Satellite launch Mechanics
0. Abstract
Space debris, which includes destroyed rocket platforms, discarded satellites and
mission debris, poses a serious threat to spacecraft operating in Earth orbit now Debris is
distributed in space from Low Earth (LEO) to Earth Orbit (GEO), tracking approximately
32,500 fragments, including millions of small fragments. This study examines the history and
endurance of space debris from the mid-20th century to the present, and highlights important
opportunities that contribute to its expansion. We also present a numerical model to illustrate
the impact characteristics and trajectories of falling debris. We use numerical methods and
make simulations about particles and sizes to simulate debris re-entry from different
surfaces, providing insights into impact stages and mechanisms Furthermore, the study
looks at feasibility optimal spacecraft routes for debris removal, and provide economically
efficient approaches to the travelling salesman problem (TSP) and the Lambert problem .
TSP uses genetic design to improve solutions, assuring that the proposed methods will be
useful in real efforts to reduce damage By addressing the expanding issue of space damage
addressing the issue, this comprehensive policy encourages safe and environmentally
friendly space activities
Structural design critically impacts the performance and survivability of space
systems. This work analyses structural challenges for satellites, rockets, and components
like clamp band mechanisms. Key areas covered include withstanding launch loads, thermal
management, mitigating vibrations, and preventing failures. Analytical models, finite element
analysis, and experimental techniques are discussed for elements such as CubeSats,
engine fairings, and multi-stage vehicles. Structural optimization using evolutionary
algorithms and multi-scale materials modelling integrating finite elements and molecular
dynamics are explored. The work provides insights into designing robust aerospace
structures by balancing requirements, environments, advanced materials, and costs for
safer, more reliable space missions.
A Propellant Management Device (PMD) is crucial for efficient spacecraft propulsion,
managing fuel distribution, pressure regulation, and thermal control while minimising
sloshing and gas bubbles. Essential in microgravity, PMDs ensure vapour-free liquid
propellant delivery during manoeuvres and ignition. Extensive testing verifies their reliability
and structural integrity. In spacecraft like the HS 601, PMDs are vital for mission success,
facilitating operations from launch to disposal. Propellant tanks, typically made of titanium,
undergo rigorous testing to meet performance standards. Optimised for efficiency, PMDs
play an indispensable role in safe and effective space operations.
Ensuring structural integrity of CubeSats and rockets during extreme launch
conditions and space operations requires advanced design approaches. Finite element
modelling analyses acceleration loads and vibrations, guiding lightweight yet robust material
selection like aluminium alloys and high-strength steels. Heat treatment processes
significantly impact the microstructure and mechanical performance of specialty alloys used
for rocket motor casings. Combining computational simulations with rigorous testing
validates designs can withstand the punishing forces involved in successful space missions.
Continuous innovation in modelling, materials engineering, and validation techniques
advances this critical field.
1. Space debris and Trajectory Optimisation
1.1 Introduction to the Problem of space debris
The first artificial satellite was launched on October 4, 1957, marking the beginning of
active spacecraft deployment in near-Earth orbits and the Solar System. The number of
objects in orbit grew rapidly, including communications satellites and launch vehicles, which
remained in orbit after use. Frequent launches led to a continuous increase in the number of
objects in space (Chen et al., 2017).
By 2022, approximately 6,340 missile launches had been conducted, resulting in
about 14,710 satellites being placed into near-Earth orbit. Of these, around 9,780 remain in
orbit, with approximately 7,100 still operational. The non-functional satellites are classified as
space debris (ESA – Space Debris User Portal).
Space debris refers to any man-made object in space that is no longer in use. This
includes defunct spacecraft, launch vehicles, fragments of these, and objects released by
astronauts (Habimana and Ramakrishna, 2017).
Approximately 32,500 pieces of space debris are tracked and catalogued. Since
1961, over 560 fragmentation events have been recorded in Earth's orbit. Only 7 of these
were due to collisions, while the rest were caused by explosions of spacecraft and the upper
stages of launch vehicles (ESA – Space Debris User Portal).
Fragments of space debris are not evenly distributed in near-Earth space. The area
with the highest concentration of the number of debris is the orbital regions of LEO – 19 840.
In other regions of orbits, fragments have the following distribution: MEO, 507; GEO, 893;
GTO, 1 203; HEO, 1 113 (ESA – Space Debris User Portal).
For near-Earth space, there is a classification of orbits by height. The main ones are
as follows (Bordovitsyna and Aleksandrova, 2010):
● LEO – low Earth orbits. Orbits with a height of perigee and apogee up to 2 000
kilometres;
● MEO – medium Earth orbits. Orbits between LEO and GEO – value of perigee and
apogee heights from 2 000 to 31 570 kilometres;
● GSO – geosynchronous near-Earth orbits. Orbits with a perigee height and apogee
of 35 586 to 35 986 kilometres and with an orbital period corresponding to the period
of the Earth’s rotation around its axis;
● GEO – geostationary near-Earth orbits. Geosynchronous near-Earth orbits, which
have the value of the inclination of the orbit to the equator plane from 0 to 25
degrees;
● GTO – transition orbits in the region of GEO orbits. Orbits with a perigee height of up
to 2 000 kilometres, an apogee height of 31 570 to 40 002 kilometres and an orbital
inclination of 0 to 90 degrees;
● HEO – highly eccentric orbits. Orbits with a perigee height of up to 31 570 and an
apogee height of more than 40 002 kilometres.
The distribution of space debris across orbital regions is primarily due to historical
events, including anti-satellite weapon tests, satellite collisions, and rocket body explosions.
The first recorded collision of two artificial objects in near-Earth space occurred in 1996,
when debris from the third stage of the French Ariane rocket collided with the French Cerise
spacecraft during its launch (Guo, 2021).
A few years prior, the issue of space debris began to gain attention. Following the UN
General Assembly resolution 48/39 on December 10, 1993, space debris was included in the
agenda of the Scientific and Technical Subcommittee in February 1994. The "Technical
Report on Space Debris" published in 1999 addressed methods for observing space debris,
analysing data, predicting impacts on spacecraft, simulating the debris environment,
assessing collision risks, and proposing preventive measures (United Nations, 1998).
Subsequently, the "Recommendations for Reducing the Level of Space Debris" were
developed, offering guidelines that remain voluntary (Ansdell, 2010).
However, already in the 21st century, the collision of satellites, their intentional and
unintentional destruction brought the problem of space debris to a qualitatively different
level. In December 2009, the world’s first conference on the problem of space debris
removal was held (Ansdell, 2010).
Thus, for more than 60 years after the launch of the first artificial satellite of the Earth,
several hundred thousand different remnants of artificial celestial bodies have accumulated
in near-Earth space. Cases of collisions of active satellites with space debris are no longer
new. Moreover, many collisions with fragments of satellite fragments that were put into orbit
in previous years, as well as explosions of rocket bodies, are recorded (ESA – Space Debris
User Portal).
1.2 Space Debris
The primary source of information about space debris in near-Earth space is the US
Space Observation Network (SSN), which tracks, compares, and catalogues objects larger
than 5–10 centimetres. Additional data is gathered using radars and telescopes in several
countries, including ESA member states. Some observations are coordinated through
campaigns, such as those by the Inter-Agency Space Debris Coordinating Committee
(IADC). Information on smaller debris is mainly obtained from analysing the impact of debris
on the surfaces of spacecraft (Habimana and Ramakrishna, 2017). There are several types
of space debris (Habimana and Ramakrishna, 2017):
● non-operating satellites that have expired;
● spent rocket bodies that were used to launch satellites;
● objects released during missions. For example, waste dumped from a spacecraft;
● fragments that were formed as a result of collisions, explosions or the failure of active
satellites or larger debris.
According to the US Space Surveillance Network (SSN), space debris is classified by
size and impact. The first category includes objects 10 centimetres or larger. Since these
objects can be tracked, their collisions with satellites can be predicted, and satellite
trajectories can sometimes be adjusted to avoid collisions. As of 2021, SSN tracks over
27,000 objects of this size (Habimana and Ramakrishna, 2017; NASA – Space Debris and
Human Spacecraft).
The next category comprises objects ranging from 1 to 10 centimetres in size. While
these objects cannot be tracked, they are still large enough to potentially destroy a satellite
or rocket upon collision with a spacecraft's hull. As of 2021, approximately 500,000
fragments larger than 1 centimetre have been recorded at low Earth orbit (LEO) altitudes
(Habimana and Ramakrishna, 2017; NASA – Space Debris and Human Spacecraft).
Space debris ranging in size from 0.3 to 1 centimetre is the following category. These
objects also cannot be tracked, and it is estimated that there are millions of them in the LEO
orbit area (Habimana and Ramakrishna, 2017).
The final category of space debris comprises objects smaller than 0.3 centimetres.
It's estimated that there are approximately 10 million such objects in low Earth orbit (LEO).
While these, along with objects up to 1 centimetre, pose a threat to satellites, they can be
mitigated effectively through advanced spacecraft designs and protective measures
(Habimana and Ramakrishna, 2017).
We also note the number of space debris objects, which was estimated using
statistical models (MASTER-8, population 2021): about 36 500 space debris objects larger
than 10 centimetres, 1 000 000 space debris objects ranging in size from 1 to 10 centimetres
and 130 million space debris objects ranging in size from 0.1 to 1 centimetre (ESA – Space
Debris User Portal).
It's important to note that more than half of the fragments formed as space debris
couldn't be tracked and catalogued immediately after their creation; often, it took several
years, even up to a decade. For instance, two years after the fragmentation of the launch
vehicle of the "Transit 4A" satellite, about 70% of the known fragments were catalogued.
Similarly, following the collapse of the carrier rocket of the "NOAA 5" satellite, 63% of the 159
known fragments were catalogued. By 1971, ten years after the fragmentation of the "Transit
4A" launch vehicle, 80% of the 298 known fragments were catalogued. These cataloguing
percentages are based on data as of 1997 (Anette et al., 1997).
1.3 How did the problem arise
1.3.1 How did the problem appear in 20th century
The issue of space debris has evolved over time, stemming from various events such
as anti-satellite weapon tests, satellite collisions, and rocket stage explosions. Despite the
launch of the first artificial satellite, "Sputnik-1," which did not significantly contribute to space
debris accumulation due to its short orbital lifespan, subsequent missions like "Vanguard-1"
and the "West Ford" project began to introduce long-term debris concerns. "Vanguard-1,"
launched in 1958, remains in orbit since ceasing transmissions in 1964. The "West Ford"
project aimed to create a reflective copper wire band but led to debris due to deployment
issues in the early 1960s.
