Performance Evaluation of the Ejection System for the RAIN Rocket
Experiment
master of science thesis for the department of mechanics, KTH
Author:
Marco Tito Bordogna
Supervisor:
Dr.Gunnar Tibert Dr.Nickolay Ivchenko Stockholm, February 2014
Department of Mechanics
Abstract
This master’s thesis work was performed at the department of Mechanics of the Royal Institute of Technology (KTH) in Stockholm as part of my Master of Science studies in Aerospace Engineering at KTH. This thesis study has two major purposes: (1) to evaluate the performance of the spring-based ejection system used in the RAIN rocket experiment and (2) to suggest improvements to reduce de-spin and tip-off of the ejected probes.
To evaluate the performance of the ejection system two sets of data have been analyzed:
on-ground tests data and flight data. Data from on-ground ejection tests have been analyzed by means of video analysis and inertial sensor analysis while for flight data only inertial sensor data were available. Moreover, simple mechanical analytical models have been created to model the behavior of the probes during the ejection.
The results from data analysis and mechanical models are able to suggests some im- provements for the ejection system. However, it is not possible to make any strong conclusion on what might have caused the de-spin and the tip-off of the probes.
First of all I would like to thank my two supervisors Dr. Gunnar Tibert and Dr. Nickolay Ivchenko who have supported me throughout this thesis work and provided me with a method to face the difficulties encountered during the last six months. A special thank goes to the whole RAIN team that provided me with the data and drawings needed for this work. Moreover, I would like to thank Antoine and David for fruitful discussions and for the time spent together in the department of Mechanics.
I would have never reached the end of my studies without the support of my family.
Thank you for having allowed me to follow my dreams and thank you to keep encouraging me in reaching my goals.
Finally, a special thank goes to Giuditta for being always by my side, especially in difficulties moments, and for the invaluable support over the last years. Thanks for having understood my decisions.
Marco Tito Bordogna September, 2013
ii
Abstract i
Acknowledgements ii
List of Figures v
List of Tables vii
Abbreviations viii
1 The RAIN Experiment 1
1.1 Experiment Description . . . 1
1.1.1 The mission . . . 2
1.1.2 Experiment design . . . 3
1.1.2.1 The Rocket Mounted Unit (RMU) . . . 3
1.1.2.2 The Free Falling Unit (FFU) . . . 4
1.2 Flight Performance . . . 5
1.2.1 Launch campaign. . . 5
1.2.2 Ejection system issues . . . 7
1.3 Thesis Objectives . . . 8
2 Simple Spring-Mass Model for the Ejection System 9 2.1 Simple Spring-Mass Model (SSMM) . . . 9
2.1.1 Phase 1 . . . 9
2.1.2 Phase 2 . . . 11
2.1.3 Results . . . 12
2.2 Ejection Steps. . . 14
3 Ejection Data Analysis 17 3.1 On-ground Ejection Tests . . . 17
3.1.1 Method . . . 17
3.1.2 Results . . . 18
3.2 Flight ejection data. . . 28
3.2.1 Inertial sensor data. . . 28
3.2.2 Summary . . . 29
3.3 Conclusion . . . 30
iii
4 Possible Causes of De-spin and Wobbling 32
4.1 Step 1 . . . 32
4.2 Step 2 . . . 32
4.2.1 Mechanical model . . . 32
4.2.2 Results . . . 34
4.2.3 Conclusion . . . 34
4.3 Step 3 . . . 35
4.3.1 Mechanical model . . . 36
4.3.2 Results . . . 38
4.4 Step 4 . . . 39
4.5 Step 5 . . . 39
5 Conclusions 40 5.1 Future works . . . 41
Bibliography 42
1.1 Experiment timeline of the RAIN Expetiment [1].. . . 2
1.2 The RAIN experiment mechanical configuration [1]. . . 3
1.3 The rocket cylinder modifications [1]. . . 3
1.4 The ejection system with all its main mechanical components [1]. . . 4
1.5 The stops preventing the push plates from leaving the rocket [1]. . . 4
1.6 The FFU and its sub-systems [1]. . . 5
1.7 The altitude and velocity in the vertical direction of the two FFUs [1]. . . 6
1.8 The acceleration in Z-direction (a) and angular rate in all three axes (b,c,d) for the two FFUs measured with the internal sensors [1].. . . 6
1.9 Definition of x, y and z-axis of the FFUs. . . 7
1.10 The velocity vectors of the FFUs 1.5 seconds after ejection from the rocket [1]. . . 8
2.1 Forces acting of the Free Falling Unit in phase 1 of the ejection. . . 10
2.2 Position of the FFU during the ejection. . . 12
2.3 Speed of the FFU in the radial direction during the ejection. . . 13
2.4 Coriolis acceleration and radial acceleration of the FFU during the ejection. 14 2.5 Contact point between the FFU and the pushing plate first part of phase 1. 14 2.6 Contact point between the FFU and the pushing plate second part of phase 1. . . 14
2.7 Step 1a. . . 15
2.8 Step 1b. . . 15
2.9 Step 2. . . 16
2.10 Step 3. . . 16
2.11 Hatch/cable effect in Step 4 of the ejections. The hatch is in red and the cable in green. . . 16
3.1 Red and white tape on FFU A. . . 18
3.2 Markers tracked by the software. . . 18
3.3 Location of position 1 and 2 on the ejection system. . . 19
3.4 History of the distance between FFU and RMU during test#2. . . 20
3.5 History of the angle of the FFU in the spin plane during test#2. . . 20
3.6 Internal sensor data during test #2 for FFU A in position 1. . . 21
3.7 Tracker: test # 3, FFU B - position 2. . . 22
3.8 Inertia sensor: test# 3, FFU B - position 2. . . 22
3.9 Cable relaxed. . . 23
3.10 Cable tensioned. . . 23
3.11 Accelerations of FFU A during tests #2, 3 and 4.. . . 23 v
3.12 Accelerations of FFU B during tests #2, 3 and 4. . . 24
3.13 Angular rates of FFU A during tests #2, 3 and 4. . . 24
3.14 Angular rates of FFU B during tests #2, 3 and 4. . . 25
3.15 Accelerations of FFU A and FFU B during tests #5 and 6. . . 26
3.16 Angular rates of FFU A and FFU B during tests #5 and 6. . . 27
3.17 Internals sensor data at ejection for FFU C. . . 28
3.18 Internals sensor data at ejection for FFU E. . . 29
4.1 Contact point between FFU and pushing plate in step 2. . . 33
4.2 Nomenclature used in the no-slip condition. . . 34
4.3 Distance that the FFU has to travel to get a certain de-spin. . . 35
4.4 Distance that the FFU has to travel to rotate without slipping. . . 35
4.5 Direction of the friction force in different instants of step 3. . . 36
4.6 Nomenclature used for the model of step 3. . . 37
4.7 Angular rate at ejection for step 3 as function of d and n1.. . . 38
4.8 Effect of the cable on the hatch and position of the center of mass of the FFU. . . 39
2.1 Values used in the simulation. . . 12
2.2 Results from the simple spring model for different values of NFFU . . . 13
3.1 Test configuration for all ejection tests.. . . 19
3.2 Results from the Tracker during test#2. . . 20
3.3 Static tests: Results from the Tracker. . . 25
3.4 Rotation speed and inertia sensors during static tests from “Tracker”. . . 27
4.1 Values used in the simulation. . . 34
vii
ACE Aerosol Collection Experiment
BC Boundary Condition
EOM Equation Of Motion
ESRANGE European Sounding rocket launching RANGE FFU Free Falling Unit
ISAAC Infrared Spectroscopy to Analyse the middle Atmosphere Composition KTH Kungliga Tekniska H¨ogskolan
MUSCAT MUltiple Spheres for Characterization of Atmpspheric Temperature RAIN Rocket deployed Atmospheric probes conducting Independent
measurements in Northern Sweden
REXUS Rocket EXperiment for University Students
RMU Rocket Mounted Unit
SPIDER Small Payloads for Investigation of Disturbances in Electrojet by Rockets SSMM Simple Spring - Mass Model
viii
The RAIN Experiment
In this chapter the RAIN Experiment is introduced and its scientific objective stated.
