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1
Design and Numerical Investigation of a
Hypersonic Waverider based Entry, Descent,
and Landing Architecture Assisted by
Supersonic Retro-Propulsion
Debdoot Ghosh
*
and Hideaki Ogawa
†
Vellore Institute of Technology (VIT), Vellore, 632014, India1
Kyushu University, Fukuoka, 819-0395, Japan2
Developing new technology for descent and soft landing of the future crewed and robotic entry, descent,
and landing (EDL) mission of high ballistic coefficient is an urgent necessity. In this paper, a new lifting body
architecture is defined, namely a hypersonic waverider capable of deceleration using supersonic retro-
propulsion (SRP) with multiple nozzles. Aerodynamic performance and flowfields are numerically investigated
using RANS-based computational simulation. Based on the preliminary aerodynamic characteristics obtained
from the numerical analysis, an optimized entry trajectory for the maximum cross-range is obtained by
employing the Hermite-Simpson direct collocation method. The SRP performance is evaluated based on the
drag augmentation and pitching moment variations at different throttling conditions. Overall, the results
obtained demonstrate advantages and improvements offered by the proposed system over conventional multi-
peripheral conical aeroshell design.
I. Nomenclature
A
=
reference area
β
=
ballistic coefficient
CD
=
coefficient of drag
CP
=
coefficient of pressure
D
=
drag
E
=
energy distribution
g
=
acceleration due to gravity
h
=
altitude
L
=
lift
M
=
Mach number
r
=
radius of Mars
ρ
=
density
PS
=
jet static pressure
PT
=
jet total pressure
Φ
=
longitude
γ
=
flight path angle
v
=
velocity
θ
=
latitude
ψ
=
azimuth
*
Undergraduate Student, School of Mechanical Engineering, AIAA Student Member.
†
Associate Professor, Department of Aeronautics and Astronautics, AIAA Member.
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26th AIAA Aerodynamic Decelerator Systems Technology Conference
May 16-19, 2022, Toulouse, FRANCE 10.2514/6.2022-2734
Copyright © 2022 by Debdoot Ghosh and Hideaki Ogawa. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
Aerodynamic Decelerator Systems Technology Conferences
2
II. Introduction
The Entry, Descent, and Landing (EDL) approach uses drag created by the body or aerodynamic drag generators
such as improved parachutes or inflatable aerodynamic decelerators (IADs) to decelerate the body from hypersonic or
supersonic speeds to subsonic speeds for soft landing. These technologies, however, are not suitable for the safe
landing of payloads with high ballistic coefficients through an environment. The ballistic coefficient of a body is
determined by Eq. (1) [1], which quantifies the amount of aerodynamic drag required to decelerate the vehicle upon
entry.
(1)
Figure 1 Previous EDL missions to Mars trajectory (adopted from [2])
If all other variables remain constant, larger ballistic coefficients result in deeper penetration into the atmosphere
before decelerating and consequently high velocities during parachute release, as shown in Fig. 1. For example, while
both the Mars Exploration Rover (MER) and the Curiosity Rover, which are part of the Mars Science Laboratory
(MSL) mission, began falling from the same velocity at the entry interface, Curiosity penetrated far deeper into the
atmosphere due to its greater ballistic coefficient. Parachutes, airbags, sky cranes, and other innovative technologies
are also being employed to safely land these advanced payloads; nevertheless, their application is still confined to a
short portion of the terminal velocity phase, as shown in Fig. 1. As a result, it is plausible to expect that for a future
robotic or crewed mission with a , the vehicles will not attain terminal velocity, rendering these
convectional approaches impractical.
