Manned Mars Flyby Mission Concept (Team Red Rock Trail Blazers)
by Eric Burnett, Donovan Chipman, Devon Garner, and Jordan Holmberg
Introduction
This document contains the response to a design competition which has been opened to
design a manned Mars flyby mission beginning sometime between the years 2018 and 2021.
The requirement is to be able to support a crew of two individuals during the course of the
mission, return them safely to earth, and to do so as simply and cheaply as possible.
This team feels that such requirements can be met by using the following:
1) low cost launch vehicles now or soon to be commercially available in the United States,
2) expandable habitats based on previous telescoping space station module developments,
3) a spinning of such habitats to create low levels of artificial gravity,
4) low weight deployable solar panels,
5) water as a propellant for use in in-space propulsion systems,
6) solar electric magneto-plasma rocket engine technology for in-space propulsion,
7) water as a source for oxygen via electrolysis,
8) polyethylene, water, food storage, and heavy propulsion equipment for radiation protection,
9) deployable radiator panels,
10) star tracking technology and electronic gyroscopes for guidance and navigation,
11) radiation hardened electronic systems,
12) omni-directional coil radio antenna for deep space communications with earth with a small
number uni-directional high gain antennae for redundancy,
13) fault tolerant s-band telemetry,
14) a highly simplified environmental control and life support system (enabled by artificial gravity
and large amounts of water “propellant”) that minimizes the requirements for recycling,
15) and soon to be available commercial manned vehicles for use during crew launch and earth reentry.
Using these technologies, a flyby mission with a total manned duration of 825 days is
possible. A notional rendering of the candidate Mars flyby spacecraft is shown in figure 1. This
document will discuss potential technologies that could be used, the overall selected mission
profile, the spaceflight trajectories that are to be used, the various systems within the candidate
spacecraft, and approximations of the financial cost of such a mission.
Launch Vehicles
The most basic requirement for a manned Mars flyby mission is the ability to
propulsively provide the Delta-V required for the particular trajectory that is to be used.
Inspiration Mars has selected a 2018 flight opportunity as its first choice for just such a flyby
mission. This trajectory, which is capable of being completed start to finish in a period of 501
days, requires a C3 energy of 38.8 km2/s2.
Various international commercial launch vehicles are available to be used for a mission
of this nature, including the European Ariane V, the Russian Soyuz and Proton launch vehicles,
the Japanese H-IIB, Chinese Long March series rockets, and potentially even the Indian PSLV,
but it is likely that ITAR restrictions would cause mission planners to use launch vehicles from
the United States. American launch vehicles large enough to be considered for such a mission
include the Atlas V, the Delta series vehicles (Delta 2 and Delta IV), the Falcon 9 rocket, and
Orbital Science’s Antares launch vehicle. NASA’s Space Launch System (SLS) is also easily
large enough, but its use is not likely to be permited by NASA. The largest of the remaining
vehicles is the Falcon Heavy, which is to have the ability to place 53 metric tonnes (mT) of
payload into LEO, 21 mT into a geosynchronous transfer orbit (GTO), and 13 mT onto a 14
km2/s2 trans-Mars injection (TMI) trajectory. A Falcon Heavy was selected for the scenario
presented herein.
In-Space Propulsion
Many propulsion systems and propellant combinations exist that can be used to propel a
mission that begins in Low Earth Orbit. In the U.S., large upper stages are available that utilize
solid propellants (usually HTPB), kerosene with liquid oxygen, and liquid hydrogen with liquid
oxygen.
There are presently restrictions on the hydrogen/oxygen upper stages, since all US
versions are made by United Launch Alliance, LLC (ULA) and this company is only allowed to
sell launch services, not independent spacecraft or rocket stages. However, if one were to
assume such availability, then a vehicle using LH2/LOX propellants (yielding a specific impulse
(Isp) of perhaps 460 seconds) would need a mass ratio of 4.2 to obtain the required 6.48 km/s of
delta-V. If a Falcon Heavy launch vehicle was used, then a 53 mT vehicle in LEO with
LH2/LOX propellants could place 12.6 mT, including the rocket stage dry mass, onto the 35.6
km2/s2 trajectory. Assuming a stage mass ratio of 11 (comparable to a Centaur upper stage), then
the rocket stage would use 3.67 of the 12.6 tonnes, leaving just under 9 mT for usable payload.
Using the same starting mass of 53 mT, a vehicle using kerosene/LOX propellants would
have an Isp of perhaps 340 seconds, and thus require a mass ratio of 7 to obtain the needed 6.48
km/s of delta-V. The total mass placed onto the fast TMI trajectory would be 7.6 mT, and a
stage mass ratio of 15 would leave a payload of only 4.5 mT. The Falcon Heavy could carry a
larger payload on the same trajectory without the extra upper stage, so consideration of anything
with a lower Isp than that achievable with LH2/LOX would be unproductive with the specified
launch vehicle. All told, the very mature state of chemical propulsion would make it a top
candidate for use in a Mars flyby mission, however, its low performance characteristics make
such a flyby difficult to do cheaply and in a timely manner. Development and testing of new
large chemical propulsion systems require large and expensive test facilities, and even if
chemical propulsion is a mature technology, the likelihood of being able to developing such
large systems in the required time frame is probably rather low.
