roll control only, the exact margin of stability in terms of the number
Since was
thesenot
tests
were for roll
control
thethe
exact
of stability
termsgeneral
of the number
of calibres,
determined.
The
mainonly,
aim of
testmargin
in Figure
9, was toinprove
stabilityof
calibres,
was not
The
aim of thedetermination
test in Figure of
9, was
to prove
general stability
so
so
that it would
bedetermined.
safe to launch.
Anmain
experimental
the center
of pressure
using this
that
it
would
be
safe
to
launch.
An
experimental
determination
of
the
center
of
pressure
using
this
method will be investigated in future work for pitch and yaw modelling.
method will be investigated in future work for pitch and yaw modelling.
Aerospace 2016, 3, 10
9 of 27
3.3. Rocket Roll Dynamics Modelling
In both launches and all wind tunnel tests in this paper, only roll dynamics were investigated.
This section outlines the modelling and parameter identification techniques used to understand and
predict the rocket roll dynamics during flight.
3.3.1. Minimal Model
The roll model is extended from a previously used model [12] which includes the effect of velocity
on the damping and normal forces in the roll axis. Ignoring the yaw term in Equation (6) of [13] and
lumping the parameter d into the coefficients of the roll fin angle and damping yields:
.
Ip p “
1 2 ”
α ı
ρ v A βu f in ptq ´ p
2
v
(1)
where the definition of the parameters is given in the Notation. Expanding out Equation (1), and
including the effects of disturbance and defining the roll angle gives the differential equation model:
.
1
1
I p p “ ´ ρ v A α p ` ρ v2 A β pu f in ptq ` udist ptqq
2
2
.
φ“p
(2)
(3)
where udist ptq udist ptq lumps the effects of fin canard interaction, thrust offsets that may impart a roll
and atmospheric effects into a single time-varying parameter. It is shown in the results section that
when there are sudden fin movements, it’s critical to allow fast changes in the disturbance at these
points to provide a good match to the data. To model these effects, the disturbance is written in
the form:
N
ÿ
udist ptq “
Yk Φk
(4)
k “1
Yk “ ud,k´1 `
pud,k ´ ud,k´1 q
pt ´ Tk´1 q
pTk ´ Tk´1 q
(5)
Φk “ Hpt ´ Tk´1 q ´ Hpt ´ Tk q
(6)
Hptq ” heaviside function, T0 , . . . , TN ” user defined time points
(7)
ud,0 , . . . , ud,N ” unknown constants identified from data
(8)
where
3.3.2. Parameter Identification
To ensure the optimum possible model is obtained with good numerical parameter identifiability,
a grid search is applied to the main parameters excluding the disturbance, which is identified using
non-linear regression. This method was applied for both an open-loop model, where u f in ptq is
measured directly by encoders on the rocket and a closed-loop model where u f in ptq is defined from
a standard proportional derivative controller plus the addition of a pre-defined input. Mathematically
these models are defined:
Open-loop :
Closed-loop :
u f in ptq “ u f in, OL ptq ” fin movement measured from encoder
u f in ptq “ u f in, CL ptq “ k p pRptq ´ φptqq ` k d pR1 ptq ´ pptqq ` uinput ptq
(9)
(10)
where
k p ” proportional gain,
k d ” derivative gain
Rptq “ pR0 ´ R1 qHpsinp2π f 0 tqq ` R1
(11)
(12)
Aerospace 2016, 3, 10
10 of 27
The reference function Rptq in Equation (12) is an alternating square wave of frequency f 0 (Hz)
between the values of R0 and R1 . This function allows multiple step responses to be analyzed from
wind tunnel tests and rocket flights. The function uinput ptq is set to 0 for the wind tunnel tests and the
first flight, but is defined as a chirp function with varying amplitudes for the second flight to increase
flight dynamics for a rigorous test of the model.
The optimization is set up by first fixing the damping α and torque constant β. Two objective
functions are defined:
OL
pUd q “ rφdata pt0 q ´ φOL pt0 q , . . . , φdata ptend q ´ φOL ptend qs
Fα,β
(13)
CL
pUd q “ rφdata pt0 q ´ φCL pt0 q , . . . , φdata ptend q ´ φCL ptend qs
Fα,β
(14)
‰T
“
Ud “ ud, 0 , . . . , ud, N
(15)
φdata ptq ” measured roll angle, t0 , . . . , tend ” data time points
(16)
φOL ptq ” roll angle solution to Equations p2q – p9q for given α, β and Ud
(17)
φCL ptq ” roll angle solution to Equations p2q – p8q , p10q – p12q , for given α, β and Ud
(18)
where
A range of values of α and β are then selected:
<α “ tαmin ` k∆α, k “ 0, . . . , Nα u , < β “ β min ` k∆β, k “ 0, . . . , Nβ
(
(19)
For each α and β from the ranges in Equation (19), the open-loop and closed-loop identified
disturbance values are defined:
ÛOL
d “ non-linear least squares solution to Equation p13q
(20)
ÛCL
d “ non-linear least squares solution to Equation p14q
(21)
The final model parameters that best fit the data are then defined:
”
ı
OL
XOL “ αOL , βOL , ÛOL
: FαOL
OL , βOL pÛd q “
d
”
ı
CL
X CL “ αCL , βCL , ÛCL
: FαCL
CL , βCL pÛd q “
d
min
ˇ
ˇ¯
ˇ OL OL ˇ
mean ˇFα,β
pÛd qˇ
(22)
min
ˇ
ˇ¯
´
ˇ CL CL ˇ
mean ˇFα,β
pÛd qˇ
(23)
´
tαP< α , βP< β u
tαP< α , βP< β u
Equations (22) and (23) represent a grid search over all the values in Equation (19), where for
each pair of α and β a non-linear regression is performed to determine the corresponding disturbance
values. This non-linear regression uses the command “lsqnonlin” in Matlab.
4. Results and Discussion
4.1. Wind Tunnel Flow Quality
Measurements from a hot wire anemometer placed at various positions from the boundary
showed that there are negligible boundary effects greater than 200 mm from the wall, with less than 5%
reduction in wind speed at 100 mm from the wall. Since the diameter of the sounding rockets in this
research are 80 mm with a 60 mm canard and fin radial distance, the outermost point of the rocket is
160 mm from the wall. Hence, the volume of the test section used in this research, has close to uniform
flow. Most importantly, the results from the prediction of rocket flight roll response from wind tunnel
derived parameters presented in the sections below, demonstrate that the test section has adequate
flow quality for this research.
this research are 80 mm with a 60 mm canard and fin radial distance, the outermost point of the
rocket is 160 mm from the wall. Hence, the volume of the test section used in this research, has close
to uniform flow. Most importantly, the results from the prediction of rocket flight roll response from
wind tunnel derived parameters presented in the sections below, demonstrate that the test section
has
adequate
Aerospace
2016, 3,flow
10 quality for this research.
11 of 27
4.1.1. Turbulence Intensity
4.1.1. Turbulence Intensity
To demonstrate the quality of the flow over time, in the wind tunnel, a Kestrel 4500 wind
To[18]
demonstrate
of the
theedge
flowatover
time, inofthe
tunnel,
4500 wind
sensor
was placedthe
200quality
mm from
the bottom
the wind
door in
Figurea1.Kestrel
This position
was
sensorthroughout
[18] was placed
200 mm from
the sensor
edge atmeasures
the bottom
of the
Figure 1.a This
fixed
the experiment.
This
every
2 door
s andin outputs
windposition
speed
was fixed throughout
experiment.
sensor
measures every
2 s andwith
outputs
a wind
speed
measurement
rounded the
to the
nearest 0.1 This
m/s. A
finer resolution
wind sensor
a higher
frequency
measurement
rounded
to the
nearestsince
0.1 m/s.
finer resolution
sensor
a higher frequency
was
not required
for this
analysis,
windAspeeds
less thanwind
0.1 m/s
havewith
a negligible
effect on
was not
required In
foraddition,
this analysis,
since wind
speeds
than 0.1 m/s
have
a negligible
effect
rocket
dynamics.
turbulence
properties
areless
independent
of the
time
scale so this
teston
is
rocket dynamics.
In addition,
turbulence
properties
are wind
independent
of the
time scaleper
so this
test
adequate
to characterize
the turbulence
intensity
in the
tunnel. The
revolutions
minute
is adequate
to characterize
the turbulence
intensity
in the wind
tunnel.
(RPM)
reference
on the fan was
set to a sequence
of values
defined
by: The revolutions per minute
(RPM) reference on the fan was set to a sequence of values defined by:
RPM ref = 570,870,1100,1400,1650,1700
(24)
[
]
RPMre f “ r570, 870, 1100, 1400, 1650, 1700s
(24)
Taking into account the controller time constant, the times when the fan reaches steady
state Taking
are:
into account the controller time constant, the times when the fan reaches steady state are:
TRPM = [100, 230,390,550, 718,858] (s)
TRPM “ r100, 230, 390, 550, 718, 858s psq
(25)
(25)
The measured wind speed is shown in Figure 10. At each steady state there are only very small
The measured wind speed is shown in Figure 10. At each steady state there are only very small
oscillations, showing that the flow is close to laminar. Figure 11a shows a plot of the RPM versus
oscillations, showing that the flow is close to laminar. Figure 11a shows a plot of the RPM versus wind
wind speed and Figure 11b plots the turbulence intensity Γ versus wind speed which is defined:
speed and Figure 11b plots the turbulence intensity Γ versus wind speed which is defined:
σ2 2(v)
Γ(v) = σ pvq , σ ≡ standard deviation, v ≡ wind speed
Γpvq “mean(v) , σ ” standard deviation, v ” wind speed
mean pvq
(26)
(26)
2
wind speed (m/s)
-1
wind speed (m s )
There is a correlation of 2R = 0.9999 for RPM versus wind speed, thus the fan controller is
There is a correlation of R = 0.9999 for RPM versus wind speed, thus the fan controller is creating
creating a very linear response. The turbulence intensity is very low and less than 0.04% over all
a very linear response. The turbulence intensity is very low and less than 0.04% over all wind
wind speeds tested.
speeds tested.
Figure 10.
Kestrel)
versus
timetime
for different
revolutions
per minute
(RPM)
Figure
10. Measured
Measuredwind
windspeed
speed(from
(from
Kestrel)
versus
for different
revolutions
per minute
values values
in the fan.
(RPM)
in the fan.
12 of 27
12 of 27
12 of 27
mean wind speed (m/s)
mean wind speed (m/s)
turbulence
intensity
(m/s)(m/s)
turbulence
intensity
Aerospace 2016, 3, 10
Aerospace 2016, 3, 10
Aerospace 2016, 3, 10
wind speed (m/s)
wind(b)
speed (m/s)
(b)
(a)
(a)
Figure 11. (a) RPM versus wind speed; (b) Turbulence intensity versus wind speed.
Figure 11. (a) RPM versus wind speed; (b) Turbulence intensity versus wind speed.
Figure 11. (a) RPM versus wind speed; (b) Turbulence intensity versus wind speed.
