EDL SEEDS VII

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Mission MILESTONE
EDL system design
Contact:
Prepared by:
Alberto FERRERO,
Gerard MORENO-TORRES BERTRAN,
Marco VOLPONI

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ENTRY, DESCENT AND LANDING (EDL)
o DESCENT CONSTRAINTS
In order to design the descend system it was necessary to take into consideration the constraints given by
other systems of the mission. The goal is to land onto the Martian surface a maximum weight of 30 tons. Also,
the total mass that would be launched from Earth cannot exceed 45 tons, meaning that the total mass of the
entry, descent and landing system must be smaller than 15 tons.
Moreover, considering the maximum volume capable to be delivered on Mars, i.e. using the SLS IIB fairing, a
further constraint on the dimensions can be considered. The EDL system (EDLS) has to fit in a cylindrical volume
of 19 m of length and 8.5 m of diameter.
1.1 EDL ARCHITECTURE
1.1.1 General Approach
Although several configurations were taken into consideration, the general approach always contains the
following steps:
- Making a Hohmann transfer from low Mars orbit to an even lower orbit, where atmospheric drag
would start the aerobraking process.
- Using an inflatable structure to increase the drag and therefore the efficiency of the aerobraking. For
this phase it is assumed that the angle between the direction of nose and the velocity vector is zero, or
in other words, that the angle of attack is zero. This can be achieved using retrorockets.
- Ejecting the TPS using springs, since they provide a simple and reliable solution for separating the
stages.
- Using retrorockets to slow down the module for the last part of the process. This is divided in two
phases. First, a more powerful retrorocket is used to completely halt the module. Subsequently,
smaller retrorockets are used to land vertically, and to control the orientation of the module.
- For the last step of the landing, it is necessary to take into consideration the unavoidable damage that
the ground will suffer due to the retrorockets. In order to ensure a safe touchdown, the module will be
granted an impulse in the horizontal direction at a certain altitude that will be optimized with a
python™ script. Then, as the module falls, wheels with be deployed. This way, the module will fly away
from the damaged ground. The wheels will have to provide a sufficiently large surface that the ground
does not crumble under the force of the impact. This force will be softened by shock absorbers.
Figure 1 shows a schematic view of the different systems of the EDLS. The external shell has to fit in the volume
constraints given by the launcher and it has to accommodate the module and the other systems related to the
descent phase. For the propelled phases, the modules are equipped with primary and secondary thrusters.
Finally for the touchdown, a landing device is activated.

Figure 1 - General Entry, Descent, Landing, sub-systems
1.1.2 EDL System Overview
Several architectures were considered. The key features are:
- Using inflatable structures: these structures will allow the aerobraking phase to be more efficient,
reducing the amount of fuel needed by the retrorockets without the need to carry a large volume from
Earth.
- Using heat shields: the heat shield will protect the module in the phase where the heat produced by
the entry is greatest and could possibly damage the structure and the payload.
- Using retro rockets: these will allow to decelerate in the later phases of the descent. Also, they will
allow orientation the model, not only to land in with the appropriate angle but also to avoid lift forces
during the descent.
- Using stages: the different stages are planned to optimize the resources that the EDL system has. For
higher altitudes, it is more efficient to use aerobraking manoeuvres whilst for lower altitudes it
becomes necessary to use retrorockets.
- Using a touchdown system: this system will have to support the impact of the touchdown when the
module finally reaches the ground. The touchdown system will also have to ensure that the pressure it
applies on the ground is lower than the bearing capacity of the landing site.

1.1.3 Entry, Descent and Landing Architectures
Figure 2 - EDL apporaches for large payloads
As can be seen in Figure 2, five different descent architectures were chosen for the trade-off. Although the
schemes for each of the configurations are similar, each of the parameters (altitudes, thrusts, inflatable radius)
are different for each case, in order to optimize each architecture.
1. Immediately after the entrance in the atmosphere, the rigid shell is ejected and the main engine is
turned on. The propelled descent is performed up to few hundred meters from the surface, where the
module is hovering; then the main engine is ejected and a vertical descent takes place with the

secondary thrusters. Just above the surface, the touchdown system is activated in order to guarantee a
non-destructive landing.
2. This configuration is similar to the previous one, except for that it uses the rigid external shell to
produce aerobraking before ejecting it and starting the main engine.
3. The third configuration also uses aerobraking, but in order to increase the efficiency a hypersonic
inflatable aerodynamic decelerator (HIAD) is deployed as the module falls. The HIAD is jettisoned
together with the external shell.
4. In the Configuration 4, the HIAD is already inflated by the time the module reaches the 100 km orbit,
increasing the aerobraking efficiency.
5. Configuration 5 differs to Configuration 4 only in the fact that the module would carry a second
inflatable to increase the aerobraking efficiency. The first HIAD would be unpacked when the descent
starts, while the second one is deployed during the process. Both HIADs are jettisoned together with
the external shield.
1.2 MATHEMATICAL MODEL
A mathematical model was created to calculate the mass of the descent system and the trajectory of the
module. The model is capable of evaluating the total mass required by the EDL system in order to land on the
Martian surface the modules of MILESTONE, which was essential to evaluate the trade-off.
1.2.1 Physics of the EDL
The crew is arriving on the Low Mars Orbit (LMO) with the CIV designed in mission ORPHEUS and lands on the
Martian surface using the landing crew vehicle, the MDV, which is similar to the habitation modules. However,
the modules that compose the base arrive separately on LMO from Earth. As described in the previous section,
the modules are protected by an external shell that allows a safe entry, descent and landing on Mars. All the
flight phases are designed to achieve a maximum acceleration lower than 10 g (Earth) due to structural design
limitation, and the touchdown phase is limited to a maximum total acceleration load of 2 g.

Figure 3 - EDL phases
Figure 3 shows the main phases of the EDL.
1. The module performs a Hohmann transfer from a 200 km LMO to a 100 km LMO, where the Martian
atmosphere starts. The entry velocity is the 𝑉𝐸(ℎ = 100𝑘𝑚) = 3.6 𝑘𝑚 𝑠⁄ .
2. The module brakes against the Martian atmosphere due to the aerodynamic forces.
3. At a certain altitude, the external shell is ejected, and the constant flight path angle (CFPA) descent
phase starts. The module activates the main thruster which acts to oppose the direction of the velocity.
4. Once the module has reached a zero velocity, the main engine is ejected. The descent phase continues
vertically, guided by the secondary engines.
5. The module lands on the Martian surface in the designed landing ellipse and the Touchdown System is
activated.
1.2.1.1 Hohmann transfer
The modules perform the Hohmann transfer from the 200 km LMO to the 100 km orbit. The mass of propellant
consumed for this manoeuvre is given by the rocket equation:
𝑚 𝑝𝑟𝑜𝑝𝐻 = 𝑚0 (1 − 𝑒
−∆𝑉
𝑐 ) (1)
where the ∆𝑉 = 0.185 𝑘𝑚 𝑠⁄ as required by the transfer trajectory, 𝑚0 is the total entry mass of up to 40 tons,
𝑐 is the specific velocity of the thruster, shown in the Table 1.
Thruster Definition
Specific Impulse, Isp [s] 360.0

Earth Gravity, g0 [m/s2] 9.8
Speed of Light, c [m/s] 3531.6
Density of Oxygen, ρOx [kg/m3] 1142.0
Density of Methane, ρCH4 [kg/m3] 464.0
Mixture Ratio 3.5
Propellant Density, ρprop [kg/m3]
(average) 862.1
Table 1 - Main thruster properties
Table 1 shows the main properties of a LOX, CH4 engine that can be used for the Hohmann transfer manoeuvre
and for the following propelled phases.
1.2.1.2 Aerobraking Phase
The aerobraking phase starts when the module reaches the 100 km orbit. In this phase the atmosphere of Mars
starts to decrease the speed of the vehicle due to the drag force. Due to the decreasing speed, the module
starts to deorbit. Figure 4 shows a model of the forces acting on the modules.
Figure 4 - Equilibrium of forces acting on the module at entry condition
In an orbital condition, the centrifugal force is equal to the gravitational force. 𝐹𝑐𝑓 = 𝑚𝑔 so therefore 𝑉𝐸
2
𝑅⁄ =
𝑔. The drag can be evaluated as:
𝐷 =
1
2
𝜌𝑉2
𝐴 𝑟𝑒𝑓 𝐶 𝐷 (2)
The density is related to the altitude 𝜌 = 𝜌(ℎ) = 𝜌0 𝑒−ℎ ℎ 𝑟𝑒𝑓⁄
with ℎ 𝑟𝑒𝑓 = 11𝑘𝑚 and 𝜌0 = 0.02 𝑘𝑔 𝑚3⁄ ; 𝐴 𝑟𝑒𝑓 is
the reference surface of the body, considered as the surface at the base of the nose.
The drag that affects the velocity induces a deceleration on the x body direction:
𝑎 𝑥 =
𝑑𝑉𝑥
𝑑𝑡
=
𝐷 𝑥( 𝜌, 𝑉)
𝑚
(3)
The module undergoes an acceleration in the y body (yb) direction, due to the fact that the centrifugal force is
not enough to balance the gravitational force:

