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70th International Astronautical Congress, Washington, USA. Copyright c
2019 by Delft Aerospace Rocket Engineering
(DARE). Published by the IAF, with permission and released to the IAF to publish in all forms.. All rights reserved.
IAC–19–D2.3
Trajectory Simulations and Sensitivity for the SPEAR Parachute Test
Vehicle
L. Pepermans, E. Menting, M. Rozemeijer, T. Britting, P.J. Derks
Parachute Research Group (PRG) of Delft Aerospace Rocket Engineering (DARE), the Netherlands,
prg@dare.tudelft.nl
The Supersonic Parachute Experiment Aboard REXUS, or SPEAR in short, is a small test vehicle that is
to fly on board the REXUS 28 rocket as part of the REXUS/BEXUS project cycle 12. The objective of the
mission is to test the Hemisflo ribbon drogue parachute of the Large Envelope Advanced Parachute System
(LEAPS) at supersonic conditions. LEAPS has been developed as the parachute recovery system for the
Aether, Stratos III and Stratos IV student build sounding rockets of Delft Aerospace Rocket Engineering.
To ensure the drogue can be tested supersonically, the vehicle shall reach at least Mach 1.5 at parachute
deployment in any possible flight case.
The trajectories are simulated using the in-house developed ParSim tool. This tool can simulate the free
fall and parachute behaviour of the vehicle during flight. In order to prove the vehicle complies with the
requirements in any possible flight case, several grid searches and Monte Carlo analyses have been performed.
During these runs, the initial conditions such as altitude and horizontal velocity are varied to simulate the
effect variations in launch conditions. The vehicle parameters such as drag coefficient, mass and area are
varied to demonstrate sensitivity to errors in production. Finally, the inflation conditions of the drogue
parachute are varied to simulate errors in the sensor and actuator subsystems.
All simulations are run separately from each other to identify the largest uncertainty and their respective
impact. Finally, one complete run is done showing the total sensitivity of SPEAR. The results of the
simulations are used to ensure SPEAR can fulfil the requirements under all expected conditions.
I. Introduction
The primary objective of the SPEAR mission is to
flight test the Stratos III and IV drogue parachute.
This Hemisflo ribbon parachute is tasked with the
stabilisation and deceleration of the nose cone. It has
to operate at supersonic conditions and high dynamic
pressures. The Stratos engineering teams could per-
form low-speed wind tunnel testing but were not able
to test at high dynamic pressures or supersonic con-
ditions.
To give the Stratos engineering teams these abil-
ities, the Parachute Research Group (PRG) of Delft
Aerospace Rocket Engineering (DARE) initiated
SPEAR. PRG is responsible for the research and de-
velopment of parachute systems within DARE. The
mission aims to flight test the drogue parachute at
supersonic conditions and is named the Supersonic
Parachute Experiment Aboard REXUS, or SPEAR
in short.
During the design cycle of SPEAR, it had to
be ensured that under all circumstances the drogue
parachute would be deployed at Mach 1.5 or higher.
Besides this, the SPEAR vehicle shall always land
with a maximum terminal velocity of 10 m/s. This
paper discusses the flight variations considered and
the effect of the variations on the Mach number at
deployment.
II. Background
II.i SPEAR mission
The SPEAR mission consists of a 7.75 kg test ve-
hicle that is to be deployed from the REXUS 28
rocket. The mission is set to fly in March 2020
from Kiruna, Sweden as part of the 12th cycle of the
REXUS/BEXUS project. The purpose of the vehicle
is to flight test the drogue parachute of the Stratos
III and IV sounding rockets at supersonic velocities.
The objectives of the SPEAR mission are shown
in Table 1.
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Table 1: The SPEAR mission objectives
Primary O.1A SPEAR shall validate the
stability performance of the drogue
parachute
O.1B SPEAR shall validate the in-
flation time predictions
O.1C SPEAR shall provide
parachute load data to validate
the ParSim parachute inflation
models
Secondary O.2A SPEAR shall provide the ther-
mal flux of the heat shield to validate
the ParSim thermal models
O.2B SPEAR shall provide a six-axis
inertial measurement data to validate
TumSim.
Tertiary O.3A SPEAR shall provide an ed-
ucational experience to the students
involved.
The SPEAR vehicle is jettisoned from the REXUS
rocket at an altitude between 50 and 80 kilometres.
This depends on the REXUS take-off mass and the
time at which SPEAR is jettisoned from REXUS.
SPEAR will then deploy an aerodynamic stabiliser,
described in Table 2. This stabiliser is deployed above
60 kilometres where the atmospheric density is low.
This stabiliser ensures the test vehicle is stable during
the atmospheric entry.