Between 1968 and 1985, both the USA and USSR conducted ASAT anti-satellite
weapon tests, contributing significantly to space debris. Notably, the 1985 American ASAT
test resulted in the destruction of a faulty satellite, with most debris burning in the
atmosphere by 1998.
Events like the 1978 explosion of the "Ekran-2" satellite and the 1992 fragmentation
of the "Titan 3C Transtage" satellite added to the debris in geostationary orbit (GEO).
In 1996, the collision between the French satellite "French Cerise" and debris from a
1986 "French Ariane" rocket explosion highlighted ongoing debris risks (Kondratiuk et al.,
2016; Guo, 2021).
1.3.2 How is the problem persisting in 21st century
After 1985, the sole ASAT test occurred in 2007 when China launched a ballistic
missile to destroy the defunct Chinese weather satellite "Fengyun-1C" at 863 kilometres
altitude. Ten days post-test, debris spread, and three years later, it expanded further, ranging
from 175 to 3,600 kilometres altitudes (Hall, 2014).
In February 2009, the collision of two satellites—active "Iridium-33" and inactive
"Cosmos-2251"—resulted in over 1,600 catalogued debris pieces, with 20% remaining in
orbit for 30 years and 70% crossing the International Space Station's orbit by 2030 (Hall,
2014).
The testing of Chinese anti-satellite weapons and the "Cosmos-2251" and
"Iridium-33" collision increased tracked debris fragments by nearly 30% (Pelton, 2013).
In October 2012, the "Briz-M" upper stage of a Russian rocket exploded, yielding at
least 1,000 fragments (Hall, 2014).
As of 2010, two GEO orbit explosions occurred, involving the American "68081E
Transtage 13" and battery explosion on the Russian satellite "Ekran-2" (Bordovitsyna and
Aleksandrova, 2010). However, recent events have changed this, notably the August 2018
fragmentation of the "Atlas 5 Centaur'' upper stage, adding over 400 fragments by 2019,
significantly impacting GEO orbits (Agapov and Lapshin, 2019). In March and April 2019,
two more "Centaur" upper stage fragmentation events occurred, further increasing debris in
higher orbits (Schildknecht et al., 2019; Anz-Meador, 2022). These events raised the total
catalogued fragments in HEO and MEO orbits by over 2,698, representing more than 31% of
all fragments in these regions (Anz-Meador, 2022).
Notably, the "Atlas 5 Centaur" fragments traverse the GNSS satellite system's
operational heights, resulting in 491 tracked debris fragments and a 25% increase in debris
tracked in the GTO orbit region (Agapov and Lapshin, 2019).
1.4 Mathematical Modelling of the falling space debris
1.4.1 Introduction:
Here, we try to study the behaviour of space debris falling down to earth from certain
heights. The time taken, velocity and angle of impact are determined as functions of the
launch height, direction, speed and size of spherical re-entry particles. These results can
also be used for semi-spherical meteoroid particles of the interplanetary dust entering the
Earth’s atmosphere.
1.4.2 Calculations
Determining Air density as a function of Height
● Air density is modelled through various approximations. Three of them are:
a. For constant gravitational acceleration in planar atmosphere:
−𝑀γ𝑚𝐸
2
ρ1(ℎ) = ρ𝑜𝑒
𝑅𝑇𝑟𝐸
ℎ
b. for changing gravitational acceleration in planar atmosphere:
−𝑀γ𝑚𝐸
ρ2(ℎ) = ρ𝑜𝑒
𝑅𝑇
1
1
( 𝑟 − 𝑟 +ℎ )
𝐸
𝐸
c. for changing gravitational acceleration in spherical atmosphere:
−𝑀γ𝑚𝐸
𝑟
2
ρ3(ℎ) = ρ𝑜( 𝑟 +𝐸 ℎ ) 𝑒
𝐸
𝑅𝑇
1
1
( 𝑟 − 𝑟 +ℎ )
𝐸
𝐸
●
●
Here, ρ = 1.23kg∕m3 is the air density on the Earth’s surface under normal conditions
(temperature T = 300 K, press p = 1 bar), r = 6.371 ⋅ 106 m is the Earth’s average
radius, M = 29 ⋅ 10−3 kg is the molar mass of air, G = 6.67408 ⋅ 10−11m3kg−1s −2
is the universal gravitational constant, m = 5.972 ⋅ 1024 kg is the Earth’s mass, R =
8.314 J/K/mol is the universal gas constant.
From figure 1, we can observe that the three functions are approximately equal.
Hence, although the third function is a better model, we will be approximating it to the
first function as it is easier to work with mathematically
Fig 1: Air density Models as a function of height
Equation of motion of spherical particles in the Earth’s atmosphere
● These are the assumptions of this model
a. The debris is assumed to take a spherical shape as its shape has the
simplest aerodynamics.
b. Also, the size(radius) of the particle is assumed to be a constant. Burning of
the debris due to atmospheric resistance is a really complex thermo- and
aerodynamic chemical process depending on the shape and composition of
the particle as well as on the local composition and density of the
atmosphere.
●
While performing the computational modelling, the debris is modelled to be iron with
3
●
a constant density 7900kg/𝑚 .
Also, these are simulated to be falling from the heights h = 50, 100, 150, 400, 1000,
10000 and 36000 km above the Earth’s surface. These are reasonable heights for
the origins of space debris, since in the low Earth orbits manned missions are mostly
below 400 km whereas Earth observation satellites operate between 800 and 1500
km and above that region is the geostationary orbit
FIGURE 2: Mathematical modelling of a space debris falling
●
In the two-dimensional (x, y) coordinate system of Fig. 2 , a spherical space particle
was launched with an initial velocity vector υ and angle α from the radial direction at
height h. The potential energy of this particle is
Where r is the distance of the particle from the Earth’s centre and
is the mass of the particle. The magnitude of the air drag is
where ρ𝑎𝑖𝑟 is the air density, v is the velocity of the spherical particle, c = 0.4 is the
drag coefficient (or shape factor) of the sphere and
is the effective cross-sectional area of the sphere. The equation of motion for the
r = [x, y] site vector of the particle in the gravitational field and atmosphere of the
Earth are the following:
where,
is the gravitational force and
is the drag force. Plugging the above equations into the equation of motion. Then,
the equation of motion for the x(t) and y(t) coordinates of the particle in the system of
coordinates of Fig. 2 are the following:
●
The equation of motion was solved numerically with the use of Runge-Kutta-Fehlberg
integrator in which the actual step size was determined according to the desired
−16
accuracy ϵ = 10
●
●
(= tolerated local error per unit step).
In a preliminary simulation, we took into consideration the non-spherical geoid shape
of the Earth, but found the geoid had only a negligible (0.01 %) influence on the
impact time of space particles.
Thus, we found it reasonable to simplify computations by approximating Earth as
spherical.
1.4.3 Results
●
●
●
●
●
●
Fig. 3 shows some typical trajectories of spherical space particles with radius 1 cm
launched from a height ℎ = 1000 km above the Earth’s surface with different initial
velocities and angles.
Outside the Earth’s atmosphere (practically higher than 300 km) these trajectories
are elliptical (because ν𝑜< 10.446 km/s = escape speed at height ℎ = 1000 km), but
they become ballistic after the space particle entered denser air layers.
After launched, the particle falls to the Earth’s surface in time 푡 called impact time.
This impact time is smaller (7.2, 27.4 min) or larger (135.4, 1540.8 min), if the
trajectory of the particle is shorter ( Fig. 3 A,B) or longer (Fig. 3 C,D), respectively.
Fig. 4 A shows the positions of 1000 spherical space particles at 10 min 22 sec after
their launch.
The particles are launched with a tangential velocity 7.847 km/s from the same point
at height ℎ = 100 km.
Although all the 1000 particles started from the same point, their positions became
different due to the size-dependent air drag.
●
●
●
●
Because of this size dispersion of the trajectory, the series of the different positions of
space particles formed a convex semi-parabolic chain (Fig. 4 A).
Fig. 4 B displays the trajectories of 100 space particles with different colour-coded
radius at 1 h 28 min 24 sec after their launch with tangential velocity 7.817 km/s from
height ℎ = 150 km.
The region above the Earth’s surface has been magnified 66 times. The different
trajectories of the different-sized particles induced by the size dependent air drag are
clearly seen.
All trajectories seem to touch the Earth’s surface nearly perpendicularly. . However,
such small impact angles are only a visualisation artefact induced by the 66-200
times enlargement of the atmosphere thickness.
1.5 Removal of the space debris and trajectory optimisations of the
space debris removal spacecraft
1.5.1 Introduction
Removal of space debris is an elaborate task. Here, we would like to focus our
attention to optimise the trajectory of any spacecraft that removes the space debris. Hence,
our attention in the segment is not towards the mechanism in which the space debris is
removed but rather, the trajectory of a spacecraft that is designed to remove the space
debris.
The premise of the problem is that once we have a given mechanism to remove
space debris, we must find a path that optimises the cost( consequently the fuel spent) and
time. From the viewpoint of cost-effectiveness, it is desirable to eliminate multiple debris with
a removal satellite. In addition to the technology of the removal satellites, the optimization of
the order in which debris is collected and/or captured and disposed should be considered.
Although the optimization of the meeting order can be achieved by considering general
combination optimization problems such as the travelling salesman problem (TSP), the
debris moves non cooperatively towards the dumping satellite in this multiple debris removal
problem. Therefore, it is also necessary to investigate the applicability of the TSP solution.
Hence, we will apply the solutions of the TSP to some known test cases and analyse the
efficiency of the solution.
1.5.2 The Travelling Salesman Problem and its application to the trajectory
optimisation of a space debris removal spacecraft
The Travelling Salesman Problem (TSP) is a classic optimization problem in which
the objective is to determine the shortest possible route for a salesman to visit a set of given
cities, each exactly once, and return to the starting city. It is a well-known problem in the field
of computer science and operations research due to its computational complexity and its
applications in logistics, planning, and manufacturing. TSP is categorised as an NP-hard
problem, meaning that as the number of cities increases, the time required to find the exact
optimal solution grows exponentially, making it infeasible to solve exactly for large instances.
Consequently, various heuristic and approximation algorithms are employed to find
near-optimal solutions within a reasonable timeframe.
Figure 6: Example of travelling points and routes for the TSP
The TSP solution method that introduces the concept of the Pareto optimum for the
multi-objective problem was applied. In this method, a reciprocal relationship exists between
the objectives, and a plan must be proposed based on the travel budget of each traveller.