Many other methods besides chemical propulsion have been considered for use in space
travel, but very few of them have reached a scale and level of maturity that would allow them to
be fielded prior to the 2018 (or even 2020) launch window at a reasonable cost. Of these, the
rules of the competition only allow for solar electric propulsion.
Electric propulsion systems produce low thrust and tend to require a spiral out maneuver
that requires a long period of time to raise a spacecraft’s orbital altitude. Electric propulsion
systems are similarly limited by the power production of current space systems. The
International Space System (ISS), for example, produces a peak power output of less than 200
kW. The largest two-wing MegaFlex solar panel arrays from ATK, if constructed and tested in
existing facilities, could only produce 250 kW.
One very mature electric propulsion technology is the gridded ion thruster. Such
thrusters have been ground tested at power levels as high as 100 kW, with specific impulse
values approaching 9,000 seconds, and efficiencies above 90%. The technology has been
successfully utilized on several unmanned spacecraft. Hall thrusters are another type of electric
engine that has been used on many satellites for station keeping. NASA is seriously considering
using these types of engines for a manned flight to near Earth asteroid in the mid- 2020s. As
such, this technology would be an excellent candidate for a mission of this nature.
Another type of electric propulsion technology is called VASIMR (Variable Specific
Impulse Magnetoplasma Rocket), built by the Ad Astra Aerospace corporation. This technology
has been tested at higher power levels than ion engines have, and its specific impulse can be
much higher (perhaps as much as 30,000 seconds), but it has a lower efficiency of only about
72% thus far, and at sub-MW power levels, it does not offer a significant weight advantage over
other electric engine technologies. Another issue is the fact that cooling of such powerful
engines is difficult, and until recently, engine designs did not account for that, relying on pulse
firings for testing. Its advantage is that it can scale up to high power levels, if large enough
space rated power systems could be developed, and at such power levels these engines weigh
considerably less than alternate electric propulsion systems.
That reasoning, however, is not immediately applicable to this mission, as test facilities
for such large engines do not exist. What is applicable is the fact that VASIMR engines can use
water as a propellant. Water does not have the toxicity issues of other propellants, does not
require cryogenic storage, is not highly explosive, and, importantly, is a requirement for the crew
consumables budget anyway. Also, according to the University of Michigan’s Plasmadynamics
and Electric Propulsion laboratory, water has a specific impulse of approximately 2,000 seconds,
which is ideal for climbing out of a gravity well, as higher thrust for a given power level is
attainable. Spinning the engines around the axis of rotation (while producing artificial gravity)
can allow for pulse firings as well. Thus VASIMR is base-lined for this mission, not because of
the potential for high relative speeds, but because of the advantages that come with having the
bulk propellant supply double as a crew consumable.
Figure 1: A notional representation of the deep space vehicle (DSV) to be used for the manned Mars flyby
mission.
Mission Overview
The Mars flyby mission herein considered begins with the launch of three SpaceX Falcon
Heavy launch vehicles spaced two months apart beginning in early June 2018. Each launch
delivers one of the three major spokes of the Mars flyby deep space vehicle (or DSV, shown in
figure 1) to low Earth orbit (LEO). Upon arrival in LEO, each vehicle is allowed a period of 21
days for system activation and checkouts. During this checkout period, each vehicle deploys its
four 28 meter diameter solar arrays (based on ATK’s Megaflex™ technology) and the radiators
for the propulsion array. The arrays sit on a small rotating platform, so that they can track the
sun. The solar panels each produce 225 MW of electricity for the electric propulsion array,
which is composed of 6 x 100 kW VASIMR engines, a 900 kW power transformer, a 600 kW
power signal conditioner, a 15 kW-hr battery bank, and a primary propellant tank. During this
period, proximity operations for docking, which will be required later, are also tested.
On January 4, 2019, the three spacecraft units fire their thruster arrays and travel in
convoy on a spiral out maneuver. (See figure 2). The thruster arrays are pulsed (12 seconds on,
8 seconds off) to allow for cooling, and are operated at 83% of their maximum power rating.
The thrusters are not fired while the spacecraft units are in the Earth’s shadow, as there is no
access to solar power. With a dry mass of 17,200 kg, an initial propellant load of 27,800 kg of
water (which is assumed to have a specific impulse of 1800 seconds for this portion of the flight)
and with a maximum propulsive power of 500,000 kW, each unit reaches the edge of Earth’s
sphere of influence (SOI) in 111.4 days, after burning 15,510 kg of propellant. Thrust in this
case is always directed 90 degrees counter-clockwise (as viewed from above Earth’s north pole)
from a line formed between the center of the Earth and the spacecraft. At this point, a total deltaV of 7.46 km/s has been applied to each unit. Thus, the official journey into deep space begins
on April 25, 2019.
Figure 2: A chart showing the path of the spiral out maneuver that each Deep Space Module (DSM) would
use to leave the sphere of influence of Earth’s gravity. Distance on each axis is shown in units of meters.