4.1.2. Swirl
4.1.2. Swirl
4.1.2.ItSwirl
was noticed that in every airframe tested in the wind tunnel, there was a roll rate with the
It was noticed that in every airframe tested in the wind tunnel, there was a roll rate with the
canards
set to
0. However,
was not
initially
known
what
percentage
was
ofwas
this aroll
caused
by
It was
that in itit
every
airframe
tested
in what
the
wind
tunnel,
there
rollrate,
rate
with
canards
setnoticed
to 0. However,
was not
initially
known
percentage
was
of this
roll rate,
caused
bythe
fin
offsets
the However,
airframe orwas
swirl
the wind
tunnel.
Topercentage
characterize
theofswirl,
several
sets of
canards
setinto
notin
known
what
was
thisseveral
roll
rate,
fin offsets
in 0.
the airframe it
or swirl
ininitially
the wind
tunnel.
To characterize
the swirl,
setscaused
of
aluminium
fins
were
machined
to
provide
a
baseline
where
there
was
no
fin
offset.
The
fins
were
byaluminium
fin offsetsfins
in the
airframe
or swirl
in thea wind
tunnel.
characterize
swirl,
several
sets
of
were
machined
to provide
baseline
whereTo
there
was no finthe
offset.
The
fins were
made
from
two
thin
sheets
of
aluminium
formed
in
a
cross.
These
fins
were
attached
to
a
steel
pipe
aluminium
were
to provide aformed
baseline
was
fin offset.
Thetofins
were
made
made fromfins
two
thinmachined
sheets of aluminium
in where
a cross.there
These
finsno
were
attached
a steel
pipe
and
by
in
tunnelin
asashown
shown
inFigure
Figure
12.
Tests
showed
the
roll
rate
from
two
thin sheets
of aluminium
formed
cross. in
These
fins
were
attached
to that
a the
steel
pipe
andsuspended
suspended
bystring
string
in the
the wind
wind
tunnel
as
12.
Tests
showed
that
roll
rateand
observed
was
highly
dependent
on
the
total
diameter
of
the
fins.
For
a
diameter
less
than
100
mm,
suspended
by string
independent
the wind tunnel
shown
in Figure
12.fins.
Tests
showed
that the
rate
observed was
highly
on theas
total
diameter
of the
For
a diameter
lessroll
than
100observed
mm,
there
was
greater
300 mm
mm
thefins.
rollrate
rate
verylow.
low.
This
result
suggests
that
there
wasno
noroll
rollrate
rateand
and
greater
than
300
the
roll
very
This
result
thatwas
was
highly
dependent
on the
totalthan
diameter
of the
Forwas
awas
diameter
less
than
100suggests
mm,
there
the
swirl
is
mainly
isolated
to
a
concentric
ring
between
100
and
300
mm
from
the
centre
of
the
wind
the
swirl
is
mainly
isolated
to
a
concentric
ring
between
100
and
300
mm
from
the
centre
of
the
wind
no roll rate and greater than 300 mm the roll rate was very low. This result suggests that the swirl is
tunnel.
The
was
detailed
analysis
had
diameter
of
200
which
maximized
tunnel.isolated
Thefin
finset
setathat
that
waschosen
chosen
detailed
analysis
had
aadiameter
200
mm
which
maximized
mainly
to
concentric
ringfor
between
100
and 300
mm
from
theof
centre
ofmm
the
wind
tunnel.
The
roll
rate.
the
roll
rate.
finthe
set
that
was chosen for detailed analysis had a diameter of 200 mm which maximized the roll rate.
Figure 12. Aluminium fin set up.
Figure 12. Aluminium fin set up.
The first test was to take a video of the 200 mm aluminium fin rocket for 5 min at the maximum
The
first
test
take
aa video
of
mm
aluminium
fin
for
min
at
maximum
wind
speed
30was
m/s to
and
visually
count
the 200
number
revolutions
work out
average
rate.
The
first of
test
was
to
take
video
of the
the
200
mm of
aluminium
fintorocket
rocket
for 55the
min
at the
theroll
maximum
wind
speed
of
30
m/s
and
visually
count
the
number
of
revolutions
to
work
out
the
average
roll
rate.
The
result
was
87.0
deg/s
which
demonstrates
there
was
certainly
a
relatively
significant
swirl
in
the
wind speed of 30 m/s and visually count the number of revolutions to work out the average roll
rate.
The
result
was
87.0
deg/s
which
demonstrates
there
was
certainly
a
relatively
significant
swirl
in
wind
tunnel.
To
overcome
this
swirl,
an
egg
crate
was
placed
up
to
a
height
of
20
cm
in
a
hexagon
The result was 87.0 deg/s which demonstrates there was certainly a relatively significant swirl in the
the
shape
on theTo
grill
at the bottom
of thean
wind
just placed
above the
shown
This
wind
tunnel.
overcome
this
egg
crate
up
to
height
of
20
cm in
in 13.
hexagon
wind
tunnel.
To
overcome
this swirl,
swirl,
an
eggtunnel,
crate was
was
placed
up fan,
to aa as
height
of in
20Figure
cm
aa hexagon
egg crate
effectively
provided
additional
flow
straightener
reducing
it was
near
shape
on the
the
grillatatthe
the
bottoman
thewind
wind
tunnel,
just
above
the
as swirl
shown
in
Figure
13.the
This
shape
on
grill
bottom
ofofthe
tunnel,
just
above
the
fan,fan,
asthe
shown
inasFigure
13.
This
egg
fan
which
caused
the
swirl.
Another
video
was
then
taken
of
the
aluminium
fin
rocket
and
the
egg
crate
effectively
provided
an
additional
flow
straightener
reducing
the
swirl
as
it
was
near
the
crate effectively provided an additional flow straightener reducing the swirl as it was near the fan
average
roll
rate
observed
was
25.7
deg/s
which
is
a
340%
reduction
in
the
swirl.
There
were
also
fan which
caused
the swirl.
Another
video
was
then
of the aluminium
fin the
rocket
and roll
the
which
caused
the swirl.
Another
video was
then
taken
of taken
the aluminium
fin rocket and
average
severalroll
periods
where
therewas
was25.7
no roll
rate.which is a 340% reduction in the swirl. There were also
average
rate
observed
deg/s
rate observed was 25.7 deg/s which is a 340% reduction in the swirl. There were also several periods
severalthere
periods
where
waswhere
no rollthere
rate.was no roll rate.
Aerospace 2016, 3, 10
Aerospace
2016,
3, 3,
1010
Aerospace
2016,
13 of 27
1327
of 27
13 of
13 of 27
Aerospace 2016, 3, 10
Figure13.
13.Egg
Egg crate
crate used
used as
Figure
Egg
crate
used
as aaa flow
flowstraightener
straightener
reduce
swirl.
Figure
13.
as
flow
straightenertoto
toreduce
reduceswirl.
swirl.
Figure 13. Egg crate used as a flow straightener to reduce swirl.
To fully characterize the impact of the flow straightener with various wind speeds on the Tasha
ToTo
fully
characterize
the
impact
the
flow
straightener
with
various
wind
speeds
Tasha
To
fully
characterize
the
impact
ofof
flow
straightener
with
various
wind
speeds
onon
thethe
Tasha
III
fully
characterize
the
impact
ofthe
the
flow
straightener
with
various
wind
III rocket,
an uncontrolled
airframe
with
the
same
dimensions
as Figure
8b
wasspeeds
placedon
in the
the Tasha
wind
III
rocket,
an
uncontrolled
airframe
with
the
same
dimensions
as
Figure
8b
was
placed
in
the
wind
rocket,
an uncontrolled
airframe
with with
the same
dimensions
as Figure
8b was
in theinwind
tunnel.
III rocket,
anairframe
uncontrolled
airframe
same
Figure
8b placed
was placed
the wind
tunnel.
This
was primarily
usedthe
to test
thedimensions
parachute as
before
implementing
the controlled
tunnel.
This
airframe
was
primarily
used
to
test
the parachute
parachute
beforeimplementing
implementing
the
controlled
This
airframe
was
primarily
used
to
test
the
parachute
before
implementing
the
controlled
launch,
so
tunnel.
This
airframe
was
primarily
used
to
test
the
before
the
controlled
launch, so had slightly different back fins as a result of natural manufacturing variations,
launch,
so
had
slightly
different
back
fins
as
a
result
of
natural
manufacturing
variations,
had
slightly
back
fins
as a result
of
natural
variations,
butfor
was
essentially
launch,
sodifferent
had slightly
different
backspecific
fins
as
a manufacturing
result
of natural
manufacturing
variations,
but
was essentially
the
same
rocket.
The
rocket
in Figure
8b was
not
available
this
test as
but
was
essentially
the
same
rocket.
The
specific
rocket
in
Figure
8b
was
not
available
for
this
test
but
was
essentially
the
same
rocket.
The
specific
rocket
in
Figure
8b
was
not
available
for
this
test
as as
the
same
rocket.
The
specific
rocket
in
Figure
8b
was
not
available
for
this
test
as
the
back
fins
were
the back fins were damaged on landing due to swinging into rocky ground with a large gust
of
thewind,
back
fins
were
damaged
on
landing
due
to
swinging
into
rocky
ground
with
a
large
gust
the
back
fins
were
damaged
on
landing
due
swinging
into
rocky
ground
with
a
large
gust
of of
damaged
on
landing
due
to
swinging
into
rocky
ground
with
a
large
gust
of
wind,
just
as
it
landed.
just as it landed.
wind,
just
as
it
landed.
wind,
just
as
it
landed.
The
canards
logging was
wasenabled.
enabled.Figure
Figure
14a
plots
rate
The
canardswere
wereset
settoto00and
androll
roll rate
rate data
data logging
14a
plots
thethe
rollroll
rate
The
canards
wereset
settoto0with
0with
andand
roll rate
rate data
datathe
logging
was
Figure
14a
plots
the
roll
rate
The
canards
were
and
roll
logging
wasenabled.
enabled.
Figure
14a
plots
the
rate
response
for
two
without
the
flowstraightener.
straightener.
The
RPM
inputs
used
in
each
response
for
twoexperiments
experiments
and
without
flow
The
RPM
inputs
used
inroll
each
response
for
two
experiments
with
and
without
flow
straightener.
The
RPM
inputs
used
in
each
response
for
two
experiments
with
and
without
the
flow
straightener.
The
RPM
inputs
used
in
each
experiment
are
plotted
in
Figure
14b.
Figure
14a
shows
that
the
flow
straightener
has
significantly
experiment are plotted in Figure 14b.
14a shows that the flow straightener has significantly
experiment
are
plotted
inFigure
Figure
14b.
Figure
14a shows
that
flow
has
significantly
experiment
are
plotted
inthe
14b.
14a
shows
that the
the
flow
straightener
has
significantly
reduced
the
roll
rateofofthe
rocket.
TheFigure
mean absolute
absolute
steady
state
roll
rate
two
experiments
reduced
the
roll
rate
rocket.
The
mean
steady
state
rollstraightener
ratefor
forthe
the
two
experiments
reduced
the
roll
rate
of
the
rocket.
The
mean
absolute
steady
state
roll
rate
for
the
two
experiments
reduced
the roll
rate the
ofthe
the
rocket. The mean
absolute
steady
statein
rate15.
for the two experiments
were
plotted
against
corresponding
mean steady
steady state
velocity
Figure
were
plotted
against
corresponding
state
velocity
inroll
Figure
15.
were
plotted
againstthe
thecorresponding
corresponding mean
mean steady
steady state
were
plotted
against
state velocity
velocityininFigure
Figure15.