The design and the mission timeline are illustrated in order to explain how the exper- iment works. Finally the results from the launch campaign are presented, commented and the thesis objectives are defined.
1.1 Experiment Description
The RAIN experiment is a student driven rocket experiment designed and manufactured at the Royal Institute of Technology (KTH), Stockholm. RAIN stands for “Rocket de- ployed Atmospheric probes conducting Independent measurements in Northern Sweden”
and the experiment is a proof-of-concept for collecting aerosol particles in the middle atmosphere using multiple free falling probes. Collection samples on each probe are exposed over varying altitude ranges between 80 and 22 km giving an altitude distribu- tion profile of aerosol particles. The experiment was launched on board the REXUS-11 sounding rocket on November 16, 2012 from Esrange Space Centre.
The primary objectives of the experiment were:
• Proof-of-concept of a multi-point aerosol collection technique in the middle atmo- sphere.
• Acquisition of the compositions and sizes of middle atmospheric aerosol particles.
The secondary objective was:
• Acquisition of middle atmospheric density and temperature profiles based on the coefficient of drag of an FFU and the velocity data calculated from raw GPS data collected during an FFUs fall.
Characterization of middle-atmospheric aerosols and their processes is of primary im- portance because of how stratospheric particles significantly influence the chemistry and radiation budget of the atmosphere [2]. During periods of high aerosol load there is evi- dence of enhanced ozone loss due to heterogeneous chemistry and tropospheric cooling.
1
Middle-atmospheric aerosol particles are also important as condensation nuclei for cloud formation in the stratosphere and mesosphere. The formation process of ice particles and solid cloud particles is still not well understood.
In-situ measurements of the aerosol composition in the middle atmosphere are rare. This is because aerosol samples are often contaminated by the balloon or the rocket itself.
Therefore, a new method for in-situ sampling of middle-atmospheric aerosol particles and successive characterization of their chemical composition is needed.
1.1.1 The mission
The experiment is composed by a rocket module, called Rocket Mounted Unit (RMU), and by two active probes for the aerosol collection, called Free Falling Units (FFUs). The RMU is composed of a rocket cylinder and an FFU housing and ejection system. The FFUs are held in the RMU during the ascent phase of the rocket flight. At an altitude of approximatively 60 km, before the rocket is de-spun, the FFUs are ejected from the sides of the rocket. When the FFUs reach an approximate apogee, they begin the Aerosol Collection Experiment (ACE) phases. A turntable collection mechanism rotates inside each FFU, exposing an aerosol collection plate to the surrounding environment via an exposure window in the base of the FFU. These grids are exposed incrementally based on their angular position within the FFU. This results in the collection of aerosols at varying heights so as to capture an aerosol distribution profile. In addition to collecting aerosol particles a secondary GPS experiment is also conducted. As the FFUs fall through the atmosphere they collect raw GPS data via a GPS front end receiver. Each FFU carries an internal parachute that is deployed at 5 km altitude and a recovery systems that allows the helicopter crew to retrieve it. After retrieving the FFUs this data is processed using a custom built software receiver. Using the velocity data derived from the raw GPS data along with assumptions of the drag characteristics of an FFU atmospheric density and temperature profiles is derived. The experiment timeline is shown in Figure1.1.
Figure 1.1: Experiment timeline of the RAIN Expetiment [1].
1.1.2 Experiment design
In this subsection the experiment design is presented (Figure 1.2) to give a better overview of the elements involved in the ejection. Most of the terminology introduced here will be used in the following chapters.
Figure 1.2: The RAIN experiment mechanical configuration [1].
1.1.2.1 The Rocket Mounted Unit (RMU)
The RMU consists of a 220 mm high and 356 mm diameter rocket cylinder and an ejection system. Its main tasks are to hold the FFUs during rocket launch and then eject them at the appropriate time during the rocket’s ascent. In order to achieve this, two large openings were made in the rocket cylinder (Figure1.3). These openings weaken the rocket structure, so reinforcements are necessary to ensure structural integrity of the experiment. The two reinforcements are attached to the rocket skin by means of screws and provide also a connection points between the rocket cylinder an the ejection system.
Figure 1.3: The rocket cylinder modifications [1].
The Ejection System In order to eject the FFUs, the RMU has a spring-based ejection system (Figure 1.4). The system is made up of six aluminum beams covered with teflon. This frame holds in place the FFUs by surrounding them: two rails below the FFUs carry the load during take off, two rails above the FFUs constrain them in the vertical direction, two side rails hold the pushing plates that constrain the FFUs tangentially. The radial force needed to eject the probes is given by four compressive springs, two for each FFU. A plate is positioned in the center of the frame and the compression springs are placed between this plate and the pushing plates can slide along the side raid and eject the probes. The ejection system is constrained by a steel
cable that is guided around the the rocket cylinder and the hatches. The steel cable is fixed to a hook on one end while the other end is clamped, after tensioning, between two plates.
Figure 1.4: The ejection system with all its main mechanical components [1].
The springs are compressed before flight and store the energy required to eject the FFUs from the rocket. The ejection is initiated by a pyro cutter positioned on the inner surface of the cylinder close to the plates holding the end of the cable, cutting the ejection constraint cable. The cable will lose its tension and no longer be able to hold the force of the springs pushing against the hatches. The springs will push the hatches and FFUs out of the rocket while the pusher plates will be stopped from leaving the rocket by stops in the form of screws, which are part of the mount structure (Figure1.5).
Figure 1.5: The stops preventing the push plates from leaving the rocket [1].
1.1.2.2 The Free Falling Unit (FFU)
The Free Falling Units are cylindrical shaped probes 116 mm in diameter, 93 mm in height and weigh 1.04 kg each. Each sub-system of the FFU is shown in Figure1.6. The FFU comprises all the essential systems needed to perform the experiments: an aerosol collection device, power and control electronics, and a parachute-based recovery system.
Figure 1.6: The FFU and its sub-systems [1].
The FFU sub-systems are housed in an aluminium alloy 7075-T6 frame. The aerosol collection plate is mounted to a central shaft underneath the separation plate of the frame, this separation plate separate the ACE from the rest of the probe to avoid contamination of the samples. The collection plate is driven by a motor and gear system, which are positioned above the separation plate. An electronics distribution board and battery are placed on the same level as the motor and gears, while the main electronics board is positioned a level above.