𝑎 𝑦 = 𝑔 −
𝑉2(ℎ)
ℎ
(4)
That implies a velocity variation on the y direction:
𝑑𝑉𝑦 = 𝑎 𝑦 𝑑𝑡 (5)
The equations are then integrated numerically up to the designed altitude ℎ = ℎ 𝑠𝑡𝑜𝑝 in which the aerobraking
system is ejected and the retro-propelled phase starts.
1.2.1.3 Retrorocket Constant Flight Path Angle Descent
The descent phase starts with the ejection of the aerobraking systems, condition in which the module has a
constant flight path angle (CFPA) determined by the velocity vector at the ending of the previous phase. The
system of forces acting on the body is shown in Figure 5.
Figure 5 - Equilibrium of forces at propelled phase
The initial conditions are:
ℎ 𝑟𝑜𝑐𝑘 = ℎ 𝑠𝑡𝑜𝑝 (6)
𝑉𝑟𝑜𝑐𝑘 = √𝑉𝑦 𝑆𝑇𝑂𝑃
2
+ 𝑉𝑥 𝑆𝑇𝑂𝑃
2 (7)
𝛾𝑆𝑇𝑂𝑃 = 𝐶𝐹𝑃𝐴 = 𝑎𝑟𝑐𝑡𝑎𝑛 (
𝑉𝑦 𝑆𝑇𝑂𝑃
𝑉𝑥 𝑆𝑇𝑂𝑃
) (8)
Knowing the ℎ 𝑟𝑜𝑐𝑘 and the CFPA, it is possible to know how many kilometres the module is going to cover
during the constant flight path angle descent, 𝑠 𝑟𝑜𝑐𝑘, as shown in Figure 6.

Figure 6 - CFPA descent
The amount of thrust requested by the thrusters is evaluated considering the conservation of energy from the
beginning of the propelled phase, until the touch down on the Martian surface. Starting from the conservation
of energy and considering the kinetic energy, the potential energy, the energy provided by the thruster and the
energy dissipated by the drag, it yields:
∆𝐾 + ∆𝑈 + 𝑇𝑠 𝑟𝑜𝑐𝑘 + 𝐷𝑠 𝑟𝑜𝑐𝑘 = 0 (9)
Setting the potential energy to be zero at ground, and requiring the kinetic energy to do the same (condition of
vehicle hovering), for 𝑉𝑔𝑟𝑜𝑢𝑛𝑑 ≈ 0 𝑚 𝑠⁄ , the previous equation can be rearranged as:
1
2
𝑉𝑟𝑜𝑐𝑘
2
+ 𝑔ℎ 𝑟𝑜𝑐𝑘 −
𝑇𝑠 𝑟𝑜𝑐𝑘
𝑚 𝑟𝑜𝑐𝑘
−
0.8𝐷𝑠 𝑟𝑜𝑐𝑘
𝑚 𝑟𝑜𝑐𝑘
= 0 (10)
The mass at the end of the aerobraking phase is the entry mass minus the external shell mass, 𝑚 𝑟𝑜𝑐𝑘 =
𝑚 𝑒𝑛𝑡𝑟𝑦 − 𝑚 𝑒𝑥𝑡𝑆ℎ𝑒𝑙𝑙. The drag is evaluated considering the density at the average altitude, 𝜌 = 𝜌 (
ℎ 𝑟𝑜𝑐𝑘
2
), and
the average velocity, 𝑉2
=
𝑉𝑟𝑜𝑐𝑘
2
2
; a scaling coefficient of 0.8 is considered for discrepancy respect to the value
numerically evaluated during the simulation.
The drag and the reduction of mass due to the consumption of propellant allow the module to achieve the zero
velocity on the direction x at a higher altitude. In the mathematical model the main thruster is firing on the
direction of the motion so the velocity on the direction of the x body axes is stopped at a higher altitude.
1.2.1.4 Retrorocket Vertical Descent
At a certain altitude, the module of the velocity 𝑉𝑟𝑜𝑐𝑘 is so low that is possible to eject the main thruster. The
descent phase continues with a vertical trajectory, guided only by the secondary thrusters. They are sized in
order to sustain 10% more of the module weight at the beginning of the propelled phase.
𝑇𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦 = 1.1𝑚 𝑟𝑜𝑐𝑘 𝑔 (11)
And the mass for this phase is the mass evaluated at the end of the constant FPA descent minus the mass of the main
engine:
𝑚 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 = 𝑚 𝑟𝑜𝑐𝑘 − 𝑚 𝑚𝑎𝑖𝑛𝑇 (12)

They were considered to have the ability to be throttled, so their thrust was rescaled during each iteration of the
simulation (if it was smaller than the nominal one) to be:
𝑇𝑥,𝑦 = 𝑀𝐼𝑁 (
𝑣 𝑥,𝑦 · 𝑚
∆𝑡
, 𝑇𝑠𝑒𝑐𝑜𝑛𝑑𝑎𝑟𝑦) (13)
1.2.1.5 Touchdown Subsystem
In order to avoid debris damage on the bottom of the module, due to the impingement of the plume on the
ground which will throw rocks up in the air, and also in order to avoid the possibility of landing inside the hole
formed after the turning off the engines (as pointed out in section 5.9 of the NASA Mars Design Reference
Architecture 5.0 – Addendum), the following touchdown approach has been chosen:
- The previous phases of the descent have left the module at an altitude of -2838 m MOLA from which
retrorockets will be used in order to ensure a slow vertical fall.
- At an altitude of 15m a horizontal impulse is performed to grant a speed of 6 m/s (TBD). This is done in
order to avoid the crater created by the vertical retrorockets. The retrorockets are then turned off,
after which a free fall starts.
- Immediately after that, the shock absorbers are released from their stowed configuration, in which
they are maintained until the shutdown of the vertical retrorocket in order to avoid heat damage to
the wheels.
- At the touchdown, the impact is softened by the shock absorbers. This will ensure that the structure of
the module does not suffer accelerations greater than its structural limit.
- As the module has a horizontal velocity, wheels are used to grant mobility in the horizontal direction
during the touchdown, as well as a pressure low enough so that the ground does not crumble.
Eventually, brakes are used to stop the module.

Figure 7 shows the touchdown phases graphically.
Figure 7 - Touchdown phases
1.3 MATHEMATICAL MODEL
The damping system has been modelled as a harmonic oscillator damped and forced, where the elastic
constant and the damping coefficient are the sum of the actual ones (considering oscillators in parallel):
𝑚𝑥̈ + 𝑐𝑥̇ + 𝑘𝑥 = 𝑚𝑔 𝑀𝑎𝑟𝑠 (14)
To minimize the oscillations (and the acceleration peaks) the system was chosen to be critically damped:
𝑐
𝑚
= √
𝑘
𝑚
= 𝜔2 (15)
The solution, parametrised respect to ω and with 𝑥(0) = 0 (at the moment of the impact, the spring shall be
fully deployed) is:
𝑥(𝑡) = (−
𝑔 𝑀𝑎𝑟𝑠
𝜔2
+ (𝑣 −
𝜔2
) 𝑡) 𝑒−𝜔𝑡
+
𝜔2
(16)
Stopping the engines at h = 15 m results in a contact velocity with the ground of:
𝑣 = √2𝑔 𝑀𝑎𝑟𝑠ℎ = 11 𝑚
𝑠⁄ (17)
The best value for ω was found to be 1.8 Hz; Figure 8 show the dynamic of the spring after the impact.

Figure 8 - Spring compression after impact
Figure 9 shows the acceleration on impact.