The crew of two is launched three days earlier, on April 22, 2019, aboard a man rated
SpaceX Dragon capsule. The capsule is placed on a trajectory parallel to that of the
aforementioned spacecraft units by a fourth and final Falcon Heavy launch. Attached to the
capsule is a four port docking module, which includes an omni-directional radio antenna for deep
space communications with Earth.
Once the three spacecraft units are flying in formation with the capsule, the three units
individually dock with the docking module. Using oxygen electrolyzed from the onboard water
supply, the habitat modules are pressurized to 3 psi and in the process expanded from their
stowed length of about 6 meters long to their full length of 15 meters. The Dragon capsule then
separates from the docking module, turns itself around, and re-docks nose first with the docking
module.
The combined spacecraft now fires its gaseous hydrogen/oxygen thrusters (also using
propellant from electrolyzed water) to spin itself up to a rotation rate of 3 rpm, creating artificial
gravity at the outer edge of the habitat modules equal to that of the moon, or about 1/6th of
Earth’s gravity. If the rotational velocity were increased to 4 rpm, then the artificial gravity
produced would be about 1/4th of Earth’s gravity, but crew comfort begins to become a concern
at such a rate of rotation. These operations need to take place over the course of about one day.
With the spacecraft fully configured for the Mars flyby, the electric propulsion arrays are
again activated to place the vehicle on a trans-Mars trajectory (see figure 3). The rates of firing
pulses change, however, from each array being on 60% of the time (while in sunlight, at least) to
only being on 33% of the time. Because the ship rotates every twenty seconds, each array is on
for 6.7 seconds, and off for the next 13.3 seconds. While extra solar arrays are required to cover
the drop in solar power availability as the spaceship moves farther away from the sun, the overall
power requirement for the ship’s entire propulsion system is only half of what it was for each
spacecraft unit while the units were spiraling out of Earth’s orbit. This reduction in the power
requirement is partially because the gravitational effect from the Earth is no longer as significant,
and partially because most of the momentum change needed has already been imparted to the
vehicle. Thus, three 600 kW propulsion arrays are available to cover a propulsive power
requirement of only 250 kW. At this power level, only three engines per array need to fire at a
time (and only at 83% of rated power), meaning that each engine is on for 6.7 seconds, and off
for 33.3 seconds, greatly simplifying the cooling requirements on the propulsion systems.
Figure 3: A graphical representation of the flight path that the DSV would use for the deep space portion of
the Mars flyby mission.
The engines continue to fire for a period of 190 days. The average thrust is constant at
25.5 N until day 181 when the available solar power drops below that required for full power.
During the remaining ten days, the average thrust drops gradually to 24.3 N. Thrust during the
outbound deep-space portion of the journey is always directed “behind” the vehicle, starting with
the engines located sixty degrees on one side away from a line formed in the direction of travel,
and continuing until the engine reaches a location 60 degrees away from the same line on the
opposing side.
The vehicle coasts through space between day 191 and day 588.
The actual flyby of Mars takes place on day 213 (see figure 4). To minimize the impact
of Mars’ gravity on the spacecraft’s trajectory, the vehicle is targeted to move no closer to Mars
than 2/3 of the radius of the planet’s sphere of influence, meaning a distance of about 250,000
km, which is a little more than half of the distance between Earth and its moon.
At this point, the crew has only been in space for a quarter of the total travel time with
609 days remaining until the crew returns to Earth. The spacecraft will continue to coast
outwards from the sun until it reaches a maximum orbital distance of 302.5 million kilometers on
day 439, at which point the orbital distance from the sun begins to decrease.
Figure 4: A graph showing the distance of the spacecraft from Mars (y-axis in meters) vs the day of the
deep space mission (shown in days on the x-axis).
On day 589, the electric propulsion arrays are again activated, though at reduced average
thrust levels and fired opposite the direction of motion, again while engines rotate between -60
degrees and 60 degrees relative to the flight path. The maximum availability of propulsive
power (which is only a percentage of the total electric power available due to inefficiencies) at
this time is 157 kW, allowing for a thrust level of 16.1 N. As the vehicle gets closer to the sun,
the propulsive power availability increases, until it reaches 205.3 kW on day 657, the last day of
the engine firing, allowing for a thrust of 20.9 N. The spacecraft then coasts for the remainder
of its journey, ending on day 822. (See figure 5.)
There is a possibility that the deep space vehicle could be placed back into a high orbit
around the Earth for later reuse. This would likely require separating the Dragon capsule with
crew on board many days prior to entering Earth’s SOI to allow for propulsive maneuvering of
the DSV. Such a maneuver would also depend on the remaining propellant load, which could be
as much 8 metric tons. No attempt was made to analyze this option, though its implementation
would seem to be highly advantageous from a cost perspective.
Based on an initial approach velocity of 4,240 m/s at Earth’s SOI, entry velocity is
predicted to be 11.8 km/s, which is well within the capabilities of the current Dragon capsule
heat shield.
Figure 5: A graph showing the distance of the spacecraft from Earth (y-axis in meters) vs the day of the
deep space mission (shown in days on the x-axis).