The recovery system consist of a cross-shaped parachute, an FFU hat, a spring-based deployment system and an interface plate that connects the recovery system to the FFU frame. The FFU hat is ejected from the FFU by means of three conical springs pushing against the hat rim. The springs are released by L-shaped clamps releasing the rim of the hat. The clamps are released from their loaded position by a thermal cutter cutting a polyethylene micro-fibre line threaded through each of the clamps.
1.2 Flight Performance
In this section data from the launch campaign are presented in order to estimate the flight performance go the RAIN experiment.
1.2.1 Launch campaign
On November 16, 2012 from Esrange Space Center, the experiment was launched on the REXUS-11 sounding rocket. All phases of the flight were nominally apart from a premature parachute deployment for both FFUs. The GPS data collected and post- processed are presented in Figure1.7and internal sensor data are presented in Figure1.8.
In the figures different phases of the flight are underlined: ejection of the FFUs at t+67s
(1), aerosol collection (ACE) phase starts (2) and stops (3) and premature parachute deployment of FFU E (4). The FFUs were ejected at 57 km altitude and reached an apogee of 78.5 km.
0 20 40 60 80
Altitude [km]
50 100 150 200 250 300 350
−500 0 500
Time [s]
Velocity Z [m/s] (3) (4)(2)(1)
FFU C FFU E
Figure 1.7: The altitude and velocity in the vertical direction of the two FFUs [1].
−10 0 10
Acc. Z [m/s2 ]
FFU C (a)
FFU E
50 100 150 200 250 300 350
−4
−2 0 2 4
Ang. X [Hz]
(d)
Time [s]
(3) (4)
(2) (1)
−4
−2 0 2 4
Ang. Y [Hz]
(c)
−4
−2 0 2 4
Ang. Z [Hz]
(b)
Figure 1.8: The acceleration in Z-direction (a) and angular rate in all three axes (b,c,d) for the two FFUs measured with the internal sensors [1].
The definition of x, y and z-axis is shown in Figure1.9, where the y-axis corresponds to the ejection direction of the FFUs.
Figure 1.9: Definition of x, y and z-axis of the FFUs.
1.2.2 Ejection system issues
The operational requirements of the ejection system are three: eject the FFUs with a total speed > 5 m/s; ejecting the FFUs so that they fall with their base plates facing towards the Earth; eject the FFUs before the rocket is de-spun so that the FFUs are spinning after ejection.
GPS data (Figure 1.10) shows that the total ejection speed was different between the two FFUs: FFU C was ejected at 5 m/s, while FFU E has an ejection speed of 6.5 m/s. Figure 1.8(a) shows that during the aerosol collection the vertical acceleration was positive. This, due to the definition of the z-axis (Figure 1.9), indicates that the bottom collecting plate of the FFUs were in the correct position: facing towards Earth.
For what concerns the spinning of the FFU Figure 1.8(b) shows that before ejection the angular rate was 3.2 Hz while after it drops till 1.8 and 1.5 Hz, respectively. From the angular rates along all three axes, presented in Figure1.8(b,c,d), it is observed that the angular momentum is not conserved and therefore an external, undesired, torque is introduced during the ejection. Even if the angular momentum is not conserved and the FFUs lose angular rate around the vertical axis the probes are still spinning and this allowed them to be spin stabilized and to fall, until the end of the aerosol collection, with the bottom plates facing towards the Earth. In Figure1.8(b,c,d) it is shown that after the ejection the FFUs have a precession motion and this motion that is larger for FFU C. This second phenomena was expected, however it is interesting to understand why FFU C was precessed more that FFU E.
It is then possible to conclude that the ejection system performed nominally and fulfilled all the three operational requirements. However, there was a significant and unexpected drop in the vertical spin rate for both FFUs and the different precession amplitudes between the probes is unclear.
−6 −4 −2 0 2 4 6
−6
−4
−2 0 2 4 6
FFU C
FFU E CoM
Rocket
Velocity east/west [m/s]
Velocity north/south [m/s]
Figure 1.10: The velocity vectors of the FFUs 1.5 seconds after ejection from the rocket [1].
1.3 Thesis Objectives
This thesis work focuses on the analysis of on-ground static and dynamic tests of the ejection system as well as on the analysis of the flight data. The objectives are to determine the causes of the de-spin and reasons of the wobbling of the FFUs. This analysis is important because spring based ejection systems, like the one used by RAIN, are the most common and reliable ejection system for sounding rocket applications.
Future KTH rocket experiments like ISAAC and SPIDER require to eject multiple probes. Both those experiments will eject bigger and heavier probes that have to be spin stabilized and have to wobble as little as possible due to the mission’s require- ments. Since the design of such ejection systems is based on RAIN’s experience, once the causes of de-spin and wobbling are discovered this thesis work will focus on how to minimize those effects and suggest improvements.
Simple Spring-Mass Model for the Ejection System
The objective of this chapter is to create a simple mechanical model for the RAIN ejection system. The ejection is divided in two main phases that are described and modeled separately. The model is used to evaluate ejection speed, duration of the ejection and to reproduce the data obtained during the on-ground and flight tests. Results from the simple spring-mass model are used to characterize different steps in the ejection process.
2.1 Simple Spring-Mass Model (SSMM)
The ejection of the Free Falling Units is divided in two phases:
• Phase 1 goes from cutter activation until the pushing plate stops its run. This phase of the ejection is characterized by the FFU being pushed by the two com- pressive springs.
• Phase 2 goes from the stop of the pushing plate until complete ejection of the FFU from the RMU. After the stop of the pushing plate the FFU is still inside the ejection system and it has to travel for 42 mm more to be out of the ejection system and thus lose contact with it.
2.1.1 Phase 1
During this phase of ejection the FFU is accelerated from a resting condition thanks to two compressive springs that push the pushing plates. The pushing plates is gliding on the two side rails of the ejection system responsible for laterally constraining the FFU.
The probe is also constrained by the upper and lower rails while inside the ejection system. Moreover the RMU is spinning during the ejection therefore centrifugal forces are acting on FFU, pushing plate and hatch.
The forces acting on the FFU in phase 1 are then:
• Spring force, FS.
9
• Centrifugal force, FC.
• Friction between cage and lateral rail, FCAGE.
• Friction between the FFU and the top and bottom rails, FFFU.
The forces are modeled as follow and values used for the variables are available in Table2.1. The centrifugal force, that acts on FFU, pushing plate and hatch, is equal to:
FC = mTΩ2y (2.1)
where mT is the mass of the FFU plus pushing plate plus hatch, Ω is the angular speed of the RMU and y is the radial position of the center on the FFU with respect to the center of the RMU. The spring force is modeled according to Hooke’s Law:
FS= k∆L = k(L0− L) (2.2)
where k is the spring constant of the two springs in parallel, L0 is the length of the uncompressed spring and L is the length of the spring when compressed. The relation between y and L is: L = y − p there p is the distance between the spring and the center of the FFU, this distance is constant. Friction between cage and lateral rail is equal to:
FCAGE = µdNCoriolis = µdmT(y ˙Ω + 2 ˙yΩ) = 2µdΩmTy˙ (2.3) where µd is the dynamic friction coefficient between aluminum and teflon, NCoriolis is the normal force between the pushing plate and the FFU and ˙Ω disappears since the angular rate of the RMU is constant during the ejection. Finally the friction between FFU and top and bottom rails is equal to:
FFFU = µdNFFU (2.4)
where NFFU is the force that compress the FFU between the top and bottom rail.