In light of this, lift-based landing systems such as waveriders [3–8] and propulsive deceleration systems using
supersonic retro-propulsion (SRP) [9–14] are attracting increasing attention as viable candidates for future high
ballistic Mars missions. A waverider is a type of hypersonic aircraft that enhances its supersonic lift-to-drag ratio by
utilizing the shock waves created by its own flight over a lifting surface. Several studies have been conducted to
investigate the suitability of waverider-type setups for missions to planets other than Earth. Anderson et al. [6]
developed waveriders that might be used on Earth, Venus, Mars, and Jupiter. On the other hand, SRP, a relatively new
EDL technique, descent necessitates the use of engine thrust to reduce a lander from supersonic to subsonic speeds by
increasing overall drag. The primary benefits of SRP include a reduction in design complexity due to the use of fewer
aerodynamic decelerators and vehicle transitions Edquist et al. [15]. Other advantages include increased flexibility
and the capacity to land higher cargo weights.
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Figure 2 Waverider hypersonic entry trajectory to supersonic descent process
In this study, taking advantage of these two advanced technologies, a hypersonic waverider capable of executing
SRP with multiple nozzles is proposed, and its characteristics and performance are numerically analyzed using RANS
(Reynolds-averaged Navier–Stokes) based computational fluid dynamics (CFD) simulation.
Fig. 2., shows an overview of the descent process of the waverider. The trajectory consists of five different phases:
Hypersonic Entry Phase, Hypersonic Gliding Phase, Supersonic Retro-Propulsion, Subsonic Retro-Propulsion, and
Freefall to Touchdown. The Hypersonic Entry Phase happens at an altitude above 125km at . In this
stage, the vehicle utilizes its drag to sufficiently reduce its velocity. Also, it keeps thermal loads in check and prepares
for the next descent phase. During the Hypersonic Gliding Phase, descending from about 75km altitude at
, the waverider employs aerodynamic lift to glide and maneuver in the upper atmosphere. It helps the waverider to
reach near a landing location and reduces its velocity to supersonic. Followed by the gliding stage, during Supersonic
Retro-Propulsion (SRP) at , it starts its retro engines to generate thrust in its opposite direction of motion
to further reduce its velocity to subsonic. Continuing the retro-propulsion process at subsonic speeds, the vehicle
reaches its freefall velocity and is ready to touchdown at a predefined location. In the current study, for the hypersonic
stages – Hypersonic Entry Phase and Hypersonic Gliding Phase – Hermite-Simpson direct collocation method, based
on aerodynamic characteristics of the waverider, is used to obtain an optimized trajectory for maximum cross-range.
For the Supersonic Retro-Propulsion (SRP) process, different differential throttling effects and the study of variations
in total axial force coefficient, coefficient of moment, thrust pitching angle, and drag augmentation are used to
establish its effectiveness during the descent process.
III. Geometric Design
A. Hypersonic Stage:
The conical waverider is designed for the hypersonic entry stage, as displayed in Fig. 3. To design the waverider,
the Taylor-Maccoll equation [16] given in Eq. (2) is solved numerically to obtain the hypersonic airflow around the
cone for conical flow. In this study, the fourth-order Runge-Kutta numerical integration method is used to solve the
equation (2).
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(a) Conical waverider design method [17]
(b) Waverider used in the present study
Figure 3 Waverider design
(2)
where is the critical speed of sound of freestream, is the total temperature, and is the specific heat ratio.
(3)
(4)
(5)
Figure 3 (a) depicts a schematic representation of a generating cone-derived waverider from a given conical
flowfield, where is the half-angle of the basic cone, is the angle of the shock wave, and is the angle measured
from the generating cone’s axis to the region of interest in the flowfield. The upper surface is produced by following
the trailing edge inversely to meet the conical shock surface, while the compression surface is made by tracing the
streamlines backward to intersect the base plane. The z-axis represents the inflow direction, whereas the x-axis is
perpendicular to the z-axis and points downward in the symmetry in this study. The y axis corresponds to the spanwise
direction.
B. Supersonic stage
Three linearly placed retro nozzles are considered along the mid-plane of the waverider to perform the SRP, see Fig.
4. Three nozzles are considered to achieve a high coefficient of thrust () and perform differential throttling.
Thrust () coefficient is given by:
(6)
Where, T is the thrust generated by each nozzle and is the freestream dynamic pressure.