Alternate Vehicle Assembly Scenario
A major risk in the previously described scenario is the limited time availability for
docking the various elements of the spacecraft together in deep space. An alternate option would
be to launch and assemble all of the spacecraft elements in low Earth orbit, and allow the vehicle
to fly in the same form it used in in deep space. The advantage of this method is that much more
time is available for docking operations, potentially weeks, instead of one day. The disadvantage
is that the spiral out maneuver would take more than a year, instead of approximately four
months. Additionally, to make up for the time lost in the spriral out maneuver, mission launches
would need to begin 8 months earlier, placing the first launch in late 2017. This scenario also
requires a fifth launch, though a smaller SpaceX Falcon 9 will suffice to carry the four metric ton
docking module into low Earth orbit, and the assumed two months between launches will not be
required because the Falcon 9 can use a different launch pad.
If the schedule risk in using this method is deemed acceptable relative to the mission risk
of a rapid deep space set of dockings, then the following scenario can be considered instead.
A Falcon 9 carrying a small docking module launches early in November 2017. This
docking module contains its own propulsion and service module for use in docking, which will
be discarded prior to the departure for Mars. The first Falcon Heavy launch carrying a deep
space module (DSM) launches in late November, 2017. December 2017 is spent activating the
two modules, and docking them together. The second Falcon Heavy launch carrying a second
deep space module takes place late in January of 2018. February can be spent checking out this
second DSM, and connecting it to the central docking module. The third launch takes place on
March 24, 2018. Three weeks later, after all checkouts have been completed on the final DSM,
it too is connected to the central docking module. The deployment of the solar panels and
radiators for the propulsion system, and the expansion of the collapsed habitat modules, are
performed for the three DSM units.
The propulsion array is fired up for the first time on April 16, 2018. (See figure 6.) The
engine arrays (each in turn) produce 34 N of thrust, but all of the engines turned off while the
vehicle is in the Earth’s shadow. After 373 days, on April 24, 2019, the mission proceeds as
previously described.
Figure 6: A chart showing an alternate path that the combined DSV would use to leave the sphere of
influence of Earth’s gravity. Distance on each axis is shown in units of meters.
Trajectory Calculation Methods
When considering spaceflight trajectories for the Mars flyby, as should be apparent at this
point, only two dimensions were used, where three dimensions can often be more appropriate.
However, due to the low orbital inclination of Earth and Mars relative to each other (less than
two degrees) only a moderate amount of delta-V should be needed to cover additional distance in
the third dimension. The deep space vehicle can begin the spiral out maneuvers in an identical
orbital plane to that used for the deep space portion of the mission, and a 17% performance
reserve was left on the launch vehicle to cover that possibility (i.e. only 45 mT of a 53 mT LEO
maximum for the Falcon Heavy was used). There are also significant power and propellant
reserves available should significant plane changes to the vehicle’s orbit around the sun be
required.
The locations of the planets were determined using the methods found at the website
http://www.stargazing.net/kepler/ellipse.html. The sample QBasic program downloaded from
the website was modified to run in Scilab. The Scilab code used is included in Appendix A. The
three dimensional locations and velocities of the Mars and Earth were calculated at an interval of
one day, beginning January 1, 2017, and ending December 29, 2021, and the two dimensional (x
and y) values of their positions and velocities were saved to a spreadsheet. Earth orbiting and
deep space portions of the mission were calculated separately, and the position and velocity of
the Earth were used as components in determining the initial orbital characteristics of the DSV
for the deep space portion of flight.
The initial low Earth orbit for the spacecraft elements was defined to begin at an altitude
of 329 km, with an initial velocity of 7,800 m/s. The initial position was chosen to occur at a
point on the coordinate system’s x-axis with a velocity normal to that axis as a matter of
convenience, since the relative position would be shifted later to match the initial position of the
deep space journey’s coordinate system. Calculation of the spacecraft’s position was done using
a brute force method – basically, Newton’s laws were applied with tens of thousands of time
steps. The only two forces considered in the Earth orbit portion of the trajectory calculations
were the thrust provided by the vehicle, and the gravitational force of the Earth. 128,000 time
steps, each 75.2 seconds in length, were used for the primary mission scenario in which the three
major spacecraft components spiraled out separately. The alternate mission scenario used time
steps of 252 seconds.
The acceleration provided by Earth’s gravity was calculated using Newton’s law of
gravitation:
in which as,E is the acceleration towards Earth’s center of mass, ME is the mass of the Earth (5.97
x 1024 kg), and rs,E is the distance of the spacecraft from the center of the Earth.
The propulsive contribution to the thrust was calculated using the following:
in which Fs, is the thrust produced by the spacecraft, PAP is the available propulsive power, and
vex is the velocity of the exhaust produced by the engines relative to the vehicle. The exhaust
velocity is calculated as follows:
where Isp is the specific impulse of the engines propellants, (in this case, approximately 2000 s),
and g is the acceleration of Earth’s gravity at sea level (9.81 m/s).