Figure 9 - Acceleration on impact
To ensure the full deployment of the shock absorbers during the free-fall phases it is important to calculate
their motion during that phase. In this case, the weight of the module will not be felt by the system, so the
equation of the motion will change:
𝑥(𝑡) = 𝑙 𝑚𝑎𝑥(1 + 𝜔 𝑡) 𝑒−𝜔𝑡 (18)
lmax is the maximum extension of the shock absorber (3m). As pictured in Figure 10, the maximum extension
occurs after 2.8 s of free fall, with this time being obtained simply using
𝑡 = √
2ℎ
, (19)
The legs will be extended by more than the 2.7 m necessary for the landing, as can be seen in Figure 10.

Figure 10 - Leg deployment, shown as the extension of the legs over time
1.3.1 Hypersonic Drag Coefficient Evaluation and Optimization
In order to evaluate the drag force acting on the entry modules is possible to evaluate analytically the drag
coefficient (17), starting from the Newtonian theory of the aerodynamic flow. The Newtonian theory
particularly fits with the hypersonic flow regime and therefore with Martian entry conditions. In fact, for a
typical entry manoeuvre on Mars, the Mach number is almost always hypersonic because of the very low speed
of sound on Mars. An assumption of the Newtonian theory for the hypersonic flux is that the motion of the
fluid is described as a system of particles traveling with rectilinear motion which, in the case of striking a rigid
surface, lose all their momentum normal to the surface and conserve only their momentum tangential to the
surface, as is shown in Figure 11.
Having an analytic approach can be useful because it allows for exact calculation of the aerodynamic
coefficients, which is currently approximated by numerical methods. This is essential above all in a conceptual
design and for global optimization, where the phase space is often large (18). From this point of view, obtaining
an analytic expression for the aerodynamic coefficients is essential in order to solve the optimization process
without solving the Navier-Stokes equations by numerical simulation. In fact it can be studied as a constrained
optimization problem, whose solution can be found or analytically or with a simpler numerical algorithm (17).

Figure 11 - Momentum of a gas particle in Newtonian assumption (18)
This behaviour of the hypersonic flows leads to one of the key hypotheses of the algorithm (18). The flow tends
to change almost instantaneously its direction from the free-stream orientation to a direction tangential to the
surface and with this consideration it's possible to simplify the study of the phenomena. In fact it is possible to
write an approximate definition of the velocity vector over the body surface, which is found by considering the
velocity on the body together with the tangential component of the free-stream velocity (18):
𝑉⃗ 𝑏𝑜𝑑𝑦−𝑙𝑜𝑐𝑎𝑙 = 𝑉⃗ 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = 𝑉⃗∞ − 𝑉⃗ 𝑜𝑟𝑡ℎ𝑜𝑔𝑜𝑛𝑎𝑙 = 𝑉⃗∞ + (𝑛⃗ ∙ 𝑉⃗∞) ∙ 𝑛⃗ (20)
Here 𝑉⃗ 𝑏𝑜𝑑𝑦−𝑙𝑜𝑐𝑎𝑙 = 𝑉⃗ 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 means that the velocity vector considered on the body has only the tangential
direction and it is possible to consider the normal component of the velocity as 𝑉⃗ 𝑜𝑟𝑡ℎ𝑜𝑔𝑜𝑛𝑎𝑙 = −(𝑛⃗ ∙ 𝑉⃗∞), for 𝑛⃗
the outward normal vector to the surface of the body. With this hypothesis it is possible to make two
assumptions:
- It is necessary to know the velocity field on the vehicle's surface to characterize the flow, so the forces
that act on the body (18).
- It is possible to obtain the inviscid pressure on the vehicle's surface, simply by considering the loss of
normal momentum in the almost instantaneous change of flow direction from normal to tangential.
This is the fundamental hypothesis of Newtonian method (2)
Starting from the second assumption, it is possible to define the pressure coefficient for the Newton flow
model, only dependent on the relative inclination that the surface has with the free-stream:
𝑐 𝑝 =
𝑝 − 𝑝∞
1
2 𝜌∞ 𝑉∞
2
= 2𝑠𝑖𝑛2
𝜃
(21)
Using conventional aircraft body axes and the corresponding free-stream velocity vector as function of angle of
attack and side-slip, it is possible to define the aerodynamic force coefficients along the body axes. Since for
the entry phase is the angle of attack and the side-slip angle are considered equal to zero, the only force acting
is the drag, so the drag coefficient along the surface is:
𝐶 𝐷 =
1
𝐴 𝑟𝑒𝑓
∬ 𝑑𝐹
𝑆
= ∬ 𝑐 𝑝 𝑛⃗ 𝑑𝑆
𝑆
(22)
For 𝐴 𝑟𝑒𝑓, the reference area of the body, considered as the surface at the base of the nose. One fundamental
result of the Newtonian flow theory is that every aerodynamic coefficient is derived from the surface integral
of the pressure coefficient (1).

So for more complex noses, the global coefficients can be calculated superpositing the effects of each of the
basic shapes in which is possible to divide the nose. The shape of common hypersonic vehicles can be
determined through a superposition of basic shapes. For example, sphere-cones can be constructed using a
spherical segment and a single conical frustum, as the shape of the entry system considered for Mission
MILESTONE, as shown in Figure 12.
Figure 12 - Side and Front view of sphere-cone nose (1)
Integrating the pressure coefficient along the cone part of the body and along the spherical termination, it is
possible to evaluate the drag coefficients of the composed shape, superpositing the two effects:
𝐶 𝐷 = 𝐶 𝐷 𝑐𝑜𝑛𝑒
+ 𝐶 𝐷 𝑠𝑝ℎ𝑒𝑟𝑒 (23)
Following the analytical calculation (1), it is shown that the drag coefficient are depending only from three
geometrical parameters: the radius at the base of the cone, 𝑅 𝑐 𝑖
; the radius at beginning of the spherical part,
𝑅 𝑐 𝑓
and the length of the conic part 𝐿 𝑐.
𝐶 𝐷 𝑐𝑜𝑛𝑒
=
−1
𝐴 𝑟𝑒𝑓
4𝜋 (𝑅 𝑐 𝑓
− 𝑅 𝑐 𝑖
)
4
𝐿 𝑐
3 ((
𝑅 𝑐 𝑓
− 𝑅 𝑐 𝑖
𝐿 𝑐
)
2
+ 1)
3
2 (24)
𝐶 𝐷 𝑠𝑝ℎ𝑒𝑟𝑒
=
−2𝜋
3𝐴 𝑟𝑒𝑓
cos (2𝑎𝑟𝑐𝑡𝑎𝑛 (
𝑅 𝑐 𝑓
− 𝑅 𝑐 𝑖
𝐿 𝑐
)) − 5
√(
𝑅 𝑐 𝑓
− 𝑅 𝑐 𝑖
𝐿 𝑐
)
2
+ 1
(25)
Using the analytical expression of the aerodynamic coefficients, the optimization process can be done
analytically. In mathematical optimization, constrained optimization is the process of optimizing an objective
function with respect to some variables in the presence of constraints on those variables.
In this work, the objective function can be considered as the ballistic coefficient, which has to be minimized in
order to obtain the maximum drag coefficient:

𝛽 =
𝑚 𝑡𝑜𝑡
𝐶 𝐷 𝐴 𝑟𝑒𝑓
=
𝑚 𝑏𝑜𝑑𝑦 + 𝑚 𝑛𝑜𝑠𝑒( 𝑥)
𝐶 𝐷( 𝑥) 𝐴 𝑟𝑒𝑓
(26)
Here x is the vector of the geometrical parameter that defines the shape of the nose, and therefore its mass.
Three constraints have been identified (17), as shown in Figure 13:
Figure 13 - Constrains on the cargo volume (a), nose radius (b) and nose mass (c).
1. The optimization has to maintain or even increase the total internal volume of the nose, in order to
have more space for the payload.
2. The optimization has to limit the total heat flux on the nose considering a maximum value.
3. The optimization has to reduce or at least maintain the total mass of the nose.
Hence the optimization problem can be written as (17):
{
𝑓𝑖𝑛𝑑𝑚𝑖𝑛𝛽( 𝑥) =
𝑚 𝑏𝑜𝑑𝑦 + 𝑚 𝑛𝑜𝑠𝑒( 𝑥)
𝐶 𝐷( 𝑥) 𝐴 𝑟𝑒𝑓
𝑉𝑜𝑙( 𝑥) ≥ 𝑉𝑜𝑙 𝑛𝑜𝑠𝑒
𝑞´( 𝑥) = 1.90 ∙ 10−4
𝑉∞
3
√
𝜌∞
𝑟𝑛( 𝑥)
≤ 𝑞´ 𝑀𝐴𝑋
𝑚( 𝑥) = 𝑆𝑙𝑎𝑡( 𝑥) 𝜌 𝑛𝑜𝑠𝑒 𝑡 𝑛𝑜𝑠𝑒 ≤ 𝑚 𝑛𝑜𝑠𝑒
(27)
Considering the three constraints, it is possible to evaluate an optimized drag coefficient for the sphere-conic
nose.
1.3.2 Simulation Implementation
In order to get sensible results from the mathematical model it was decided to implement a numerical
simulation with Python3™. Originally this was done with scripting spirit although later in the development
some object-oriented techniques were used in order to make the mode more reusable and flexible.