15.
(a)
(a)
(b)
(b)
Figure 14. Tasha III results
with and without flow straightener (a) RPM inputs;(b)
(b) roll rate response.
(a) with
Figure
14.14.
Tasha
(a)RPM
RPMinputs;
inputs;(b)
(b)roll
rollrate
rate
response.
Figure
TashaIIIIIIresults
results withand
andwithout
without flow
flow straightener
straightener (a)
response.
ss ss
mean
|p
-1 | (deg/s)
ss | (deg/s)
mean
mean
|p|p
mean|p
| (deg
) -1s -1 )
ss s|ss
mean|p
| (deg/s)
(deg
ss
mean|p
| (deg
s )
Figure 14. Tasha III results with and without flow straightener (a) RPM inputs; (b) roll rate response.
mean wind speed (m/s)
mean wind speed (m/s)
Figure 15. Mean steady state roll rate with and without flow straightener.
wind
speed
(m/s)
Figure
roll rate
with
andwithout
withoutflow
flowstraightener.
straightener.
Figure15.
15.Mean
Meansteady
steady state
statemean
with
and
Figure 15. Mean steady state roll rate with and without flow straightener.
Aerospace 2016, 3, 10
14 of 27
As2016,
a final
Aerospace
3, 10analysis
of these experiments, the effective steady state fin offset is computed14using
of 27
known values of the damping α and torque constant β of the airframe as discussed in the next
section. Specifically, at steady state, the roll rate p&, so assuming that u fin , ss = 0 , the disturbance in
As a final analysis of these experiments, the effective steady state fin offset is computed using
Equation
(2) can
be solved
to yield:
known
values
of the
damping
α and torque constant β of the airframe as discussed in the next section.
.
Specifically, at steady state, the roll rate p, so assumingαthat
p u f in,ss “ 0, the disturbance in Equation (2)
u fin offset = ss
(27)
can be solved to yield:
βαp
vssss
u f in o f f set “
(27)
βvss
where “ss” refers to the steady state value for each steady state wind speed vss which is computed
where “ss” refers to the steady state value for each steady state wind speed vss which is computed
from the average of the velocity during the steady state period of interest. This analysis allows a
from the average of the velocity during the steady state period of interest. This analysis allows
characterization of the swirl in terms of the effective canard angle. Note that the canards and extra
a characterization of the swirl in terms of the effective canard angle. Note that the canards and extra
fin area in Tasha III, as well as a larger diameter airframe would cause significantly more damping in
fin area in Tasha III, as well as a larger diameter airframe would cause significantly more damping
Tasha III than in the aluminium fin rocket of Figure 12. Therefore, it’s reasonable to assume that the
in Tasha III than in the aluminium fin rocket of Figure 12. Therefore, it’s reasonable to assume that
very small amount of swirl remaining after the addition of the flow straightener would have a
the very small amount of swirl remaining after the addition of the flow straightener would have
negligible effect on the Tasha III rocket. The aluminium fin rocket also has a very low moment of
a negligible effect on the Tasha III rocket. The aluminium fin rocket also has a very low moment of
inertia, so the threshold of torque required to overcome the damping in the fins, would be much
inertia, so the threshold of torque required to overcome the damping in the fins, would be much lower
lower in this rocket and thus much more sensitive to swirl than Tasha III.
in this rocket and thus much more sensitive to swirl than Tasha III.
A plot of u
versus vss for both experiments, is given in Figure 16. This figure shows that
A plot of u f infinooffset
f f set versus vss or both experiments, is given in Figure 16. This figure shows that in
in the
of flow
no flow
straightener,
the swirl
a greater
the lower
velocities.
the
casecase
of no
straightener,
the swirl
has ahas
greater
effecteffect
at theatlower
velocities.
This This
resultresult
was
was expected
since
the vertical
component
in the
windwould
tunnelnot
would
not be sufficiently
high to
expected
since the
vertical
component
in the wind
tunnel
be sufficiently
high to overcome
overcome
the horizontal
induced
from However,
the swirl. with
However,
withstraightener
the flow straightener
the
horizontal
componentcomponent
induced from
the swirl.
the flow
there was
therelittle
wasdifference
very littlein
difference
in the
finall
offset
over allwhich
velocities,
which
provides
further
very
the fin offset
over
velocities,
provides
further
evidence
thatevidence
there is
that there swirl
is negligible
swirlSubtracting
in this case.the
Subtracting
curves
in Figure
16 provides
a measure
negligible
in this case.
two curvesthe
in two
Figure
16 provides
a measure
of the
swirl in
−1, there is an average
of theof
swirl
in termscanard
of the offset.
effective
canard
Afteris20
of in
about
2° of
terms
the effective
After
20 m¨offset.
s´1 , there
anm·s
average
of about 2˝ of swirl
the wind
swirl inThis
the value
wind will
tunnel.
will need
be subtracted
from
future
tests to
better
tunnel.
needThis
to bevalue
subtracted
fromtofuture
tests to get
a better
estimate
of get
the atrue
fin
estimate
the prediction.
true fin offset for flight prediction.
offset
for of
flight
wind speed (m/s)
Figure
Figure 16.
16. The
The equivalent
equivalent fin
fin offset
offset versus
versus velocity
velocity representing
representingswirl
swirlin
inthe
thewind
windtunnel.
tunnel.
4.2.
4.2. Tasha
TashaIII—Launch
III—Launch11
Tasha
Tasha III
III from
from Figure
Figure 8b
8b was
was launched
launched from
from Kaitorete
Kaitorete Spit
Spit on
on 22
22July
July2015.
2015. The
The aim
aim of
of this
this
launch
was
primarily
to
test
the
new
avionics
stack
and
fibreglass
rear
fins.
In
the
previous
flight
launch
test the new avionics stack and fibreglass rear fins. In the previous flight of
of
Smokey
[12],
finswere
were3D
3Dprinted.
printed.The
Thereason
reasonfor
forthe
the fibreglass
fibreglass was
was to provide further
Smokey
[12],
thethefins
further
strengthening
strengthening suitable
suitable for
for supersonic
supersonic flights
flights in
in future
future research.
research. In
In addition,
addition, to
to gain
gain some
some useful
useful data
data
from
the
launch,
a
PD
controller
was
implemented
during
flight
in
both
the
thrust
and
coast
periods.
from the launch, a PD controller was implemented
Since
Since the
the vehicle
vehicle was
was finished
finished only
only days
days before
before the
the launch,
launch, there
there was
was not
not sufficient
sufficient time
time to
to do
do aa full
full
Aerospace 2016, 3, 10
Aerospace 2016, 3, 10
15 of 27
15 of 27
wind tunnel test, analysis of data and rigorous testing of gains. The only wind tunnel test performed
was the stability test of Section 3.2.
wind tunnel test, analysis of data and rigorous testing of gains. The only wind tunnel test performed
For the flight, the gains chosen were k p = 1, kd = 0.1 , which were known to give a reasonable
was the stability test of Section 3.2.
response
from
previous
wind
tunnelwere
testing
with
the were
gimbal
frameto[12].
reference
For the
flight,
the gains
chosen
k p “of1,Smokey
k d “ 0.1,
which
known
giveThe
a reasonable
was chosen
to previous
be a series
of responses
starting
at 0° forwith
a pre-determined
amount
afterreference
clearingwas
the
response
from
wind
tunnel testing
of Smokey
the gimbal frame
[12]. The
launch to
guide,
by an alternation
between
and 15° every
second.
As clearing
a precaution,
since
chosen
be a followed
series of responses
starting at
0˝ for a−15°
pre-determined
amount
after
the launch
this was
the first
with thebetween
avionics,
a ˝maximum
limitsecond.
of 6° was
in since
each this
canard.
guide,
followed
by flight
an alternation
´15
and 15˝ every
As a enforced
precaution,
was
˝
Unfortunately,
there
a significant
fin limit
offsetof in
the airframe
which
was greater
than the
the
first flight with
thewas
avionics,
a maximum
6 was
enforced in
each canard.
Unfortunately,
canards
compensate
for with
maximum
so onlythan
about
s of oscillatory
data was
there
wascould
a significant
fin offset
in thethis
airframe
whichlimit,
was greater
the1canards
could compensate
obtained.
However,
this
data
set
was
sufficient
to
identify
parameters
and
thus
analyse
the
rocket
for with this maximum limit, so only about 1 s of oscillatory data was obtained. However, this data
set
roll response.
was
sufficient to identify parameters and thus analyse the rocket roll response.
The apogee
apogeefor
forthis
thisflight
flightwas
was522
522
time
apogee
s and
the maximum
velocity
The
m,m,
thethe
time
to to
apogee
waswas
10.210.2
s and
the maximum
velocity
was
−1
−1
´
1
´
1
was
. The
wind
speed
was
very
low
day,
varying
between
1 and
2 m·s
97
m¨97s m·s
. The
wind
speed
was
very
low
onon
thethe
day,
varying
between
1 and
2 m¨
s on
on the
the ground.
ground.
The flight
flight was
was successful
successful and
and the
the rocket
rocket safely
safely recovered
recovered apart
apart from
from aa couple
couple of
of broken
broken canards
canards that
that
The
were
easily
replaced.
Figure
17
shows
video
stills
from
the
ignition,
take-off,
onboard
footage
and
were easily replaced. Figure 17 shows video stills from the ignition, take-off, onboard footage and
parachute recovery.
recovery.
parachute
Figure
recovery.
Figure 17. Tasha
Tasha III launch 1 stills (a) ignition; (b) take-off; (c) onboard video; (d) recovery.
Since there
there was
Since
was only
only one
one step
step response
response from
from 0°
0˝ to
to −15°,
´15˝the
, thecontrol
controlreference
referenceisismodeled
modeledbybya
asingle
singleHeaviside
Heavisidefunction
functionand
andthe
theproportional
proportionalderivative
derivative(PD)
(PD)control
controlcommand
commandisisdefined:
defined:
u
= max{min{uˆ
, u }, u }H (t − T )
cmd
cmd
max
min
u , umin
u Hpt ´ TPD
ucmd
“ max tmin tûcmd
, umax
PD q
umax “u
uˆcmd = k p ( R(t ) − φ(t )) + kd ( R1′(t ) − p(t ))
ûcmd “ k p pRptq ´ φptqq ` k d pR ptq ´ pptqq
(29)
(29)
R(t )“=RR00´−pR
( R00´−RR11qHpt
) H (t´−TTPD
−1q
1)
Rptq
PD ´
(30)
(30)
6 π 6π
´6 π
´15π
, u , u“ = −6, π ,R0 R
“ 0,
R1R“= −15π, , kkp “= 1,
1,
min 180
0 = 0,
1
p
180= 180min
180
180
180
max
(28)
(28)
“ 0.1,
0.1, TTPD= “
0.42
kkdd =
0.42
PD
(31)
(31)
The Heaviside function in Equation (28) provides a delay of TPD after the launch detect to ensure
TPD after
The Heaviside
in Equation
(28) provides
a delayFor
of launch
the launch
detect
to
the rocket
is well clearfunction
of the launch
guide before
starting control.
detection
to occur,
the on
ensureaccelerometer
the rocket is on
well
of the
launch
guide
starting
control.2 For
to
board
theclear
rocket’s
vertical
axis
needsbefore
to detect
a consistent
g orlaunch
higher detection
acceleration
occur,0.2the
on board
accelerometer
onsensor
the rocket’s
vertical
needs
to detect
a consistent
2 g or
over
s. This
requirement
prevents
errors or
motoraxis
misfires
from
triggering
launch control.
highertheacceleration
over 0.2thes. rocket’s
This requirement
sensor
errors or motor
misfires
from
Once
launch is detected,
vertical axisprevents
acceleration
is transformed
to the earth
reference
triggering
launch
control.
