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:

𝑚𝑝𝑟𝑜𝑝𝐻 = 𝑚0 (1 − 𝑒−∆𝑉𝑐 ) (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 𝑉𝐸2 𝑅⁄ =

𝑔. The drag can be evaluated as:

𝐷 =1

2𝜌𝑉2𝐴𝑟𝑒𝑓𝐶𝐷 (2)

The density is related to the altitude 𝜌 = 𝜌(ℎ) = 𝜌0𝑒−ℎ ℎ𝑟𝑒𝑓⁄ with ℎ𝑟𝑒𝑓 = 11𝑘𝑚 and 𝜌0 = 0.02 𝑘𝑔 𝑚3⁄ ; 𝐴𝑟𝑒𝑓 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:

𝑎𝑥 =𝑑𝑉𝑥𝑑𝑡

=𝐷𝑥(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:


𝑎𝑦 = 𝑔 −𝑉2(ℎ)

ℎ (4)

That implies a velocity variation on the y direction:

𝑑𝑉𝑦 = 𝑎𝑦𝑑𝑡 (5)

The equations are then integrated numerically up to the designed altitude ℎ = ℎ𝑠𝑡𝑜𝑝 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:

ℎ𝑟𝑜𝑐𝑘 = ℎ𝑠𝑡𝑜𝑝 (6)

𝑉𝑟𝑜𝑐𝑘 = √𝑉𝑦𝑆𝑇𝑂𝑃2 + 𝑉𝑥𝑆𝑇𝑂𝑃

2 (7)

𝛾𝑆𝑇𝑂𝑃 = 𝐶𝐹𝑃𝐴 = 𝑎𝑟𝑐𝑡𝑎𝑛 (𝑉𝑦𝑆𝑇𝑂𝑃𝑉𝑥𝑆𝑇𝑂𝑃

) (8)

Knowing the ℎ𝑟𝑜𝑐𝑘 and the CFPA, it is possible to know how many kilometres the module is going to cover

during the constant flight path angle descent, 𝑠𝑟𝑜𝑐𝑘 , 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 + 𝑇𝑠𝑟𝑜𝑐𝑘 +𝐷𝑠𝑟𝑜𝑐𝑘 = 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 ≈ 0𝑚 𝑠⁄ , the previous equation can be rearranged as:

1

2𝑉𝑟𝑜𝑐𝑘2 + 𝑔ℎ𝑟𝑜𝑐𝑘 −

𝑇𝑠𝑟𝑜𝑐𝑘𝑚𝑟𝑜𝑐𝑘

−0.8𝐷𝑠𝑟𝑜𝑐𝑘𝑚𝑟𝑜𝑐𝑘

= 0 (10)

The mass at the end of the aerobraking phase is the entry mass minus the external shell mass, 𝑚𝑟𝑜𝑐𝑘 =

𝑚𝑒𝑛𝑡𝑟𝑦 −𝑚𝑒𝑥𝑡𝑆ℎ𝑒𝑙𝑙. The drag is evaluated considering the density at the average altitude, 𝜌 = 𝜌 (ℎ𝑟𝑜𝑐𝑘

2), and

the average velocity, 𝑉2 =𝑉𝑟𝑜𝑐𝑘2

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 = 1.1𝑚𝑟𝑜𝑐𝑘𝑔 (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:

𝑚𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 = 𝑚𝑟𝑜𝑐𝑘 −𝑚𝑚𝑎𝑖𝑛𝑇 (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 (𝑣𝑥,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):

𝑚�̈� + 𝑐�̇� + 𝑘𝑥 = 𝑚𝑔𝑀𝑎𝑟𝑠 (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) = (−𝑔𝑀𝑎𝑟𝑠𝜔2

+ (𝑣 −𝑔𝑀𝑎𝑟𝑠𝜔2

) 𝑡)𝑒−𝜔𝑡 +𝑔𝑀𝑎𝑟𝑠𝜔2

(16)

Stopping the engines at h = 15 m results in a contact velocity with the ground of:

𝑣 = √2𝑔𝑀𝑎𝑟𝑠ℎ = 11𝑚𝑠⁄ (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) = 𝑙𝑚𝑎𝑥(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

𝑔𝑀𝑎𝑟𝑠 , (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):

�⃗� 𝑏𝑜𝑑𝑦−𝑙𝑜𝑐𝑎𝑙 = �⃗� 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = �⃗� ∞ − �⃗� 𝑜𝑟𝑡ℎ𝑜𝑔𝑜𝑛𝑎𝑙 = �⃗� ∞ + (�⃗� ∙ �⃗� ∞) ∙ �⃗� (20)