Python3™ was chosen for several reasons:
- Free
- Multiplatform
- Readability
- Big community with lots of libraries available
Specifically, numpy and matplotlib were used in the development. Numpy provides several scientific tools as
well as a fast iterable array. Matplotlib allows to plot data easily, which was used to assess the validity of the
results. In a later stage, the data was output to a csv file that was imported to Excel® to ease the work pipeline
with other Microsoft® Office products.
1.3.2.1 Numerical Model
The problem consists in solving the equation presented in the mathematical model section above: since this
problem cannot be solvable analytically, a numerical solution was calculated using the semi-implicit Euler
method. This method has shown to maintain the stability of orbits considering a small enough step. Although
this method is not as fast as Runge-Kutta methods, its implementation is trivial and as it was later seen,
performance was not a big concern for this simulation.
The first part of the program takes into account the aerobraking descent. With a step size of 1s, position,
velocity, acceleration and forces were updated; the aerodynamic pressure and the heat flux were also
calculated at each step. A control on the acceleration was performed at each step, in order to assure that the
module was never experiencing a load bigger than their structural limit (in this case, 10gEarth).
Once the desired altitude is reached, the program calculated the mass of the aerobraking system (HIAD, TPS,
etc.) based on the maximum aerodynamic pressure, the maximum heat flux and the heat load, and updated
the mass by subtracting these values from it, in order to simulate the ejection of the external shell.
Next, the retrorocket descent took place: the thrust was estimated as shown in the mathematical model, and
(also here with a time step of 1s) the trajectory of the module was calculated, but this time the frame of
reference was simply a 2d plane where the y-axis was the altitude and the x-axis was the Martian surface,
which was considered to be flat. A very easy attitude control was implemented, keeping the flight path angle
confined within a range of 3° about the initial angle. Also here a check was performed at every cycle that the
maximum acceleration was never exceeding the structural limit (this time, 2gEarth). At each step the mass of
propellant used was calculated and the system mass updated.
When the speed was smaller than a chosen value (25m/s) the main thruster was jettisoned (and its mass
subtracted) and the vertical descent was started. In this phase, a simple control was put on the speed in order
to have a more real descent and to better estimate the fuel consumption.
1.3.2.2 Object Oriented Programming
Using the abstractions provided by object orientation, it was possible to write the code in a way that it would
easily accept changes, such as new forces that add a bigger degree of precision, or even adapt it for other
needs of the mission such as the ascending phase.

The most important abstraction of this program is the definition of a “solid body” class that would encapsulate
the mass, the position and velocity vectors agreeing with the abstractions of classical mechanics. It is also
worth mentioning that the concept of force was associated to a common interface that for our case was
sufficiently well represented with a lambda function accepting a “solid body” as only parameter. Also, the
simulation itself was reified into a class that holds the results for the different phases, allowing for the
concatenation of different configuration seamlessly.
These were carried out in such a way that the physics of the problem can be given abstracted from the specifics
of the problem. Hence, it was possible to apply this software to other parts of the program (i.e. the ascent)
since the physics of the rocket are essentially the same but with different starting conditions.
1.3.2.3 Optimization
Once the simulation was implemented, it was necessary to find an optimum configuration of parameters that
would allow the module to reach the touchdown phase with a minimum speed while carrying the maximum
amount of weight. Different approaches were used in order to have validate the results.
The parameters that were given to optimize are:
- Thrust of the main thruster
- Thrust of the retrorockets
- Altitude at which the aerobreaking stops
- Altitude at which the main thruster is ejected
- Altitude at which retrorockets are started
- The diameter of the HIAD
The value used for the optimization is 𝑣/𝑚2
, where 𝑣 stands for the speed with which you arrive, and 𝑚 is the
mass that was landed when the touchdown took place.
1.3.2.3.1 Brute Force
The first method that was implemented was a rather naive but effective one. Iterating over each parameter
and comparing all results allows for a simple optimization. The computational cost of this method grows
quickly as more parameters are added, but it quickly offered a solution close to the optimal one. It also has the
problem that the accuracy of the solution is limited by the initial size of the grid.
1.3.2.3.2 Monte Carlo Optimization
A Monte Carlo method was also implemented. This algorithm offers higher precision than its predecessor, at
the cost of an equally slow computation time. Using both methods it was possible to see that the solution
doesn’t have a single solution but a series of combinations that together reach similar performances.
1.3.2.3.3 Recursive Brute Force
This method consists of a brute force optimization in which the optimization is done recursively over intervals
of the size of the previous divisions. This allows for an arbitrary level of precision. Also, since the process is

recursive, it was not necessary to have small divisions. It was seen that 10 divisions allow for a very fast
convergence.
As this method would be prohibitively long for iterating over all the parameters, only the thrusts were analysed
with it. The rest of the parameters were given by the results of the Monte Carlo. Using both methods it was
possible to find minima. However, given the complexity of the equations it is hard to assess if they are the
global minima or rather local minima.
1.3.3 Mass Breakdown
The EDL system mass can be evaluated considering all the subsystems that it composes of, related to the five
phases of the global entry and landing manoeuvre. It is possible to define the global mass as it is composed of
the mass of the aerobraking system, the propellant, the engine and the tanks for the propelled phase, the mass
of the reaction control system, and the mass of the landing devices:
𝑚 𝐸𝐷𝐿 = 𝑚 𝑎𝑒𝑟𝑜𝑏𝑟𝑎𝑘𝑖𝑛𝑔 + 𝑚 𝑝𝑟𝑜𝑝 + 𝑚 𝑡𝑎𝑛𝑘𝑠 + 𝑚 𝑒𝑛𝑔𝑖𝑛𝑒 + 𝑚 𝑅𝐶𝑆 + 𝑚𝑙𝑎𝑛𝑑 (28)
The total module mass can then be written as:
𝑚 𝑜𝑛𝑀𝑎𝑟𝑠 = 𝑚 𝑚𝑜𝑑𝑢𝑙𝑒 + 𝑚 𝐸𝐷𝐿 ≤ 40𝑡𝑜𝑛𝑠 (29)
The EDL mass can be eventually divided considering the different phases of the manoeuvre:
𝑚 𝐸𝐷𝐿 = 𝑚 𝐸𝐷𝐿𝐻 + 𝑚 𝐸𝐷𝐿𝑎𝑒𝑟𝑜 + 𝑚 𝐸𝐷𝐿𝑟𝑜𝑐𝑘 + 𝑚 𝐸𝐷𝐿𝑙𝑎𝑛𝑑 (30)
1.3.3.1 Hohmann Transfer Mass Budget
Knowing the properties of the engine used for the Hohmann transfer, the propellant mass used in this phase is
simply evaluated considering the rocket equation:
𝑚 𝑝𝑟𝑜𝑝𝐻 = 𝑚0 (1 − 𝑒
−∆𝑉
𝑐 ) (31)
where the ∆𝑉 = 0.051 𝑘𝑚 𝑠⁄ is the delta-V required by the transfer trajectory, 𝑚0 is the total entry mass, up
to 40 tons, and 𝑐 is the specific velocity of the thruster, as shown in the Table 2.
Thruster definition
Specific Impulse Isp [s] 360,0
g0 [m/s2] 9,8
c [m/s] 3531,6
Density of Oxygen ρOx [kg/m3] 1142,0
Density of Methane ρCH4 [kg/m3] 464,0
Mixture ratio 3,5
Propellant Density ρprop [kg/m3] (average) 862,1
Table 2 - Main thruster properties