Once to
thedetermine
launch isthe
detected,
rocket’s
axisguide.
acceleration
is
frame
and then
double
integrated
rocket’s the
height
abovevertical
the launch
Using the
transformed
to the
earth reference
and then
double
integrated
to determine
the rocket’s
height
two
conditions
of launch
detectionframe
and launch
guide
clearance
enables
safe conditions
for actuating
above
the launch
guide. Using the two conditions of launch detection and launch guide clearance
the
rocket’s
canards.
enables
for actuating
thekey
rocket’s
canards.
Thesafe
rollconditions
rate data including
all the
points
of the launch are given in Figure 18, where t “ 0
The rollto
rate
including
allThe
the control
key points
the launch
Figurewas
18, 2where
t =the
0
corresponds
1.5data
s before
launch.
wasof
started
whenare
thegiven
rocketinheight
m above
4corresponds
m launch guide.
However,
due
to
the
specified
0.2
s
delay
in
the
launch
detect,
the
actual
altitude
to 1.5 s before launch. The control was started when the rocket height was 2 m above
when control started was 7 m which was 0.63 s after lift-off.
Aerospace 2016, 3, 10
16 of 27
Aerospace 2016, 3, 10
16 of 27
the 4 m launch guide. However, due to the specified 0.2 s delay in the launch detect, the actual
the 4 m2016,
launch
guide.started
However,
to thewas
specified
0.2 s lift-off.
delay in the launch detect, the 16
actual
altitude
when
control
was 7due
m which
0.63 s after
Aerospace
3, 10
of 27
altitude when control started was 7 m which was 0.63 s after lift-off.
200
200
control
starts
control
starts
true
launch
true
time
100 launch
time
0
100
end of
thrust
end of
thrust
parachute
deployment
parachute
deployment
0
-100
-100 launch
detect
launch
-200 detect
-200
-300
-3000
2
4
0
2
4
6
8
10
12
8
10
12
time
6 (s)
time (s)
Figure 18. Roll rate response for Tasha III launch 1 including key points in the launch.
Figure
III launch
launch 11 including
including key
key points
points in
in the
the launch.
launch.
Figure 18.
18. Roll
Roll rate
rate response
response for
for Tasha
Tasha III
The commanded and encoder measured canard roll angle are defined as the average of all
The
commanded
encoder
measured
canard
inputs
which is and
standard
in the
literaturecanard
[19]: roll angle are defined as the average of all
The commanded and encoder measured canard roll angle are defined as the average of all canard
canard inputs which is standard in the literature [19]:
inputs which is standard in the literature
[19]:+ cmd + cmd + cmd
cmd
ucmd = cmd1 + cmd2 + cmd3 + cmd4
(32)
4 cmd 3 ` cmd 4
ucmd = cmd11 ` cmd22 `
(32)
3
4
ucmd “
(32)
4
enc1 + enc2 +4 enc3 + enc4
uenc = enc + enc + enc + enc
(33)
4 enc33 ` enc44
enc11 ` enc22 `
uuenc
=
(33)
(33)
enc “
44
The data is analyzed from just before control starts up to a couple of seconds before the
The data
isisanalyzed
from justjust
before
control
startsstarts
up to aup
couple
seconds
thebefore
parachute
The
data
analyzed
before
to a of
couple
of before
seconds
the
parachute
deployment.
Thefrom
roll rate and
fincontrol
angle u
enc which is computed from Equation (33)
deployment.
The
roll
rate
and
fin
angle
u
which
is
computed
from
Equation
(33)
using
the
encoder
enc fin angle u
parachute deployment. The roll rate and
is computed from Equation (33)
enc which
using
theenc
encoder
outputs enc1 , …, enc
for eachin
canard,
in Figure
where
time
is
4 plotted
outputs
are
Figureare
19,plotted
where the
time is19,
reset
to 0.the
Note
that
1 , . . . , enc4 for each canard,
enc
,
…
,
enc
using
the
encoder
outputs
for
each
canard,
are
plotted
in
Figure
19,
where
the
time
is
for some
the thrust
period
all thrust
of the4 coast
period
all of
thethe
canards
are set at
maximum
reset
to 0.ofNote
that for
someand
of1the
period
and all
coast period
alltheir
the canards
arevalues
set at
˝
˝
reset
to
Note
some
of the roll
thrust
period
allisofaThe
the
period
all
canards
are
at
their
values
of
6°,negative.
yet
staysisand
negative.
reason
is there
isthe
a fin
offset
which
is
of 6 ,maximum
yet0.the
rollthat
ratefor
stays
Therate
reason
there
fin coast
offset
which
is larger
than
the
6 set
that
their
maximum
values
of
6°,
yet
the
roll
rate
stays
negative.
The
reason
is
there
is
a
fin
offset
which
is
larger
than the
that the canards
the canards
can6°compensate
for. can compensate for.
larger than the 6° that the canards can compensate for.
(deg/s)
roll roll
raterate
(deg/s)
measured
canard
angle
(deg)
measured
canard
angle
(deg)
6
(a)
(a)
6
4
4
2
2
0
0
-2
-2
-4
-4
-6
-60
2
4
6
8
0
2
time4 (s)
(b)
time (s)
6
8
(b)
Figure 19. Data for analysis (a) Roll rate response; (b) Measured canard angle from encoders.
Figure 19. Data for analysis (a) Roll rate response; (b) Measured canard angle from encoders.
Figure 19. Data for analysis (a) Roll rate response; (b) Measured canard angle from encoders.
To identify the torque constant β, damping α and disturbance udist (t ) from the roll model of
To identify the torque constant β, damping α and disturbanceuudist(ptq
the roll model of
) from
To identify
the
torque
constant
β, damping
α and
disturbance
from the
roll model of
dist tas
Equations
(2)–(8),
the
first
step
is
to
specify
the
range
in
the
β
and
α
values
given
Equations (2)–(8), the first step is to specify the range in the β and α values as givenin
inEquation
Equation(19).
(19).
Equations (2)–(8),
the first step is to specify the range in the β and α values as given in Equation (19).
These
These ranges
ranges are
are defined:
defined:
These ranges are defined:
<α “ t1, 2, . . . , 60u , < β “ t5, 5.5, 6.5, 7, . . . , 15u
(34)
Aerospace 2016, 3, 10
17 of 27
ℜα = {1, 2,…, 60} , ℜβ = {5,5.5, 6.5, 7,…,15}
(34)
The next step is to define the time values for the disturbance changes in Equation (7). These
Aerospace 2016, 3, 10
17 of 27
values are equally spaced in both the thrust period and the coast period of the data which are
denoted in Figure 19a. Let Nthrust be the number of time points in the thrust period and Ncoast the
The next step is to define the time values for the disturbance changes in Equation (7). These values
number of time points in coast period. The values in Equation (7) are defined:
are equally spaced in both the thrust period and the coast period of the data which are denoted in
T points in the thrust period and Ncoast the number of time
Figure 19a. Let Nthrust be the number of time
Ti = i thrust , i = 1,…, Nthrust
(35)
points in coast period. The values in Equation
N (7) are defined:
thrust
Tthrust
(Tend, −i “
Tthrust
1, . .).,, Njthrust
i “ i+ j
TNthrust + j = TTthrust
= 1, …, N coast
Nthrust
N coast
(35)
(36)
pT ´ Tthrust q
TNthrust ` j in
“ the
Tthrust
` j end
“ 1, . .is
. , set
Ncoast
(36)
Since there are no dynamics
canards
during
coast,, jN
to the minimum possible
coast
N
coast
value Since
whichthere
obtains
a reasonable
match
in the coast
period.
found empirically that higher
are no
dynamics in
the canards
during
coast,ItNwas
coast is set to the minimum possible
values
than
2
do
not
help
identifiability
due
to
the
lack
of
dynamics
during
period, and
value
value which obtains a reasonable match in the coast period. It was foundthis
empirically
thata higher
ofvalues
1 gavethan
a consistently
large
error. Therefore
setdynamics
to 2 for all
the analysis
on this
launch.
2 do not help
identifiability
due to N
the
lackisof
during
this period,
and
a valueThe
of 1
coast
value
alsoerror.
minimized
andNcoast
it was
found
that
alsolaunch.
a goodThe
choice.
gave aofconsistently
Therefore
is set
to 2 for
all the
analysis
on this
value
N thrust waslarge
Nthrust
= 2 was
of
N
was
also
minimized
and
it
was
found
that
N
=
2
was
also
a
good
choice.
Higher
values
thrust
Higher
values gave a progressively better match to thrust
the data in the thrust period as would be
gave
a
progressively
better
match
to
the
data
in
the
thrust
period
as would
butgave
were
expected, but were much slower computationally. Specifically,
the values
frombeNexpected,
thrust = 2, …,6
much slower computationally. Specifically, the values from Nthrust = 2,¨ ¨ ¨ ,6 gave virtually identical
virtually identical results with an improvement in the match to the roll angle˝ by less than 0.1°. More
results with an improvement in the match to the roll angle by less than 0.1 . More importantly, the
importantly, the identified damping remained unchanged and the torque constant only varied by a
identified damping remained unchanged and the torque constant only varied by a maximum of 0.05.
maximum of 0.05. The results for Nthrust = 2 and N coast = 2 are defined:
The results for Nthrust = 2 and Ncoast = 2 are defined:
αbest ,OL = 8.5, βbest ,OL = 10.0
αbest,OL “ 8.5, β best,OL “ 10.0
(37)
(37)
μ|µp|,OL ≡ mean
absolute error in roll rate = 9.82 deg/s
” mean absolute error in roll rate “ 9.82 deg{s
(38)
(38)
μµ|φ||,φOL|,OL≡ ”mean
rate =“1.51
meanabsolute
absoluteerror
error in
in roll
roll angle
1.51 deg/s
deg{s
(39)
(39)
| p|,OL
Themodel
modelresponse
responseisisplotted
plottedagainst
againstthe
themeasured
measuredvalues
valuesfor
forboth
boththe
theroll
rollrate
rateand
androll
rollangle
angle
The
in
Figure
20.
A
zoomed
in
plot
of
Figure
20a
is
given
in
Figure
21a
and
the
identified
time-varying
in Figure 20. A zoomed in plot of Figure 20a is given in Figure 21a and the identified time-varying
disturbanceisisplotted
plottedininFigure
Figure21b.
21b.
disturbance
200
0
model
data
roll rate (deg/s)
-200
-400
-600
-800
-1000
-1200
-1400
0
2
4
6
time (s)
(a)
(b)
Figure
Figure20.
20.Model
Modelresponse
responseversus
versusdata
data(a)
(a)Roll
Rollangle
angleresponse;
response;(b)
(b)Roll
Rollrate
rateresponse.
response.