Here �⃗� 𝑏𝑜𝑑𝑦−𝑙𝑜𝑐𝑎𝑙 = �⃗� 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 �⃗� 𝑜𝑟𝑡ℎ𝑜𝑔𝑜𝑛𝑎𝑙 = −(�⃗� ∙ �⃗� ∞), for �⃗�

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:

𝑐𝑝 =𝑝 − 𝑝∞12𝜌∞𝑉∞

2= 2𝑠𝑖𝑛2𝜃 (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:

𝐶𝐷 =1

𝐴𝑟𝑒𝑓∬ 𝑑𝐹𝑆

=∬ 𝑐𝑝�⃗� 𝑑𝑆𝑆

(22)

For 𝐴𝑟𝑒𝑓 , 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:

𝐶𝐷 = 𝐶𝐷𝑐𝑜𝑛𝑒 + 𝐶𝐷𝑠𝑝ℎ𝑒𝑟𝑒 (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, 𝑅𝑐𝑖; the radius at beginning of the spherical part,

𝑅𝑐𝑓 and the length of the conic part 𝐿𝑐.

𝐶𝐷𝑐𝑜𝑛𝑒 =

−1

𝐴𝑟𝑒𝑓

4𝜋 (𝑅𝑐𝑓 − 𝑅𝑐𝑖)4

𝐿𝑐3 ((

𝑅𝑐𝑓 − 𝑅𝑐𝑖𝐿𝑐

)

2

+ 1)

32

(24)

𝐶𝐷𝑠𝑝ℎ𝑒𝑟𝑒 =−2𝜋

3𝐴𝑟𝑒𝑓

cos (2𝑎𝑟𝑐𝑡𝑎𝑛 (𝑅𝑐𝑓 − 𝑅𝑐𝑖

𝐿𝑐)) − 5

√(𝑅𝑐𝑓 − 𝑅𝑐𝑖

𝐿𝑐)

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 =𝑚𝑡𝑜𝑡

𝐶𝐷𝐴𝑟𝑒𝑓=𝑚𝑏𝑜𝑑𝑦 +𝑚𝑛𝑜𝑠𝑒(𝑥)

𝐶𝐷(𝑥)𝐴𝑟𝑒𝑓 (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) =

𝑚𝑏𝑜𝑑𝑦 +𝑚𝑛𝑜𝑠𝑒(𝑥)

𝐶𝐷(𝑥)𝐴𝑟𝑒𝑓𝑉𝑜𝑙(𝑥) ≥ 𝑉𝑜𝑙𝑛𝑜𝑠𝑒

�́�(𝑥) = 1.90 ∙ 10−4𝑉∞3√

𝜌∞𝑟𝑛(𝑥)

≤ �́�𝑀𝐴𝑋

𝑚(𝑥) = 𝑆𝑙𝑎𝑡(𝑥)𝜌𝑛𝑜𝑠𝑒𝑡𝑛𝑜𝑠𝑒 ≤ 𝑚𝑛𝑜𝑠𝑒

(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:

𝑚𝐸𝐷𝐿 = 𝑚𝑎𝑒𝑟𝑜𝑏𝑟𝑎𝑘𝑖𝑛𝑔 +𝑚𝑝𝑟𝑜𝑝 +𝑚𝑡𝑎𝑛𝑘𝑠 +𝑚𝑒𝑛𝑔𝑖𝑛𝑒 +𝑚𝑅𝐶𝑆 +𝑚𝑙𝑎𝑛𝑑 (28)

The total module mass can then be written as:

𝑚𝑜𝑛𝑀𝑎𝑟𝑠 = 𝑚𝑚𝑜𝑑𝑢𝑙𝑒 +𝑚𝐸𝐷𝐿 ≤ 40𝑡𝑜𝑛𝑠 (29)

The EDL mass can be eventually divided considering the different phases of the manoeuvre:

𝑚𝐸𝐷𝐿 = 𝑚𝐸𝐷𝐿𝐻 +𝑚𝐸𝐷𝐿𝑎𝑒𝑟𝑜 +𝑚𝐸𝐷𝐿𝑟𝑜𝑐𝑘 +𝑚𝐸𝐷𝐿𝑙𝑎𝑛𝑑 (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:

𝑚𝑝𝑟𝑜𝑝𝐻 = 𝑚0 (1 − 𝑒−∆𝑉𝑐 ) (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:

𝑚𝑡𝑎𝑛𝑘𝐻 =𝑝𝑉𝑝𝑟𝑜𝑝𝐻

𝑔0Ф (32)

In equation 26, g0 stands for the Earth gravity. The volume of propellant can be evaluated in the following way:

𝑉𝑝𝑟𝑜𝑝𝐻 =𝑚𝑝𝑟𝑜𝑝𝐻

𝜌 (33)