After a set time the drogue parachute is deployed.
The flight phase under the drogue parachute is the
primary flight phase of interest for the SPEAR mis-
sion. At an altitude of 1 km above the ground, the
main parachutes are deployed, ensuring a safe landing
of the test vehicle. All flight phases of the SPEAR
test vehicle can be seen in Fig. 1.
II.ii ParSim
To help DARE recovery engineers in the design
of the Stratos III recovery system work was started
on the Parachute Simulation Tool. This tool, named
ParSim, had the goal to predict the landing velocity
and structural loads of the Stratos III nose cone. The
ParSim v3 tool has been presented at the IAC2018.1
With added requirements for Stratos IV and SPEAR,
ParSim has been upgraded to v4, which is used for
this research.
II.iii SPEAR vehicle
The SPEAR test vehicle is a cylinder with a semi-
sphere cap of 500mm long and 220mm in diameter.
The total vehicle mass is 7.75 kg. SPEAR has four
parachutes on board. These can be found below and
are described in Table 2.
•1x Stabiliser
•1x Drogue parachute
•2x Main parachutes
For these simulations, the pilot chutes for the main
parachutes are not simulated. As the pilot chutes will
only extract the main parachutes from the parachute
bag, they are assumed to have no contribution to the
deceleration of the vehicle.
The stabiliser parachute is designed to keep the
test vehicle in a close to zero angle of attack flight
path. This ensures that the simulations can be done
using ParSim and that the maximum terminal veloc-
ity is reached. The drogue parachute is a one-on-
one copy of the Stratos III and Stratos IV drogue
parachutes.2The two main parachutes ensure a safe
landing velocity such that the flight data can be re-
trieved.
Table 2: Parachute Parameters
Parameter Value
Type parachute Ballute
Area [m2] 0.088
CD [-] 0.3
Deployment altitude [m] 60.000+
Type parachute Hemisflo ribbon
Area [m2] 0.2
CD [-] 0.29
Deployment time [s] Variable
Type parachute Disk Gap Band
Number of parachutes 2
Total Production Area [m2] 2.6
CD [-] 0.50
Deployment altitude [m] 1000
III. Simulations
III.i Variations
Even though the detailed design of the SPEAR
vehicle has finished, there are still unknowns in the
design. These unknown parameters are beyond the
control or current knowledge of the team. The first
includes the atmospheric conditions and the ejection
conditions. The second include parameters such as
the supersonic performance of the test vehicle and
ballute. An overview of all uncertain parameters,
called variations, has been made. These variations
come in three categories: vehicle parameters (I), en-
vironment (II), and initial conditions (III). A detailed
IAC–19–D2.3 Page 2 of 10
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Fig. 1: The SPEAR flight trajectory
breakdown of the variations can be seen in Table 3.
This table shows in which case a certain parameter is
considered (Case), what the nominal value is (Nom)
and what the considered variation is (Var).
The variations in the performed simulations con-
tain all unknowns in the design of the Free Falling
Unit (FFU). This includes variations in the vehicle
mass due to unknowns in the design and production
errors. The uncertainties of the parachute areas all
occur because of production errors. Similar to the
ballute stabiliser, the drag coefficient of the drogue
parachute is unknown at high Mach numbers.
Variations in the atmosphere are included only in
the air density and air temperature. These varia-
tions are included as the atmospheric conditions dur-
ing launch are unknown and can vary greatly.
The variations in initial conditions come from two
factors. Firstly, the performance of the REXUS
rocket is dependent on the total final mass, which
is unknown at the moment of writing. Secondly, the
ejection moment of SPEAR is unknown at this mo-
ment. The moment of ejection is determined by the
REXUS launch crew and in agreement with the other
experiments. In the REXUS 28 rocket, there is a
need to maximise microgravity time; thus, an ejec-
tion at apogee might not be feasible. This would
mean SPEAR is ejected between 50 and 60 km dur-
ing ascent.
Table 3: Variations considered
Parameter Case Nom Var
Mass [kg] I 7.75 ±0.75
Drogue parachute area
[m2]
I 0.2 ±5%
Drogue parachute CD
[−]
I 0.29 ±5%
Ballute area [m2] I 0.085 ±0.005
Ballute CD [−] I 0.3 ±20%
Initial altitude, apogee
[km]
II a 82.5 ±7.25
Initial altitude, ascent
[km]
II b 55 ±5
Initial flight path angle
[deg]
II b 75.2 ±3.0
Initial vertical velocity,
ascent [m/s]
II b 706 ±139
Air density [kg/m3] III 1.304 ±11%
Air temperature [K] III 270.7 ±10%
Distributions mentioned in Table 3 are given as ei-
IAC–19–D2.3 Page 3 of 10
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ther a uniform or normal distribution. Uniform dis-
tributions are given as a range of the minimum to the
maximum value with a step size (min:stepsize:max).