8
Aerospace 2016, 3, 10
Aerospace 2016, 3, 10
18 of 27
18 of 27
0
10
model
data
0
Second PD
controlled
response
(reference -15 deg)
First PD
controlled
response
(reference 0 deg)
-10
-20
-2
fin offset
dominates
response
-4
-6
-30
-40
canard-fin interaction
dominates response
0
0.5
1
1.5
-8
0
2
4
time (s)
time (s)
(a)
(b)
6
8
Figure
21.21.
(a)(a)
Zoomed
inin
roll
angle
response
versus
data;
(b)
Identified
Figure
Zoomed
roll
angle
response
versus
data;
(b)
Identifieddisturbance.
disturbance.
Figure 21a shows that although there is some error in the first controlled response, the overall
Figure 21a shows that although there is some error in the first controlled response, the overall
trends are captured accurately. For example the data drops 27.2°˝from the local maximum at t = 0.49 s
trends are captured accurately. For example the data drops 27.2 from the local maximum at t = 0.49 s
to the local minimum at t = 1.02 s where the model predicts a drop of 26.15° ˝which corresponds to
to the local minimum at t = 1.02 s where the model predicts a drop of 26.15 which corresponds to
less than 4% error. The model also captures all the coast period, in both the roll angle and roll rate, as
less than 4% error. The model also captures all the coast period, in both the roll angle and roll rate, as
shown in Figure 20. The disturbance is quite low initially in the first 0.5 s of the data. This behavior is
shown in Figure 20. The disturbance is quite low initially in the first 0.5 s of the data. This behavior is
caused due to low velocity and therefore the canard–fin disturbance dominates the dynamics, as the
caused due to low velocity and therefore the canard–fin disturbance dominates the dynamics, as the
fin offset takes some time to take effect. After about 1 s the disturbance rapidly converges to a near
fin offset takes some time to take effect. After about 1 s the disturbance rapidly converges to a near
constant value around −7° which
remains for the rest of the flight with only a minor increase at the
constant value around ´7˝ which remains for the rest of the flight with only a minor increase at the
end. The results of Figures 20 and 21 and Equations (38) and (39) show that quite a simple model
end. The results of Figures 20 and 21 and Equations (38) and (39) show that quite a simple model with
with a relatively smooth disturbance function, is very effective in capturing the rocket roll response.
a relatively smooth disturbance function, is very effective in capturing the rocket roll response.
Note that the second PD controlled roll response in Figure 21a has a very large steady state
Note that the second PD controlled roll response in Figure 21a has a very large steady state error,
error, since the reference was
−15°. The reason for this error is that the fin offset is having a major
since the reference was ´15˝ . The reason for this error is that the fin offset is having a major effect due
effect due to the increased velocity and the maximum and minimum canard constraints do not
to the increased velocity and the maximum and minimum canard constraints do not provide enough
provide enough actuation to overcome this fin offset. However, the goal of this launch was not
actuation to overcome this fin offset. However, the goal of this launch was not control, but to test the
control, but to test the logistics of the new launch vehicle and avionics and provide an initial
logistics of the new launch vehicle and avionics and provide an initial proof-of-concept of the model
proof-of-concept of the model and methods.
and methods.
The final validation of the model and methods for this launch is to match the closed-loop model
The final validation of the model and methods for this launch is to match the closed-loop model
of Equations (28)–(31) to the data. The results are:
of Equations (28)–(31) to the data. The results are:
αbest ,CL = 7.5, βbest ,CL = 10.0
(40)
αbest,CL “ 7.5, β best,CL “ 10.0
(40)
μ| p|,OL ≡ mean absolute error in roll rate = 9.76 deg/s
µ| p|,CL ” mean absolute error in roll rate “ 9.76 deg{s
μ|φµ|,OL ≡ mean
absolute error in roll rate = 1.50 deg
” mean absolute error in roll angle “ 1.50deg
|φ|,CL
(41)
(41)
(42)(42)
These
Theseresults
resultsare
arevery
veryclose
closetotothe
theopen-loop
open-loopresponse
responsewith
withaamean
meanerror
errordifference
differenceofof0.06
0.06deg/s
deg/s
˝
ininthe
roll
rate
and
0.01°
in
the
roll
angle.
However,
there
are
some
small
differences
in
the
the roll rate and 0.01 in the roll angle. However, there are some small differences in thethrust
thrust
period
periodininthe
theroll
rollangle
angleasasshown
shownininFigure
Figure22a,
22a,but
butthe
theoverall
overallbehavior
behaviorofofthe
thetwo
tworesponses
responsesare
are
very
similar.
In
addition,
apart
from
a
small
period
in
the
thrust,
the
identified
closed
and
open-loop
very similar. In addition, apart from a small period in the thrust, the identified closed and open-loop
disturbances
disturbancesare
arevirtually
virtuallyidentical
identicalasasshown
shownininFigure
Figure22b.
22b.
Hence, in summary, there is no noticeable change in the output responses and identified
parameters when using the closed-loop model over of the open-loop model, although the
closed-loop model typically takes about 50% longer to simulate. The advantage of the open-loop
model computationally is that the roll rate is decoupled from the roll angle which is simpler to
handle numerically.
Aerospace 2016, 3, 10
19 of 27
Aerospace 2016, 3, 10
19 of 27
10
closed-loop model
measured
(deg)
0
dist
-10
u
-20
Aerospace
-302016, 3, 10
19 of 27
10
-40
0
0.5
1 closed-loop model
1.5
time (s)
0
measured
(b)
(deg)
(a)
-10
Figure 22. (a) Roll angle closed loop response versus data; (b) Identified disturbance comparison.
dist
Figure 22. (a) Roll angle closed loop response versus data; (b) Identified disturbance comparison.
u
-20
4.3. Tasha
III—Launch 2
Hence, in summary, there is no noticeable change in the output responses and identified
A-30
new vehicle was manufactured for the second launch including fibreglassing the rear fins and
parameters when using the closed-loop model over of the open-loop model, although the closed-loop
3D printing two new canards to replace the ones that were broken during the Tasha III launch 1, see
model
typically
abouta number
50% longer
to simulate.
The advantage
of the
open-loop
model
Figure
8c. For takes
this vehicle,
of controlled
step responses
were performed
in the
wind tunnel
-40
0
0.5
1
1.5
computationally
theHence,
roll rate
from
thetoroll
angle
which
is simpler
to
shortly before is
thethat
launch.
there is
is adecoupled
good amount
of data
identify
torque,
damping
and
time (s)
handle
numerically.
disturbances
and to analyze
the
capability
of
the
wind
tunnel
tests
to
predict
flight
response.
(a)
(b)
Figure
22. (a)2Roll
closed loop response versus data; (b) Identified disturbance comparison.
4.3. Tasha
4.3.1. III—Launch
Wind
Tunnel
Stepangle
Responses
Thevehicle
rocket
wasmanufactured
string,
andlaunch
8 stepincluding
responsesfibreglassing
were performed
withfins
a and
A
new
was
for athe
second
the rear
4.3.
Tasha
III—Launch
2suspended from
−1. The highest wind speed of 30 m·s−1 was not used in
magnitude
45°, canards
at a windtospeed
of 22
m·s
3D printing
twoofnew
replace
the
ones
that were broken during the Tasha III launch 1, see
A new
vehicle
manufactured
for the second
launch
the rear
fins and
and
this
case,
it vehicle,
was was
found
that thisofairframe
also step
had
a fin including
offset,were
so fibreglassing
it performed
was spinning
rapidly
Figure
8c.
For as
this
a number
controlled
responses
in launch
the
wind
tunnel
3D
printing
two
new
canards
to
replace
the
ones
that
were
broken
during
the
Tasha
III
1,
see
starting to swing backwards and forwards, risking damaging the canards. The gains and frequency
shortly
before
the
launch.
Hence,
there
is
a
good
amount
of
data
to
identify
torque,
damping
Figure
8c. For and
this vehicle,
a number
of controlled
were performed in the wind tunnel and
were
reduced
the parameters
in Equations
(11)step
andresponses
(12) are defined:
disturbances
and
to
analyze
the
capability
of
the
wind
tunnel
tests
predicttorque,
flight response.
shortly before the launch. Hence, there is a good amount of data totoidentify
damping and
45π
disturbances and to analyze
the capability
of the
response. (43)
k p = 0.5,
kd = 0.05,
f 0 wind
= 0.1,tunnel
R0 =tests to,predict
R1 = flight
0
4.3.1. Wind Tunnel Step Responses
180
4.3.1. Wind Tunnel Step Responses
The rocket
suspended
from
a string,
8 step
responses
The rollwas
angle
and roll rate
responses
areand
plotted
in Figure
23. were performed with a magnitude
rocket
was
fromhighest
a string,
andspeed
8 step
werenot
performed
withcase,
a as
of 45˝ , at aThe
wind
speed
of suspended
22 m¨ s´1 . The
wind
of responses
30 m¨ s´1 was
used in this
50
−1. The highest wind speed of 30 m·s−1 was not used in
magnitude
of
45°,
at
a
wind
speed
of
22
m·s
it was found that this airframe also had a fin offset, so it was spinning rapidly and starting to swing
40 as it was found that this airframe also had a fin offset, so it was spinning rapidly and
this case,
backwards
and forwards, risking damaging the canards.
50 The gains and frequency were reduced and
starting
30 to swing backwards and forwards, risking damaging the canards. The gains and frequency
the parameters in Equations (11) and (12) are defined:
were reduced
and the parameters in Equations (11) and (12) are defined:
20
0
45π
45
π
k p k“ =
0.5,
k
“
0.05,
f
“
0.1,
0
d
= 180 ,,
0.5, kd = 0.05, f 0 = 0.1, RR00 “
p
10
180
0
RR11=“0 0
(43)
-50
-10 angle and roll rate responses are plotted in
The roll
Figure23.
23.
The
roll angle and roll rate responses are plotted in Figure
-20
50
-30
400
20
40
60
80
time (s)
30
-100
0
50
20
60
80
time (s)
(a)
20
40
(b)
Figure 23. Wind tunnel 45 degree step responses
(a) Roll angle; (b) Roll rate.
0
10
0
Figure
23 shows there are significantly different overshoots and rise times for each step
-50
response
as
well
as a major difference in dynamics depending
on the direction of rotation, which is
-10
likely caused
by
the
fin
offset
in
the
airframe.
To
account
for
these
variations, the model of Equations
-20
(2)–(12) is identified for each individual step response. Since the oscillations reduce quite quickly
-30
0
20
40
time (s)
(a)
60
80
-100
0
20
40
60
80
time (s)
(b)
Figure 23. Wind tunnel 45 degree step responses (a) Roll angle; (b) Roll rate.
Figure 23. Wind tunnel 45 degree step responses (a) Roll angle; (b) Roll rate.
Figure 23 shows there are significantly different overshoots and rise times for each step
response as well as a major difference in dynamics depending on the direction of rotation, which is
likely caused by the fin offset in the airframe. To account for these variations, the model of Equations
(2)–(12) is identified for each individual step response. Since the oscillations reduce quite quickly
(43)
Aerospace 2016, 3, 10
20 of 27
Figure 23 shows there are significantly different overshoots and rise times for each step response
as
well
as a major difference in dynamics depending on the direction of rotation, which is likely caused
Aerospace 2016, 3, 10
20 of 27
by the fin offset in the airframe. To account for these variations, the model of Equations (2)–(12) is
identified
for each
step half
response.
oscillations
reduce quite
quickly
after
the first
after
the first
peak,individual
only the first
of theSince
data the
in each
step response
is used
for the
parameter
peak,
only
the
first
half
of
the
data
in
each
step
response
is
used
for
the
parameter
identification.