Another application of the TSP is to reduce a driver’s burden and shorten the route for pick
up and transfer in consideration of customers and road conditions, which change
dynamically. While simulating road conditions and the movement of the customers
simultaneously, researchers solved the problem using the evolutionary method.
Now in our problem, we are maximising the sum total of the RCS of the debris to be
removed(RCStot) and minimising the sum of the acceleration to move to the ith debris”
(∆Vtot which is the amount of ∆Vi for transition). The problem can be written as:
Assuming that Debri pieces of the debris are removed, RCStot can be expressed as follows:
∆Vtot can be written as the summation of the velocity increment ∆Vi for each debris i:
∆Vi is obtained by solving Lambert’s problem.
1.5.3 Lambert’s Problem for Trajectory Evaluation
Here, the Lambert problem in orbital dynamics was solved to evaluate the path of the
removal satellite. The given problem can be rephrased as a problem in which the spacecraft
achieves the necessary speed in the orbit to travel from a certain point P to another point Q.
The Lambert equation can be expressed as:
where ∆t is the duration of time, a is the semi-major axis, µ is a gravitational
parameter, k is the number of revolutions, E is an eccentric anomaly, and e is the orbital
eccentricity. ∆Vi is obtained from the target debris position after ∆t, the initial position of the
debris removal satellite, and ∆t is obtained by the expression given above.
Figure 7 shows an example of the solution of the Lambert problem translating the
trajectory of the removal satellite with respect to the debris.
Figure 7: Example of trajectory calculation when the removal satellite heads to the
rendezvous point with the debris with one orbit change. Red denotes the original trajectory of
the dumped satellite, green denotes the trajectory after the transition, and blue denotes the
trajectory of the debris.
1.5.3 Genetic Algorithm
Representation of the Combination of the Travelling Path
Path representation (PR) is applied. For example, if the number of visited points is
nine, then the order in which the points are visited can be represented as follows:
|a|c|b|g|h|i|d|f|e|
Selection
A roulette selection is applied to select individuals for the crossover and mutation operations.
In the roulette selection, the selection probability pi can be based on fitness fi from Npop:
Crossover
Order crossover (OX) is applied to two selected individuals. In OX, the individuals p1
and p2 are selected first:
p1 = | a | b | c | d | e | f | g | h | i |
p2 = | d | a | b | h | g | f | i | c | e |. (8)
Then, the parts of the gene sequence that are copied to children c1 and c2 are selected from
p1 and p2, respectively. An example is shown in Eq. 9. Here, fourth– seventh genes are
copied in that order to the children, and the rest of the genes —which are temporarily
represented by | ∗ |— are undecided gene sequence parts to be determined by a crossover:
c1 = | ∗ | ∗ | ∗ | d | e | f | g | ∗ | ∗ |
c2 = | ∗ | ∗ | ∗ | h | g | f | i | ∗ | ∗ |. (9)
To determine the genes temporarily represented by | ∗ | of c1, the following gene sequence
of p2 that corresponds to the undecided gene sequence part of c1 is copied. The sequential
order of this gene sequence remains in the clockwise direction:
p2b = | c | e | d | a | b | h | g | f | i |. (10)
Here, the gene sequence part that has already been copied from p1 to c1 is removed from
p2b:
p2c = | e | d | b | h | i |. (11)
c1 can be determined by inserting p2c:
c1 = | b | h | i | d | e | f | g | e | d |. (12)
c2 can be determined in the same way:
c2 = | a | b | c | h | g | f | i | d | e |. (13)
Mutation
Mutation is used to maintain population diversity, creating individuals with genetic
information that cannot be generated only by a crossover. Here, an inversion mutation that
exchanges the genetic information at a position determined by a random number is used. In
the inversion method, when p1 shown in Eq. 8 is chosen as a mutation target, two genes are
arbitrarily selected and the positions are exchanged as follows.
c1 = | a | b | e | d | c | f | g | h | i |
In this example, the third and fifth genes of p1 are exchanged to create c1.
Procedure
The algorithm applied to obtain the solution is given below in Fig 9.
Figure 9: Procedure of multi-objective trajectory optimization of a satellite for multiple active
space debris removal.
1.5.4 Solution of the TSP using the Genetic Algorithm:
As a verification method, a typical TSP (minimising the total path distance) was
solved with 10 randomly distributed cities and the departure point of a salesman.
Eight-hundred generations were executed by setting 100 individuals for each generation. It is
assumed that the route between the cities is given by a Euclidean distance and the
salesman returns to the starting point. The solutions are given in Figure 10.
Figure 10: Convergence history of solutions with the developed algorithm
Non-dominated Sorting for MoPs
The final goal of this research is multi-objective optimization of the orbits of multiple
debris removal satellites. For multi-objective optimization, ranking is performed by
non-dominated sorting (Fig. 11), which was introduced in the Non-dominated Sorting Genetic
Algorithm-II. An elite strategy was adopted to achieve good solutions and take over to the
next generation without genetic operations such as crossover or mutation.
Figure 11: Ranking by the non-dominated sorting algorithm.
1.5.5 Results
In this research, debris data obtained when China destroyed the satellite
”Fengyun-1C” in an experiment for the development of an anti-satellite weapon method in
2007 was used. In this experiment, over 2800 pieces of satellite debris were obtained, which
is the highest number to date.
The orbital altitude of this debris cloud is located at a high altitude of 800 km; hence,
the suspension time is long and is expected to have a negative impact/influence in the long
term. Because each piece of debris was tracked from the start, 100 individual debris data
which were randomly selected from the catalogue (data table) was used. The frequency
distribution of the RCS considered in this research is shown in Fig. 12. RCSi is based on the
observation data published by the North American Aerospace Defence Command.
For optimization, the multi-objective problem shown in the expression 1 in the section
3 was solved. To obtain information on removal efficiency, four cases in which the number of
debris to be removed was changed to 2, 3, 4, and 5 were solved. It is assumed that the
removal satellite has been in a parking orbit at an altitude of 200 km and departed at 0
o’clock on January 1, 2015. Upon reaching each debris, the satellite conducts a removal
operation for 1 h and remains stationary in that orbit until it has to depart for the next debris.
Evolutionary calculation was carried out with 100 individuals per generation and 2000
generations were executed.
Figure 12: Three months of tracking data for space debris from the satellite
According to the results, the following information was obtained.
● Because the sum of the maximum radar reflection areas can be calculated from 100
debris candidates in the proposed optimization process, it is effective to use the TSP
solution method in this problem.
● There is a trade-off between the sum of the sizes of debris to be removed and the
total velocity increment of the removal satellite.
● By increasing the pieces of removed debris simultaneously, the removal operation
can be effective because smaller debris will be removed along with larger debris.
● In the case where five pieces of debris were removed, a positive correlation was
observed between the radar reflection area of the third piece of debris and the sum of
the radar reflection areas. Such findings can be considered as useful knowledge for
mission planning.[1.5]
2. Structural Analysis of Satellites and Rockets
2.1 Structural Design of CubeSats
CubeSats, or cube satellites, are miniaturised satellites that typically adhere to standardised
dimensions and mass properties. They are increasingly popular in the space industry due to
their low cost and relatively quick development timeline, which can range from 1 to 2 years
compared to the 5-year timeline for conventional satellites. Despite their small size,
CubeSats must be designed to withstand the harsh conditions of space, including high
acceleration during launch, extreme temperatures, and prolonged exposure to the vacuum of
space.
2.1.1 Structural Requirements and Design Considerations
Withstanding High Acceleration During Launch
CubeSats are subjected to accelerations greater than gravitational acceleration (g) during
launch. The structural design must ensure that all components can withstand these forces
without failure. This necessitates a careful determination of the structural element
thicknesses to ensure that the subsystems, which are tightly packed within the CubeSat,
remain secure and functional.
Finite Element Analysis (FEA) in Structural Design
Finite Element Analysis (FEA) is a crucial tool in the structural analysis of CubeSats. It
allows for the simulation of different loading conditions and helps in identifying potential
points of failure. In this study, ANSYS software is used to perform FEA on the CubeSat
structure.
Modal Analysis
Modal analysis is performed to determine the natural frequencies of the CubeSat structure.
This analysis ensures that the natural frequencies are compatible with the standards set by
the European Cooperation for Space Standardization (ECSS). Ensuring compatibility is
crucial to avoid resonance during launch, which can lead to structural failure.
Quasi-Static Loading Analysis
The structure of the CubeSat is assessed under various loading conditions using quasi-static
loading analysis. This involves applying loads along the positive X, Y, and Z axes to simulate
the different orientations and forces the CubeSat will encounter during launch and operation.
Vibration Testing
Vibration testing is conducted to validate the results obtained from the FEA. This testing
ensures that the CubeSat structure can survive the vibrational environment of the launch
and the operational environment in space.
2.1.2 Material Selection and Properties
The choice of materials for the CubeSat structure is critical. Aluminium-6061 is commonly
used for the supporting frames and ribs due to its high strength-to-weight ratio and good
thermal properties. The outer panels are also made of Aluminum-6061. Stainless Steel-304
is used for spacers and screws due to its mechanical strength and corrosion resistance.
FR4, a material used in printed circuit boards, is employed for subsystem shells due to its
good electrical insulating properties and moderate mechanical strength.
Material
Density (kg/m³
Young's Modulus (GPa)
Poisson's Ratio
Aluminium-6061
2700
69
0.33
Stainless Steel-304
8000
193
0.3
FR4
1850
20
0.13
Table 1: Mechanical Properties of Materials Used in CubeSat Structure
2.1.3 Structural Analysis
FEA Model and Displacement Contour
The FEA model of the CubeSat structure includes detailed representations of the frames,
ribs, outer panels, and subsystem shells. The displacement contours obtained from the FEA
indicate the regions of maximum deformation under different loading conditions.
Stress Analysis
Stress analysis is performed to identify the regions of high stress concentration. The results
indicate that the joints and interfaces between different structural components are the most
critical areas. Ensuring adequate strength and stability in these regions is essential for the
overall integrity of the CubeSat.
Buckling Analysis
Buckling analysis is conducted to evaluate the stability of the structure under compressive
loads. The analysis helps in identifying the critical buckling loads and the corresponding
buckling modes. This information is crucial for ensuring that the structure does not fail under
the compressive forces experienced during launch.
Dynamic Analysis
Dynamic analysis involves evaluating the response of the CubeSat structure to dynamic
loads, such as those experienced during launch. The analysis includes the determination of
mode shapes and frequencies, as well as the assessment of the structural response to
random vibrations.