Figure 2.1: Forces acting of the Free Falling Unit in phase 1 of the ejection.
The forces acting on the system are shown in Figure2.1and the equation of motion for the simple spring model in phase 1 is:
mTy = F¨ S+ FC− FCAGE− FFFU (2.5) introducing Equations (2.1) − (2.4) it is possible to obtain:
¨
y + (2Ωµd) ˙y + k mt
− Ω2
y = k(L0+ p) − µdNFFU mT
(2.6) This second order differential equation describes the dynamics of the Free Falling Unit in phase 1 of the ejection. To solve it the boundary conditions used are:
y(t = 0) = y0
˙
y(t = 0) = 0 (2.7)
where y0 is the position of the FFU before cutter activation and the starting speed is zero. From Equation (2.6) it is possible to obtain the time (t1) at which the pushing plate stops its run and the speed (v1) of the FFU at the end of phase 1:
y(t = t1) = LstopCAGE+ p
v1= ˙y(t = t1) (2.8)
where LstopCAGE is where the pusher plate stops.
2.1.2 Phase 2
During this phase of the ejection the FFU is not pushed anymore by the pushing plate.
The probe is able to complete the ejection thanks to the speed it gained in phase 1 and it is assumed to continue the ejection straight forward. In this second phase the only force acting on the FFU is the friction force between the probe and the top and bottom rails.
The equation of motion of the system is then:
m¨y = −FFFU (2.9)
where, in this case, m is the weight of only the FFU since the pusher plate is stopped inside the rocket and the hatch is ejected and not in touch with the side rails. Using Equation (2.4) the EOM can be written in the form:
¨
y = −µdNFFU
m (2.10)
To solve the equation the boundary conditions used are:
y(t = t1) = LstopCAGE+ p
˙
y(t = t1) = v1 (2.11)
the BC states that phase 2 starts where phase 1 ended both in terms of position and speed of the FFU and this ensure continuity between the two phases of the ejection.
From Equation (2.10) it is possible to obtain the time (texit) when the FFU is completely ejected and the radial speed vexit at which the FFU leaves the ejection system:
y(t = texit) = Lexit+ p
vexit= ˙y(t = texit) (2.12)
where Lexit the total length of the ejection system.
2.1.3 Results
The value used to obtain the following results are shown in Table 2.1 Variable Value
Ω 20.1 rad/s
k 5411 N/m
mT 1.5 kg
m 1 kg
L0 0.115 m
LstopCAGE 0.111 m Lexit 0.194 m
x0 0.097 m
p 0.060 m
µd 0.18
Table 2.1: Values used in the simulation.
The model created gives an idea of the ejection time and speed of the Free Falling Unit.
However there is no known value of the compression of the FFUs between the upper and lower rails (NFFU) therefore the results is a function of NFFU. Figures2.2and2.3shows the estimated ejection time and speed for NFFU= 50 N. In the figures the first vertical black line indicates the end of phase 1 and the second indicates the end of phase 2.
0.005 0.010 0.015 0.020 0.025 Time@sD 0.05
0.10 0.15 Distance@mD
Distance of the FFU from the center og the RMU
Figure 2.2: Position of the FFU during the ejection.
Table 2.2 shows the effect of NFFU on the ejection time, ejection speed in the radial direction and the total ejection speed. The total ejection speed is obtained by adding
0.000 0.005 0.010 0.015 0.020 0.025 Time@sD 1
2 3 4 5 Speed@msD
Figure 2.3: Speed of the FFU in the radial direction during the ejection.
to the radial speed the tangential speed due to the rotation of the RMU. The value of NFFU is unknown but it is estimated to be lower that 100 N. As shown in Table2.2the error of an incorrect value of NFFU can be up to 2.5% for the ejection time, −4.9% for the radial ejection speed and −3.3% for the total ejection speed. These error values are considered good enough for the qualitative studies of this thesis work, therefore from now on the NFFU used in all future calculation is set to 50 N.
NF F U Ejection Time Radial Speed Total Speed
[N] [s] [%] [m/s] [%] [m/s] [%]
0 0.0282 0 5.0930 0 6.1466 0
10 0.0282 0 5.0688 −0.48 6.1264 −0.33
20 0.0283 0.35 5.0445 −0.96 6.1061 −0.66 30 0.0284 0.70 5.0201 −1.44 6.0858 −0.99 40 0.0284 0.70 4.9956 −1.92 6.0655 −1.32 50 0.0285 1.06 4.9709 −2.40 6.0450 −1.66 60 0.0286 1.41 4.9462 −2.89 6.0245 −1.99 70 0.0287 1.77 4.9213 −3.38 6.0040 −2.32 80 0.0287 1.77 4.8963 −3.87 5.9833 −2.66 90 0.0288 2.12 4.8711 −4.36 5.9626 −3.00 100 0.0289 2.48 4.8458 −4.86 5.9419 −3.34 Table 2.2: Results from the simple spring model for different values of NFFU
.
The SSMM can be used to determine the accelerations the FFU is subjected to during the ejection during phase 1 and 2. While the FFU is pushed by the spring the forces acting on it are the ones mentioned in Sec2.1.1in the radial direction plus the Coriolis forces perpendicular to the ejection direction. Figure 2.4shows the accelerations of the FFU for NFFU = 50 N.
Figures 2.3 and 2.4 show that there is a discontinuity in the speed and acceleration fields between phase 1 and phase 2: in phase 1 the radial forces are pushing the FFU in the ejection direction while in phase 2 the friction force is decelerating the FFU.
Moreover in phase 1 between 0 and 0.0128 s the radial acceleration is larger than the
0.005 0.010 0.015 0.020 0.025 Time@sD
5 10 15 20 25 30
Acceleration@gD Radial acceleration Vs Coriolis acceletation
Radial Acceleration Coriolis Acceletation
Figure 2.4: Coriolis acceleration and radial acceleration of the FFU during the ejec- tion.
Coriolis acceleration meaning that in this part of phase 1, the contact points between the FFU and the pushing plate are the one shown in Figure 2.5. After 0.0128 s the Coriolis acceleration prevails on the radial acceleration, therefore in this part of phase 1 the contact point of the FFU are assumed to be the one shown in Figure2.6.
Figure 2.5: Contact point between the FFU and the pushing plate first
part of phase 1.
Figure 2.6: Contact point between the FFU and the pushing plate sec-
ond part of phase 1.
2.2 Ejection Steps
From the results of SSMM and ejection tests (Sec3) it is possible to divide the ejection in six different steps, each of them well defined by time frame and forces acting on the FFU. This division of the ejection in different steps allows to focus on each event of the ejection separately defining step by step the boundary conditions and the contact points between the FFU and the ejection system.
Step 1a: This step corresponds to the first part of phase 1 and it is therefore charac- terized by high radial acceleration, mainly due to spring forces, that push the FFU by
the pushing plate as shown in Figure 2.7. It goes from cutter activation until 0.0128 s when the magnitude of radial acceleration and Coriolis acceleration is equal.