The
identification. The remaining half is essentially disturbances in the wind tunnel, and there are very
remaining
is essentially
disturbances
in the wind
tunnel, and there
are very
few
dynamics
few
canardhalf
dynamics
so it does
not contribute
to identifiability.
The time
points
incanard
the disturbance
so
it
does
not
contribute
to
identifiability.
The
time
points
in
the
disturbance
model
of
Equations
model of Equations (4)–(8) were chosen to be simply the beginning and end points with (4)–(8)
N =1
were
chosen(4).
to be
simply
the
beginning
with
N =is1 reset
in Equation
(4).time,
Sincethe
5 stime
is analyzed
in
Equation
Since
5 s is
analyzed
in and
eachend
datapoints
set, and
time
to 0 each
points
in each
data set, and time is reset to 0 each time, the time points are defined:
are
defined:
T00 “
= 0,
T
0,
T
T1 =
“ 55
(44)
(44)
For
For the
the grid
grid search
search and
and non-linear
non-linear regression
regression algorithm,
algorithm, the
the ranges
ranges of
of the
the parameters
parameters are
are taken
taken
from
Equation
(34).
The
results
identified
parameters
and
mean
model
response
errors
for
from Equation (34). The results identified parameters and mean model response errors for the
the
open-loop
of Equation
Equation (9)
(9) are
aregiven
givenin
inTable
Table2.2.An
Anexample
exampleset
setofofmodel
model
responses
plotted
open-loop model
model of
responses
is is
plotted
in
in
Figure
which
is the
sixth
response
in Figure
23. Both
the angle
roll angle
roll match
rate match
Figure
24,24,
which
is the
sixth
stepstep
response
in Figure
23. Both
the roll
and and
roll rate
very
very
closely
the measured
even awith
very simple
for disturbance
the
closely
to thetomeasured
data, data,
even with
veryasimple
linear linear
model,model,
for disturbance
across across
the whole
whole
data
set
considered.
data set considered.
50
model
measured
40
30
20
10
0
-10
-20
0
1
2
3
4
5
time(s)
(a)
(b)
Figure 24. Open-loop model response versus measured data (a) Roll angle; (b) Roll rate.
Figure 24. Open-loop model response versus measured data (a) Roll angle; (b) Roll rate.
Table 2. Summary of the identified model parameters for each of the 8 wind tunnel step responses.
Table 2. Summary of the identified model parameters for each of the 8 wind tunnel step responses.
Step Response
Step Response
1
12
2
3
3
44
55
66
77
8
8
Mean
Mean
α
α
13
1315
15
22
22
1515
2525
2323
1515
27
27
19.4
19.4
β
β
10.5
10.5
6.5
6.5
10.5
10.5
6.0
6.0
12.5
12.5
10.5
10.5
10.5
10.5
10.0
10.0
9.6
9.6
[ud 0 , ud 1 ]
rud0 , ud1 s
[−5.59,−7.71]
[´5.59,´7.71]
[−5.82,−6.10]
[´5.82,´6.10]
[−6.04,−6.35]
[´6.04,´6.35]
[−4.18,−7.16]
[´4.18,´7.16]
[−5.90,−6.51]
[´5.90,´6.51]
[´5.12,´6.25]
[−5.12,−6.25]
[´6.11,7.41]
[−6.11,7.41]
[´5.47,´5.44]
[−5.47,−5.44]
[´5.47,6.62]
[−5.47,6.62]
[μ”| p|,OL , μ|φ|,OL ] ı
µ
,µ
|p|,OL |φ|,OL
[1.64,6.23]
[1.64,6.23]
[0.70,2.38]
[0.70,2.38]
[1.13,4.40]
[1.13,4.40]
[0.42,2.08]
[0.42,2.08]
[0.82,2.92]
[0.82,2.92]
[0.26,1.66]
[0.26,1.66]
[1.43,5.84]
[1.43,5.84]
[0.60,2.66]
[0.60,2.66]
[0.88,3.52]
[0.88,3.52]
Table
showsthere
there
a significant
variation
of parameters
the
step responses.
The
Table 22shows
is is
a significant
variation
of parameters
acrossacross
the step
responses.
The average
˝ andwas
average
model
over
3.52
angle and roll
model error
overerror
all tests
wasall
0.88tests
3.520.88°
deg/sand
for the
rolldeg/s
anglefor
andthe
roll roll
rate respectively.
The rate
size
˝
respectively.
The size of
the45step
was 45°,
so the
average
model
errorsfrom
in Table
vary
from
of the step response
was
, soresponse
the average
model
errors
in Table
2 vary
0.6%2 to
3.6%
of
0.6%
to 3.6%
change
in roll
angle. and
Hence,
the model
andeffective
methodsat are
very effective
at
the change
in of
rollthe
angle.
Hence,
the model
methods
are very
capturing
rocket roll
capturing rocket roll response in the vertical wind tunnel. The disturbances in column 4 of Table 2
show a trend for a lower disturbance in the first period, which was similar to the flight in Figure 22b,
showing that the canard-fin interaction effects can minimize the effect of fin offset in the airframe.
The average fin offset across all tests was −6.1°, so taking into account the swirl this value
corresponds to −4.1°. The wide range of values of the damping, torque constant and fin offsets in
Aerospace 2016, 3, 10
21 of 27
response in the vertical wind tunnel. The disturbances in column 4 of Table 2 show a trend for a lower
disturbance in the first period, which was similar to the flight in Figure 22b, showing that the canard-fin
interaction effects can minimize the effect of fin offset in the airframe. The average fin offset across all
˝ ,10
Aerospace
2016, 3,
21 of 27 of
tests
was ´6.1
so taking into account the swirl this value corresponds to ´4.1˝ . The wide range
values of the damping, torque constant and fin offsets in Table 2 give the range of uncertainty in the
Table 2 give the range of uncertainty in the launch, and will be compared with the flight data in the
launch, and will be compared with the flight data in the next section.
next section.
4.3.2. Flight Data
4.3.2. Flight Data
Tasha III from Figure 8c was launched from Kaitorete Spit on 4 December 2015. The aims of this
Tasha III from Figure 8c was launched from Kaitorete Spit on 4 December 2015. The aims of this
launch included testing the rocket under a greater amount of actuations and to overcome the fin offset
launch included testing the rocket under a greater amount of actuations and to overcome the fin
problem that occurred in the July launch as detailed in Section 4.2. Importantly, the launch provided
offset problem that occurred in the July launch as detailed in Section 4.2. Importantly, the launch
a characterization
of the ability of the wind tunnel to predict flight dynamics far outside the wind
provided a characterization of the ability of the wind tunnel to predict flight dynamics far outside
speeds
that
can
be
generated
by the fan.
Since
wind
for the
tunnel
datadata
was
only
the wind speeds that
can be generated
by the
fan.the
Since
the speed
wind speed
forwind
the wind
tunnel
was
1 , this launch provided a rigorous test of how well the model could be extrapolated to higher
22 only
m¨ s´22
m·s−1, this launch provided a rigorous test of how well the model could be extrapolated to
´1 which
wind
speeds.
apogee
this flight
was
422was
m, and
maximum
velocity
was 81was
m¨ s81
higher
windThe
speeds.
Thefor
apogee
for this
flight
422 the
m, and
the maximum
velocity
m·s−1
were
much
lower
than
the
July
launch,
due
to
the
increased
weight
from
the
more
robust,
supersonic
which were much lower than the July launch, due to the increased weight from the more robust,
capable
avionics
stack.avionics
The wind
speed
reasonably
on the day
an day
average
speed
supersonic
capable
stack.
Thewas
wind
speed waslow
reasonably
lowwith
on the
withground
an average
−1. Figure
of ground
3 m¨ s´1speed
. Figure
shows
several
stills of
the rocket
moving
up and
leaving
the launch
of 325m·s
25 shows
several
stills of
the rocket
moving
up and
leaving guide.
the
launch
guide.
Thewas
overall
launchalthough
was a success
although
the damaged
back fins were
damaged
ontolanding,
The
overall
launch
a success
the back
fins were
on landing,
due
a sudden
due
a sudden
gust of wind
that pushed
the rocket
onto stony ground.
gust
ofto
wind
that pushed
the rocket
onto stony
ground.
Figure
Sequenceofofstills
stillsshowing
showing Tasha
Tasha III
III rocket
rocket moving
guide.
Figure
25.25.Sequence
movingup
upand
andleaving
leavinglaunch
launch
guide.
The controller for this launch was a single step response from 0° to −20°, which occurred 2 s
The controller for this launch was a single step response from 0˝ to ´20˝ , which occurred 2 s after
after the controller was switched on. The canard limits were increased
to ±9° in this launch to
the controller was switched on. The canard limits were increased to ˘9˝ in this launch to overcome
overcome the fin offset from the first launch. In addition, some open-loop oscillatory inputs were
theincluded
fin offsetinfrom
the first launch. In addition, some open-loop oscillatory inputs were included in the
the PD control signal of Equation (10). This input signal was implemented 0.4 s after the
PDcontrol
controlstarted
signaland
of Equation
(10). 5This
input
wasresponse.
implemented
0.4 s after
control chirp
started
was stopped
s after
thesignal
−20° step
The input
was athe
modified
˝
and
was defined:
stopped 5 s after the ´20 step response. The input was a modified chirp signal defined:
signal
(t ) “
= (pA
A00 +`Δ∆Aptqqsin
A(t )) sin (ppω
(ω00(ptq
t ) +`Δω
(t ))t )
uuinput
∆ωptqqtq
input ptq
=
AA00 “
4π
4π
tt
(t )“= 2πp2
2π(2´− q,), ∆Aptq,
ΔA(t ), Δω
(t ) ≡”random
,, ωω00ptq
∆ωptq
randomvariation
variation on
on signal
signal
180
10
180
(45)(45)
(46)(46)
AA
plot
ofof
the
applied
26.
plot
the
appliedinput
inputsignal
signalisisgiven
given in
in Figure
Figure 26.
The
roll
rate
data
including
all
the
key
points
of
the
launch
given
in Figure
27, where
The roll rate data including all the key points of the launch
areare
given
in Figure
27, where
t = 0t = 0
corresponds
to 1.5 s before take-off. For this launch, two accelerometers were used to improve
corresponds to 1.5 s before take-off. For this launch, two accelerometers were used to improve the
therobustness
robustnessininthe
thelaunch
launchdetect
detectand
andthe
thedelay
delaythreshold
threshold
was
reduced
addition,
was
reduced
to to
0.10.1
s. s.In In
addition,
thethe
accelerometer
threshold
increased
to
2.5
g.
Similarly
to
the
Tasha
III
launch
1,
the
control
was
started
accelerometer threshold increased to 2.5 g. Similarly to the Tasha III launch 1, the control was started
when
thethe
rocket
height
when
rocket
heightwas
was2 2mmabove
abovethe
the44m
mlaunch
launch guide.
guide.
