2.3 Descent Stage
Jeremy Davis
Nomenclature
HAB = Habitation Module
ERV = Earth Return Vehicle
CTV = Crew Transfer Vehicle
G = Force due to Earth Gravity of 9.81 m/s2
LRE = Liquid Rocket Engine
h = Acceleration of spacecraft towards Mars during descent
T = Thrust provided by the LRE during descent
mo = Initial mass of spacecraft prior to LRE burn
 = Propellant mass flow of the LRE during descent
m
t = time
gm = Acceleration due to Martian gravity (~ 3/8 G)
FAI/IPC = Fédération
Aéronautique
Internationale
/
International Parachuting
Commission
2.3.1 Descent Stage
In this section, we address the problem of decelerating the spacecraft from their
post-entry velocities (of ~ Mach 3) to their final touchdowns at the destination planet.
The analysis is presented in chronological order, beginning with the ERV descent to
Mars and ending with the CTV's Earth entry.
2.3.1.1 ERV Descent
Before analyzing the problem of the ERV entry it is necessary to first look at the
constraints. The ERV being launched first and carrying no humans makes the
constraints less critical than those of the HAB. However, the nature of the landing is
more complicated than that of the HAB. Because the ERV does not contain the crew,
the constraints are geared more towards mission-critical systems unlike the HAB entry,
which will be centered on life-critical systems.
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Constraints
The vehicle must not be subjected to more than 7 G’s for more than 20 seconds.
The velocity of the ERV at touchdown must be less than 1.0 m/s.
The ERV must have enough fuel for 20 seconds of hovering.
The third constraint is slightly trivial to the analysis because the appropriate
amount of propellant can just be added to the final results to allow for the hover.
It is our goal to optimize certain variables while working around these constraints.
Variables of Interest
The mass of the propellant.
The mass of the parachutes.
The risk of life-critical and mission-critical failures during the descent, which will
be assessed in Sec. 2.3.1.4.
With all the constraints and variables of interest in mind, the analysis was
completed for the HAB and the following results were obtained.
When the vehicle reaches Mach 1, the descent stage begins and five subsonic
ringsail parachutes, each 49m in diameter are deployed. At the moment of the subsonic
chute deployment, bolts connecting the ERV and the garage (which contains the rover)
are cut. The snatch force from the chute deployment pulls the two craft apart and the
garage quickly separates itself from the ERV. Soon after the separation, three ringsail
parachutes, also 49m in diameter deploy from the garage and large balloons inflate
from the craft to prepare it for landing. Because the ERV chutes are deployed first, but
the ERV weighs much more than the garage, the ERV overtakes the garage soon after
the parachute deployments. This, however, does not mean that the two spacecraft
collide. Because they separate while still traveling at about 236 m/s, their longitudinal
positions are slightly different; enough so that a collision is virtually impossible. At
approximately 1.47km above the surface, the subsonic parachutes of the ERV are cut
and the retro rockets are fired, providing a constant thrust of 330kN. Over the course of
the trajectory, the engine consumes 4.62 tonnes of propellant to set the ERV onto the
surface at a velocity of 0.385 m/s. The garage however, hits the surface of Mars at 21
m/s. Normally this would be a jarring landing that would be catastrophic to the garage
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and rover, but the balloons located around the garage dissipates the energy and causes
minimal loading on the garage during the landing.
Figure 2.3.1 shows the altitude history of this complicated descent. The solid line
represents the ERV and the dashed line represents its garage.
Figure 2.3.1 ERV Mars Descent - Altitude History [J. Davis]
Figure 2.3.2 shows the velocity history during descent of both the ERV and the
garage. Notice that the ERV has a much steeper velocity gradient than the garage.
This can be seen as an effect of the ratio of the parachute size to the vehicle weight. If
the parachute size to vehicle weight is relatively small, the parachutes will have a large
terminal velocity and small snatch force. If the ratio is relatively great, the parachutes
will have a small terminal velocity (which is a design goal for the garage) and a large
snatch force. Because we are designing the garage descent system to have as a small
terminal velocity as possible, we are forced to deal with a large snatch force. In the
case of the garage, the number of parachutes being used (three) is the greatest that
can be used without causing a snatch force too great for the structure to withstand.