The available propulsive power is determined by multiplying the total power input from
the solar panels by an efficiency value. For the VASIMR engines being considered, this
efficiency is approximately 72% at the optimal power level, which can be achieved by the
described vehicle even at low power levels due to the use multiple engines that can be turned on
and off as needed. An additional inefficiency that applies in this mission scenario is that of
“cosine losses”, which occur when the thrust applied does not occur in exactly the opposite
direction of intended acceleration. As the vehicle spins, the thrust is applied over a rotational
range of 120 degrees. This means that only about 82% of the impulse imparted to the vehicle is
gainfully converted into a change in momentum. Also, there is the fact that only one third of the
solar panels are producing power at any given time, because the remaining 2/3 of the panels are
facing away from the sun. (While each panel is not actually facing the sun directly that full 1/3
of the time, the other panels also provide some contribution during this time, so the 1/3 factor is
fairly accurate.) Thus relative to the total power production capability of the vehicle, the
available propulsive power is:
where ηen is the 72% engine efficiency, ηrot is the 33% of the total power availability caused by
the panels not always facing the sun, and ηcos is the 82% thrust cosine loss factor.
Total power production capability of the spacecraft is dependent on the solar panel
surface area, the solar power flux, which varies as a distance from the sun, and the efficiency of
the panels themselves. The total spacecraft power availability is thus:
where P”sol,E - bar is the average power flux from the sun at Earth’s position (1,370 W), Apan is
the area of the solar panels (6,568 m2 total for 12 x 28 m diameter panels with inner 1/3 radius
removed open), and ηpan is the efficiency of the solar panels (assumed to be 30%), which at
Earth’s orbital position means a total power production capability of of 2.7 MW.
With this information, the engine thrust can be calculated. The acceleration created by
the engine thrust is found by dividing the thrust by the vehicle mass.
where aS,en is the acceleration of the spacecraft created by the engine and mS is the mass of the
spacecraft.
The spacecraft mass, however, is not constant – it is reduced as propellant is burned. The
propellant consumption is found by using the following formula:
in which m_dot is the mass flow rate of the propellant. Thus the mass is calculated at any time
step by taking the mass at the previous time step and subtracting the product of the mass flow
rate and the length of the time step, shown as:
where mnew is the mass of the vehicle at the current time step mold is the mass of the vehicle at the
preceding time step, and t is the length of the timestep. To determine the maximum theoretical
change in velocity that can be produced by burning a given amount of fuel on a particular
vehicle, the following equation can also be used:
in which v is the change in velocity, minit is the total mass of the vehicle including propellants
at the start of the burn, and mfinal is the mass of the vehicle at the end of the burn, or the initial
vehicle mass minus the consumed propellant mass. As described earlier, the average direction of
the thrust is defined in the mission scenario as being either normal to the vector between the
Earth and the spacecraft (for the earth orbit portion of the mission) or as being in line with the
vehicles direction of flight for the deep space portion of the journey. The gravitational and
propulsive total accelerations are then broken down into x and y components, and added
together.
The velocity at any point is found by adding the product of the acceleration and the time
step to the velocity at the previous timestep, as follows:
in each direction, where vnew is the updated velocity for the current time step, vold is the velocity
at the previous time step, and anew is the acceleration at the present time step.
Position is determined in a similar manner, by adding the product of the velocity and the
length of the time step to the previous velocity as follows:
in which snew is the position at the current time step and sold is the position at the previous
timestep.
The total power availability, and thus the thrust, is always zero while the vehicle is in the
Earth’s shadow. The Earth’s shadow was defined as being a stationary triangular wedge 9.213 x
10-4 radians wide with a termination point 1.385 x 106 km away from the center of the Earth.
The vehicle was defined as being in the shadow if for a given y location value, the distance from
the y axis was less than the shadow width at that y value.
The deep space trajectory design process began by rotating the LEO trajectory about the
Earth on the coordinate system of the deep space simulation by a user specified angle. The thrust
was taken to be the maximum amount possible based on either engine thrust limitations or solar
power availability, whichever was lower. The only gravitational force accounted for in this part
of the mission was that of the sun. The first and last day of engine firing could be entered
manually. A time step of one day, much longer than that used for the Earth orbit portion of the
trip, was possible because the deep space orbit is much larger – only one orbit around the sun
was completed compared to 590 orbits around the Earth .
By trial and error, it was shown that the best results were obtained when the first day of
firing was on day 1 of the deep space journy, which is not surprising because that is when the
largest amount of power is available. The last day of engine firing was then modified until the
spacecraft trajectory came nearest to the Earth after approximately two years. Additional course
corrections were found to be necessary, however, so a retro-burn period was included. This
required more trial and error, but it was obvious that the retro-burn needed to take place on the
inbound leg of the voyage. Once an acceptable general trajectory was established, the entire
trajectory was then rotated about the solar system by altering the mission start date until the
vehicle flew an acceptably close distance to Mars. (This distance had to be close enough to get a
good view of Mars, but no so close that the planet’s gravity would seriously alter the vehicle’s
trajectory – a limitation imposed by the model used.) Additional minor changes had to be made
to the burn schedule each time the mission start date was changed due to the minor eccentricity
of Earth’s orbit.