Table 2 shows the main properties of a LOX, CH4 engine that can be used for the Hohmann transfer manoeuvre
and for the following propelled phase.
The tank mass can be evaluated considering titanium tanks with a specific mass factor of Ф=5000 m, at a
pressure of p=1.4 MPa:
𝑚 𝑡𝑎𝑛𝑘𝐻 =
𝑝𝑉𝑝𝑟𝑜𝑝𝐻
𝑔0Ф
(32)
In equation 26, g0 stands for the Earth gravity. The volume of propellant can be evaluated in the following way:
𝑉𝑝𝑟𝑜𝑝𝐻 =
𝑚 𝑝𝑟𝑜𝑝𝐻
𝜌
(33)
In the end the mass of the EDL system for the first phase is:
𝑚 𝐸𝐷𝐿𝐻 = 𝑚 𝑝𝑟𝑜𝑝𝐻 + 𝑚 𝑡𝑎𝑛𝑘𝐻 (34)
Giving the entry mass as:
𝑚 𝑒𝑛𝑡𝑟𝑦 = 𝑚 𝑚𝑜𝑑𝑢𝑙𝑒 + (𝑚 𝐸𝐷𝐿 − 𝑚 𝐸𝐷𝐿𝐻) (35)
1.3.3.2 Aerobraking Phase Mass Budget
The module delivered to Mars is packed inside the rigid shell that protects it during the interplanetary
trajectory and during the first phases of the entry. Depending on the type of the aerobraking phase, the mass
budget can be divided in structural mass and mass of the Thermal Protection System (TPS) (3).
1.3.3.2.1 Rigid Shell Mass
The rigid shell mass can be divided into a front and back shell. The front shell protects the module from the
entry heat and stresses. It is made of a structural part, related to the maximum aerodynamic pressure that the
module faces during the entry phase, and a heat shield which is related to the total heat load of the manoeuvre
(19):
𝑚 𝑓𝑟𝑜𝑛𝑡 = 𝑚 𝑠𝑡𝑟𝑢𝑐𝑡 + 𝑚 𝑡𝑝𝑠 = (0.0232𝑞 𝑀𝐴𝑋
−0.1708
)𝑚 𝑒𝑛𝑡𝑟𝑦 + (0.00091𝑄0.51575
)𝑚 𝑒𝑛𝑡𝑟𝑦 (36)
The maximum aerodynamic pressure is expressed in Pa, 𝑞 =
1
2
𝜌𝑉2
; the total heat load is expressed in [J/cm2
]
and it is evaluated along all of the aerobraking phase, 𝑄 = ∫ 𝑞´ 𝑑𝑡 = ∫ 1.90 ∙ 10−4
𝑉∞
3
√
𝜌∞
𝑟 𝑛
𝑑𝑡.
The back shell mass can be evaluated from historical data, considering its thermal and structural mass:
𝑚 𝑏𝑎𝑐𝑘 = 0.14𝑚 𝑒𝑛𝑡𝑟𝑦 (37)

1.3.3.2.2 Inflatable Front Shell
In case of the configuration requires the inflatable technology, a HIAD (Hypersonic Inflatable Aerodynamic
Decelerator) of 23 m of diameter of deployable structure, and 9m of diameter of rigid part has been considered
(20). The mass of these two parts can be derived even in this case from the maximum aerodynamic pressure
and from the total heat load, as shown in Figure 14.
In case of having a double inflatable technology, the second inflatable shell has been considered as 20% larger
than the one depicted in the Figure 14.
In general, the mass of the HIAD can be written as:
𝑚 𝐻𝐼𝐴𝐷 = 𝑚 𝐻𝐼𝐴𝐷𝑠𝑡𝑟𝑢𝑐𝑡 + 𝑚 𝐻𝐼𝐴𝐷𝑡𝑝𝑠 (38)
So the EDL mass system for the second phase, 𝑚 𝐸𝐷𝐿𝑎𝑒𝑟𝑜 can be written as the sum of rigid and inflatable part,
depending on the chosen configuration.
Figure 14 - Structural (left) and TPS (right) Mass for the HIAD (20)
All the systems related to the aerobraking phase are ejected before the propelled phase begins. So the mass to
land with the retrorocket phase can be written as:
𝑚 𝑟𝑜𝑐𝑘 = 𝑚 𝑒𝑛𝑡𝑟𝑦 − 𝑚 𝐸𝐷𝐿𝑎𝑒𝑟𝑜 = 𝑚 𝑚𝑜𝑑𝑢𝑙𝑒 + ( 𝑚 𝐸𝐷𝐿 − 𝑚 𝐸𝐷𝐿𝐻 − 𝑚 𝐸𝐷𝐿𝑎𝑒𝑟𝑜) (39)
1.3.3.3 Retrorocket Descent Mass Budget
The retrorocket descent phase is made in two different parts: a constant flight path angle descent that stops
the module in the x body direction, and a vertical descent. For both of these manoeuvres, it is necessary to
maintain the orientation of the module, through a system of reaction thrusters. The total mass of this system
can be estimated as (19):
𝑚 𝑅𝐶𝑆 = 𝑚 𝑡ℎ𝑟𝑢𝑠𝑡 + 𝑚 𝑝𝑟𝑜𝑝 ≅ 0.0151𝑚 𝑟𝑜𝑐𝑘 (40)

The mass of the main and of the secondary engines can be evaluated knowing the thrust, in N, that they have
to apply during the manoeuvre (3):
𝑚 𝑒𝑛𝑔𝑖𝑛𝑒 = 0.00144𝑇 + 49.6 (41)
Considering the same propellant used for the Hohmann transfer, the propellant used in this phase is:
𝑚 𝑝𝑟𝑜𝑝𝑟𝑜𝑐𝑘 = ∫ 𝑑𝑚 = ∫
𝑇𝑑𝑡
𝑐
(42)
And for the tanks it is possible to use the same formulation considered for the Hohmann transfer:
𝑚 𝑡𝑎𝑛𝑘𝑟𝑜𝑐𝑘 =
𝑝𝑉𝑟𝑜𝑐𝑘
𝑔0Ф
(43)
So for the retrorocket descent phase, the EDL system mass is:
𝑚 𝐸𝐷𝐿𝑟𝑜𝑐𝑘 = 𝑚 𝑅𝐶𝑆 + 𝑚 𝑒𝑛𝑔𝑖𝑛𝑒1 + 𝑚 𝑒𝑛𝑔𝑖𝑛𝑒2 + 𝑚 𝑝𝑟𝑜𝑝𝑟𝑜𝑐𝑘 + 𝑚 𝑡𝑎𝑛𝑘𝑟𝑜𝑐𝑘 (44)
In case of ejection of the main engine after the constant flight path angle descent, the mass can be considered
as:
𝑚 𝐸𝐷𝐿𝑟𝑜𝑐𝑘 = 𝑚 𝑅𝐶𝑆 + 𝑚 𝑒𝑛𝑔𝑖𝑛𝑒2 + 𝑚 𝑝𝑟𝑜𝑝𝑟𝑜𝑐𝑘 + 𝑚 𝑡𝑎𝑛𝑘𝑟𝑜𝑐𝑘 (45)
1.3.3.4 Landing Devices Mass Budget
The definition of the landing system mass budget has been made considering the mass of the wheels and of
the shock absorber system.
𝑚𝑙𝑎𝑛𝑑 = 𝑚 𝑤ℎ𝑒𝑒𝑙𝑠 + 𝑚 𝑑𝑢𝑚𝑝𝑒𝑟 (46)
The touchdown on the Martian surfaces causes a deceleration of 3.5 g. The energy is considered to be shared
equally between all of the wheels. Each module is built with 3 lines of wheels, with 4 wheels in each line,
reaching a total of 12 wheels as shown in Figure 15.