Aerospace 2016, 3, 10
Aerospace 2016, 3, 10
Aerospace 2016, 3, 10
22 of 27
22 of 27
22 of 27
6
6
4
4
2
2
0
0
-2
-2
-4
-4
-6
-6
-8
-8
0
2
4
6
8
0
2
time4 (s)
time (s)
6
8
(deg/s)
roll roll
raterate
(deg/s)
Figure 26. Input signal applied to PD Controller ( t = 0 corresponds to start of controller).
Figure
26. Input signal applied to PD Controller (t = 0 corresponds to start of controller).
Figure 26. Input signal applied to PD Controller ( t = 0 corresponds to start of controller).
Figure 27. Roll rate response for Tasha III launch 2 including key points in the launch.
Figure
27.27.Roll
includingkey
keypoints
pointsininthe
thelaunch.
launch.
Figure
Rollrate
rateresponse
responsefor
forTasha
TashaIII
III launch
launch 2 including
For this launch, the data is split into the two PD controlled responses with the set point of 0°
followed
bylaunch,
−20°
which
was
2ississplit
later.
A
sharp
roll rate can
be seen for
this
second
set point
this
launch,
thedata
data
splitinto
into
thechange
two PD
PDincontrolled
controlled
responses
with
the
set
ofof
0°0˝
ForFor
this
the
the
two
responses
with
the
setpoint
point
at
aboutby
4by
s´20
in
Figure
27.was
The2first
period
ofsharp
analysis
isinstarted
at 2.4
in
Figure
27
which
is 0.4
afterset
followed
−20°
which
AA
sharp
change
roll
can
seen
this
second
setspoint
˝ which
followed
was
2s slater.
later.
change
in rate
roll
ratesbe
can
befor
seen
for
this
second
the
control
starts
and27.
corresponds
to theofimplementation
of at
the2.4
input
signal 27
from
Figure
26.s after
This
at
about
4
s
in
Figure
The
first
period
analysis
is
started
s
in
Figure
which
is
0.4
point at about 4 s in Figure 27. The first period of analysis is started at 2.4 s in Figure 27 which is
starting
point
wasand
chosen
since there
oscillatory
dynamics
in thefrom
canards
which
will
the control
starts
corresponds
to are
thesignificant
implementation
of the
input signal
Figure
26. This
0.4 s after the control starts and corresponds to the implementation of the input signal from Figure 26.
ensure
of the
model
The second
period of
starts
at 4 will
s in
startinggood
pointidentifiability
was chosen since
there
are parameters.
significant oscillatory
dynamics
in analysis
the canards
which
This starting point was chosen since there are significant oscillatory dynamics in the canards which
Figure
27,
which
is
when
the
set
point
changes
from
0°
to
−20°.
ensure good identifiability of the model parameters. The second period of analysis starts at 4 s in
will ensure good identifiability of the model parameters. The second period of analysis starts at 4 s in
Figure
which
when athe
set point
changes
0° to −20°.
For27,the
first is
period,
similar
approach
tofrom
the Tasha
III launch 1 model is applied, where N1
Figure 27, which is when the set point changes from 0˝ to ´20˝ .
For
the
first
period,
a
similar
approach
to
the
Tasha
IIIuntil
launch
1 model issignificantly
applied, where N1
equally
pointsa similar
are chosen,
and toNthe
increased
For thespaced
first period,
approach
III launch
1 there
modelisis no
applied, where Nfurther
1 isTasha
1 equally
N
equally
spaced
points
are
chosen,
and
is
increased
until
there
is
no
significantly
further
spaced
points
are
chosen,
and
N
is
increased
until
there
is
no
significantly
further
improvement
1
Forthe
improvement in the fit to the1 data. The values
of N1 investigated were from 1 to 6 points. in
fit to
the data. The values
N
were of
from
to 6 points. For
N1from
= 1,¨ 1¨ ¨ to
,4, 6the
best model
1 investigated
N11angle
investigated
were
points.
For
improvement
fit of
to
the
data.
The average
values
N1 = 1,…, 4 , in
thethebest
model
fits had
roll
errors of
2.36,
2.15, 0.57
and 0.26°
fits had
average roll angle errors of 2.36, 2.15, 0.57 and 0.26˝ respectively. There was no significant
N1 = 1,…, 4 There
, the best no
model fits had
average roll
of
2.36,
2.15, 0.57 and 0.26°
N1 virtually
= 5errors
respectively.
improvement
for angle
and 6identical
and
the parameters
improvement
for N1 =was
5 and significant
6 and the parameters
remained
for N1 = 3,¨ remained
¨ ¨ ,6. Hence
N
=
5
respectively.
There
was
no
significant
improvement
for
and
6
and
the
parameters
remained
1
a value of N1 = 4 is chosen for the final model. The results are
defined:
Aerospace 2016, 3, 10
23 of 27
virtually
identical
Aerospace
2016,
3, 10
for
N1 = 3,…, 6 . Hence a value of N1 = 4 is chosen for the final model.
23 ofThe
27
results are defined:
αbest ,OL = 23.0, βbest ,OL = 9.0
μ| p|,OL ≡ mean absolute error in roll rate = 4.10 deg/s
(47)
(47)
(48)
(48)
μµ|φ|φ|,OL
≡ mean absolute error in roll angle = 0.26 deg/s
|,OL ” mean absolute error in roll angle “ 0.26 deg{s
(49)
(49)
αbest,OL “ 23.0, β best,OL “ 9.0
µ| p|,OL ” mean absolute error in roll rate “ 4.10 deg{s
The
The model
model response
response for
for the
the roll
roll angle
angle and
and roll
roll rate
rate are
are shown
shown in
in Figure
Figure 28
28 and
and the
the offset
offset angle
angle is
is
plotted
plotted in
inFigure
Figure29.
29.
6
model
measured
4
2
0
-2
-4
-6
-8
0
0.5
1
1.5
time (s)
(a)
(b)
Figure 28.
28. Modelled
Modelled roll
roll angle
angle (a)
(a) and
and roll
roll rate
rate (b)
(b) versus
versus the
the measured
measured data
datafor
forfirst
firstanalysis
analysisperiod.
period.
Figure
-1
-2
-3
-4
-5
-6
-7
-8
0
0.5
1
1.5
time (s)
Figure29.
29.Identified
Identifiedtime-varying
time-varyingoffset
offsetangle
angle uuoffset for
first analysis period.
Figure
offset for first analysis period.
The
toto
thethe
average
wind
tunnel
predicted
values
of 19.4
andand
9.6
The results
resultsofofEquation
Equation(47)
(47)are
areclose
close
average
wind
tunnel
predicted
values
of 19.4
in
2, with
of 15.7%
4.4%,
The offset
angles
in angles
Figure 29
all within
9.6Table
in Table
2, errors
with errors
of and
15.7%
andrespectively.
4.4%, respectively.
The
offset
in are
Figure
29 arethe
all
range
of
values
of
the
wind
tunnel
tests
as
well.
There
is
also
a
similar
trend
of
lower
offset
angles
for
within the range of values of the wind tunnel tests as well. There is also a similar trend of lower
the
smaller
finfor
movements
was
the case inas
the
wind
Thewind
meantunnel.
offset angle
of Figure
29angle
was
offset
angles
the smallerasfin
movements
was
the tunnel.
case in the
The mean
offset
˝
˝
˝
4.9
which29
is was
0.8 4.9°
greater
thanisthe
4.1 the
predicted
wind
tunnel.inThis
of Figure
which
0.8°average
greaterofthan
averageinofthe
4.1°
predicted
thevalue
wind corresponds
tunnel. This
to
an
error
of
16.3%
but
well
within
the
expected
variation
of
Table
2.
value corresponds to an error of 16.3% but well within the expected variation of Table 2.
A similar procedure was applied to the second period of data corresponding to a reference angle
of ´20˝ . In this case, a value of N2 = 2 was sufficient for the modelling and the identified parameters
are defined:
αbest,OL “ 23.0, β best,OL “ 9.0
(50)
A similar procedure was applied
A similar procedure was applied
angle of −20°. In this case, a value of
angle of −20°. In this case, a value of
parameters are defined:
parameters are defined:
to the second period of data
to the second period of data
N 2 = 2 was sufficient for the
N 2 = 2 was sufficient for the
corresponding to a reference
corresponding to a reference
modelling and the identified
modelling and the identified
αbest ,OL = 48.0, βbest ,OL = 8.0
αbest
,OL = 48.0, βbest ,OL = 8.0
μ OL ≡”mean
absolute
error
in
roll rate“=8.32
8.32 deg/s
meanabsolute
absoluteerror
error in
in roll
|,OL≡ mean
μµ|| pp||,|,pOL
roll rate
rate = 8.32deg{s
deg/s
μµ OL
mean
roll angle
angle“=0.99
0.99deg{s
deg/s
meanabsolute
absoluteerror
error in
in roll
|,OL≡”
μ||φφ||,|,φOL
≡ mean absolute error in roll angle = 0.99 deg/s
Aerospace 2016, 3, 10
24 of 27
(50)
(50)
(51)
(51)
(51)
(52)
(52)
(52)
The
3030
and
the
offset
angle
is
The model
model responses
responsesfor
forthe
theroll
rollangle
angleand
androll
rollrate
rateare
areshown
shownininFigure
Figure
and
the
offset
angle
Theinmodel
responses
for the roll angle and roll rate are shown in Figure 30 and the offset angle
plotted
Figure
31.
is plotted in Figure 31.
is plotted in Figure 31.
5
5
0
0
-5
-5
-10
-10
-15
-15
-20
-20
-25
-25
-30
-30 0
0
model
model
measured
measured
1
1
2
3
2 time (s) 3
4
4
5
5
time (s)
(a)
(a)
(b)
(b)
Figure 30. Modelled roll angle (a) and roll rate (b) versus the measured data for second analysis period.
Figure30.
30.Modelled
Modelledroll
rollangle
angle(a)
(a)and
androll
roll rate
rate (b)
(b) versus
versus the
the measured
measured data
Figure
data for
for second
secondanalysis
analysisperiod.
period.
-8.5
-8.5
-9
-9
-9.5
-9.5
-10
-10
0
0
1
1
2
2
time (s)
time (s)
3
3
4
4
5
5
Figure 31. Identified time-varying offset angle uoffset for second analysis period.
Figure31.
31.Identified
dentifiedtime-varying
time-varyingoffset
offsetangle
angle u
uoffset
Figure
forsecond
secondanalysis
analysisperiod.
period.
offset for
The modeled torque constant in Equation (50) is reasonably close to the wind tunnel predicted
The modeled torque constant in Equation (50) is reasonably close to the wind tunnel predicted
value of 9.6 with an error of 16.7%, however the damping is significantly larger than all the damping
value of 9.6 with an error of 16.7%, however the damping is significantly larger than all the damping
values of Table 2. This extra damping is likely due to the rocket pitching over with an increasing
values of
damping
is likely
duedue
to the
rocket
pitching
over over
with with
an increasing
angle
of Table
Table2.2.This
Thisextra
extra
damping
is likely
to the
rocket
pitching
an increasing
angle of attack as well as the higher velocity. On the other hand, the average identified offset of
of attack
as wellas
aswell
the higher
On the other
hand,
thehand,
average
offset of Figure
angle
of attack
as the velocity.
higher velocity.