After several attempts, it was determined that an acceptable rotation angle for the LEO
trajectory was approximately -1.5 radians relative to the Earth’s direction of motion, though is
varied between about -1.48 and -1.53 radians depending on the start date. If the engine burn
began on April 24, 2019, as was selected for this scenario, then the best day to end the burn was
found to be October 30, 2019. With a retro-burn starting date of November 30, 2020 and a retroburn ending date of February 6, 2021, the vehicle came within 121,000 km of Earth at the exact
time of the time step. With smaller time steps, a refined burn schedule would easily make it
possible to hit the Earth directly, since an additional day added to the retro-burn would cause the
vehicle to undershoot, rather than overshoot, the Earth’s position.
Spacecraft Design
The DSV is composed of three DSM units and a docking module, as has already been
described. The DSM units are composed of the propulsion arrays and the habitat modules,
including the toroidal water tank. Total interior volume of the spacecraft is approximately 365
cubic meters.
Habitat Modules
Each habitat module is composed of three telescoping sections with an approximate
diameter of 3 m, and lengths of 5 m for the lower section, 4.5 m for the middle section, and 5.5
m for the upper section. The difference is length of each section is due to the need to fit the
barrels on top of the end domes, but still stay within the 6 m toroidal water tank height limit.
The design of the habitat is based very heavily on the “Expandable Space Structure”
development (Interim Technical Documentary Report Nr. ASD.TDR.7-943a(1), Martin Marietta
Corporation, 1963) done by the US Air Force between 1962 and 1963. In that development
project, a 5 section boiler plate ground test unit measuring 4.57 meters long and 2.42 meters in
diameter was built and ground tested. Deployment was done by pressurizing the internal volume
of the spacecraft. Pressure inside was maintained by the use of either grooved v-tongue seals or
o-ring seals on flanges placed at the top of bottom of each interior section. A similar system is
recommended for use on the DSV habitat modules.
While stowed for launch, the habitat has a total length of 6 meters, but it expands to 15
meters when deployed. (See figure 7)
Figure 7: The habitat module design, shown in a stowed configuration for launch on the right, and in its deployed
form for use in space.
The habitat is set up with two floors in the lower section and one floor in each in the
middle and upper sections. The crew lives, for the most part on the bottom level of the lower
section, where there are sleeping arrangements, food preparation areas, and hygiene facilities
(see figure 8). The cabin is not roomy, but it is large enough for two astronauts to sleep, cook,
and maintain themselves. The smaller volume makes it easier to provide the necessary radiation
protection. The upper floor of the lower section is used for food and supply stowage during
launch, and is used primarily for short term storage needs during the mission. There is a thin
radiation shield composed of polyethylene plastic located between the upper and lower floors of
this section. Its density is about 10 g/cm^2
Additional food storage kept on the upper floor helps to augment to radiation protection
during much of the journey. The middle section is also used for storage of less commonly used
items, or longer term food supply, or even just packaging waste.
The upper section has a single 18 inch viewing port. The direction of the viewing port
depends on the module, as one has the port on top, another on the bottom, and the third on the
side (as viewed from above the docked crew capsule). This upper section also contains the
electrolysis unit for the life support system, the docking ring, and vital module interfaces.
Transport between floors of the habitat is done by climbing small extendable ladders.
Figure 8: Layout of the lower level of a habitat module, where the crew will spend most of the mission.
Stowage for Launch
Figure 9 shows a single DSM in its configuration stowed for launch. The U.S. aerospace
industry only has facilities to process payloads that fit into volume 5 meters in diameter by about
15 meters long. A similar restriction applies to the payload fairings on Falcon Heavy launch
vehicles. (Actually, current Falcon Heavy launch fairings are limited to payloads 10 meters in
length, but it is likely that future military launch contracts, if awarded to SpaceX, would require
longer fairings, so this should hopefully not be an issue by the time of this mission.)
Additionally, test facilities are limited to spacecraft components less than 30 meters in
diameter. Thus, the solar panels used on the DSV are only 28 meters in diameter, and the
radiators are likewise not more than 30 meters long.
The habitat module collapses down for this reason as well, though under a different
vehicle architecture, the 15 meter length could be accommodated without the need for
telescoping segments.
Figure 9: A DSM shown with propulsion array, toroidal water tank, and hidden habitat module in stowed
configuration for launch.
ECLSS
At the present time, Inspiration Mars is working with Paragon Aerospace to develop a
life support system for the flyby mission. If such a unit is not overly heavy, then its use would
be recommended.
However, a potentially simplified system based on the usage of electrolyzed water to
provide oxygen, and a membrane based system to separate out non-oxygen components from the
air could be utilized. The advantage of such a system for this particular vehicle, is that waste
gases can be pumped through the VASIMR engines and used as propellant for a large part of the
journey. Separated hydrogen could be used either for the reaction control system or for the
primary propulsion engines. Additional oxygen would be made available from the RCS
propellant production process anyway, because hydrogen/oxygen rockets do not usually run at
stoichiometric fuel to oxidizer ratios, instead running fuel rich, leaving excess oxygen.
However, such a process would not produce enough oxygen alone for the crew.