Step 1b: This step is the second part of phase 1. The FFU is still pushed by the pushing plate, however in this step the Coriolis acceleration prevails on the radial acceleration leading to different contact point between FFU and pushing plate (Figure2.8). It goes from 0.0128 s to the stop of the pushing plate, when the radial acceleration became negative.
Figure 2.7: Step 1a. Figure 2.8: Step 1b.
Steps 1a and 1b together form the phase 1 of the simple spring model, where the FFU gains kinetic energy thanks to spring force and centrifugal force.
Step 2: This step is characterized by the stop of the pushing plate. The pushing plate is not ejected and its run ends when it hits the reinforcement collars mounted on the RMU skin (Figure 1.5). In this step the Coriolis acceleration is at its maximum value and the FFU rests as shown in Figure2.9. In this configuration the FFU rolls and slides out from the pushing plate.
Step 3: This step corresponds to the phase 2 of the simple spring model. The FFU is not pushed anymore by the pushing plate and it continues its ejection thanks to the kinetic energy it gained in step 1a and 1b. The FFU is in contact only with the upper and lower rail of the ejection system (Figure 2.10). This creates a friction force that slows the ejection of the FFU. Step 3 goes from the stop of the pushing plate until the FFU is totally ejected from the ejection system.
There are other two steps, not modeled in the simple spring model, that can be defined:
Step 4: In this step the FFU is outside the ejection system. However there are inter- actions between the FFU and the hatch due to the presence of the cable all around the RMU Figure2.11.
Step 5: The FFU is in free fall, the only forces acting on it is the air drag.
Figure 2.9: Step 2. Figure 2.10: Step 3.
Figure 2.11: Hatch/cable effect in Step 4 of the ejections. The hatch is in red and the cable in green.
Ejection Data Analysis
In this chapter on-ground ejection tests data and flight data are analyzed. Results from this analysis will be useful to identify unexpected behavior of the ejection system and at which step of the ejection the de-spin occurs.
3.1 On-ground Ejection Tests
The RAIN Ejection Test took place on October 15, 2011 in the Space and Plasma Physics workshop where four static tests and two dynamic tests were performed. In all tests the FFUs were loaded inside the RMU and then ejected by cutting the steel cable constraining the hatches. What differentiate the static tests from the dynamic ones is that in the dynamic tests the experiment is placed on a spinning table to simulate the rotation of the rocket at ejection.
The objectives of the ejection test were:
• Ensure that no electrical or mechanical failures occur during ejection.
• Test the spring compression and cable tensioning mechanism.
• Estimate the ejection performance.
To estimate the performance of the ejection system video footages with 240 fps were taken and FFUs’ inertial sensors were recording accelerations and angular rates during all tests. In this section, data from ground tests are analyzed to determine ejection speed, angular speed of the probes and to evaluate if any unexpected behavior occurs.
3.1.1 Method
In order to be able to track the FFUs during the ejection two tapes were place on the lid of the probes and were used as tracking points for the video analysis. The two tapes were:
a red square tape positioned in the middle of the lid, used to track the ejection speed of the FFU; and a rectangular white tape in order to capture the rotation of the probe
17
(Figures 3.1 and 3.2). A free software “Tracker” [3] was used to determine, frame by frame, the position of the tracking points on the FFUs with respect to a reference frame, a known length in the video and the frame rate of the video. By deriving the position of the reference points in each frame is it possible to calculate speed and angular speed of the probes. This kind of analysis is possible only when the camera is perpendicular to the ejection since any other angle generates distortions in the field of view of the camera and therefore errors in the results. This requirement is fully satisfied in the all static tests, however during the dynamic tests it was not possible to place the camera over the experiment, therefore no reliable videos are available for those tests.
To be consistent in the report and to be able to present the results correctly, the starting positions of the FFUs in the ejection system and the name of the FFU are given according to the following convention. The position in the ejection system close to the location of the cutter is called position 1 and the position close to the location of the hook that constrain one end of the cable, is called position 2 (Figures 3.3). In order to recognize the FFUs during the ejection tests a sign was put on the white tape: the FFU with the signed white tape is called FFU A while the one without sign is called FFU B.
Figure 3.1: Red and white tape on FFU A.
Figure 3.2: Markers tracked by the software.
The FFUs’ internal sensors recorded accelerations and angular rates during the ejection.
From those data it is possible to estimate the time for ejection of the probes and angular rotation of the FFUs. Results from video footage and inertial sensor are then compared with the expected behavior of the system.
3.1.2 Results
Table3.1present the test configuration for each test stating where each FFU was posi- tioned, the position of the camera and, for the dynamic test, the spin direction.
Static Test
Time history of the FFUs position and rotation angle in the spin plane during Test #2 are shown in Figures3.4and 3.5. In the figure the plot starts when the FFU is outside the ejection system and ends when the FFU touches the protective net that was placed
Figure 3.3: Location of position 1 and 2 on the ejection system.
Test Type FFU position Camera
1 Static No FFU Camera on top, record-
ing spring extension 2 Static FFU A - Pos 1, FFU B - Pos 2 Camera on top, record-
ing both FFUs
3 Static FFU A - Pos 1, FFU B - Pos 2 Camera on top, record- ing FFU B
4 Static FFU B - Pos 1, FFU A - Pos 2 Camera on top, record- ing FFU B
5 Dynamic CW FFU A - Pos 1, FFU B - Pos 2 Camera NOT on top, recording both FFUs 6 Dynamic CCW FFU B - Pos 1, FFU A - Pos 2 Camera NOT on top,
recording both FFUs Table 3.1: Test configuration for all ejection tests.
around the ejection system. Therefore, using the definitions of the ejection steps, the figures show step 4 and 5.
In Figure 3.4 the position of the FFU with respect to the center of the RMU is not a straight line and the speed reduces gradually. This is due to the fact that, while in free fall, the FFUs are moving away from the camera. To have a good estimation of the ejection speed the linear fitting has been done taking into account only the data from the first 10 samples. To obtain the angular speed of the FFU the position of the two ends of the white tape has been tracked (Figure3.2, cyan and violet points). Measuring how the relative position of the two point change during the free fall is is possible to estimate the angular rate of the probe. Ejection speed and angular rate for test #2 are shown in Table 3.2.
Data from the inertial sensor of FFU A in test #2 are shown in Figure 3.6, where:
y-axis is aligned with the ejection direction, z-axis is aligned with the rotational axis
0 0.01 0.02 0.03 0.04 0.05 0.06 150
200 250 300 350 400
Distance of the FFU from the center of the RMU
Time [s]
Distance [mm]
FFU A − Pos 1 FFU B − Pos 2
Figure 3.4: History of the distance between FFU and RMU during test#2.
0 0.01 0.02 0.03 0.04 0.05 0.06
135 140 145 150 155 160 165
Angle of the tape marker on top of the FFU
Time [s]
Angle [deg]
FFU A − Pos 1 FFU B − Pos 2
Figure 3.5: History of the angle of the FFU in the spin plane during test#2.