The uniform distribution is given as an average and
a 3σpercentage (Average ±Average* 3σ).
III.ii Outputs
•Landing velocity
•Mach number at drogue parachute deployment
•Dynamic pressure at drogue parachute deploy-
ment
•Flight time during which the drogue parachute
is at supersonic conditions ∗
For every simulation run, a table will be presented
showing the minimum and maximum values. Every
simulation run will present a total number of fail-
ures.
IV. Results
Five separate runs will be performed to confirm
the performance of the SPEAR vehicle. These are
four grid searches with the variations mentioned in
Table 3. The final simulation run is a Monte Carlo
analysis to show the distribution of the results.
IV.i Variations in vehicle parameters
Because the design of the SPEAR vehicle is not
yet fixed, it is likely that some parameters, such as
vehicle mass, will change towards the launch. Other
variables such as the drag coefficients of the main,
drogue and stabiliser parachutes are not fixed. This
is due to the uncertainty of the performance of the
parachute in flight. Especially the drag behaviour of
the stabiliser at high altitude, supersonic conditions
has significant uncertainty. The production area is
also very likely to deviate from it’s designed value,
mainly due to the production challenges of such a
small ballute.
Table 4: Variations of vehicle - Inputs
Parameter Value
Mass [kg] 7:0.5:8.5
Area Drogue [m2] 0.2
CD Drogue [-] +- 10 %
Area Stabiliser [m2] 0.08:0.001:0.09
CD Stabiliser [-] +-20 %
∗Supersonic conditions are considered to be Mach 1.2 or
higher
Fig. 2: Altitude-Time plot for the the variations
given in Table 4.
What can be seen in Fig. 2 is that the main dif-
ferences are visible around 25km when the drogue
parachute deploys. The differences for the Ballute
are negligible in this altitude-time plot.
In the velocity plot, Fig. 3, a deviation in the ve-
locity is visible at about 150 s. This deviation can
be attributed to the Ballute variations. However,
this is less than 5% difference to the mean value, be-
ing 890 m/s. The high final velocities are the result
of the fact that the main parachutes are not simu-
lated in this case. This is due to ParSim only being
able to simulate two parachutes. For this simulation
the parachute 1 is set to the ballute stabaliser, and
parachute 2 is set to the Hemisflo drogue.
In the envelope, Fig. 4, it can be seen that the
Ballute, as well as the Hemisflo drogue parachute,
remain within their respective envelopes. The Mach
number at drogue deployment varies between 2.1 and
2.5. The time when the Hemisflo drogue parachute is
deployed at supersonic conditions is about 5.9 s with
a variation of 0.23s in the most extreme cases. The
dynamic pressure at deployment varies more, being
in the range of 7.9 to 11.4 kPa. This large spread is
caused by the low density at 25km as well as the high
velocities. A small change in velocity causes a large
variation in dynamic pressure due to the quadratic
relation.
IAC–19–D2.3 Page 4 of 10
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Fig. 3: Velocity-Time plot for the the variations given
in Table 4.
Table 5: Variations of vehicle - Outputs
Parameter Min Max
Landing Velocity [m/s] 9.23 9.23
Mach number deployment [-] 2.1 2.5
Supersonic flight time [s] 5.67 6.13
Dynamic pressure [kPa] 7.9 11.4
IV.ii Variations in Initial Conditions
The largest uncertainty which influences the tra-
jectory of SPEAR is the variations in the initial flight
conditions. Since the REXUS rocket always flies on
the Improved Orion motor, the mass of the experi-
ments on-board determine the final weight and there-
fore also the final altitude it can reach. The moment
of ejection has to be determined in agreement with
the other experiments on-board. In order to take this
into account two variations for the initial conditions
will be performed. One where SPEAR is ejected at
apogee the other case is where SPEAR is ejected dur-
ing the ascent.
Ejection at apogee
The preferable ejection is at apogee since at this
point the velocity is relatively predictable and the
horizontal separation is the primary mode. The vari-
ations for the ejection at apogee are given in Ta-
ble 6. These values are determined by the historical
flight data of REXUS. Since the ejection happens at
apogee, the flight path angle (FPA) is equal to zero.
Fig. 4: Envelope plot for the the variations given in
Table 4
Table 6: Variations for Ejection at apogee - Input
Parameter Value
Altitude [km] 75:5:90
Velocity [m/s] 180
Flight path angle [deg] 0
Using the values in Table 6 three figures are given:
Fig. 5 and Fig. 6 with respectively the altitude and
velocity over time as well as the envelope of the sys-
tem in Fig. 7.