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Figure 4 Waverider three retro-nozzles configuration for SRP phase
IV. Numerical Scheme
Steady-state three-dimensional CFD simulations are performed to analyze the aerodynamic characteristics and
performance. To solve the governing equations, mathematically defined polyhedral volumes are used for the
computational mesh. The main advantage of a polyhedral mesh is that each individual cell has a large number of
neighboring, allowing for the accurate calculation of gradients. Polyhedrons are also less susceptible to stretching than
tetrahedrons, resulting in enhanced mesh quality and numerical stability. Furthermore, due to mass interchange across
multiple faces, numerical diffusion is decreased, which enables the acquisition of precise solutions with a lower cell
count. The computational mesh comprises 188,739 cells and 207,612 cells for the hypersonic and SRP stages,
respectively, as shown in Fig. 5.
(a) Mesh used for hypersonic stage
simulation
(b) Mesh used for supersonic stage
simulation
Figure 5 Computational mesh used for (a) Hypersonic Stage (b) Supersonic Stage - SRP
A density-based solver along with an advection upstream splitting method (AUSM) is employed to approximate
the flux functions. Second-order upwind and first-order implicit Euler schemes are used for spatial and temporal
discretization, respectively. Two-equation shear stress transport (SST) k-ω model is adopted for turbulence modeling
because of its ability to predict accurately the near-wall and far-wall regions. The numerical setup has been verified
in comparison with experimental data in Fig. 6 for the hypersonic waverider with ref. [18] and supersonic retro-
propulsion with ref. [19].
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(a) Hypersonic waverider
(b) Supersonic Retro-Propulsion
Figure 6 Validation of numerical simulation in comparison with experiment [18,19]
The transport equations [20] that defines the SST k- turbulence model are:
Turbulent kinetic energy:
(7)
Specific Dissipation Rate:
(8)
The closure coefficients and auxiliary relations are given by:
The production term is given by
The function blends the k-ω and k-ε turbulence models as follows:
(9)
The cells with the values of and are solved for the and model equations, respectively. The
smooth transition between these models is achieved by the function’s hyperbolic nature, expressed as
where is the distance to the nearest wall and is the positive portion of the cross-diffusion term given by
is an addition to blending equations together, it also blends the empirical constants of the turbulence models by the
linear interpolation given by the following equation:
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
-10 0 10 20 30 40
L/D
Angle of Attack, α°
Numerical
Experimental
-0.25
-0.2
-0.15
-0.1
-0.05
0
-0.5 0 0.5 1
Cp
r/R
Experimental
Numerical
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(10)
(11)
Where,
It has been reported that the SST turbulence model overpredicts the viscosity near the wall where the shear
stress is more using the relation
, and so a viscosity limiter is used to limit the value of viscosity,
depending on the value of the product , where is another blending hyperbolic function that facilitates gradual
change of viscosity, depending on the distance from the wall .
V. Results - Hypersonic Stage
A. Preliminary aerodynamic performance
The aerodynamic performance of the waverider is evaluated by varying angle of attack at Mach 10 flight
condition at and . Linear regression and quadratic regressions, given in Eq. (12) and Eq.
(13) are calculated for and variations, respectively, used for trajectory optimization discussed in the following
sections.
(a) Lift coefficient
(b) Drag coefficient
Figure 7 Variations of aerodynamic coefficients with angle of attack
It can be observed from the above plots that there is an abrupt change in the magnitude of aerodynamic coefficients
from . To probe into this behavior, the wall shear stress distributions along the midplane of the waverider for
are plotted in Fig. 7. In Fig. 8, wall shear stress plot depicts a similar trend, from which it can be inferred
that the tangential force exerted by the friction between the flow and body is higher for a lower non-zero angle of
attack.
Figure 8 Wall shear stress distributions with the angle of attack
Regression equations obtained from the and variations are as follows:
(12)
-1
0
1
2
3
020 40 60 80
CL
Angle of Attack ()
0
1
2
3
020 40 60 80
CD
Angle of Attack ()
-10000
0
10000
20000
30000
40000
50000
60000
70000
80000
-4 -2 0 2 4 6 8 10
Wall shear stress, Pa
Distance from nose, m
0-deg
10-deg
20-deg
30 deg
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(13)
Figure 9 Aerodynamic phenomena around the hypersonic stage
B. Trajectory
The Hermite-Simpson direct collocation method [21] is employed to optimize the trajectory for maximum cross
range based on the lift coefficient CL approximated by Eq. (12) and the drag coefficient CD by Eq. (13) in the Martian
atmosphere, such that are the control variables. Here, the cross-range is defined equivalent to
maximizing the final latitude.