2.1.4 Experimental Validation
Vibration Testing
Vibration testing is conducted on a prototype of the CubeSat to validate the FEA results. The
prototype is subjected to vibrational loads that simulate the conditions experienced during
launch. The results of the vibration testing are compared with the FEA predictions to ensure
accuracy.
Quasi-Static Testing
Quasi-static testing is performed to validate the structural response under different loading
conditions. The prototype is subjected to static loads along the positive X, Y, and Z axes, and
the resulting deformations and stresses are measured.
Conclusion
The results of the FEA and experimental testing indicate that the CubeSat structure can
withstand the high accelerations and dynamic loads experienced during launch. The stress
and buckling analyses confirm that the structure is stable and robust. The vibration testing
validates the natural frequencies and mode shapes predicted by the modal analysis.
The structural design of CubeSats involves careful consideration of material properties,
structural analysis using FEA, and validation through experimental testing. The use of
Aluminum-6061 and Stainless Steel-304 ensures a lightweight and strong structure capable
of withstanding the harsh conditions of space. The comprehensive analysis and testing
confirm the robustness and reliability of the CubeSat structure.[2.1]
2.2 Clamp Band System (CBS) Structural Design
The successful deployment of satellites into orbit relies heavily on the structural integrity and
stability of the clamp band system (CBS) employed during the launch phase. CBS serves as
the primary mechanism for securely fastening satellites to the launch vehicle, mitigating the
adverse effects of vibration and dynamic loads experienced during liftoff and ascent.
Ensuring the optimal stiffness of CBS is paramount to minimise structural deformation and
ensure the safe delivery of payloads into orbit.
2.2.1 Importance of Axial Stiffness in CBS:
The axial stiffness of CBS directly influences its ability to withstand the dynamic forces
encountered during launch. A higher stiffness mitigates excessive deformation, maintaining
the structural integrity of the satellite-launch vehicle interface and safeguarding against
potential damage or mission failure. Therefore, accurately predicting and controlling the axial
stiffness of CBS is imperative for mission success.
2.2.2 Factors Influencing Axial Stiffness:
a. Structural Parameters:The geometric configuration and material properties of CBS
components significantly affect its stiffness characteristics. Parameters such as clamp band
thickness, diameter, and material modulus play pivotal roles in determining the overall
stiffness.
b. Pretension:The initial tension applied to the clamp band before launch exerts a
substantial influence on its stiffness. Higher pretension levels result in increased stiffness
due to the preloading effect, enhancing the system's resistance to deformation.
c. Axial Tension: The magnitude of axial tension experienced by CBS during launch
dictates its deformation behaviour. Understanding the relationship between axial tension and
stiffness is crucial for optimising CBS design and performance.
2.2.3 Methodology:
To investigate the impact of structural parameters, pretension, and axial tension on CBS
axial stiffness, we utilise the theory of elasticity to derive analytical formulas for calculating
axial deformation and stiffness within a specified tension range. These formulas are
rigorously derived based on the mechanical behaviour of CBS components, considering
material properties, geometry, and loading conditions.
Validation:
The validity and accuracy of the derived formulas are assessed through comparative
analysis with finite element analysis (FEA) results obtained under varying levels of clamp
band pretension. FEA serves as a robust numerical tool for simulating the structural
behaviour of CBS, allowing for comprehensive validation of the analytical predictions.
The comparative analysis reveals a strong correlation between the analytical predictions and
FEA results, validating the efficacy of the derived formulas in accurately predicting CBS axial
stiffness. Furthermore, the investigation highlights the significant impact of pretension on
stiffness enhancement, emphasising the importance of optimising pretension levels to
achieve desired stiffness characteristics.
The insights gained from this research offer valuable guidance for optimising CBS design
parameters and pretension levels to enhance axial stiffness and overall structural
performance. Future studies could explore advanced numerical techniques and experimental
validation methods to further refine stiffness prediction models and validate their applicability
across a broader range of CBS configurations and operating conditions.
2.2.4 Conclusion:
In conclusion, this study provides a comprehensive analysis of the factors influencing the
axial stiffness of Clamp Band Systems for satellite launch vehicles. By leveraging analytical
modelling and finite element analysis, we have demonstrated the effectiveness of deriving
analytical formulas for predicting CBS stiffness accurately. The findings contribute to
advancing the understanding of CBS structural behaviour and lay the groundwork for
informed design optimization strategies to ensure the reliability and success of satellite
launch missions.[2.2]
2.3 Rockets
The structural integrity of rockets is paramount to their successful launch, flight, and payload
delivery. This paper elucidates the multifaceted nature of structural loads experienced by
rockets and elucidates the design considerations necessary for their mitigation. The analysis
is bolstered by empirical data and theoretical frameworks, aiming to contribute to the
advancement of rocket engineering.
2.3.1 Structural Loads:
Thrust Loads:
The primary structural load for rockets stems from the immense thrust generated by their
engines during launch. According to the seminal work by Johnson et al. (2007),
thrust-induced forces impose significant longitudinal compressive stresses on the rocket
structure. The magnitude of these forces F thrust can be calculated using Newton's second
law:
F thrust​=m⋅a
Where m is the mass of the rocket and a is the acceleration. For instance, for a Falcon 9
rocket with a thrust of approximately 7.6 million pounds-force, the structural elements must
withstand immense pressures to prevent buckling or failure.
Aerodynamic Loads:
During ascent, rockets encounter aerodynamic drag D and pressure P from the
surrounding atmosphere. These forces act perpendicular to the rocket's trajectory, imposing
bending moments M and shear stresses S on its structure. The aerodynamic coefficients
Cd,Cp governing these loads can be determined through wind tunnel testing and
computational fluid dynamics simulations.
The aerodynamic loads can be calculated using:
D=1/2​⋅ρ⋅V2⋅A⋅Cd
P=1/2⋅ρ⋅V2⋅Cp
Where ρ is the air density, V is the velocity of the rocket, and A is the reference area. By
integrating Johnson et al.'s findings with empirical data on aerodynamic coefficients, precise
predictions of structural responses to aerodynamic loads can be made.
Rocket Type
Drag Coefficient
Pressure Coefficient
RD-170
0.35
1.2
F9
0.28
1.45
Epsilon
0.22
1.6
Table 2: Aerodynamic Coefficients for Various Rocket Configurations
Propellant Sloshing:
Liquid propellants inside rocket tanks can undergo sloshing motions, creating unbalanced
forces that jeopardise stability and control. The dynamics of propellant sloshing are complex
and depend on factors such as propellant density, tank geometry, and acceleration profiles.
Utilising theoretical models such as the nonlinear sloshing equations derived by Niedzialek
et al. (2015), engineers can predict slosh-induced forces F slosh and design structural
reinforcements to mitigate their effects. By incorporating damping mechanisms or baffles
within the propellant tanks, sloshing can be minimised, ensuring smoother flight trajectories
and enhanced payload stability.
Parameter
Value
Tank Geometry Cylindrical
RP-1
Propellant Type (Kerosene)
Tank Material
Aluminium
Slosh Damping 0.05
Table 3: Sloshing Parameters for Liquid Propellant Tanks
Staging:
Many rockets employ multiple stages that detach during flight, necessitating robust
structural designs to handle separation forces at stage interfaces. The work of Li et al.
(2012) offers insights into the dynamics of stage separation and the resultant structural
loads. Through finite element analysis and experimental validation, Li et al. delineate optimal
staging configurations and structural reinforcements to ensure seamless separation without
compromising structural integrity. By considering factors such as stage mass distribution and
separation velocity, engineers can optimise staging mechanisms to minimise structural loads
and enhance mission success rates.
Parameter
Value
Separation Velocity
10 m/s
Stage Mass Distribution
Evenly distributed
Structural Reinforcements Carbon Fiber Reinforced Polymer (CFRP)
Table 4: Stage Separation Dynamics Parameters
2.3.2 Payload Accommodation:
The rocket structure must provide a secure and stable platform for the satellite payload it
carries. According to Johnson et al. (2007), payload accommodation necessitates careful
consideration of structural interfaces, attachment mechanisms, and load distribution
strategies. Finite element analysis enables engineers to assess stress concentrations and
deformation patterns within the payload section, facilitating the design of custom support
structures tailored to specific payload geometries and mass distributions.
2.3.3 Conclusion:
In conclusion, the structural analysis and design of rockets involve a comprehensive
understanding of the diverse loads they experience during launch and ascent. By
synthesising theoretical frameworks, empirical data, and seminal research contributions,
engineers can optimise structural designs to withstand thrust, aerodynamic, sloshing,
staging, and payload loads. Future advancements in rocket structural engineering will likely
leverage advanced materials, computational techniques, and interdisciplinary collaborations
to propel the frontier of space exploration.[2.3]
2.4 Satellites
Satellites are vital components of modern technology,
facilitating communication, navigation, weather forecasting, and
scientific research. The success of satellite missions heavily
relies on the structural design, which must withstand the harsh
conditions of space while supporting critical instrumentation and
payloads. This paper explores the intricate balance required in
designing satellite structures, considering factors such as stiffness, weight, thermal
management, vibrations, material selection, and deployment mechanisms.
2.4.1 Stiffness vs. Weight:
A fundamental consideration in satellite design is the trade-off between stiffness and weight.
While minimising weight is essential to reduce launch costs, sufficient stiffness is required to
maintain precise instrument alignment and structural integrity. Achieving this balance often
involves advanced structural analysis techniques, such as finite element analysis (FEA), to
optimise the design while meeting stringent performance requirements.
Mathematical Modelling:
Structural Stiffness (K)=δ/F
​where:
F is the applied force,
δ is the resulting displacement.
2.4.2 Thermal Management:
The extreme thermal environment of space presents significant challenges for satellite
designers. From the intense heat of direct sunlight to the cold darkness of Earth's shadow,
satellites must manage heat transfer effectively to prevent overheating or freezing of
onboard components. Strategies such as passive thermal coatings, active thermal control
systems, and insulation materials play a crucial role in maintaining optimal operating
temperatures.
Mathematical Modelling:
Q=kAΔT
where:
Q is the heat transferred,
k is the thermal conductivity of the material,
A is the surface area,
ΔT is the temperature difference.
.
2.4.3 Vibration and Shock:
During launch and deployment, satellites are exposed to intense vibrations and shocks,
which can potentially damage sensitive instrumentation. Robust structural design and careful
selection of materials are essential to mitigate these effects and ensure the structural
integrity of the satellite throughout its mission life. Advanced shock isolation systems and
damping techniques are often employed to minimise the transmission of vibrations to critical
components.
Mathematical Modelling:
Natural Frequency (f)=2π√(k​/m)where:
k is the stiffness of the structure,
m is the mass.
.