In the end the mass of the EDL system for the first phase is:

𝑚𝐸𝐷𝐿𝐻 = 𝑚𝑝𝑟𝑜𝑝𝐻 +𝑚𝑡𝑎𝑛𝑘𝐻 (34)

Giving the entry mass as:

𝑚𝑒𝑛𝑡𝑟𝑦 = 𝑚𝑚𝑜𝑑𝑢𝑙𝑒 + (𝑚𝐸𝐷𝐿 −𝑚𝐸𝐷𝐿𝐻) (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):

𝑚𝑓𝑟𝑜𝑛𝑡 = 𝑚𝑠𝑡𝑟𝑢𝑐𝑡 +𝑚𝑡𝑝𝑠 = (0.0232𝑞𝑀𝐴𝑋−0.1708)𝑚𝑒𝑛𝑡𝑟𝑦 + (0.00091𝑄

0.51575)𝑚𝑒𝑛𝑡𝑟𝑦 (36)

The maximum aerodynamic pressure is expressed in Pa, 𝑞 =1

2𝜌𝑉2; the total heat load is expressed in [J/cm2]

and it is evaluated along all of the aerobraking phase, 𝑄 = ∫ �́� 𝑑𝑡 = ∫1.90 ∙ 10−4𝑉∞3√

𝜌∞

𝑟𝑛𝑑𝑡.

The back shell mass can be evaluated from historical data, considering its thermal and structural mass:

𝑚𝑏𝑎𝑐𝑘 = 0.14𝑚𝑒𝑛𝑡𝑟𝑦 (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:

𝑚𝐻𝐼𝐴𝐷 = 𝑚𝐻𝐼𝐴𝐷𝑠𝑡𝑟𝑢𝑐𝑡 +𝑚𝐻𝐼𝐴𝐷𝑡𝑝𝑠 (38)

So the EDL mass system for the second phase, 𝑚𝐸𝐷𝐿𝑎𝑒𝑟𝑜 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:

𝑚𝑟𝑜𝑐𝑘 = 𝑚𝑒𝑛𝑡𝑟𝑦 −𝑚𝐸𝐷𝐿𝑎𝑒𝑟𝑜 = 𝑚𝑚𝑜𝑑𝑢𝑙𝑒 + (𝑚𝐸𝐷𝐿 −𝑚𝐸𝐷𝐿𝐻 −𝑚𝐸𝐷𝐿𝑎𝑒𝑟𝑜) (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):

𝑚𝑅𝐶𝑆 = 𝑚𝑡ℎ𝑟𝑢𝑠𝑡 +𝑚𝑝𝑟𝑜𝑝 ≅ 0.0151𝑚𝑟𝑜𝑐𝑘 (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):

𝑚𝑒𝑛𝑔𝑖𝑛𝑒 = 0.00144𝑇 + 49.6 (41)

Considering the same propellant used for the Hohmann transfer, the propellant used in this phase is:

𝑚𝑝𝑟𝑜𝑝𝑟𝑜𝑐𝑘 = ∫𝑑𝑚 = ∫𝑇𝑑𝑡

𝑐 (42)

And for the tanks it is possible to use the same formulation considered for the Hohmann transfer:

𝑚𝑡𝑎𝑛𝑘𝑟𝑜𝑐𝑘 =𝑝𝑉𝑟𝑜𝑐𝑘𝑔0Ф

(43)

So for the retrorocket descent phase, the EDL system mass is:

𝑚𝐸𝐷𝐿𝑟𝑜𝑐𝑘 = 𝑚𝑅𝐶𝑆 +𝑚𝑒𝑛𝑔𝑖𝑛𝑒1 +𝑚𝑒𝑛𝑔𝑖𝑛𝑒2 +𝑚𝑝𝑟𝑜𝑝𝑟𝑜𝑐𝑘 +𝑚𝑡𝑎𝑛𝑘𝑟𝑜𝑐𝑘 (44)

In case of ejection of the main engine after the constant flight path angle descent, the mass can be considered

as:

𝑚𝐸𝐷𝐿𝑟𝑜𝑐𝑘 = 𝑚𝑅𝐶𝑆 +𝑚𝑒𝑛𝑔𝑖𝑛𝑒2 +𝑚𝑝𝑟𝑜𝑝𝑟𝑜𝑐𝑘 +𝑚𝑡𝑎𝑛𝑘𝑟𝑜𝑐𝑘 (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 = 𝑚𝑤ℎ𝑒𝑒𝑙𝑠 +𝑚𝑑𝑢𝑚𝑝𝑒𝑟 (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:

𝐹𝑤ℎ𝑒𝑒𝑙𝑀𝑎𝑟𝑠 = 3.5𝑔 𝑚𝑙𝑎𝑛𝑑/𝑛𝑤ℎ𝑒𝑒𝑙 (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.