Oxygen requirements vary depending on the level of crew activity, but generally, an
astronaut uses 0.8 kg of oxygen per day. A crew of two over a span of 825 days would thus use
1,320 kg of oxygen, electrolyzed from 1,485 kg of water.
Left over hydrogen, if not being used in the RCS, could be used in a Sabatier reactor to
react with exhaled carbon dioxide and produce methane and water. This would require that the
atmospheric membrane separator be able to distinguish carbon dioxide as well as oxygen and
water. The produced methane could then be stored for later use in the main propulsion system,
or if necessary vented. The water produced could then be returned to the water storage tanks to
continue to provide radiation protection and propellant reserves. In essence, using this system,
the oxygen comes free, so long as energy is available for the electrolysis and membrane units.
The presence of artificial gravity is very helpful in processes such as water/solid
separation. It also simplifies the processes of showering and the use of restroom facilities.
Finally, in regards to the environmental control systems, it reduces the reliance on circulation
fans, which are necessary in micro-gravity to move air, and thus exhaled carbon dioxide, away
from the crew.
Water usage management is important as well. Over the first 190 days of the manned
mission, the crew has the option to use more than 21 metric tons of water, which is the amount of
propellant used for the outbound engine burn. This means that each astronaut can use 50 kg of
water, or 14 gallons, each day. This is nearly five times as much water as is used by current
astronauts, who use about 3 gallons per day. For the remainder of the mission, there are 32
metric tons of water left on board. If the entire allotment were to be used, then each crew
member would have access to 25 kg of water per day, nearly 7 gallons, which is still above
nominal levels. However some of that water should preferably be kept in the toroidal tank for
radiation protection purposes.
The retroburn consumes an additional 5.5 metric tons of water, so the total water still on
board at the end of the mission should be just over 20 metric tons. This requires some
management regarding with toroidal tanks get emptied when. The only major requirement is that
at the end of the mission, there is one tank with about 6 mT of potable water left. This is easily
managed by using the other modules for the first 700 days of the mission.
Waste management is also important. There is an abundance of volume aboard once the
modules are fully expanded to store packaging waste, especially in the middle modules.
Packaging waste is actually quite helpful for radiation protection, so, as long as it is isolated,
keeping it on board is an advantage. Human waste however, needs to be cared for more
properly. Liquid waste can just be filtered and then dumped into the waste tank. Solid waste
should be screened out as well, but it can be handled by dumping it into the vacuum of space.
The plumbing system contains isolation valves above and below the filters, so that anything solid
that is trapped above the filters can be flushed out into space through a third valve.
Item
Water
Solar Panels
Engines
Power Transformer
Signal Conditioner
Spherical Water Tank
Toroidal Water Tank
Propulsion Structure
Furnishings
Food
RCS systems
Radiators
Habitat Structure (kg/m)
Controls
Navigation
Communication
Deep Space
Communication
Additional Power Systems
Instrumentation
Environmental Controls
Rendezvous and Docking
Cabin Upper Radiation
Shield (10 g /cm^2)
TOTAL
Unit Mass
(kg)
1125
150
453.5
453.5
800
1950
1500
250
5 (kg/day)
50
450
150 (kg/m)
46.4
46.4
57.7
70
368.2
147.7
351.4
24.5
700
Number of
Units
12
18
3
3
3
3
3
3
825 (days)
18
6
45 (m)
3
3
3
1
3
3
3
8
3
Mass (kg)
82517.5
13500
2700
1360.5
1360.5
2400
5850
4500
750
4125
900
2700
6750
139.1
306
173.2
70
1104.5
443.2
1054.1
196.4
2100.0
135000
Table 1: Table showing mass estimates for the three DSM units combined. The 10 metric ton mass of the
docking module and crew return capsule is not included.
Mass Estimates
The mass breakdown estimates for the three DSM units combined are shown in Table 1.
The mass of the solar panels was estimated based on ATKs analysis showing that they could
produce Megaflex solar panels weighing 200 W / kg, meaning 5 kg / kW. Multiplying that
number by the 2,700 kW production capacity gives 13,500 kg. This is an area where significant
improvements could be made in mass efficiency. Thin film solar panels, produced by KaiserThrede and test deployed at NASA’s Plumbrook Facility in 2006, have been manufactured that
produce nearly 6000 W / kg, and it is estimated that a specific power of 1250 W / kg could be
achievable with structural supports added to the thin film panels.
Ad Astra Aerospace’s most recent large VASIMR engine, the VX-200, has achieved a
specific power of 1.5 kg / kW. With 1,800 kW of engines on the vehicle, the mass for the
engines alone should be about 2,700 kg. A similar specific power was cited for the power
processing unit (which includes the control electronics and power transformer). The specific
power of the PPU was for a 200 kW unit. A 2.5 MW PPU is estimated by Ad Astra to mass only
0.54 kg / kW, or 1,320 kg. If the PPU mass is assumed to increase logarithmically with power,
then the interpolated trendline is:
Mass = 403.84 * ln(Power) - 1839.7
and thus, a 900 kW PPU should weigh 907 kg, or three units should weight 2721 kg. Table 1
divides that mass equally between the power transformer and the signal conditioner.