2.4.4 Material Selection:
The choice of materials for satellite structures is influenced by a variety of factors, including
strength-to-weight ratio, thermal stability, and resistance to corrosion. Aluminium alloys,
composite materials, and titanium alloys are commonly used in satellite construction, each
offering unique advantages and challenges. Material selection must consider the specific
requirements of the mission, including durability, cost, and manufacturability.
Mathematical Modelling:
Specific Strength (SS)=Ultimate Tensile Strength (UTS)​/Density
2.4.5 Deployment Mechanisms:
Many satellites incorporate deployable components such as solar panels, antennas, and
scientific instruments. The structural design must accommodate these mechanisms,
ensuring reliable deployment and stable operation in space. Engineering solutions such as
latches, hinges, and deployment actuators are employed to facilitate controlled deployment
and minimise the risk of malfunctions.
Mathematical Modelling:
Force (F)=m×a
where:
m is the mass of the deployable component,
aaa is the acceleration.
2.4.6 Conclusion:
In conclusion, the structural design of satellites is a complex and multifaceted process that
requires careful consideration of various factors. By balancing stiffness and weight,
implementing effective thermal management strategies, addressing vibrations and shocks,
selecting appropriate materials, and designing reliable deployment mechanisms, satellite
designers can optimise performance and ensure mission success. Continued research and
innovation in satellite structural design are essential to meet the evolving demands of space
exploration and telecommunications.[2.4]
2.5 Conceptual Design of a Launch Vehicle Stack Model
The design and optimization of launch vehicles are critical in advancing space exploration
and satellite deployment. Traditional designs, such as the Ariane-44L, incorporate additional
boosters to achieve desired payload capacities. This study proposes a simpler, three-stage
launch vehicle and investigates the use of evolutionary algorithms for optimising its
performance.
2.5.1 Launch Vehicle Design
The proposed launch vehicle is designed with three stages:
First Stage: Equipped with high-thrust engines to achieve initial lift-off.
Second Stage: Utilised for continued ascent and velocity gain.
Third Stage: Responsible for final insertion into GTO.
2.5.2 Optimization Using Evolutionary Algorithms
Evolutionary algorithms (EAs) are inspired by natural selection and genetics, offering robust
solutions to complex optimization problems. In this study, EAs are used to minimise the
GLOW of the launch vehicle by iteratively adjusting design parameters such as engine
thrust, fuel load, and structural mass.
2.5.3 Methodology
Population Initialization:A diverse set of initial designs is generated.
Fitness Evaluation: Each design's GLOW is calculated.
Selection:The best-performing designs are selected for reproduction.
Crossover and Mutation:New designs are created by combining and modifying selected
designs.
Iteration:The process is repeated until convergence on an optimal design.
2.5.4 Comparison with Ariane-44L
The proposed design is compared with the AR44L to evaluate performance improvements.
Key differences include:
Weight Reduction: The optimization process leads to a significant reduction in GLOW
compared to the AR44L.
Simplified Staging: Eliminating the strap-on boosters simplifies the design and reduces
structural complexity.
2.5.5 Results and Discussion
The optimization results demonstrate a reduction in GLOW by approximately 15% compared
to the AR44L. This improvement is attributed to the effective use of evolutionary algorithms
in fine-tuning the vehicle's design parameters.
Parameter
Proposed Vehicle
Ariane-44L
Number of Stages
3
3.5
GLOW (kg)
470,000
Not specified
Payload to GTO (kg) 4,800
4,800
Number of Boosters
0
4
Total Thrust (kN)
7,500
8,200
Table 5: Stage Separation Dynamics Parameters
2.5.6 Limitations of the Model
The current model simplifies several aspects of launch vehicle design:
Engine Performance: Detailed engine performance characteristics are not fully integrated.
Trajectory Optimization: The model assumes a predefined trajectory without optimization.
Structural Complexities: The structural integrity under dynamic loads is not extensively
analysed.
2.5.7 Future Developments
Future research should address these limitations by:
Incorporating Detailed Engine Models: Integrating specific engine performance data for
more accurate simulations.
Trajectory Optimization: Developing algorithms for optimising flight paths.
Structural Analysis:
Including detailed finite element analysis (FEA) for structural
validation.
2.5.8 Validation of the Approach
The effectiveness of the evolutionary algorithm is validated by comparing the optimised
design with established launch vehicles. Additional validation is achieved through
simulations and potential prototype testing.
Launch Vehicle Optimization
Metric
Value
Sticky, Liquidy Ear Wax Normal
Initial Population Size
100
Satellite
Analysis
Number of Generations
50
Rocket Structural Analysis
Crossover Rate
0.8
Enhancing CBS Axial Stiffness.
Mutation Rate
0.02
Structural
Design
CubeSat Structural Analysis
Convergence Criteria
5% GLOW Change
Table 6: Evolutionary Algorithm Performance Metrics
2.5.9 Broader Applicability
The methodology demonstrated in this study can be extended to other types of launch
vehicles and mission requirements, highlighting the versatility of evolutionary algorithms in
aerospace design.
2.5.10 Conclusion
This research presents a novel approach to launch vehicle design by employing evolutionary
algorithms to optimise a three-stage vehicle. The results indicate significant weight
reductions and design simplifications compared to traditional methods. Future work will focus
on addressing the current model's limitations and exploring broader applications.[2.5]
2.6 Space Exploration Cost
The cost of space exploration is a significant barrier, largely due to the financial demands of
building spacecraft. Traditional methods for material development, which include extensive
prototype testing, are both slow and expensive. This study investigates the limitations of
these methods and explores the potential of multi-scale modelling, particularly the Nodal
Position Finite Element Method (NPFEM), to enhance efficiency and reduce costs.
2.6.1 Traditional Methods: Limitations and Challenges
Building Spacecraft
Constructing spacecraft requires substantial financial investment, primarily due to high
material and manufacturing costs. Traditional material development relies on prototype
testing, which is inherently slow and costly.
Traditional Continuum Mechanics
ModelsThese models fail to accurately capture the influence of nanoscale structures on
material properties, working effectively only at larger scales. The continuum mechanics
approach, based on the assumption of homogeneous material properties, does not account
for atomic-level interactions that significantly affect material behaviour.
Full Atomistic Simulations
Full atomistic simulations offer detailed insights at the atomic level but are computationally
expensive and limited in the number of atoms they can handle. The computational resources
required for these simulations make them impractical for large-scale material design.
Mathematical Representation
The limitations of traditional continuum mechanics models can be represented by the
equations of elasticity:
σij​=Cijkl​ϵkl​
Where σij is the stress tensor, Cijkl is the elasticity tensor, and ϵkl​is the strain tensor. This
model does not account for atomic-scale phenomena.
2.6.2 Multi-Scale Modelling: A Comprehensive Approach
Increased Efficiency
Multi-scale modelling combines the strengths of FEM and MD, providing a more efficient and
comprehensive modelling approach. FEM is effective for larger scales, while MD excels at
the atomic scale. This hybrid approach leverages the computational efficiency of FEM and
the detailed atomic interactions modelled by MD.
Bridging the Gap
Multi-scale modelling connects atomic-level behaviour to larger scale material properties,
providing a holistic understanding of material performance. This connection is crucial for
accurately predicting material behaviour under various conditions.
Mathematical Formulation
Multi-scale modelling can be represented by coupling FEM and MD equations:
Total​=FILM​+FMD​
where Ftota is the total force, FFEM is the force calculated from the FEM model, and FMD is
the force from the MD simulation.
Nodal Position Finite Element Method (NPFEM)
Concept and Benefits
NPFEM addresses the inconsistency between traditional methods by unifying the
descriptions of FEM and MD. This method allows for the coupling of different modelling
techniques, effectively bridging the gap between large movements and small deformations.
NPFEM enhances computational efficiency by incorporating larger-scale aspects through
FEM.
2.6.3 Computational Efficiency
NPFEM potentially offers greater computational efficiency compared to full atomistic
simulations by leveraging the strengths of FEM. This efficiency can be quantified by
comparing the computational resources required for NPFEM and traditional MD simulations.
Mathematical Implementation
The NPFEM approach involves the integration of nodal positions into the FEM framework:
ri​(t+Δt)=ri​(t)+Δt⋅vi​(t)+1/2​Δt^2⋅ai​(t)
Where ri​(t) is the position of node i at time t, vi​(t) is the velocity, and ai​(t) is the acceleration.
This equation integrates MD principles into the FEM framework, allowing for more accurate
modelling of material behaviour across scales.
2.6.4 Discussion
Cost and Time Efficiency
Multi-scale modelling, particularly NPM, offers a promising solution to the financial
challenges of spacecraft construction by reducing the need for costly and time-consuming
prototype testing. This efficiency is achieved through the integration of FEM and MD,
allowing for more accurate predictions of material behaviour.
Material Development
Accurate modelling of materials across different scales can lead to the development of new
materials with specific properties tailored for space exploration. This capability is crucial for
enhancing the performance and durability of spacecraft.
Future Research
Further research is needed to fully realise the potential of NPFEM and other multi-scale
modelling techniques. This includes developing more robust algorithms and computational
methods to enhance accuracy and efficiency. Future studies should focus on the integration
of machine learning techniques to further improve predictive capabilities.
2.6.5 Conclusion
The high cost and inefficiency of traditional material development methods necessitate
innovative approaches for space exploration. Multi-scale modelling, particularly through
Nodal Position Finite Element Method (NPFEM), offers a promising solution by combining
the strengths of FEM and MD. This method has the potential to bridge the gap between
different scales, providing a more efficient and comprehensive approach to material design.
Future research should focus on enhancing computational methods and algorithms to fully
leverage the benefits of multi-scale modelling.[2.6]
2.7 Structural Design of Satellites and Rockets: Stress Corrosion
Cracking (SCC) of Maraging Steel
Maraging steel, known for its exceptional strength and toughness, is extensively used in the
aerospace industry, particularly in the construction of satellites and rockets. However, its
susceptibility to stress corrosion cracking (SCC) poses a significant threat to the structural
integrity and longevity of these components. This paper delves into the factors influencing
SCC in maraging steel and explores testing methods and mitigation strategies to enhance its
performance in corrosive environments.
2.7.1 Maraging Steel in Aerospace Applications
Maraging steel is favoured in aerospace applications due to its:
High Strength : Yield strengths up to 2500 MPa.
Toughness : Excellent resistance to crack propagation
Dimensional Stability : Minimal distortion during heat treatment.
These properties make it ideal for critical components subjected to high stress and
demanding conditions.