𝑚𝑤ℎ𝑒𝑒𝑙 = 𝑚𝑤ℎ𝑒𝑒𝑙𝐸𝑎𝑟𝑡ℎ

𝐹𝑤ℎ𝑒𝑒𝑙𝑀𝑎𝑟𝑠𝐹𝑤ℎ𝑒𝑒𝑙𝐸𝑎𝑟𝑡ℎ

𝑛𝑤ℎ𝑒𝑒𝑙 (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):

𝐴𝑐𝑜𝑛𝑡𝑎𝑐𝑡 = 𝑎 ∙ 𝑏 = √𝐹𝑛𝑟𝑏(𝜃𝑤ℎ𝑒𝑒𝑙 + 𝜃𝑀𝑎𝑟𝑠)

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 − 𝜈𝑖2)/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

𝐴𝑐𝑜𝑛𝑡𝑎𝑐𝑡𝑛𝑤ℎ𝑒𝑒𝑙 < 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:

𝐴𝑐𝑜𝑛𝑡𝑎𝑐𝑡 = √𝐹𝑛𝑟𝑏(𝜃𝑤ℎ𝑒𝑒𝑙 + 𝜃𝑀𝑎𝑟𝑠)

𝜋>

𝐹𝑛𝑛𝑤ℎ𝑒𝑒𝑙𝐵𝑒𝑎𝑟𝑖𝑛𝑔 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:

𝐸𝑤ℎ𝑒𝑒𝑙 =

4(1 − 𝜈2)

𝐴𝑐𝑜𝑛𝑡𝑎𝑐𝑡2

4𝐹𝑛𝑏𝑟𝜋− 𝜃𝑀𝑎𝑟𝑠

=4(1 − 𝜈2)

𝐹𝑛4𝑏𝑟𝜋(𝐵𝑒𝑎𝑟𝑖𝑛𝑔 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦)2

− 𝜃𝑀𝑎𝑟𝑠

(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:


𝑚𝑑𝑢𝑚𝑝 = 6𝑚𝑠𝑢𝑠𝑝𝑒𝑛𝑠𝑖𝑜𝑛 (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 =𝑚𝑠𝑦𝑠𝑡𝑙𝑖𝑛𝑓𝑙−𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑

𝑙𝑚𝑜𝑑𝑢𝑙𝑒+𝑚𝑠𝑡𝑟𝑢𝑐𝑡 = 16000𝑘𝑔

4.4 𝑚

15.7 𝑚+ 1700 𝑘𝑔 = 6184 𝑘𝑔 (54)

𝑔𝑀𝑎𝑟𝑠 = 3.71 𝑚/𝑠2 (55)

𝑞𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑 =𝑚𝑖𝑛𝑓𝑙 𝑔𝑀𝑎𝑟𝑠

𝑙𝑖𝑛𝑓𝑙−𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑= 5.48

𝑘𝑁

𝑚 (56)

𝑉𝐴 = 𝑉𝐵 =𝑚𝐻𝐴𝐵

4𝑔𝑀𝑎𝑟𝑠 = 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 =𝑞𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑𝑙𝑖𝑛𝑓𝑙−𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑

2

2− 𝑉𝐵𝑙𝑖𝑛𝑓𝑙−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 =𝑀𝐴𝐽𝑑𝑖 (59)

Where the inertia can be evaluated knowing the position of the booms, supposing all with the same area:

𝐽 =∑𝐴𝑖𝑑𝑖2 = 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

2𝑀𝐴𝜎𝑦𝑖𝑒𝑙𝑑𝑑

= 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:

𝑚𝑏𝑜𝑜𝑚 = 4𝜌𝐴𝑙𝑖𝑛𝑓𝑙−𝑏𝑜𝑜𝑚 = 4 2800𝑘𝑔

𝑚3 33.84 10−4𝑚2 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:

𝑢𝑦 =5

384

𝑞𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑𝑙𝑖𝑛𝑓𝑙−𝑖𝑛𝑓𝑙𝑎𝑡𝑒𝑑4

𝐸𝐽= 1.6 10−5𝑚 (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 𝑔𝐸𝑎𝑟𝑡ℎ = 34.3 𝑚/𝑠2 (66)

𝑞𝑝𝑎𝑐𝑘 =𝑚𝑖𝑛𝑓𝑙𝑔𝑙𝑜𝑎𝑑

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:

𝑢𝑦 =1

8

𝑞𝑝𝑎𝑐𝑘𝑙𝑖𝑛𝑓𝑙−𝑝𝑎𝑐𝑘4

𝐸𝐽= 2.5 10−5𝑚 (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

Documents

EDL SEEDS VII