(14)
In direct collocation the trajectory optimization is discretized and converted into a non-linear program (NLP) as
represented by Eq. (14) and the following relations:
The collocation or transcription process comprises discretization of time, choosing an initial guess, creating an
augmented state, calculating the constraints, solving the NLP, and interpolation.
The Simpson approximation is defined for a generic integral as:
(15)
where
is the midpoint of the interval.
With the Hermite-Simpson method the midpoints of the intervals to get second-order approximation as:
(16)
The integral form of the cost function is approximated as:
(17)
with
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Figure 10 Representation of exemplary trajectory for maximum cross range [21]
The 3-DOF (degree of freedom) equations of motion are expressed by
(18)
(19)
(20)
(21)
(22)
(23)
The dynamic pressure is constrained by
(24)
For reference, the aerodynamic and atmospheric forces on the vehicle are given by the following relations (English
units):
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Figure 9 Schematic of association of different terms with waverider's motion and trajectory, adapted from
[22]
The entry trajectory begins at an altitude where the aerodynamic forces are quite small with a weight of
(Ib) and mass slug , where . The initial conditions are as follows:
The final point on the entry trajectory occurs at a time (unknown a priori), which is defined by the conditions
(a) Angle of attack
(b) Bank angle
0
20
40
60
80
0 200 400 600 800 1000 1200 1400
Angle of attack, α°
Time, s
-100
-50
0
50 0 200 400 600 800 1000 1200 1400
Bank angle, β°
Time, s
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(c) Velocity
(d) Flightpath angle
(e) Latitude
(f) Longitude
0
2
4
6
8
0 200 400 600 800 1000 1200 1400
Velocity, 1000 m/s
Time. s
-20
-10
0
10
20
0 200 400 600 800 1000 1200 1400
Flight path angle,
γ°
Time, s
-20
0
20
40
60
80
0 200 400 600 800 1000 1200 1400
Latitude, θ°
Time, s
0
5
10
15
20
25
30
0 200 400 600 800 1000 1200 1400
Longitude, Φ°
Time, s
0
0.5
1
1.5
0 200 400 600 800 1000 1200 1400
Altitude, 100,000 m
Time, s
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(g) Altitude
(h) Azimuth
Figure 11 Waverider entry state variable variations with elapsed time for optimized trajectory
To travel along the obtained optimum trajectory, the time required to decelerate to a suitable velocity of 620 m/s
at a suitable altitude of 15 km to perform the SRP process is found to be 1,400 seconds or 23.33 minutes. It can be
seen that the trajectory is overall smooth with some ripples at the beginning until the first 400 seconds see Fig. 11.
C. Aerodynamic performance of the waverider along the obtained trajectory
The following Martian atmospheric model
‡
is chosen to examine the aerodynamic performance, see Table 1, of
the waverider following the obtained trajectory:
(25)
(26)
(27)
Table 1 Time elapsed, vehicle attitude, aerodynamic performance, and freestream conditions along the
optimum trajectory
Time
elapsed
(min)
Angle of
attack
)
Bank
angle
)
Pressure
freestream,
kPa
Mach No.
freestream,
)
Temperature
freestream
(), K
Lift
coefficient
(
Drag
coefficie
nt ()
L/D
ratio
0
31.85
86.73
0.01
40.43
-27.06
0.0911
0.1257
0.725
200
22.54
28.43
12.87
37.59
151.07
0.4233
0.3306
1.281
400
17.30
12.33
21.15
31.68
163.31
0.4241
0.2625
1.615
600
16.14
4.02
29.01
26.46
171.11
0.4404
0.2731
1.613
800
16
0.97
38.90
20.97
178.34
0.4133
0.2412
1.713
1000
16
0.274
54.572
15.582
186.69
0.4132
0.2412
1.713
1200
15.85
0.3
85.702
10.099
197.83
0.4096
0.2377
1.723
1400
13.09
0.145
184.596
5.471
216.75
0.3552
0.1855
1.915
VI. Results - Supersonic Stage
To examine the effectiveness of the linearly placed muti-jet SRP process, quantities such as total axial force
coefficient, coefficient of moment, thrust pitching angle, and drag augmentation are calculated for different throttling
conditions at Pa and , is represented in Fig. 12.