On the
other
the identified
average identified
offset 31
of
Figure ˝31 is −4.7°, which is even closer to the wind tunnel average
of 4.1°. Hence, although the
˝ . Hence,
is
´4.7
,
which
is
even
closer
to
the
wind
tunnel
average
of
4.1
although
the
damping
is
Figure 31 is −4.7°, which is even closer to the wind tunnel average of 4.1°. Hence, although the
damping is less accurate in the post-thrust period, the torque constant and the offset angles are both
less accurate
in the
post-thrust
period, the period,
torque constant
and
the offset
are both
accurately
damping
is less
accurate
in the post-thrust
the torque
constant
andangles
the offset
angles
are both
accurately predicted for all stages of the flight, which are more important for control design. A
predicted
all stagesfor
of the
more which
important
control
design.for
A similar
accuratelyfor
predicted
all flight,
stageswhich
of theare
flight,
are for
more
important
controlanalysis
design.has
A
been performed for the closed-loop responses, but since the results were very similar to the open-loop
analysis above, these results are not shown.
Note that the torque constant values of β = 8 and β = 9 in this second Tasha III launch are
reasonably close to value of β = 10 identified in the first Tasha III launch. However, both of the values
of damping in the second launch are considerably larger than the damping from the first launch.
Aerospace 2016, 3, 10
25 of 27
This result is probably because there were a lot less dynamics in the first launch so the damping was
less identifiable.
5. Conclusions
A vertical wind tunnel has been designed and built at the University of Canterbury. This wind
tunnel has been specifically customized for sounding rocket research and has a unique feature of
allowing the rocket to be suspended by string for accurate prediction of roll dynamics. It is also
very useful for testing stability before flight. The flow of the wind tunnel was analyzed in detail and
turbulence intensity was estimated to be less than 0.04%. However, there was a reasonable amount of
swirl equivalent to 2˝ of canard fin. This swirl was dramatically reduced to a negligible amount by
using an egg crate at the bottom of the wind tunnel near the fan to straighten the flow.
Two new airframes were developed in this research with a supersonic capable avionics stack
in the second vehicle. Both rockets had reinforced fiberglass to give strength to the fins, but it was
found that they had significant fin offset, with post-thrust average values of about 7˝ for the first
vehicle and 5˝ for the second. Wind tunnel tests on the second vehicle revealed a high roll rate, which
suggested a combination of swirl and fin offset. After the second flight, tests with and without the
flow straightener using a similar airframe, showed that swirl could be modeled by the equivalent
canard offset. This value was then used to compare the wind tunnel tests of the second vehicle to the
flight data.
A minimal modelling approach for roll dynamics was developed using a velocity dependent
model and a piecewise-linear time-varying canard offset function. Open and closed loop models were
considered with PD control, with encoders used to measure the canard movements. A combination
of a grid search and non-linear regression provided a rigorous way of identifying the parameters.
The models identified gave an excellent match to the flight data in both launches, with quite a smooth
varying canard offset profile. It was found that with high dynamic movement in the canards the
identified fin offset was lower, showing that canard–fin interaction dominates during these periods.
This phenomenon occurred in both the wind tunnel tests and flight.
A significant outcome of this paper was proving that wind tunnel tests give accurate predictions
of the torque constant and fin offset and importantly, the resulting minimal roll models predict flight
behavior closely. The damping is typically underestimated in the wind tunnel so a greater uncertainty
should be included in this parameter for future control design.
In summary, the vertical wind tunnel at the University of Canterbury is a unique facility and
a key part of the success of UC Rocketry. A combination of wind tunnel tests and rocket launches have
allowed a thorough understanding of rocket flight and control.
Acknowledgments: Funded by the Rutherford Discovery Fellowship, Royal Society New Zealand; Callaghan
Innovation PhD Fellowships; and Rocket Lab Ltd.
Author Contributions: Hoani Bryson, Hans Philipp Sültrop, George Buchanan, Christopher Hann,
Malcolm Snowdon, Avinash Rao, Adam Slee, Kieran Fanning, David Wright: developed the hardware, did the
experiments, analyzed the data, developed models and wrote the paper. Jason McVicar, Brett Clark, Graeme Harris
and Xiao Qi Chen: helped to construct the wind tunnel including setting up the fan and controller, provided
expertise and advice on the flow quality and instrumentation and sensors for the wind tunnel tests, and contributed
to writing the paper.
Conflicts of Interest: The authors declare no conflict of interest.
Notation
Ip
ρ
α
β
u f in
Inertia in roll axis (kg/m2 )
Air density (kg/m3 )
Damping constant (m2 )
Torque constant (m)
Roll fin angle (rad)
Aerospace 2016, 3, 10
A
p
v
k p , kd
Rptq
ud,0 , . . . , ud,N
φdata
φOL , φCL
<α , < β
Γ
σ
ucmd
uenc
cmd1 , . . . , cmd2
enc1 , . . . , enc2
umin , umax
µ| p|,OL , µ| p|,CL
µ|φ|,OL , µ|φ|,CL
uinput
26 of 27
Cross sectional area (m2 )
Roll rate (rad/s)
velocity (m/s)
Proportional and derivative gains
Reference angle (rad)
Time-varying disturbance offset angle parameters (rad)
Measured roll angle (rad)
Open and closed loop numerical solutions to roll equations (rad)
Ranges for α, β in the grid search for parameter identification
Turbulence intensity (m/s)
Standard deviation of wind speed (m/s)
Commanded canard angle (rad)
Measured canard angle by encoder (rad)
Individual canard commands (rad)
Individually measured encoders (rad)
Minimum and maximum canard limits for actuation (rad)
Mean absolute roll rate for open loop and closed loop controllers
Mean absolute roll angle for open loop and closed loop controllers
Open loop input signal into PD controller
Abbreviations
PD
NASA
UC
CFD
RPM
OL
CL
Proportional-derivative
The National Aeronautics and Space Administration
University of Canterbury
Computational Fluid Dynamics
Revolutions per minute
Open loop
Closed loop
References
1.
2.
3.
4.
5.
6.
UC Rocketry Project. Available online: http://ucrocketry.org/ (accessed on 1 March 2016).
Schrijer, F.; Bannink, W. Description and Flow Assessment of the Delft Hypersonic Ludwieg Tube.
J. Spacecr. Rocket. 2010, 47, 125–133. [CrossRef]
Spirito, J.D.; Vaughn, M.E., Jr.; Washington, W.D. Numerical Investigation of Canard-Controlled Missile with
Planar and Grid fins. J. Spacecr. Rocket. 2003, 40, 363–370. [CrossRef]
Silton, S.I.; Fresconi, F. Effect of Canard Interactions on Aerodynamic Performance of a Fin-Stabilized
Projectile. J. Spacecr. Rocket. 2015, 52, 1430–1442. [CrossRef]
Curfman, H.J.; Grisby, C.E. Longitudinal Stability and Control Characteristics of a Canard Missile Configuration for
Mach Numbers from 1.1 to 1.93 as Determined from Free-Flight and Wind-Tunnel Investigations; Technical Report for
NASA Langley Aeronautical Laboratory: Hampton, VA, USA, 1952. Available online: http://ntrs.nasa.gov/
archive/nasa/casi.ntrs.nasa.gov/19930087105.pdf (accessed on 1 March 2016).
Dollyhigh, S.M. Subsonic and Supersonic Longitudinal Stability and Control Characteristics of an Aft-Tail Fighter
Configuration with Cambered and Uncambered Wings and Cambered Fuselage; Technical Report for NASA
Langley Research Center: Hampton, VA, USA, 1977. Available online: http://ntrs.nasa.gov/archive/nasa/
casi.ntrs.nasa.gov/19770024149.pdf (accessed on 1 March 2016).
Aerospace 2016, 3, 10
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
27 of 27
Blair, A.B., Jr.; Hernandez, G. Effect of Tail-Fin Span on Stability and Control Characteristics of a Canard-Controlled
Missile at Supersonic Mach Numbers; Technical Report for NASA Langley Research Center: Hampton, VA, USA,
1983. Available online: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19830019688.pdf (accessed
on 1 March 2016).
Dillenius, M.F.E.; Lesieutre, D.J.; Hegedus, M.C.; Perkins, S.C., Jr.; Love, J.F.; Lesieutre, T.O. EngineeringIntermediate- and High-Level Aerodynamic Prediction Methods and Applications. J. Spacecr. Rocket. 1999, 36,
609–620. [CrossRef]
Lesieutre, D.J.; Love, J.F.; Dillenius, M.F.E. Prediction of the Nonlinear Aerodynamic Characteristics of
Tandem-Control and Rolling-Tail Missiles. In Proceedings of the AIAA Atmospheric Flight Mechanics
Conference and Exhibit, AIAA 2002-4511, Monterey, CA, USA, 6 August 2002.
Beresh, S.J.; Smith, J.A.; Henfling, J.F.; Grasser, T.W.; Spillers, R.W. Interaction of a Fin Trailing Vortex with
a Downstream Control Surface. J. Spacecr. Rocket. 2009, 46, 318–328. [CrossRef]
Lesieutre, D.J.; Quijano, O. Studies of Vortex Interference Associated with Missile Configurations.
In Proceedings of the 52nd Aerospace Sciences Meeting, AIAA SciTech (AIAA 2014-0213), National Harbor,
MD, USA, 13–17 January 2014.
Buchanan, G.; Wright, D.; Hann, C.E.; Bryson, H.; Snowdon, M.; Rao, A.; Slee, A.; Sültrop, H.P.;
Jochle-Rings, B.; Barker, Z.; et al. The Development of Rocketry Capability in New Zealand—World Record
Rocket and First of its Kind Rocketry Course. Aerospace 2015, 2, 91–117. [CrossRef]
Hann, C.E.; Snowdon, M.; Rao, A.; Winn, O.; Wongvanich, N.; Chen, X.Q. Minimal Modelling Approach to
Describe Turbulent Rocket Roll Dynamics in a Vertical Wind Tunnel. Proc. Inst. Mech. Eng. G J. Aerosp. Eng.
2012, 226, 1042–1060. [CrossRef]
Assato, M.; Moraes, L.F.; Chisaki, M. Investigation of a Boundary-Layer Control System by Air Blowing in
a Closed-Circuit Subsonic Wind Tunnel. In Proceedings of the 45th AIAA Aerospace Sciences Meeting and
Exhibit, Aerospace Sciences Meetings, Reno, NV, USA, 8–11 January 2007.
Seo, Y. Effect of hydraulic diameter of flow straighteners on turbulence intensity in square wind tunnel.
HVAC R Res. 2013, 19, 141–147.
Wind Tunnel Design. Available online: http://www-htgl.stanford.edu/bradshaw/tunnel/index.html
(accessed on 1 March 2016).
BBS Timbers Ltd. Available online: http://bbstimbers.co.nz/flexible-plywood-bendy-plywood/ (accessed
on 1 March 2016).
Kestrel AU Pocket Weather Instruments. Available online: http://kestrelmeters.com.au/ (accessed on
1 March 2016).
Sioruis, G.M. Missile Guidance and Control Systems; Springer-Verlag Inc.: New York, NY, USA, 2004.
© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons by Attribution
(CC-BY) license (http://creativecommons.org/licenses/by/4.0/).