Figure 15 - Landing system equipment definition

1.3.3.4.1 Wheels Sizing
The sizing of the wheels has been firstly designed considering the volume available in the fairing. The wheels
have been designed with a radius of 0.5 m and a width of 0.4 m.
Figure 16 - Landing system geometrical properties (dimensions in [mm])
Considering the wheel dimension, a research was been performed in order to identify commercial wheels with
similar properties. The M843 from Bridgestone Corporation was selected, and a linear sizing has been
performed in order to evaluate the mass of the landing tires, considering the impact force acting on each wheel
as:
𝐹 𝑤ℎ𝑒𝑒𝑙 𝑀𝑎𝑟𝑠
= 3.5𝑔 𝑚𝑙𝑎𝑛𝑑/𝑛 𝑤ℎ𝑒𝑒𝑙 (47)
The maximum load capacity of the tires on Earth application has been then used to identify the mass of the
tires for Martian landing.
𝑚 𝑤ℎ𝑒𝑒𝑙 = 𝑚 𝑤ℎ𝑒𝑒𝑙 𝐸𝑎𝑟𝑡ℎ
𝐹 𝑤ℎ𝑒𝑒𝑙 𝑀𝑎𝑟𝑠
𝐹 𝑤ℎ𝑒𝑒𝑙 𝐸𝑎𝑟𝑡ℎ
𝑛 𝑤ℎ𝑒𝑒𝑙 (48)

Table 3 summarizes the characteristic of the wheels.
Landing tires
Radius [m] 0.5
Width [m] 0.4
Mars load/wheel [N] 76395,375
Earth load/wheel [N] 40221
Earth wheel mass [kg] 70
Mars wheel mass [kg] 133
Total mass of the tires [kg] 1595,5
Table 3 - Landing tires mass
The definition of the material properties of the wheels is going to be selected knowing the characteristic of the
soil of the landing site. In fact, the module would sink into the ground if the impact pressure that each wheel
exerts on the soil was greater of the bearing capacity of the soil itself. This implies that each wheel needs a
contact surface that allows the soil to sustain the touch down. The minimum area can be defined knowing the
bearing capacity of the landing site, the impact force, and the elastic properties of the tire material (21)
The contact area can be defined as (21):
𝐴 𝑐𝑜𝑛𝑡𝑎𝑐𝑡 = 𝑎 ∙ 𝑏 = √
𝐹𝑛 𝑟𝑏( 𝜃 𝑤ℎ𝑒𝑒𝑙 + 𝜃 𝑀𝑎𝑟𝑠)
𝜋
(49)
In the equation above, a is the contact length, b is the wheel width, Fn is the load on the wheel at the touch
down, r is the wheel radius, θ is a coefficient depending on the Young’s module and the Poisson coefficient of
the two bodies that are in contact, 𝜃𝑖 = 4 (1 − 𝜈𝑖
2
)/𝐸𝑖. In this way the contact surface depends on the material
of the wheels, considering the Martian soil with an average elastic modulus and Poisson ratio given in
Table 4.
Table 4 - Martian soil elastic properties
The bearing capacity of the soil is from 10 kPa to 100 kPa depending on the landing site, the total contact area
has to be:
10 𝑘𝑃𝑎 <
𝐹𝑛
𝐴 𝑐𝑜𝑛𝑡𝑎𝑐𝑡
𝑛 𝑤ℎ𝑒𝑒𝑙 < 100 𝑘𝑃𝑎 (50)
Mars, soil properties
E [Pa] 1,44E+11
vu 0,268
θ Mars [1/Pa] 2,57E-11

Or the required contact area:
𝐴 𝑐𝑜𝑛𝑡𝑎𝑐𝑡 = √
𝐹𝑛 𝑟𝑏( 𝜃 𝑤ℎ𝑒𝑒𝑙 + 𝜃 𝑀𝑎𝑟𝑠)
𝜋
>
𝐹𝑛 𝑛 𝑤ℎ𝑒𝑒𝑙
𝐵𝑒𝑎𝑟𝑖𝑛𝑔 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦
(51)
From the last formula it is possible to evaluate the material of the wheel, related to the definition of the
landing site as:
𝐸 𝑤ℎ𝑒𝑒𝑙 =
4(1 − 𝜈2
)
𝐴 𝑐𝑜𝑛𝑡𝑎𝑐𝑡
2
4𝐹𝑛 𝑏𝑟𝜋 − 𝜃 𝑀𝑎𝑟𝑠
=
4(1 − 𝜈2
)
𝐹𝑛
4𝑏𝑟𝜋( 𝐵𝑒𝑎𝑟𝑖𝑛𝑔 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦)2 − 𝜃 𝑀𝑎𝑟𝑠
(52)
Table 5 gives the Elastic modulus for the extreme condition of the soil.
Range Of Materials For Landing Site
Bearing [Pa] Contact Area [m2] contact length [m] E wheel [Pa]
Min soil bearing 100000 0,764 1,90 1,43E+06
Max soil bearing 1000000 0,076 0,19 1,43E+08
Table 5 - Range of material for tire system, referred to landing site bearing capacity
1.3.3.4.2 Shock Absorber Sizing
As described in section 3.1.5, the modules need a damping system in order to absorb the deceleration at
impact, concerning the structural limit of 3.5 g with the properties previously analyzed. Knowing the maximum
compression of the dumber under the impulse given by the touch down, it has been possible to select a shock
absorber with the given characteristics.
A shock absorber similar to the ACE SDH50-1000EU (22) has been selected.
Figure 17 - Shock absorber geometry (22)
With the selected suspension, one shock absorber for each leg of the module can dissipate the impact energy
and consequently the mass of the damping system:

𝑚 𝑑𝑢𝑚𝑝 = 6𝑚 𝑠𝑢𝑠𝑝𝑒𝑛𝑠𝑖𝑜𝑛 (53)
1.3.3.4.3

1.3.3.4.4 Landing Devices Final Mass Budget
According to the standard on the margins adopted in this work, the Table 6 summarizes the contingency
margins that have been applied on the different components. The general approach implies a 20% margin on
brand new solution, a 10% margin on technologies already existing but that have to be adapted to the mission.
Moreover a margin of 50 % has been applied to the propellant for the descent phase and a 100 % margin for
the Attitude and Orbital Control System propellant mass.
Contingency margins (ESA approach)
DV 1,05
AOCS prop 2
Prop Maneuver 1,05
Final landing prop 1,5
HIAD 1,2
TPS 1,1
Landing devices 1,2
Table 6 - Contingency margins definition

1.4 FINAL MODEL
1.4.1 Mass Trade-Off
After the development of the mathematical model for the different architectures of the EDL phases and the
definition the mass of the components of the EDL system, a trade-off was performed in order to understand
which of the five configuration has the most benefits:
Figure 18 - Trade-off EDL configurations

Configuration 1 2 3 4 5
M Propellant Hohmann [kg] 638.0 638.0 638.0 638.0 638.0
Entry Mass (kg) 43361.0 43361.0 43361.0 43361.0 43361.0
MAX Dynamic Pressure [Pa] 9197 5981 625 661 222
Heat Load [MJ/m^2] 34.40 29.50 2.46 3.39 2.49
HIAD [ref.]
TPS [kg] 0.000 3400 3400
Structure
[kg] 1500.000 1500 1800
Front Shield
TPS [kg] 2630.999094 2132.0 1550.000 0 0
Structure
[kg] 211.6393922 199.0 309.000 0 0
Back Shield [kg] 5600.0 5600.0 5600.0 0.0 0
Mass END of free flight [kg] 34918.4 35430.0 34402.0 38461.0 38161.0
Mass reaction system [kg] 594.4 594.4 594.4 594.4 594.4
Mas Thruster Main [kg ] 1908.0 598.000 694 516
Mass Thruster Secondary (19)
[kg ] 229.0 223.000 245 243
Mass Propellant [kg] 11984.0 3867.000 3135 2945
Mass Tank [kg] 397.0 128.000 104 97
Landing System Mass (kg) 2040 2040.0 2040.000 2040 2040
Mass Landed [kg] 12993.12232 17819.6 26505.6 31158.6 31239.6
Entry Time [min] 28.17 28.85 16.03 18.33
Max g-load Exceeded yes yes no no no
Complexity (low=better) 1 2 4 3 5
Table 7 - Trade-off parameters
For simplicity, all these numbers are calculated without taking into account margins. It can be seen from the
table that only two configurations are actually capable of landing our modules: but since the difference in mass
is almost negligible, the configuration 4 has been chosen because of the lower complexity.
1.4.2 Configuration 4 Definition
1.4.2.1 Simulation Results
The results of the simulation are presented in this section. The graphs shows the trajectory of a payload, of 39
tons in LMO, entering in the Martian atmosphere, following the physics of configuration 4. The landing altitude
is supposed to be at MOLA level of -3000 m. In the first phase the HIAD is deployed in order to brake against
the Martian atmosphere, reducing the velocity up to an altitude of -2000 m. At this point the module ejects the

HIAD and continues the descent with the retrorockets with a constant FPA up to an altitude of 200m; then, the
main engine is ejected and a vertical descent is performed. The total entry phase lasts around 1000 s.
Figure 19 - Schematic definition of the EDL phases
Considering the topographic values given by MOLA satellite form NASA, it is possible to identify the areas on
Mars where land with the selected system can take place. Further considerations on the bearing capacity of the
soil and the possible presence of resources are necessary.