‡
NASA. (n.d.). Mars atmosphere model - metric units. NASA. Retrieved April 9, 2022, from
https://www.grc.nasa.gov/www/k-12/airplane/atmosmrm.html
0
20
40
60
80
100
0 200 400 600 800 1000 1200 1400
Azimuth, ψ
Time, s
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Figure 12 Deception of different SRP throttling cases, where PT and PS are jet total pressure and static
pressure, respectively, measured in psi
1. Evaluation of Total Axial force coefficient and coefficient of moment:
The variations of and with the angle of attacks, , for different throttling cases are plotted in Fig. 13. It
can be seen there are abrupt increments in and magnitudes at and . To investigate the
reason behind these increments, the thrust pitching angle is calculated at these angles of attack.
The forebody axial force coefficient is
(28)
where thrust coefficient is
The total axial and force coefficient is given by
(for 3 engines)
(29)
(a) Total axial force coefficient
1.07
1.08
1.09
1.1
1.11
1.12
1.13
1.14
1.15
-70 -50 -30 -10 10 30 50 70
Total axial force
coefficient, CAT
Angle of Attack, α°
Case 1
Case 2
Case 3
Case 4
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(b) Coefficient of moment
Figure 13 Variation of coefficients with angle of attack.
2. Evaluation of thrust pitching angle:
To evaluate the performance, the thrust pitching angle is considered based on the momentum ratio in the fluidic
thrust vectoring (FTV) nozzle in the vertical direction to the axial direction [23].
(30)
(31)
The thrust pitching angle is given by
where is and are the x- and y-component of force, respectively,
is density, u and v are the x- and y-component
of velocity, respectively, p is the static pressure of cells in the x direction, is the freestream pressure, and A is the
nozzle exit area.
(a) 45°
(b) 15°
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
-70 -50 -30 -10 10 30 50 70
Co-efficient of Moment, Cm
Angle of Attack, α°
Case 1 Case 2 Case 3 Case 4 Case 5 case 6 No Throtlling
-4
-2
0
2
4
6
8
10
135
Thrust pitching angle δ,°
Cases
Tail Middle Nose
9
9.5
10
10.5
11
11.5
12
12.5
13
13.5
135
Thrust pitching angle δ, °
Cases
Tail Middle Nose
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(c) 5°
(d) Combined representation of thrust pitching
angle for different cases
Figure 14 Evaluation of thrust pitching angle at various angles of attack at (a) 45°, (b) 15°, (c)
5°, and (d) Combined representation of thrust pitching angle for different cases
(a) No throttling
(b) Case 1
(c) Case 2
(d) Case 3
(e) Case 4
(f) Case 5
-60
-50
-40
-30
-20
-10
0
10
20
123456
Thrust pitching angle δ, °
Cases
Tail Middle Nose
-80
-60
-40
-20
0
20
40
Thrust pitching angle δ, °
Cases
CASE 1 CASE 2 CASE 3
CASE 4 CASE 5 CASE 6
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(g) Case 6
(h) for case 4
(i) for case 4
(j) at for no throttling case
Figure 15 Multi-jet interaction of SRP flowfields for different cases at for (a) no throttling, (b) case
1, (c) case 2, (d) case 3, (e) case 4, (f) case 5, (g) case 6; (h) , (i) for case 4 and (j)
It can be seen from the various contour plots of multi-jet flow interaction (Fig.15) at different throttling conditions
that the flowfield is subject to the Coandă effect, which refers to a fluid’s tendency to adhere to a curved wall due to
lower pressure induced by high velocities. The convex wall curvature of the waverider causes the centrifugal forces
to take over and operate in the opposite direction as the pressure forces. As the jet exits from the nozzle, the pressure
in the contact zone with the curved wall rises until it reaches the ambient pressure. The jet detaches when the pressure
has reached the value of the pressure force and centrifugal force [24]. This phenomenon accounts for the tendency of
the jet plumes to flow towards the wall of the waverider body according to local pressure gradients.