Ejection Speed Rotation Speed
FFU A Position 1 3.6 m/s 0.11 Hz CCW
FFU B Position 2 3.4 m/s 0.23 Hz CCW
Table 3.2: Results from the Tracker during test#2.
of the RMU and x-axis is perpendicular to the y-and z-axes. In Figure 3.6, step 1 (1a plus 1b), step 2 and step 3 are underlined by means of vertical dashed lines: from zero to the first dashed lines there is step 1 that ends when the radial acceleration (y-axis) goes to zero, between the first and the second dashed line there are step 2 and 3. The
plot starts at cutter activation, so at zero seconds the ejection starts, and it ends when the FFU touched the protective net. From this data it is possible to see that, even if no intentional torque is applied on the FFU, there is non-zero angular rate around the x-and y-axis after the ejection. Moreover the angular rate along z-axis is almost zero and this does not agree with the video footage.
0 0.05 0.1 0.15 0.2
−1
−0.5 0 0.5 1
Time [s]
Angular rate [Hz]
x−axis y−axis z−axis
0 0.05 0.1 0.15 0.2
−2 0 2
Time [s]
Acceleration [g]
x−axis y−axis z−axis
Figure 3.6: Internal sensor data during test #2 for FFU A in position 1.
An interesting behavior can be found in the rotation speed of test #3, where FFU B is in position 2. In Figure3.7between 0 and 0.034 s after the ejection the rotation is almost zero, then it rises up to 0.23 Hz. By looking at the ejection video for test #3 it can been seen that before 0.034 s the cable around the hatch is relaxed and it get tensioned at 0.034 seconds. This tensioning of the cable (Figures3.9and 3.10) induces a rotation in the hatch that is in front of the FFU. This rotation is then partially transmitted to the FFU and this explains why rotation of the FFU suddenly starts. This change in rotation speed is also measured by the inertial sensors (Figure 3.8) where it is possible to see a peak in the acceleration and a change of slope in the angular rate at 0.036 s after the ejection.
Comparison between internal sensor results. Internal sensor data show different behavior of the FFU during ejection and free fall in different test. Sensor data from all the static tests are shown in Figures 3.11,3.12, 3.13 and 3.14. In all these figures the time interval is the same and a third dashed line has been added to indicate when the free fall ends.
In Figures 3.11 (c) and 3.12 (a,b) it can be seen that the FFU placed in position 2 presents spikes during the free fall. Those spikes derive from tensioning and relaxing of the cable (Figures 3.9 and 3.10) that pulls the hatch while the FFU is outside the RMU. At each spikes there is a change in angular rate around the z-axis as shown in Figures3.13(c) and3.14(a,b). Figures3.13and3.14show also that there is a non-zero angular rate in all the axis for most of the ejections even if no intentional torque is applied on the FFUs. As a consequence of the pulls created by the cable the angular
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 88
90 92 94 96 98 100 102 104
Angle of the tape marker on top of the FFU
Time [s]
Angle [deg]
FFU B − Pos 2
0.034
Figure 3.7: Tracker: test # 3, FFU B - position 2.
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
−1 0 1
Test#3
Time [s]
Angular rate [Hz]
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
−2 0 2
Test#3
Time [s]
Acceleration [g] 0.036
Figure 3.8: Inertia sensor: test# 3, FFU B - position 2.
rates for the FFUs in position 2 are not constant and varies during the free fall while the FFUs ejected from position 1 have constant angular rate after the ejection. This lead to the conclusion that for static tests step 4 occurs only for the FFU in position 2 while for position 1 there is no interaction between the FFU and the hatch after step 3.
In the SSMM the deceleration in step 3 in the radial direction is almost negligible, however in the tests there are two different behaviors: when the FFU is in position 1 the deceleration is similar to that of the simple spring model and the deceleration is hard to see, when the FFU is in position 2 the deceleration is larger. This effect might be due to the presence of the cable on the hatch in position 2 while hatch in position 1 lost contact with the cable immediately after cutter activation. The presence of the cable with its
Figure 3.9: Cable relaxed. Figure 3.10: Cable tensioned.
0 0.05 0.1 0.15 0.2 0.25
−2 0 2
Test#2:FFU A − Pos 1
Time [s]
Acceleration [g]
(a)
0 0.05 0.1 0.15 0.2 0.25
−2 0 2
Test#3:FFU A − Pos 1
Time [s]
Acceleration [g]
(b)
0 0.05 0.1 0.15 0.2 0.25
−2 0 2
Test#4:FFU A − Pos 2
Time [s]
Acceleration [g]
(c)
Figure 3.11: Accelerations of FFU A during tests #2, 3 and 4.
mass and inertia impede the ejection of the FFU and this leads to higher deceleration in step 3 when the FFU is not pushed by the cage anymore.
Dynamic Test
Due to the fact that the camera was not on top of the RMU during the dynamic tests only the internal sensor results are shown in this section. In Figure 3.16 the gyros are saturated at 1.29 Hz in the CW direction and 1.55 Hz in CCW direction, therefore it is not possible to evaluate the ejection detail. Nevertheless, it is possible to see that in test #5, where the RMU was spinning CW, the drop in angular rate is lower that in test #6. Furthermore in all tests there is non-zero lateral rate after ejection.
An interesting behavior is observed in Figure 3.15. Based on the SSMM and on the re- sults from the static ejection a non-negligible deceleration was expected in both tests #5
0 0.05 0.1 0.15 0.2 0.25
−2 0 2
Test#2:FFU B − Pos 2
Time [s]
Acceleration [g]
(a)
0 0.05 0.1 0.15 0.2 0.25
−2 0 2
Test#3:FFU B − Pos 2
Time [s]
Acceleration [g]
(b)
0 0.05 0.1 0.15 0.2 0.25
−2 0 2
Test#4:FFU B − Pos 1
Time [s]
Acceleration [g]
(c)
Figure 3.12: Accelerations of FFU B during tests #2, 3 and 4.
0 0.05 0.1 0.15 0.2 0.25
−1 0 1
Test#2:FFU A − Pos 1
Time [s]
Angular rate [Hz]
(a)
0 0.05 0.1 0.15 0.2 0.25
−1 0 1
Test#3:FFU A − Pos 1
Time [s]
Angular rate [Hz]
(b)
0 0.05 0.1 0.15 0.2 0.25
−1 0 1
Test#4:FFU A − Pos 2
Time [s]
Angular rate [Hz]
(c)
Figure 3.13: Angular rates of FFU A during tests #2, 3 and 4.
and #6 for the FFU in Pos 2. However, the inertial sensors show that negligible decel- eration occurred in tests #5 for both Pos 1 and Pos 2 and a non negligible deceleration occurred in tests #6 for both Pos 1 and Pos 2. Once again the reason for this can be found in the cable/hatch/FFU interaction during the ejection. During CCW ejection the cable is forced, by the ejection system configuration, to follow the rotation of the RMU since the hook is pulling the cable. This lead to the fact that the cable is then
0 0.05 0.1 0.15 0.2 0.25
−1 0 1
Test#2:FFU B − Pos 2
Time [s]
Angular rate [Hz]
(a)
0 0.05 0.1 0.15 0.2 0.25
−1 0 1
Test#3:FFU B − Pos 2
Time [s]
Angular rate [Hz]
(b)
0 0.05 0.1 0.15 0.2 0.25
−1 0 1
Test#4:FFU B − Pos 1
Time [s]
Angular rate [Hz]
(c)
Figure 3.14: Angular rates of FFU B during tests #2, 3 and 4.
pressing over both hatches, while in the static tests it was only pressing over the hatch in Pos 2. Moreover it can be seen that the length of step 3 for Pos 2 is longer for CCW dynamic tests that for the static tests, this agrees with the idea of the cable impeding the ejection. For CW test there was no decrease of speed since the hook was not pulling the cable, therefore the effect of the cable on the hatches is lower and the deceleration negligible.