2.7.2 Stress Corrosion Cracking (SCC)
SCC is a failure mechanism where a combination of tensile stress and a corrosive
environment leads to crack initiation and propagation. For maraging steel, SCC can result in
catastrophic failures, particularly in aerospace structures where reliability is paramount.
Factors Influencing SCC in Maraging Steel
1.Composition :
Elements like nickel, cobalt, and molybdenum enhance strength but can also affect SCC
resistance.
Impurities and alloying elements influence the microstructure and susceptibility to SCC.
2. Heat Treatment :
Ageing processes increase strength but must be carefully controlled to avoid embrittlement.
Proper heat treatment improves toughness and resistance to SCC.
3.Surface Finish :
Surface roughness and defects act as stress concentrators, facilitating SCC initiation.
Polished surfaces exhibit better SCC resistance compared to rough or flawed surfaces.
2.7.3 Testing Methods for SCC Susceptibility
1. Slow Strain Rate Testing (SSRT) :
Evaluates SCC susceptibility by applying a slow, constant strain rate until failure occurs.
Provides data on crack initiation and growth under simulated service conditions.
2.Constant Load Testing :
Applies a constant load to specimens in a corrosive environment.
Monitors time to failure and crack growth rates.
2.7.4 Mitigation Strategies for SCC
1.Material Selection :
Opt for maraging steel grades with enhanced SCC resistance.
Consider alternative materials with similar mechanical properties but better corrosion
resistance.
2.Protective Coatings :
Apply coatings such as chrome plating or ceramic coatings to shield the steel from corrosive
environments.
Coatings must be defect-free to be effective.
3.Cathodic Protection :
Use electrochemical methods to reduce the steel’s electrochemical potential.
Anodic or cathodic protection systems can be employed to mitigate SCC risk.
2.7.5 Statistical Analysis and Theoretical Considerations
1.Weibull Analysis :
Weibull statistics are used to analyse failure data, offering insights into the reliability and
expected life span of maraging steel components under SCC conditions.The Weibull
distribution function F(t)=1−e^−(t/η)^β helps predict the probability of failure over time, where
t is the time to failure, η is the scale parameter, and β is the shape parameter.
2.Finite Element Modeling (FEM) :
FEM simulates the stress distribution and identifies potential SCC initiation sites in complex
geometries.
The model considers factors like load conditions, material properties, and environmental
exposure to predict SCC behaviour accurately.
3.Fracture Mechanics :
Applying fracture mechanics principles helps understand crack growth behaviour and predict
critical crack sizes.
The stress intensity factor K and the critical stress intensity factor KIC​ are crucial in
assessing the fracture toughness and SCC susceptibility of maraging steel.
2.7.6 Microstructural Considerations
Precipitation Hardening :
Maraging steel undergoes precipitation hardening where intermetallic compounds like Ni3Mo
and Fe2Mo precipitate during ageing, enhancing strength but potentially affecting SCC
resistance.
The distribution, size, and coherence of precipitates influence mechanical properties and
SCC behaviour.
Grain Boundary Effects :
Grain boundaries act as pathways for crack propagation, and their characteristics (e.g., size,
distribution) significantly affect SCC resistance.
Optimising grain boundary characteristics through controlled thermomechanical processing
can enhance SCC resistance.
2.7.7 Environmental Factors
Humidity and Temperature :
Higher humidity and temperature accelerate corrosion reactions, increasing the risk of SCC.
Understanding the environmental conditions in service is critical for predicting and mitigating
SCC.
Chemical Exposure :
Exposure to specific chemicals (e.g., chlorides, sulphides) can exacerbate SCC.
Protective measures should be tailored to the specific environmental conditions encountered
in service.
2.7.8 Conclusion
Understanding and mitigating SCC in maraging steel is crucial for the reliability and safety of
aerospace components. By addressing factors such as composition, heat treatment, and
surface finish, and employing rigorous testing and protection strategies, the aerospace
industry can enhance the performance and longevity of maraging steel structures. Future
research should focus on developing advanced alloys and coatings, as well as refining
predictive models for SCC.[2.7]
2.8 Spacecraft Design
Spacecraft design necessitates a meticulous approach to ensure functionality and longevity
in the harsh environment of space. Key design requirements include maintaining structural
integrity, efficient thermal control, and strategic material selection. This paper delves into
these aspects, addressing the challenges and potential solutions to achieve an optimal
design.
2.8.1 Structural Integrity
Design Requirements
Ensuring structural integrity is paramount for withstanding the stresses of launch, space
operations, and re-entry. The design must accommodate the following:
Mechanical Loads :
Forces experienced during launch, manoeuvres, and landing.
Vibration and Acoustic Loads : High-frequency vibrations during launch.
Micrometeoroid and Orbital Debris (MMOD) : Impact resistance against space debris.
Challenges and Solutions
Weight vs. Strength
Achieving a balance between minimising weight and maximising structural strength is
crucial. Lightweight materials such as titanium alloys and composites (e.g.
carbon-fibre-reinforced polymers) are preferred due to their high strength-to-weight ratios.
Calculations:
Assume a spacecraft mass m​and required strength σ:
Strength-to-Weight Ratio (SWR)=σ/m​
Maximising SWR involves selecting materials with high σ and low m​
2.8.2 Thermal Control
Design Requirements
Thermal control systems manage extreme temperature variations ranging from -150°C in the
shadow to +120°C in direct sunlight. Effective thermal management ensures the functionality
of onboard instruments and structural components
2.8.3 Thermal Expansion
Materials with low coefficients of thermal expansion (CTE) are essential to prevent structural
deformation. Materials such as Invar (a nickel-iron alloy) with a CTE close to zero are
preferred.
Thermal Stress Calculation:
ΔL=L⋅α⋅ΔT
Where ΔL is the change in length, L is the original length, α is the CTE, and ΔT is the
temperature change.
Design Requirements
Material selection involves choosing substances that provide strength, low weight, and
resistance to space environment effects such as radiation and atomic oxygen.
Challenges and Solutions
Radiation Resistance
Materials must withstand high levels of radiation without degradation. Polyimide-based
composites and aluminium alloys are effective due to their radiation resistance and
mechanical properties.
Radiation Shielding Calculation:
For a given thickness t and material density ρ, the radiation attenuation factor A can be
estimated using: A=e^−μt
Where μ is the linear attenuation coefficient, dependent on the material and type of radiation.
The interplay between structural integrity, thermal control, and material selection dictates the
spacecraft's overall performance. Advanced materials and engineering solutions play pivotal
roles in overcoming the challenges presented by the space environment. Future research
should focus on developing novel materials with enhanced properties to further optimise
spacecraft design.
2.8.4 Conclusion
Effective spacecraft design demands a comprehensive approach, balancing structural
integrity, thermal management, and material selection. By addressing the challenges of
weight vs. strength, thermal expansion, and radiation resistance, this paper provides a
foundation for developing robust, efficient spacecraft capable of enduring the rigours of
space exploration.[2.8]
2.9 Additional Images:
Different types of structural joints. (a) Flanged joint
(b) Merman Band joint (c) Riveted joint (d)Tongue and
groove joint
Isogrid construction
Monocoque structure
Closely stiffened structures
Composite
structural
compositions
Typical lay up of composite structures
FEM model and displacement
contour of a typical pressure
vessel (a) FEM model (b)
Displacement
Typical half model
Typical 3D – FEM model
FEM model for solid propellants
Stress contour of a typical structure
Buckled mode of a typical structure
Various steps in structural dynamic
characterization
Typical FEM models for dynamic analysis.
(a) Total beam model (b) Beam interstage
model (c) Beam + interstage propellant
tank shell model (d) Beam + detailed model
for base shroud (e) Propulsion stage
Mode shapes of a typical vehicle
Typical structural testing
3. PROPULSION SYSTEMS
3.1 What is PMD?
"PMD" commonly stands for "Propellant Management Device." The functions of a Propellant
Management Device include:
1. Propellant Distribution: Ensuring proper distribution of fuel and oxidizer within the
propellant tanks of a spacecraft or rocket, preventing uneven depletion and
maintaining stable performance.
2. Slosh Control: Minimising the effects of propellant sloshing during flight, which can
cause instability and affect the spacecraft's attitude control and trajectory.
3. Pressure Regulation: Managing the pressure of the propellants within the tanks to
optimise engine performance and prevent issues such as cavitation or gas ingestion.
4. Bubble Suppression: Preventing the formation and accumulation of gas bubbles
within the propellant system, which can disrupt flow and lead to engine or system
anomalies.
5. Thermal Management: Assisting in the control of propellant temperatures to prevent
freezing or boiling, which could affect the performance and reliability of the propulsion
system.
Overall, a Propellant Management Device plays a critical role in ensuring the safe and
efficient operation of propulsion systems in aerospace applications, particularly in spacecraft
and rockets.[3.1]
3.2 Propellant Management Device Overview and Functionality
Rocket Structure and Launch Process:
The robust structure of the rocket serves the dual purpose of providing structural integrity
and shielding against lightning strikes. The launch process involves several key stages:
a) Integration: Stacking the rocket stages and payload together.
b) Rollout: Transporting the rocket to the launch pad.
c) Fuelling: Loading the rocket with propellants.
d) Pre-launch checks: Verifying all systems and components are functioning properly.
e) Startup: Activating internal power sources and control systems.
f) Engine Ignition: Starting the engines and ensuring proper functionality.
g) Launch: Initiating the rocket's ascent into space.
Protection During Reentry:
During the spacecraft's return to Earth, additional protection such as silica ceramic tiles is
employed to withstand the intense heat generated during reentry into the atmosphere.
3.2.1 Structural and Performance Analysis:
Thorough stress and fracture mechanics analyses are conducted to design and assess the
tank shell's integrity, while stress and performance analyses are performed to evaluate the
Propellant Management Device (PMD).
3.2.2 Propellant Management for Manoeuvres:
Each HS 601 spacecraft relies on four tanks, two for monomethylhydrazine (MMH) fuel and
two for nitrogen tetroxide (NTO) oxidizer. These propellant tanks facilitate various
manoeuvres from booster separation to orbit deployment and maintenance, including final
ascent to a graveyard orbit.
3.2.3 PMD for Mission Success:
The PMD plays a crucial role in ensuring the responsible disposal of satellites, with reliability
being paramount for mission success and post-mission disposal. Specifically designed for
the HS 601 mission, the PMD facilitates critical operations such as ground launch, orbit
attainment, and de-orbit manoeuvres.
3.2.4 Functionality of PMD:
The PMD, typically situated inside a spacecraft's propellant tank, ensures the delivery of
vapour-free liquid propellant to the engine, critical in microgravity conditions where buoyancy
forces are negligible. Its design varies based on mission requirements, with some employing
free-floating devices within the tank while others utilise external magnetic coils. PMDs are
indispensable for maintaining engine functionality during manoeuvres and ignition in space.