The altitude plot clearly shows that the different
cases converge through time. The difference in al-
titude tends to fade away throughout descent, es-
pecially after the drogue deployment. After main
parachute deployment, the difference is hardly no-
ticeable.
The velocity plot however, clearly shows a dif-
ference in maximum velocity for the different cases.
Similarly to the altitude plot, this difference decreases
with time. The only discrepancy is visible in the de-
lay of main parachute deployment.
The envelope plot shows a noticeable difference in
the maximum Mach number. The moment of drogue
and main parachute deployment are both still within
their respective envelopes. IT can however be seen
that the dynamics pressure constraint of the main
parachute is only just met. The other ranges can be
found in Table 7.
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Fig. 5: Altitude-Time plot for the variations given in
Table 6.
Fig. 6: Velocity plot for the the variations given in
Table 6.
Table 7: Variations for Ejection at apogee - Outputs
Parameter Min Max
Landing Velocity [m/s] 9.15 9.17
Mach number deployment [-] 2.07 2.38
Supersonic flight time [s] 6.05 6.82
Dynamic pressure [kPa] 7.2 9.5
Ejection during ascent
It is likely that the SPEAR vehicle will be ejected
before apogee in order not to compromise the zero-
g phase of the other experiments on-board REXUS.
The ejection altitude, vertical velocity and flight path
angle are all varied, as can be seen in Table 8. The
results of runs using variations during ascend can be
Fig. 7: Envelope plot for the the variations given in
Table 6.
found in Table 9.
Table 8: Variations for Ejection during ascent - Input
Parameter Value
Altitude [km] 50:5:60
Horizontal Velocity [m/s] 173
Vertical Velocity [m/s]
50km - 695:15:845
55km - 653:13.6:789
60km - 567:11.5:682
Flight Path Angle [deg]
50km - 75.5:0.27:78.2
55km - 74.6:0.27:77.3
60km - 72.2:0.31:75.3
Note the FPA has been computed by the vertical
and ground velocity. This is required as ParSim re-
quires total input and FPA as input.
The altitude-time plot, Fig. 8, shows a wide range
of apogee altitudes. Similarly to the variations in
initial conditions at apogee, the differences tend to
disappear over time. This convergent behaviour is
visible in both the altitude-time and the velocity-time
plot, Fig. 9. Fig. 9 has a different shape compared
to the other velocity plots in this article. This comes
from the fact that the vehicle first slows down during
ascent, after which it reaches a local minimum, the
apogee velocity. From then on, the general shape of
the plot is similar to the other velocity-time plots in
this article. The envelope for varying ascend initial
conditions, presented in Fig. 10, shows that the dif-
ferences in initial altitude and velocity are translated
to a difference in maximum Mach number at roughly
35 km altitude. The drogue and main deployment
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Fig. 8: Altitude-Time plot for the variations given in
Table 8
Fig. 9: Velocity-Time plot for the variations given in
Table 8
both fall within their respective envelopes for all con-
sidered variations in initial conditions during ascend.
Table 9: Variations for Ejection at ascent - Outputs
Parameter Min Max
Landing Velocity [m/s] 9.14 9.19
Mach number deployment [-] 1.8 2.1
Supersonic flight time [s] 4.12 6.54
Dynamic pressure [kPa] 6.7 8.8
IV.iii Variations in Atmosphere
For the atmospheric conditions, the ambient tem-
perature and density are varied. Table 10 shows the
outermost ambient temperature conditions that can
Fig. 10: Envelope plot for the the variations given in
Table 8
be expected for SPEAR, ranging from -30deg Cto
25 deg C. The air density at the launch site is var-
ied from 1.18kg/m3to 1.45 kg/m3. The percentage-
wise deviations from the international standard at-
mosphere at sea level are applied for all altitudes.
Table 10: Variations of atmospheric conditions - In-
puts
Parameter Value
Ambient air density [kg/m3] 1.18 : 0.14 : 1.45
Ambient air temperature
[deg C]
-30 : 27.5 : 25
The variations in temperature mainly influence the
Mach number as they determine the local speed of
sound. This effect is visible in the envelope plot,
Fig. 13, where the Mach number changes with the
different temperature variations. This is most ex-
plicit between 10 and 40 km altitude. Therefore the
Mach number at drogue deployment varies notably,
with a maximum difference of 0.43. The change in
density has the most impact on the landing velocity
and dynamic pressure, as can be seen in Table 11.