Summary
Static test Results from the video footage analysis for all static tests are summarized in Tables3.3and3.4. In Table3.3the ejection speed and rotation speed calculated with the “Tracker” are presented. In Table3.4the rotation speed calculated by the “Tracker”
is compared with the one recorded by the inertial sensor.
Ejection Speed [m/s] Rotation Speed [Hz]
TEST#2
FFU A Position 1 3.6 0.11 CCW
FFU B Position 2 3.4 0.23 CCW
TEST#3
FFU B Position 2 4.2 0.23 CCW
TEST#4
FFU B Position 1 4.8 0.07 CCW
Table 3.3: Static tests: Results from the Tracker.
Tables3.3shows that, apart from the rotation speed of FFU in Pos 2, the other results differ a lot between test#2 and tests#3-4. For what concerns the ejection speed the
0 0.05 0.1 0.15
−2 0 2
Test#5:FFU A − Pos 1
Time [s]
Acceleration [g]
(a)
0 0.05 0.1 0.15
−2 0 2
Test#6:FFU A − Pos 2
Time [s]
Acceleration [g]
(b)
0 0.05 0.1 0.15
−2 0 2
Test#5:FFU B − Pos 2
Time [s]
Acceleration [g]
(c)
0 0.05 0.1 0.15
−2 0 2
Test#6:FFU B − Pos 1
Time [s]
Acceleration [g]
(d)
Figure 3.15: Accelerations of FFU A and FFU B during tests #5 and 6.
difference is up to 25% for Pos 1 and 33% for Pos 2 and for the rotation speed of Pos 1 the error is up to 40%. The difference in results in the ejection speed might be explained by the camera not placed in the same position in test#2 and tests#3-4. A difference in the distance from the RMU and the camera leads to different measurement errors, moreover between test#2 and tests#3-4 the camera was also moved from the center of the RMU to the side and this might lead to additional errors. Even if the results do not match it is possible to appreciate a systematic behavior of the system: Pos 2 has always lower ejection speed and higher rotation speed of the FFU. This different behavior can be attributed to the cable/hatch/FFU interaction during step 3 and 4 of the ejection.
Tables 3.4shows good qualitative matching between the results from the video footage and from the sensor data. All results shows a systematic behavior of the FFU to rotate CCW after the ejection, moreover it is confirmed that the FFU ejected from position 2 has higher angular rate.
0 0.05 0.1 0.15
−1 0 1
Test#5:FFU A − Pos 1
Time [s]
Angular rate [Hz]
(a)
0 0.05 0.1 0.15
−1 0 1
Test#6:FFU A − Pos 2
Time [s]
Angular rate [Hz]
(b)
0 0.05 0.1 0.15
−1 0 1
Test#5:FFU B − Pos 2
Time [s]
Angular rate [Hz]
(c)
0 0.05 0.1 0.15
−1 0 1
Test#6:FFU B − Pos 1
Time [s]
Angular rate [Hz]
(d)
Figure 3.16: Angular rates of FFU A and FFU B during tests #5 and 6.
Rotation Speed [Hz]
- Sensor
Rotation Speed [Hz]
- Video TEST#2
FFU A Position 1 0.02 CCW 0.11 CCW
FFU B Position 2 0.19 CCW 0.23 CCW
TEST#3
FFU A Position 1 0.11 CCW -
FFU B Position 2 0.25 CCW 0.23 CCW
TEST#4
FFU A Position 2 0.18 CCW -
FFU B Position 1 0.09 CCW 0.06 CCW
Table 3.4: Rotation speed and inertia sensors during static tests from “Tracker”.
Dynamic test From the dynamic tests is possible to conclude that the spinning di- rection of the RMU significantly influences the ejection. As shown in Figure3.16 when the RMU is spinning CCW the de-spin is bigger than for spinning in CW direction.
However, no conclusive explanation has been found to explain this phenomena. Another phenomena that is related to the rotation direction of the RMU is the different deceler- ations of the FFUs in step 3. In fact, in the CCW direction the hook pulls the cable and force it to follow the RMU in its rotation, therefore the cable is pressed on the RMU skin partially impeding the ejection of the FFUs.
3.2 Flight ejection data
In this section data from the flight are analyzed and compared with the results from the SSMM and the on-ground tests.
3.2.1 Inertial sensor data
Flight data of acceleration in z-direction and the angular rate in all three axes direction from FFUs’ ejection until parachute deployment were presented in Figure 1.8. From the figure it was possible to observe a de-spin of the FFUs at ejection and a different wobbling of the probes after ejection. During the launch the FFUs used were not the test FFUs A and B but the flight FFU C and E where: FFU C was is position 2 and FFU E in position 1. The data for the ejection are shown in Figures 3.17and 3.18.
67.25 67.3 67.35 67.4
−4
−2 0 2 4
Time [s]
Angular rate [Hz]
Angular rate at ejection
(a)
x−axis y−axis z−axis
67.25 67.3 67.35 67.4
−2
−1 0 1 2
Acceleration at ejection
Time [s]
Acceleration [g]
(b)
Figure 3.17: Internals sensor data at ejection for FFU C.
In Figures 3.17 and 3.18 the first dashed line corresponds to the cutter activation, the second line is the stop of the pushing plate and the third one the complete ejection of the FFU from the ejection system. In Figure 3.17 (a) it is possible to see the de-spin
67.25 67.3 67.35 67.4
−4
−2 0 2 4
Time [s]
Angular rate [Hz]
Angular rate at ejection
(a)
x−axis y−axis z−axis
67.25 67.3 67.35 67.4
−2
−1 0 1 2
Acceleration at ejection
Time [s]
Acceleration [g]
(b)
Figure 3.18: Internals sensor data at ejection for FFU E.
of the FFU in the z-direction (1.5 Hz) and that at ejection both angular rates in x and y-direction are non-zero. Therefore, there is an external torque that generates a tip-off on the FFU. Figure3.18 (a) shows that de-spin occurs for FFU E (1.8 Hz) and in this case there is no tip-off of the FFU since the lateral rate are zero at ejection.
Figures3.17 and3.18 show also than for FFU C the ejection takes longer time that for FFU E. Moreover, while Figure 3.17 (b) shows the same acceleration tendency shown in the ground tests, Figure 3.18 (b) has a change of sign in the x-direction where the Coriolis force is pointing. This phenomena has never been seen in any of the ground tests.
3.2.2 Summary
Comparing the data from the two FFUs one can see that in position 2 the ejection takes longer and, as shown in Figure 1.10, the ejection speed is lower, moreover there is a tip-off of the FFU at ejection. All these observations agree with the on-ground test where the cable/hatch/FFU interaction in the dynamic test was responsible for the bigger deceleration in step 3 of the ejection. During the flight the spin of the rocket was higher than during the on-ground test, this leads to bigger deceleration of the probe since the cable is more attached to the RMU.