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Figure 2.3.2 ERV Mars Descent - Velocity History [J. Davis]
Throughout the ERV descent, the G-forces incurred by the ERV and garage are
brief impulses of 8 and 12 G's respectively.
Figure 2.3.3 shows the mass breakdown for the descent stage of the ERV and
garage landings.
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ERV Descent Stage Weight Breakdown
357.7
594.4665
Subsonic Parachute Mass [kg]
Retro-Rocket Propellant Mass [kg]
Garage Parachutes [kg]
4.62E+03
Figure 2.3.3 Mass Breakdown of ERV Stage
2.3.1.2 HAB Descent
Upon entry, the HAB encounters a velocity of Mach 3 at an altitude of
approximately 17.5 km. At this point, three supersonic conical ribbon parachutes, each
30m in diameter, are deployed. Upon deployment, the crew will experience a peak of 5
G’s, which exponentially decays to about 1 G over a 20 second period. 42 seconds into
the descent stage, the HAB reaches Mach 1. At that time, the risers of the supersonic
parachutes are cut and five subsonic, ringsail parachutes, each with a diameter of 49m,
are deployed. As with the supersonic deployment, there is a snatch force that imposes
5 G's on the crew. That snatch force imposes an average g-load of approximately 3 G’s
for a period of 10 seconds. The subsonic parachute deployment decelerates the HAB
from 236 m/s to a terminal velocity of about 63 m/s, which takes about 57 seconds to
complete. When terminal velocity is reached, which is at an altitude of about 1.2km, the
subsonic chutes are cut and the retro liquid rocket engine (LRE) is fired. Over a time
span of almost 35 seconds, the LRE uses a constant thrust of 335.2 kN and 3.85 tonnes
of propellant to lower the HAB to the surface with a touchdown velocity of 0.89 m/s.
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Retro-Rocket Analysis Method
In order to simplify the problem, a constant thrust, and therefore constant
propellant mass flow is assumed. Using Newton’s 2nd Law, we find an EOM for the
descending rocket system, shown below.
h 
T
 gm
m0  m  t
(2.3.1)
By integrating the EOM, an analytical solution was found (see the Appendix for
details solution) and implemented into the code to solve for the trajectory.
Figure 2.3.4 shows an altitude history of the trajectory described above.
Figure 2.3.4 HAB Mars Descent - Altitude History [J. Davis]
From the above figure, the three stages of the descent are obvious. Each stage
reduces the slope of the trajectory by an amount enough to significantly reduce the
velocity at touchdown without increasing the g-loading beyond what our constraints
require.
Figure 2.3.5 below shows the velocity history of the HAB descent. This shows
more clearly how each stage contributes to setting the large spacecraft on the surface
of Mars. Figure 2.3.6 shows the g-load history during the descent. Note that the largest
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contributor to g-loading during the descent stage is the deployment of the supersonic
parachutes. This is because the spacecraft is moving at Mach 3 when the parachutes
are deployed, in contrast to the velocity at subsonic parachute deployment of slightly
less than Mach 1. Also notice the plateau at the end of the g-load history. This plateau
corresponds approximately to the gravity felt by the astronauts while on Mars.
Figure 2.3.5 HAB Mars Descent - Velocity History [J. Davis]
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Figure 2.3.6 HAB Mars Descent - G-load History [J. Davis]
HAB Descent Stage Weight Breakdown
Mass Breakdow n of HAB Descent Stage
135.667
594.4665
Supersonic Parachut e Mass [ kg]
Subsonic Parachut e Mass [ kg]
Ret ro-Rocket Propellant Mass [ kg]
3847.4045
Figure 2.3.7. Mass Breakdown of HAB Stage
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2.3.1.3 CTV Descent
The CTV descent is most difficult for the orbital mechanics (high incoming
velocities) but due to the atmospheric density of Earth, the main job of the descent
analyst is done by blunt body aerodynamics. It is because of this that we forego the
supersonic parachutes for the CTV and use subsonic ringsail parachutes when the CTV
reaches a velocity of Mach 1. Also, much like the Apollo capsule, the CTV uses no
retro rockets and instead, splashes down in the ocean. This reduces the weight by
relieving the need for an LRE and propellant but requires that we minimize the
touchdown velocity. In order to minimize the impact at splash down, the parachute
system is reefed. Reefing is a staging system where the parachutes are deployed but
the skirt of each parachute is kept constricted for a period of time.