A higher density causes the dynamic pressure to be
higher, which in its turn causes an increase in drag.
This effect is most clearly visible at lower altitudes,
as can be seen in the altitude-time plot, Fig. 11. The
delay caused by the change in drag is visible at the
main parachute deployment in the velocity-time plot
in Fig. 12.
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Fig. 11: Altitude-Time plot for the variations given
in Table 10
Table 11: Variations of atmospheric conditions - Out-
puts
Parameter Min Max
Landing Velocity [m/s] 8.26 9.19
Mach number deployment [-] 1.31 1.74
Supersonic flight time [s] 1.47 3.7
Dynamic pressure [kPa] 7.30 9.54
IV.iv Monte Carlo Analysis
By using the same inputs as for the grid search us-
ing variations of all inputs, the Monte Carlo analysis
is executed. The results are presented in Table 12.
Table 12: Variations for Monte Carlo - Outputs
Parameter Min Max
Mach number deployment [-] 2.38 2.62
Supersonic flight time [s] 4.15 6.32
Dynamic pressure [kPa] 10.1 12.2
As the variations focused mainly on the drogue de-
ployment conditions, the main parachute and there-
fore the landing velocity has not been included in Ta-
ble 12. From the table, one can see that the drogue
deploys at Mach 2+, this is desirable as the dynamic
stability of the vehicle is uncertain. A dynamically
unstable vehicle will result in lower velocities during
drogue parachute inflation.
Fig. 12: Velocity-Time plot for the variations given
in Table 10
Fig. 15: Velocity-Time plot for the variations given
in Table 8 and Table 4
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Fig. 13: Envelope plot for the variations given in Ta-
ble 10
Fig. 14: Velocity-Time plot for the variations given
in Table 8 and Table 4
Fig. 16: Envelope plot for the variations given in Ta-
ble 8 and Table 4
Fig. 14 and Fig. 15 show the SPEAR flight paths in
terms of Altitude-time and Velocity-ime. One can see
that the apogee of the vehicle varies between 70 and
90 kilometres, which results in a maximum velocity
variation of 800 to 990 m/s. It is desirable to reduce
this variation for the final flight to understand the
final SPEAR trajectory better.
V. Conclusion
In conclusion, it can be seen that SPEAR will,
under all conditions, land with a landing velocity of
below 10 m/s. Furthermore, it can be seen that the
supersonic flight as expected by the simulations is at
least four seconds when only looking at the varia-
tions in the vehicle and the initial conditions. When
looking at the atmospheric variations, the supersonic
flight time could be reduced to 1.47 seconds. This
is still more than sufficient for the experiment. This
observation however does stretch the importance of
measuring the atmospheric conditions pre-flight and
running final simulations with these measurements.
With these simulations the team is confident that
SPEAR can achieve the objective of testing the
Large Envelope Advanced Parachute System’s drogue
parachute at supersonic conditions. It is however rec-
ommended to attempt to reduce the uncertainties on
the various parameters.
VI. Next Steps
The team will continue in the development and
production of the SPEAR vehicle, aiming for the
complete experiment to be done end of November.
This complies with the Experiment Acceptance Re-
view imposed by the REXUS timeline. After this, the
experiment will be sent for flight acceptance testing
at ZARM in December. Even though the team can
no longer modify the design for the flight in March
2020, the team can take this time to reduce the uncer-
tainties in the simulations. These tests will include
a wind tunnel test to confirm the stability and drag
coefficient of the parachutes at low-speed conditions.
The team proposes to perform a subsonic and super-
sonic wind tunnel to get better values for the aero-
dynamic coefficients for the vehicle itself. With these
coefficients the team can attempt a simulation run of
SPEAR in the TumSim tool. TumSim is capable of
running a 6 degrees of freedom simulations, and can
make a better estimation of the aerodynamic stability
of SPEAR.
IAC–19–D2.3 Page 9 of 10
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Acknowledgments
The team would like to thank all people that
worked on ParSim v3 and ParSim v4. Without their
efforts in the development and validation of the tool
this paper would not have been possible.
Finally, we would like to thank all the organisers
of the REXUS/BEXUS program: SNSA, DLR, ESA,
Zarm, and SSC for their contribution to the SPEAR
project.
References
[1] L. Pepermans et al. (2018). Flight Simulations
of the Stratos III Parachute Recovery System.
International Astronautical Congress 2018.
[2] L. Pepermans, M. Rozemeijer, E. Menting, N.
Suard, S. Khurana, ”Systematic Design for a
Parachute Recovery System for the Stratos III
Student Build Sounding Rocket”, AIAA Avia-
tion Forum 2018.
IAC–19–D2.3 Page 10 of 10