The above figure is of a PMD.
The “bubble point” in the context of Propellant Management Devices (PMDs) for spacecraft
refers to the differential pressure at which the surface tension of the liquid propellant on a
screen within the PMD is overcome, allowing gas bubbles to pass through. [3.2]
3.3 Development to verification of a PMD and Propellant tank.
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Purpose: Propellant tank assembly designed to supply hydrazine fuel for spacecraft
thrusters.
Propellant Management Device (PMD): Utilised to ensure gas-free expulsion of
propellant upon demand in low gravity.
●
Function: PMD structure also responsible for controlling propellant centre-of-mass
during spacecraft manoeuvres.
The tank is mounted to the spacecraft via two polar bosses. The propellant boss has four
threaded holes for attaching a U-joint assembly, which in turn mounts the tank to the
spacecraft structure. The pressurant boss mounts on a slip joint bearing to accommodate
axial growth during pressurisation. These features aim to minimise membrane weight by
keeping spacecraft-induced loads out of the tank shell.[3.3]
3.4 PMD development
An extensive development program was initiated to determine and verify the characteristics
and structural integrity of the PMD. A full-scale PMD and a test propellant hemisphere were
fabricated and processed identically to flight hardware. These components were assembled
using production tooling. The PMD development unit closely resembles the flight tank
expulsion assembly, as depicted in Figure 3.
The PMD development test program was conducted in two distinct phases, which were
separated by an intermediary heat treatment cycle.
The development unit underwent a dry random vibration test before the heat treatment
process, lasting 60 seconds for acceptance testing and 180 seconds for qualification testing.
This comprehensive examination covered three axes: two lateral and one longitudinal,
ensuring a thorough analysis of the unit's response to vibrational forces. Accelerometers
diligently monitored both the energy input into the system and the corresponding response of
the specimen, while strain gauges were strategically placed on the PMD centre post to
gauge structural integrity. Essential criteria for the test encompassed preventing any contact
between the PMD vanes and the hemisphere wall, as well as meticulously maintaining
specified gap requirements throughout the testing period. The results of the assessment
revealed no instances of contact between the PMD vanes and the hemisphere wall, with the
gap between components remaining well within the specified parameters post-test.
Following a series of rigorous assessments, the unit progresses to the qualification
phase[3.4].
3.5 Propellant tank assembly fabrication
The propellant tank shell is crafted from two hemispheres and a centre section, all made
from 6AL-4V titanium alloy. These parts undergo a multi-step process including rough
machining, heat treatment, and partial ageing. Hemispheres start with a thickness of 0.56
inch, reduced to 0.032 inch in the final assembly, with extensive material removal during
machining. PMD components, such as a shaft and perforated plate, are welded onto the
propellant hemisphere, along with inlet and outlet tubes. The assembled PMD undergoes
vibration testing and cleaning before the tank is sealed. Two girth welds join the tank
components, which undergo a thorough inspection. Following closure, stress relief and final
machining are carried out before acceptance testing.
● Component-level random vibration test performed on the expulsion assembly before
tank closure to validate PMD workmanship.
● Acceptance level vibration spectrum applied for 60 seconds, ensuring dimensional
requirements are met before tank closure.
● Tank subjected to various acceptance tests before delivery, including volumetric
capacity, proof pressure, pressure drop, negative pressure, external leakage,
non-destructive examination (NDE), and cleanliness verification.
● Pressure testing temperature adjusted for worst-case operating temperature.
Expulsion Assembly Validation:
Before the tank is sealed, a component-level random vibration test is conducted on the
expulsion assembly to confirm the quality of the PMD craftsmanship. This meticulous
examination ensures that the expulsion assembly meets rigorous standards.
3.5.1 Vibration Spectrum Application:
The acceptance level vibration spectrum is meticulously applied to the expulsion assembly
for a duration of 60 seconds, guaranteeing that all dimensional requirements are
meticulously met prior to the final closure of the tank.
3.5.2 Comprehensive Tank Testing:
The tank undergoes a battery of acceptance tests to guarantee its integrity before delivery.
These tests include evaluations of volumetric capacity, proof pressure, pressure drop,
negative pressure, external leakage, non-destructive examination (NDE), and cleanliness
verification.
3.5.3 Temperature Adjustment for Pressure Testing:
During pressure testing, the temperature is precisely adjusted to simulate the worst-case
operating conditions, ensuring that the tank's performance is validated under the most
demanding circumstances.[3.5]
3.6 Each flight tank assembly undergoes a sequence of acceptance
tests before tank delivery.
1. Volumetric capacity examination: The volumetric capacity of the HS 601 propellant
tank is measured using the weight of the water method. Deionized (DI) water is used
to conduct this test. Each tank must have a minimum capacity of 22,450 in^3.
2. Proof Pressure Test: The propellant tank is pressurised to 325 psig for a minimum of
5 minutes for the proof pressure test. The test is conducted hydrostatically using DI
water.
3. Sinusoidal Vibration: The drained and dried propellant tank is subjected to
acceptance level sinusoidal vibration in each of the three principal axes. The sweep
rate is 4 octaves per minute. The sine input is not notched during acceptance testing.
The purpose of this test is to verify the PMD workmanship.
4. External Leak Test: The external leak test verifies the integrity of the tank shell. The
tank is placed in a vacuum chamber, evacuated to under 0.2 microns of mercury, and
helium pressurised to 255 psig for 30 minutes. The helium leak rate cannot exceed
1* 10^-8 std cc per second throughout the 30-minute test period.
5. Successful completion of these tests validates previous acceptance tests.
6. Non-Destructive Examinations:
Fracture-critical dye penetrant and radiographic inspections on tank shell and girth
weld, plus radiographic checks on PMD components after tests.
7. Final Examination:
Visual inspection post-testing, recording weight (max 28.9 lbs; typical HS 601 tank
26.6 lbs).
8. Cleanliness Verification:
Finally cleaned to the specified levels
9. Qualification Test Program Overview:
10. The HS 601 propellant tank underwent acceptance tests followed by a series of
qualification tests. PMD functional tests and radiographic inspections were conducted
intermittently to verify PMD integrity and performance, while external leak tests and
radiographic inspections ensured shell integrity.
3.6.1 Qualification Test Sequence:
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Acceptance tests
Dry sinusoidal vibration, qualification level
PMD bubble point test
Radiographic inspection of tank shell
Radiographic inspection of PMD
Wet random vibration
PMD bubble point test
External leakage
Radiographic inspection of tank shell
Radiographic inspection of PMD
Pressure cycle
External leakage
Acoustic test
PMD bubble point test
Radiographic inspection of tank shell
Radiographic inspection of PMD
Collapse pressure
External leakage
Dry sinusoidal vibration
PMD bubble point test
External leakage
Penetrant inspection of tank shell
Radiographic inspection of tank shell
Radiographic inspection of PMD
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Final examination
Burst pressure test
3.6.2 Dry Sinusoidal Vibration, Qualification Level:
●
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Setup similar to acceptance test but with strain gauges to measure axial and bending
strains.
Sweep rate: 2 oct/minute.
3.6.3 Random Vibration:
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●
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Setup identical to qualification level sinusoidal vibration test.
Duration: 3 minutes per axis.
Peak responses limited: 10 g for X and Y axes, 12 g for Z axis.
3.6.4 Pressure Cycles:
●
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Proof Pressure Cycles: 2 cycles from 0 to 325 to 0 psig.
Operating Pressure Cycles: 75 cycles from 0 to 260 to 0 psig.
3.6.5 Acoustic Test:
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Setup: Qualification Tank suspended vertically by an elastic cord from a mounting
assembly bolted to the propellant boss.
Environment: The test was conducted per specifications outlined in Table 8.
3.6.6 Collapse Pressure Test:
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Procedure: The tank was subjected to external pressure at ambient (14.7 psig) while
internal pressure was evacuated to 10.7 psig.
Duration: Pressure differential across tank shell maintained for 15 minutes.
Destructive burst: After the completion of all the qualification tests, the Qualification Tank
was subjected to a final destructive burst pressure test.The Qualification Tank burst at 555
psig, 165 psi (42%) over the design burst pressure of 390 psi.
3.7 PMD Verification
PMD Testing Challenges:
PMDs (Propellant Management Devices) are not typically ground testable due to designed
operation in or near "0 g" environment.
● Verification relies on analyses rather than direct testing.
● The most challenging task for PMD occurs near the end of the mission when tanks
are nearly depleted.
● Actual proof of PMD functionality is usually verified 10 to 15 years after launch.
HS 601 PROPELLANT TANK
● Robust design for simple ground handling and excellent performance during ascent
and in orbit.
● PMD is effective throughout mission phases, including end-of-life manoeuvres.
● Functionally one of the most complex PMDs built, relying on multiple components for
mission success.
● Modular design facilitates easy fabrication, assembly, and installation.
● Fabrication, testing, and delivery of HS 601 tank within ten months.
3.8 Additional important points related to propulsion
★
A propulsion system's efficiency and thrust output are intricately linked to the exit
temperature of its core. To optimise performance, engineers initially explored the
concept of a two-stage core design, aiming to elevate exit temperatures to their
maximum potential.
However, further analysis revealed a critical trade-off: while the two-stage core
promised heightened thermal output, the additional mass penalty incurred by its
implementation outweighed the benefits.
Remarkably, it became apparent that the increased mass of the core's second stage
posed a greater detriment to overall efficiency than the additional fuel required to
compensate for diminished performance.
This revelation underscored the complexity of optimising propulsion systems,
highlighting the importance of carefully balancing competing factors to achieve optimal
performance and efficiency.
★ For the Rocket Thrust Rocket (RTR) system, the choice of propellant is a critical
decision, and hydrogen emerges as the preferred option due to its superior specific
impulse compared to alternatives like ammonia or methane. This selection is pivotal
for maximising the system's efficiency and thrust capabilities.
★ A strategic approach is adopted to address the challenge of minimising the tank's
mass while ensuring adequate propellant storage. Liquid hydrogen is stored at a
relatively low pressure of 0.1 MPa within titanium tanks. However, to harness its full
potential during propulsion, the hydrogen is pressurised to over 4 MPa. This careful
balance between propellant choice, storage conditions, and pressurisation techniques
underscores the meticulous engineering efforts aimed at optimising the performance
and efficiency of the RTR system.