There is no concrete explanation why the acceleration in the x-direction changes sign for the FFU in position 2. However one might think that the change of sign in the x-axis direction is due to step 4 of the ejection, where the FFU is in touch with the hatch that is pulled by the steel cable. Therefore, between the second and the third dashed line there are steps 2, 3 and 4. Let us assume that when the acceleration in the x-axis direction gets positive the FFU is in step 4, it is then possible to see that the de-spin
occurs before step 4 and that step 4 is actually increasing the spin as in the static tests.
It is also possible to see that in step 4 the lateral rates go from zero to non zero values.
Therefore, if the assumptions are correct, step 4 is responsible for the tip-off of FFU C. It has already been mentioned that in step 4 the steel cable is pushing the hatch (Figures 3.9 and 3.10), due to the fact that the hatch is acting on the FFU in middle of the height of the probe and the center of mass of the FFU is below the ideal center of mass of the cylinder, the whip effect of the cable on the hatch can generate a torque that creates the tip-off shown in Figure3.17 (b).
Finally, the de-spin in position 2 is lower that in position 1, this agrees with the static tests where the FFU in position 2 had higher angular rate in CCW direction than in position 1. Figures 3.17 (a) and 3.18 (a) agrees on the fact that the de-spin do not occurs in step 1 of the ejection, therefore the source of de-spin has to be found in steps 2 and 3.
3.3 Conclusion
From the on-ground test data and flight data it is possible to make some conclusions concerning ejection speed, de-spin and the tip-off of the FFUs:
• Ejection speed:
– Ejection speed is always higher for the FFU ejected from position 1. This is due to the presence of the cable over the hatch of FFU in position 2, the cable adds mass and inertia therefore the FFU is slowed down before ejection.
Moreover, there is energy dissipation, due to friction, when the cable slides against the hatch.
– The effect of the presence of the cable is seen in step 3 where for the FFU ejected from position 2 there is higher deceleration. The magnitude of the deceleration varies between static and dynamic tests since the presence of the cable has greater effect in CCW dynamic ejection.
• De-spin:
– The ejection system has the tendency to introduce a systematic rotation of the FFUs in the CCW direction regardless of the FFU and of the position the FFU occupies.
– In static tests the FFU ejected from position 2 has always higher spin rate that the FFU elected from position 1. This is the results of the cable/hatch/FFU interaction that happens in position 2 where friction between cable and hatch creates a rotation in the FFU.
– For dynamic tests the direction of spin of the RMU influences the de-spin of the FFUs since in one direction the hook pulls the cable pressing it on the RMU.
– From both video and internal sensors the de-spin occurs only during steps 2 and 3 while, if the assumptions made are correct, step 4 helps in increasing the spin of the FFU.
• Tip-off for FFU C:
– The tip-off of FFU C is due to the fact that the FFU was in position 2 and therefore was subjected to step 4. During this step the force introduced by the cable in the FFU is in the middle of the height of the FFU while the center of mass of the FFU is in the lower part of the probe. This creates a lever arm and a torque that generates the tip-off.
Possible Causes of De-spin and Wobbling
In this chapter possible causes of the de-spin and wobbling for the RAIN FFUs are analyzed and mechanical analytical models are utilized to evaluate the effect of those causes. Each step of the ejection is treated separately and its effect on the FFU’s spin and wobbling are described and analyzed when possible.
4.1 Step 1
In step 1 the FFU is pushed by the pushing plate and no rotation has been identified during both ground tests and flight of the experiment. Moreover the high accelerations (Figure2.4 ) which the FFU is subjected to ensure that friction between the FFU and the pushing plate can avoid any undesired rotation of the probe during both steps 1a and 1b. For what concerns the wobbling or the tip-off of FFU C there is no cause here that can influence those phenomena since the FFU is constrained in all directions by the rails of the ejection system and the pushing plate and the hatch.
4.2 Step 2
Step 2 is characterized by the stop of the pushing plate while the FFU is resting on the pushing plate as shown in Figure 4.1since the Coriolis force pulls the FFU perpen- dicularly to the ejection direction at both points 1 and 2. Therefore the normal force to the side of the pushing plate is considerably high and this leads to friction force at point 2. This friction force plus the fact that the pushing plate stops its run and the FFU continue straight create a moment that produces a rotation with sliding in the direction of the de-spin of the FFU.
4.2.1 Mechanical model
The objective of this model is to determine how long time it takes for the FFU to start to roll without slipping and how long distance it has travelled starting from the end of
32
Figure 4.1: Contact point between FFU and pushing plate in step 2.
step 1. Moreover for a given length of the side bar of the pushing plate it is important to know the rotational speed of the FFU [4] [5].
Model
The forces acting on the system are the friction forces between the FFU and the side of the pushing plate in point 2 and the friction force between the FFU and the upper and lower rails (Figure4.1). Therefore the equations of motion describing the step 2 are:
m¨y = −FFFU− FFr
J ¨θ = FFr r (4.1)
where r is the radius of the FFU, J the inertia of the FFU (mr2/2) and FFr is the friction force between the FFU and the side bar of the pushing plate. This friction force is a function of the dynamic friction coefficient and the normal force between the FFU and the side bar:
FF r= µdNCoriolis = 2µaldΩm ˙y (4.2) where Ω is the angular speed of the rocket and µald is the dynamic friction coefficient aluminum-to-aluminum. The resulting equations of motion to solve are:
¨
y = −µdNFFU
m − 2µaldΩ ˙y θ =¨ 4µaldΩy0
r
(4.3)
Figure 4.2shows that the speed of the center of the FFU can be calculated as:
˙
y = vC = vP+ ωr (4.4)
The FFU stops slipping when the speed of the contact point between the lateral bar and the FFU is zero (vP = 0). Therefore, the no-slip condition is obtained when:
˙
y = ωr (4.5)
C
P r
vC
vP
y
Figure 4.2: Nomenclature used in the no-slip condition.
4.2.2 Results
The value used to obtain the following results are shown in Table 4.1 Variable Value
Ω 20.1 rad/s
m 1 kg
r 0.058 m
µd 0.18
µald 1.4 [6]
Table 4.1: Values used in the simulation.
Figure 4.3 shows the de-spin obtained from the stop of the cage as a function of the distance travelled by the FFU in the radial direction, assuming contact between the FFU and the side bar of the pushing plate. The model used assumed slipping condition between the FFU and the side bar therefore the dynamic friction coefficient between aluminum and aluminum has been used, this assumption in fact is correct as Figure4.4 shows that the no-slipping condition is fulfilled only after 30 mm. The FFU will start slipping and rolling after the stop of the pushing plates and, after 30 mm, it will roll without slipping.
4.2.3 Conclusion
The de-spin the FFUs experienced during the launch campaign is 1.5 for FFU C and 1.8 Hz for FFU E. To reach that magnitude of de-spin the FFUs has to travel 4.8 and and 5.8 mm respectively. However the side bar of the pushing plate is approximatively as long as the radius of the FFU and less that 1 mm is available for sliding, giving a maximum de-spin of 0.3 Hz in CW direction.