3. Drag augmentation:
Drag is a critical factor responsible for sufficient reduction of the waverider’s velocity to a safe level before
landing. In order to quantify the effectiveness, the drag augmentation factor for the vehicle is calculated using the
following equation:
(32)
where is the drag generated by the body at no throttling condition, , and at .
The study of drag augmentation is crucial, as it imperative that any increase in deceleration by drag reduces the
thrust requirements of SRP, saving propellant mass and increasing payload mass.
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The geometry of supersonic plumes is comparable to that of "hard" geometry [25]. A bow shock system forms
around the effective body of the waverider when the plumes penetrate the supersonic freestream, wrapping around the
jet plumes. As a result of the post-shock pressure rise, the bow shock is a primary decelerative physical mechanism;
nevertheless, stagnation losses caused by this shock substantially diminish the maximum recoverable pressure on the
body, severely limiting the capacity for creating huge quantities of drag [19]. However, in this new design, the
following plots indicate positive drag augmentation for all cases except few instances in case number 1, demonstrating
notable effectiveness of SRP for soft landing of the vehicle.
(a) Case 1
(b) Case 2
(c) Case 3
(d) Case 4
(e) Case 5
(f) Case 6
Figure 16 Drag augmentation for different angle of attacks for (a) Case 1, (b) Case 2, (c) Case 3, (d) Case 4,
(e) Case 5, (f) Case 6
VII. Conclusion
This paper has presented the results of a numerical investigation for a new landing architecture for descent and
soft landing on the Martian surface. Upon hypersonic entry, it glides through the Martian atmosphere until reaches a
suitable velocity and altitude for supersonic retro propulsion (SRP) through an optimized trajectory. The Hermite-
Simpson direct collocation method based on aerodynamic characteristics of the waverider is used to determine the
optimum trajectory for maximum cross range.
0
2
4
6
8
10
12
14
-70 -20 30 80
Drag Augmentation
Angle of Attack (α°)
0
2
4
6
8
10
12
14
-70 -20 30 80
Drag Augumentation
Angle of Attack (α°)
0
5
10
15
20
25
-60 -10 40 90
Drag Augumentation
Angle of Attack (α°)
0
5
10
15
20
-80 -30 20
Drag Augumentation
Angle of Attack (α°)
0
2
4
6
8
10
12
14
-80 -30 20 70
Drag Augumentation
Angle of Attack (α°)
0
2
4
6
8
10
12
14
-100 -50 0 50 100
Drag Augumentation
Angle of Attack (α°)
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It has been found that it takes 23.3 seconds for the waverider to reach a suitable velocity to perform SRP. This will
not only help the waverider to undergo lower thermal loads but also provide a provision for performing exploratory
studies of the Martian atmosphere. The SRP system is designed comprising three linearly placed retro nozzles. Its
effectiveness during the descent process is determined based on different differential throttling effects and the study
of the variations of total axial force coefficient, coefficient of moment, thrust pitching angle, and drag augmentation.
Overall, the results are indicative of favorable performance and flexibility of the proposed architecture to realize
successful soft landing of high ballistic payloads on the Martian.
References
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Mars Entry Systems.” Journal of Spacecraft and Rockets, Vol. 47, No. 5, 2010, pp. 836–848.
https://doi.org/10.2514/1.49803.
[2] Ghosh, D., and Gunasekaran, H. “Large Eddy Simulation (LES) of Aerospike Nozzle Assisted Supersonic
Retro-Propulsion (SRP).” AIAA AVIATION 2021 FORUM, 2021. https://doi.org/10.2514/6.2021-2489.
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