This can be
compared to a choice between taking a staircase with 50 steps between two floors and
simply jumping down the elevator shaft to get to the lower floor. Taking one large step
may be simpler, but taking it in steps causes a reduction in snatch force.
After the appropriate time has passed, the reefing line is then cut and the
parachutes are allowed to fully deploy. This enables the parachute system to provide a
small landing velocity without an excessive snatch force.
For the CTV, the altitude at which Mach 1 is obtained is 63km. Five subsonic
ringsail parachutes are then deployed but reefed. It is at this point where analysis (at
this level) becomes beyond our scope. Because of the increased atmosphere, reducing
the g-loading using reefing is not as simple as staging. Instead, the reefing lines would
be "let out" over a time period until the lines would be let loose completely and the
parachutes would be fully deployed. Returning to our stairway analysis, this would be
the equivalent of replacing the stairs with a slide, affording nearly no impact at all to go
from one for to the next. For analysis however, the touchdown velocity and parachute
weights remain the same. The touchdown velocity for such a descent is only 3.2 m/s
and the weight of the parachutes are 594 kg.
2.3.1.5 Risk Analysis
Parachute analysis by nature is experimental. The turbulence of the flow and
absence of structural rigidity of the parachutes makes it virtually impossible to do
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analysis (such as risk analysis) on the systems without looking at historical data. The
following are possible modes of failure occurring within the parachute system:
-
Electronic failure (i.e., sequencers, timers, etc.)
-
Mechanical failure (i.e., bay doors, door latches, etc.)
-
Actual parachute failure (i.e., risers snapping, fabric tearing, etc.)
With respect to the relative rate of occurrence of these three failure modes,
Manley C. Butler, Jr., President of Butler Parachutes Systems, Inc. remarks, “In my
experience with a wide variety of recovery systems, the electronic components have the
highest failure rate (sequencers, timers, etc.) followed by the mechanical items (door
releases, etc.) then followed a long way back by the parachute components (actual
textiles).”
In order to get an estimate of the occurrence of the most infrequent failure mode
in recovery systems, we found statistics pertaining to catastrophic failures of personal
parachute systems.
According to FAI/IPC Technical and Safety Subcommittee
Congress meeting, 74 catastrophic failures were experienced during 4,848,025
recorded parachute deployments. This results in a failure rate of .0015%. This means
that for one parachute deployment, the odds that the parachute will fail catastrophically
are 1 in 65,500. For the purposes of our mission, there are 13 parachute deployments
that are life-critical (and mission critical) and 8 deployments that are mission-critical
only.
If any one parachute fails during the descent, the failure would result in a
catastrophic failure of the descent stage and mission. With this in mind, the odds of a
life-critical failure (anomaly resulting in loss of crew due only to parachute failure) are
0.00195%. The odds of a mission-critical failure are 0.00315%. These figures mean
that, statistically, we would need to fly 513 missions (clear of any non-parachute-related
failures) before the crew would be killed by parachute-failure. Also, we would need to
fly 317 missions before we had a mission-critical parachute failure (i.e., one of the ERV
parachutes failing, ending the mission but not killing the crew still on Earth).
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References
Knacke, T.W., “Parachute Recovery Systems: Design Manual”, Para Publishing, Santa
Barbara, CA, 1992
Humble, R.W., Henry, G.N., Larson, W.J., “Space Propulsion Analysis and Design”,
McGraw Hill
Fédération Aéronautique Internationale / International Parachuting Commission,
http://www.afn.org/skydive/sta/stats.html
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