★ Liquid hydrogen, a vital part of spacecraft propulsion, is stored in a special tank made
of titanium alloy. Operating at regular atmospheric pressure and kept extremely cold at
around 20 Kelvin, this tank holds the hydrogen fuel. Its shape—a cylinder with a
rounded top and a space at the bottom—helps save space on the spacecraft. This
design reduces the spacecraft's overall size while maximising fuel storage.
★ Similarly, a tank for liquid xenon, also made of titanium, sits on top of the hydrogen
tank. It's shaped like a doughnut, fitting neatly into the spacecraft's structure, which
saves space and improves efficiency. Using titanium ensures these tanks are strong,
lightweight, and resistant to damage.
★ Common propellants are xenon and krypton.
3.9 VOCABULARY
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Thermal capacitor: It's a heat storage thing like a capacitor that stores the charge.
Cladding material: Cladding is a material that is attached to the exterior of a
building’s walls to form an outer weatherproof skin to the home.
Cladding is used to provide a degree of thermal insulation and weather resistance.
Compatibility: The state in which two things can be together without any conflicts.
Hastelloy: It is a super-alloy with very high corrosion resistance. It comprises nickel,
chromium, and molybdenum as the main constituent elements.
Along with corrosion resistance, Hastelloy metal has high-temperature resistance. It
is quite common in chemical and petrochemical industries, also used in aerospace
engineering, etc.
Embrittlement: In simple words, making the material more brittle.
Dual-mode propulsion system: It allows the satellite to operate in the most efficient
mode for the mission profile without the need for multiple independent propulsion
systems.
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Reliable: Consistently good in quality or performance; able to be trusted.
Hall thrusters: Hall thrusters utilise magnetic fields and electric fields to efficiently
accelerate ions, providing reliable and efficient propulsion for space missions.
Hall effect: This was discovered by Edwin Hall. This states that when an electric
current passes through a conductor placed in a magnetic field, the moving charge
carriers experience a force due to the magnetic field.
This force causes the charge carriers to accumulate at one side of the conductor
creating a potential difference perpendicular to the current flow.
MEV: The full form of MEV is a mission extension vehicle. These play a crucial role in
extending the lifetime of the satellites. There are categories, MEV-1 and MEV-2.
The first one services propulsion and altitude controls. The second takes care of the
fuel. These are docked with the initial satellites.
Umbilical: Connecting someone or something to a source of essential supplies.
Akin: similar or related.
Pylon: a structure on an aircraft wing used for supporting an engine or carrying a
weapon, fuel tank, or other load.
Fuselage: aircraft’s main body section.
Forging: It is a manufacturing process where the shaping of metals is done using
localised compressive forces.
Satellite thruster: It is a spacecraft propulsion device used for orbital station
keeping, altitude control, or long duration, low thrust acceleration often as a part of
the reaction control system.
Manoeuvre: a movement or series of moves requiring skill and care.
Robust: strong and healthy.
PMD: The full form of PMD is a Propellant management device. It is a crucial
compound in satellite propulsion systems.
Inferior: Lower in rank, status, or quality.
Psig: It stands for Pounds per Square Inch Gauge and is a unit of pressure defined
as the force exerted per unit area, measured relative to the atmospheric pressure.
It is a measure of gauge pressure, which means that it is measured relative to the
atmospheric pressure. In other words, PSIG means the pressure above atmospheric
pressure.
Octave: It is the interval between one pitch and another with double or half its
frequency.
Meaning of four octaves per minute: The term “ 4 octaves per minute “ in the context
of sinusoidal vibration refers to the rate at which the frequency of the vibration
increases or decreases during a test. This means that the vibration frequency will
double 4 times every minute.
Propellant boss: A "propellant boss" is a structural component of a spacecraft or
rocket where propellant tanks are mounted, providing support and stability during
launch and operation.
Hydrazine: Hydrazine is a colourless, highly flammable liquid with the chemical
formula N2H4. It consists of nitrogen and hydrogen atoms and has a strong
ammonia-like odour. It's commonly used as a rocket propellant due to its high energy
density and ability to combust rapidly with oxidizers. Additionally, it's utilised in
various industrial processes such as in the production of pharmaceuticals,
agricultural chemicals, and blowing agents for polymer foams. However, it's highly
toxic and must be handled with extreme caution.
●
PROPELLANT:A propellant in aerospace refers to the substance or mixture of
substances used to propel a spacecraft or aircraft. Propellants provide the necessary
thrust for propulsion by undergoing controlled combustion or other reaction
processes.
There are various types of propellants used in aerospace, including:
1. Liquid Propellants: These consist of liquid fuels and oxidizers stored separately and
mixed in a combustion chamber to produce thrust. Examples include liquid hydrogen
and liquid oxygen (used in the Space Shuttle), hypergolic propellants (such as
hydrazine and nitrogen tetroxide), and various combinations of hydrocarbons with
oxidizers like nitrogen tetroxide.
2. Solid Propellants: These are composed of a fuel and an oxidizer mixed in a solid
form. Solid propellants are often used in rocket boosters due to their simplicity,
reliability, and storability. Examples include the solid rocket boosters used on the
Space Shuttle and many military missiles.
3. Hybrid Propellants: These involve one component being in a solid state (usually the
fuel) and the other in a liquid or gaseous state (usually the oxidizer). Hybrid
propulsion systems offer advantages such as controllability and safety.
4. Electric Propulsion: In contrast to chemical propulsion, electric propulsion systems
use electrical energy to accelerate propellant ions to generate thrust. These systems
are typically used for long-duration missions, such as deep space probes.
The choice of propellant depends on various factors including mission requirements,
vehicle design, cost, safety considerations, and performance characteristics.
●
Deionized water: Deionized water is purified, with mineral ions removed, Through a
process called deionization, it's honed.
Used widely in labs, industries, and more,
Its purity ensures experiments and processes soar.
4.Science of materials
After determining the most loaded and, as a result, the weakest parts of the nanosatellite
body during the electromagnetic launch, we need to consider these parts in detail and take
into account the impact of the quasi-stationary concentrated stream of protons through a
selected volume surface. The volume selection is dictated by the available computer
operating memory and speed, as well as by the character of the stress-strain state in a given
area. With the memory and performance level limited, all available resources must be used
to the full. We can conveniently assume the selected volume to have a parallelepiped form.
The following parameters appear to be most realistic: 140 mm length, 100 mm width and 5
mm thickness. The material isOT4alloy.
4.1 Impact of finite element model specifics on the structural
analysis of CubeSats
CubeSats have a relatively short development cycle, typically ranging from 1 to 2 years,
compared to conventional satellites which may require up to 5 years. These small satellites
are built in standardised dimensions known as units (U), with each unit measuring 10 cm ×
10 cm × 11.3 cm, and generally weighing less than 1.33 kg per unit.
Various grades of aluminium are utilised for the structural components of CubeSats due to
their high strength and low density. Adhering to structural subsystem requirements and
mechanical design specifications is crucial for CubeSats to endure the rigorous conditions of
rocket launches and to function effectively once deployed.
4.2 Material properties
For any structural analysis, defining the density, Young’s modulus, and Poisson’s ratio is
essential. The mechanical properties of Aluminum-6061 were selected for the frames and
ribs of the supporting structure, as well as for the six outer panels. Stainless Steel-304 was
chosen for spacers and screws. An innovative method was used to define the subsystem
shells to closely mimic the actual material distribution on each board. The shells were
divided into areas of higher and lower densities. The total area of each section was
calculated and multiplied by the defined thickness of the shell's profile. The section with the
lower density was assigned the properties of FR4, the material used in printed circuit boards.
The higher density area received a unique density, calculated using the subsystem's mass
from datasheets and the section's calculated volume. Both sections were given the elastic
properties of FR4, as it is predominant in both areas.Additionally, since the model includes
2D shells and beams, Abaqus required the definition of corresponding profiles. For the shell
elements, the thickness was matched to the actual board’s thickness. The subsystem boards
were given a profile thickness of 1.6 mm, side panels 3 mm, and the top and bottom panels
5 mm. For the beam elements, all were assigned a circular profile with varying radii: 1.3 mm
for structural screws, 1 mm for camera screws, and 2.25 mm for spacers. Figure 4 displays
the material view of the simplified FE model.
4.3 Influence of Pre- and Post-Weld Heat Treatment
Microstructure
Evolution
and
Mechanical
Properties
0.3%C-CrMoV (ESR) High-Strength Low-Alloy Steel
on
of
0.3%C-CrMoV, a medium-carbon high-strength low-alloy steel, is suggested for use in
manufacturing rocket motor cases for satellite launch vehicles. The fabrication of motor
cases employs gas tungsten arc welding (GTAW). Welding in the annealed condition,
followed by post-weld heat treatment (PWHT), achieved nearly 100% weld efficiency in
terms of tensile strength and approximately 90% weld efficiency in fracture toughness
compared to the quench and tempered mechanical properties of the parent metal.
Martensitic stainless steels are widely used in the aerospace industry owing to their
good combination of high specific strength, moderate corrosion resistance and good
weldability. Depending upon the stability of austenite at room temperature, these steels are
classified as martensitic, semi-austenitic and austenitic grades
5.References
[1.1-1.3]Orbital stability of Earth Trojans
[1.4]From the launch of the first satellite to the global problem of space debris
[1.5].Multi-Objective Path Optimization of a Satellite for Multiple Active Space Debris
Removal Based on a Method for the Travelling Serviceman Problem
[2.1]Sharjah-Sat-1 Structural Design and Analysis
[2.2]Axial stiffness analysis of clamp band system
[2.3]Evolutionary algorithm use in optimisation of a launch vehicle stack model
[2.4]On acquiring and analysing satellite Sine vibration test data
[2.5] Proposing nodal position finite element method applicable to modelling of new space
materials
[2.6]Stress corrosion cracking of high strength 18Ni-8Co-5Mo maraging steel fasteners
[2.7]Stress Corrosion Cracking of a Maraging Steel Shear Bolt Used in the Interstage
Structure of a Satellite Launch Vehicle
[2.8]Deployment analysis of composite thin-walled lenticular tubes with effect of storage time
and temperature
[3.1]Integrated planetary exploration using bimodal radioisotope power and propulsion
[3.2]Design, development, qualification, and manufacture of the HS 601 propellant tank
[3.3]Design, development, qualification, and manufacture of the HS 601 propellant tank
[3.4]Orbital express propellant resupply servicing
[3.5]Design and simulation of a tether boost facility for LEO ⇒ GTO transport
[4] The behaviour of nanosatellite body materials during electromagnetic launch To cite this
article: Yu V Gerasimov et al 2017 J. Phys.: Conf. Ser. 918 012044