Figure 20 - Definition of possible landing area related to MOLA altitude (23)
Here some graphs of quantities related to the first phase are displayed.

Figure 21 - Aerobraking trajectory defintion
Figure 22 - Velocity variation during aerobraking deceleration

Figure 23 - g-load variation during aerobraking deceleration
Figure 24 - Aerodynamic pressure variation during aerobraking deceleration

Figure 25 - Heat flux variation during aerobraking deceleration
The maximum dynamic pressure that the module experiences is 447 Pa, reached around at 35 km after ~780
seconds. The maximum deceleration instead is about 1.8 gEarth, reached at similar values of altitude and time.
The heat peak occurs at an altitude ~57 km. Table 8 summarizes the results obtained with the simulation.
Parameter Value Altitude [km] Time [sec]
Total Heat flux 2.48W/m2
57 690
Maximum Aerodynamic pressure 447 Pa 35 780
Maximum g load 1.8 35 780
Table 8 - Maximum thermal, aerodynamic and structural loads during aerobraking phase

The following graphs, instead, refers to the propelled descent phase:
Figure 26 - Graphical representation of the propelled descent phase
Figure 27 - The variation of velocity of the propelled descent phase
1.4.2.2 Landing Ellipse
The landing ellipse was evaluated using the same simulation, taking into consideration the uncertainties for the
position and velocity of the rocket when the descent starts. The current value is 5 m/s for the velocity and 400 m
for the position. Using the simulation as a propagator and considering these errors, it was possible to roughly
estimate the size of the landing ellipse to an ellipse with a semi-major axis of 10 km, and a semi-minor axis of 3
km.

1.4.2.3 HIAD Subsystem
Figure 28 - HIAD dimensions and packed configuration
Figure 28 shows the dimensions of the HIAD (both deployed and packed) once they were optimized by the
simulation. The inflatable part of the HIAD packages like an umbrella. The material used is based on SIRCA-15,
as shown in Figure 29. There possibility of using it as acoustic shielding during launch
The rigid part of the HIAD has the structure shown by Figure 30, and unlike the inflatable part, it is based on the
PICA material. The ablative part can be even used for a previous phase of aerocapture. The sizing of the
material has been made considering the total heat load for the both phases: the aerocapture and the
aerobraking.
Figure 29 - HIAD inflatable material

Figure 30 - Rigid TPS Material definition
The thrusters were sized according to the results of the configuration, as was seen in the trade-off. Results
presented in the tables are related to the EDL phases of the heaviest payload of 40 tons on LMO. The inflation
gas can be considered to be stored in the main thruster assembly so it is ejected after the first propelled phase.
To size the propulsion system accurately, it was taken into account not only the mass of the propellant but also
the mass of the tank, the cryocooler system, the MM protection and the insulation system (as seen in Table 9).
Propellant [kg] 3135
Tank [kg] 104
Cryocooler system [kg] 17
MM protection [kg] 38
Insulation system [kg] 38
Table 9 - Propellant system mass budget
The thruster used by the system is sized as seen in Table 10:
Isp [s] 360
c [m/s] 3532
rho Ox [kg/m3] 1142
rho CH4 [kg/m3] 464
MR 3,5
Thrust [kN] 428
Nozzle length [m] 2,5
Nozzle diameter [m] 2,7
Engine mass [kg] 694
Table 10- Main thruster definition
Finally, the general architecture of the thrusters, the tanks the HIAD and the landing system can be seen in
Figure 31.

Figure 31 - EDL sub-systems definition
1.4.2.4 Sensing Subsystem
For sensing, it will be necessary to provide the system with several different sensors, as well has having a better
understanding of the Martian surface and atmosphere. Some of the sensors that will be used are:
 Inertial navigation system
- Using gyroscopes and accelerometers it is possible to estimate the position of a spacecraft via
dead reckoning. This method is susceptible to cumulative errors, which is why it is combined to
other sensors to provider further precision.
 Barometric sensor
- This sensor is used as an altimeter in Earth based aircraft. However it will be necessary to study
the Martian atmosphere to much greater depth in order to ensure a sufficiently high TRL for
this sensor.
 Radar
- Using a radar it is possible to estimate the altitude of the module.
 Lidar
- Using the same principles as a radar, it is possible to estimate the altitude of the module using
a light beam and measuring the scattered light.

In Table 11 the sensing sub-systems budget is presented (24).
Sensor Mass [kg] Power [W]
Radar Altimeter 0.4 8
IMU 3.65 12
LIDAR scanner 12 25
Sun Sensor 0.25 1
Radial Accelerometers 0.02 0.5
Star Tracker 2.7 7.5
Horizon Sensor 4 7
Barometric Sensor TBD TBD
Total 23.02 61
Table 11 - Attitude and Control system mass and power budget (24)
1.4.2.5 Heat Shield Ejection Subsystem
Leaf springs will be used to force the heat shield apart upon release. They offer a simple and reliable solution
for a low weight. The speed of the ejected bodies will be of 1 m/s, which will offer enough time to separate
from the module before the landing takes place.
1.4.3 EDL Mass Budget
After having evaluated all the masses related to the systems that are included in the EDL, it was possible to
evaluate the global mass budget. A system margin has been applied to all the systems considering the TRL of the
solution that have been taken into account. The data in Table 12 and Figure 32 are refers to the EDL system for a
payload of around 27 tons.
System Mass [kg] Margin % Mass with margin [kg]
Propulsion system 950 10% 1045
EDL system 11233 20% 13480
EDL avionics 969 10% 1066
Communication/Avionics 25 15% 29
Total 13178 18,5% 15620

Table 12 - EDL system mass budget definition
Figure 32 - EDL System Mass Budget
1.4.4 Landing Loads, Structural Considerations
As introduced in Mission MILESTONE, Turin Final Report, the inflatable part needs four booms in order to
sustain the impact load of the landing and the operational load in the inflated configuration.
The design case is the heaviest of our modules. The operational loads are the most critical in terms of bending,
since the inflatable part has to sustain all the subsystems allocated in the internal volume. For structural
stability, a fourth line of wheels are deployed after that the module has landed. Since these wheels have to
sustain the mass of the module on Mars, their weight has been scaled from the landing tires, considering the
different load factor. The mass of the inflatable support system is summarized in the Table 13.
Device Mass
Tire (x4) 80 kg
Shock Absorber (x2) 14 kg
Total 94 kg
Table 13 - Inflatable support system wheels mass budget
Considering the inflated configuration, the inflatable part can be assumed as a boom fixed on the rigid part,
lying on the support system, as shown in Figure 33. Since all the 8 legs are sustaining the same load, the force
acting on the inflatable part is given by the weight of its own structure, the subsystem allocated inside and the
force on the support.

Figure 33 - Inflated Configuration, Operational Loads
For a first approximation the mass of the module is considered equally distributed along the structure, the
mass of the inflatable part and the loads acting on it are:
𝑚𝑖𝑛𝑓𝑙 =
𝑚 𝑠𝑦𝑠𝑡 𝑙𝑖𝑛𝑓𝑙−𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑
𝑙 𝑚𝑜𝑑𝑢𝑙𝑒
+ 𝑚 𝑠𝑡𝑟𝑢𝑐𝑡 = 16000𝑘𝑔
4.4 𝑚
15.7 𝑚
+ 1700 𝑘𝑔 = 6184 𝑘𝑔 (54)
𝑔 𝑀𝑎𝑟𝑠 = 3.71 𝑚/𝑠2 (55)
𝑞𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 =
𝑚𝑖𝑛𝑓𝑙 𝑔 𝑀𝑎𝑟𝑠
𝑙𝑖𝑛𝑓𝑙−𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑
= 5.48
𝑘𝑁
𝑚
(56)
𝑉𝐴 = 𝑉𝐵 =
𝑚 𝐻𝐴𝐵
4
𝑔 𝑀𝑎𝑟𝑠 = 24.1 𝑘𝑁 (57)
So it is possible to evaluate the bending moment at the conjunction between the inflatable and the rigid part
as:
𝑀𝐴 =
𝑞𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 𝑙𝑖𝑛𝑓𝑙−𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑
2
2
− 𝑉𝐵 𝑙𝑖𝑛𝑓𝑙−𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 = 57 𝑘𝑁𝑚 (58)
Using the formulation of Navier, it is possible to determine the tensile tension acting on the i-th boom, on the
most stressed section, so at the point A, the connection between inflatable and rigid part:

𝜎𝑖 =
𝑀𝐴
𝐽
𝑑𝑖 (59)
Where the inertia can be evaluated knowing the position of the booms, supposing all with the same area:
𝐽 = ∑ 𝐴𝑖 𝑑𝑖
2
= 4𝐴𝑑2
(60)
Considering the same aluminium of the boom of the rigid part, the area of the boom has to sustain two times
the maximum yield stress, equal to 145 MPa.
𝐴 =
1
4
2𝑀𝐴
𝜎 𝑦𝑖𝑒𝑙𝑑 𝑑
= 1.5 10−4
𝑚2
(61)
To size the booms some other considerations are necessary. From an industrial point of view, the dimensions
previously evaluated do not fit with the requirements of the deployment approach. The booms for the
inflatable part have to be inserted in the boom of the rigid part and then extracted during the inflation of the
structure. The minimal area that allows this procedure has been geometrically evaluated as 33.84 cm2
with a
similar C-shape of the others. The length has been set as 5 m in order to guarantee the connection between
the booms of the two parts when the inflatable part is inflated. Figure 34 shows the connection mechanism.
Figure 34 - Boom connection mechanism between rigid and inflatable part
So the total mass for the four booms can be easily evaluated, considering the density of the aluminum of 2800
kg/m3
:
𝑚 𝑏𝑜𝑜𝑚 = 4𝜌𝐴𝑙𝑖𝑛𝑓𝑙−𝑏𝑜𝑜𝑚 = 4 2800
𝑘𝑔
𝑚3
33.84 10−4
𝑚2
5 𝑚 = 182 𝑘𝑔 (62)
So the inertia:
𝐽 = 0.0236 𝑚4 (63)

With this design, it is interesting to understand the amount of the deflection of the inflatable structure,
reinforced by the booms. Considering the equation of the elastic line and the constraints conditions, the
maximum displacement is evaluated in the middle of the inflatable part, at 2.2 m:
𝑢 𝑦 =
5
384
𝑞𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 𝑙𝑖𝑛𝑓𝑙−𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑
4
𝐸𝐽
= 1.6 10−5
𝑚 (64)
For the Young’s modulus of 71.7 GPa. It is then possible to assume that the displacement of the section in the
middle is negligible.
Finally, it is interesting to evaluate the displacement of the inflatable part packed, during the entry touch
down. In this configuration, the inflatable part is only sustaining its own structural mass, since in the packed
configuration it is internally empty. The mass and the loads, as they are shown in Figure 35, can be evaluated
as:
𝑚𝑖𝑛𝑓𝑙 = 1700 𝑘𝑔 (65)
𝑔𝑙𝑜𝑎𝑑 = 3.5 𝑔 𝐸𝑎𝑟𝑡ℎ = 34.3 𝑚/𝑠2 (66)
𝑞 𝑝𝑎𝑐𝑘 =
𝑚𝑖𝑛𝑓𝑙 𝑔𝑙𝑜𝑎𝑑
𝑙𝑖𝑛𝑓𝑙−𝑝𝑎𝑐𝑘
= 32.4 𝑘𝑁 (67)
Figure 35 - Packed configuration, operational loads

Considering again the equation of the elastic line and the constraints conditions, the maximum displacement is
evaluated at the free part of the inflatable part, at 1.8 m:
𝑢 𝑦 =
1
8
𝑞 𝑝𝑎𝑐𝑘 𝑙𝑖𝑛𝑓𝑙−𝑝𝑎𝑐𝑘
4
𝐸𝐽
= 2.5 10−5
𝑚 (68)
It is finally possible to assume that even at the touch down, the inflatable part of the structure does not suffer
a critical modification due to the load of the impact.
1.4.5 Human Descent Phase
The MDV is supposed to arrive in Mars orbit attached to the CIV. The interplanetary trip ends when a 500 km
LMO is achieved and stabilized. Following the mission scenarios definition, the crew enters in the MDV, the CIV
is switched in unmanned mode and the EDL phase starts.
The MDV consists of a scaled habitable module that would allow a crew of six members for 21 days. This
accounts for the possibility that the MDV lands far from the designated point, given that the landing ellipse has
semi-axis of 10km and 3km. With this approach the MDV has the same entry, descend and landing system as
the other modules.
The EDL system so far designed achieves decelerations limit compatible with the manned entry requirements.
It is moreover possible to assume its safety level is acceptable, since the crew arrival is supposed to be around
2 year after the first module landings. In this way around 10 modules have already safety landed on Mars with
this system. Further considerations on improving the precision of the landing ellipse for human descent can be
done.
After the landing phase, the collection rover will go to the MDV landing site in order to pick up the crew and
bring them to the base location. The worst case scenario would be that the crew lands in the furthest extreme
of the landing ellipse. In that case the rover would have to cover around 20km, as shown in Figure 36.
Due to the fact that the MDV has wheels (used for the landing), it can be carried by the rover to the base
location. During the initial assembly and set up phase of the base, the crew would perform EVA activities
through the MDV’s suit-lock while living in the MDV itself. 4 suit locks are present on the MDV since a 4 crew
member EVA is foreseen.
Figure 36 – MDV landing ellipse (worst case scenario)

In case of failure of the 4 suit lock, the MDV is equipped also with six EVA suits that allow the crew to exit
directly from the MDV to the Martian surface. This scenario foresees the MDV depressurization and it is taken
in consideration only in case of critical failures.
1.4.5.1 MDV Sizing
In order to size the MDV, the habitable module has been scaled considering the shorter duration of the
mission; 21 days instead of 60 days. The 21 days ensure a contingency margin period to complete the set up of
the base, while this is not operational. The dimension of the module has been reduced, as can be seen in Table
14. For simplicity, the module only has a rigid structure.
Module diameter 4 m
Module length 6.0 m
Table 14 – MDV dimensions
All the subsystems related to the human support were sized from the equivalent habitable module systems,
considering the reduced stay. Table 15 and Figure 37 show the masses of the different subsystems (based on
Turin phase report). Considering the reduced duration of the mission, the MDV has different subsystems. For
example for the Air Revitalization System, only oxygen tanks have been considered.
Moreover, the MDV is designed to have 4 deployable solar arrays in order to produce the amount of power
required for the subsystems, estimated around 2 kW. The power is guaranteed by 4 solar arrays with a radius
of around 1.3 m, considering the solar constant on Mars of 98 W/m2
, and a spefic mass of the array of 36 W/kg.
This mass is allocated in the Autonomous Electric Power System section (AEPS).
As it will be better analysed in the rover section, for mission MILESTONE the MDV can be brought by the rover
far from the base as an exploration habitat for the crew, after the completion of the base assembly. In the
mass budget, the systems related to the EVA activity are also considered.
Mass (kg) Percentage of Total Mass
PRIMARY STRUCTURE 5397 56%
SECONDARY STRUCTURE 472 5%
ECLSS 2827 29%
ATCS 467 5%
AEPS 283 3%

COMMUNICATION 29 0%
SPACE SUIT 175 2%
Total 9650 100%
Table 15 – MDV habitable mass budget
56%
5%
29%
5%3%0%2%
MDV Mass Budget
PRIMARY STRUCTURE
SECONDARY STRUCTURE
ECLSS
ATCS
AEPS
COMMUNICATION
SPACE SUIT
Figure 37 – MDV habitable mass budget

1.4.6 EDL Modules Tailoring
Demonstrated the capability of landing big payload on the Martian surface with the selected architecture,
configuration 4, simulations have been run in order to define properly the EDL sub-system mass for each
module of Mission MILESTONE.
Firstly, several simulations have been performed varying the mass in LMO from 10.5 tons up to 44 tons,
evaluating the total mass on the Martian surface. For each configuration, the code optimizes the different
sensitive parameters (amount of thrust of the primary and secondary thrusters and HIAD diameter) to achieve
the biggest possible landed mass. As shown in Figure 38, the simulations show EDL system mass can be
considered as proportional to the entry mass.
Figure 38 - EDL and landed Mass related to the mass in LMO

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