A water / tankage ratio of 20 was assumed for the spherical water tank. With a diameter
of 3 m, the tank can hold 14.1 metric tons of water – meaning the tank should weigh 705 kg.
Assuming some additional mass is required for structural attachments and fittings, the tank can
be estimated to weigh about 800 kg. The toroidal water tank is six meters high, with a 3.75
meter outer diameter and a 3 meter inner diameter. The inner tank wall is conformal with the
outer wall of the habitat section, and so its mass is already included. The outer tank wall and
upper and lower toroidal surfaces have a surface area of 75.4 m^2. The spherical tank has an
area mass of 25 kg / m^2. Thus each toroidal tank should weigh approximately 1,885 kg.
Again, assuming some additional mass for structural attachments and fittings, each tank should
weigh 1,950 kg, or 5,850 kg for all three toroidal tanks.
Radiator mass was based on the conservative that all 2.7 MW of solar energy would be
need to be dissipated simultaneously, and on the optimistic assumption that a specific radiator
mass of 1 kg / kW thermal could be achieved. In reality, only about 30% of the utilized solar
energy will need to be dissipated as most of it will be carried away in the engine exhaust, and
only about 900 kW at most will be utilized at any given time.
The estimate for the habitat structure came from the “Expanded Space Structures” study
mentioned earlier. That document showed a structural mass of 1,263 lb. for a fifteen foot long
structure, including end domes, bulkheads, and all other structural components. This is
approximately 120 kg / m of length. Because the DSM units have a diameter 25% larger, the
120 kg/m was multiplied by 1.25 to get 150 kg /m length. The structure also has to support the
additional weight of remaining water and the propulsion array while in deep space, but at 1/6th
gravity, that is only about 3.5 metric tons force equivalent. The vehicle from the study was
designed for 15 psi, which with a 2.4 meter diameter would produce 93 metric tons force
equivalent tension on the structure.
The upper radiation shield mass was found by multiplying the cross sectional area of the
space craft by the 10 g / cm2 area density shown in the table.
All other mass values came from the “Expanded Space Structures” study, just multiplied
by three to account for the fact that there are three units. Again, these values are likely to be
somewhat conservative as electronics technology especially has improved over the ensuing
decades.
Radiation Protection
The vehicle is designed to provide radiation protection to the crew by the use of liquid
water in tanks surrounding the crew cabin, propulsive equipment and water tanks below the
cabin, and a polyethylene radiation shield on top of the cabin. The polyethylene shield provides
10 g/cm2 of shielding. At any point in the mission, at least one of the habitat modules will have a
water column 2.5 meters high (enough to reach the ceiling) and 37.5 cm thick, providing 37.5
g/cm of shielding. Along the bottom of the cabin, there is 5 tonnes of propulsion equipment (not
counting the solar panels), providing some 70 g/cm2 of shielding. This mass is not all adjacent to
the cabin, though, so an estimate of 10 g/cm2 aluminum will be used, though there will usually
be a significant amount of water in the spherical tank to augment the protection. (Using a
conformal tank instead of a spherical tank would improve the protection even more, as well as
possibly reduce the actual tank mass, allowing for more propellant to be stored.)
According to P.D. Campbell (“Crew Habitable Element Space Radiation Shielding for
Exploration Missions”, Lockheed Engineering and Sciences, 1992) at 10 g /cm2, aluminum
allows exposure to approximately 61.4 cSv per year. Water at 37.5 cm thickness allows
exposure to 12.62 cSv/year (interpolated). Polyethylene at 10 g/cm2 allows for 17.36 cSy/yr.
The highest radiation exposure value should be used. Thus over a period of 822 days in
deep space, the crew would be exposed to 138.3 cSv (1.38 Sv) of radiation. This estimate is
likely high because of the low protection level assumed at the base of the habitat modules.
Using the BEIR based estimates specified in the competition rules, which state that the
risk of fatal cancer increases by 1% for each 0.6 Sv of exposure, this equates to a 2.3% increase
in fatal cancer risk over the course of the mission. This number is below NASA’s 3% lifetime
risk requirement.
Cost Analysis
The cost estimates for this mission are shown in table 2. The total is nearly $1.7 billion.
There were a few cases where estimates for items, or information that could help with estimates,
were available in the public domain, and those items are referenced in the table. For the most
part, however, a heuristic called “10K plus One Fourth” was used, meaning the development
cost of any aerospace system is expected to cost $10,000 per pound, and that, for low volume
production rates, the cost per additional unit is about 1/4th of the development cost. (This is a rule
perhaps more applicable to commercial aerospace than to military, but since this mission would
be done as a commercial endeavor, hopefully this rule would apply.) Thus, for example, the 3
meter diameter water tank, which weighs 800 kg, would cost $17.6 million to develop. Each unit
would then cost $4.4 million, so that the total would come to:
$17.6 million + 3 * $4.4 million = 30.8 million. For three tanks, that averages to $10.27 million
dollars per tank.
Item
Number
Falcon Heavy
Rocket
Space Capsule
4
Unit Cost ($
Millions)
135
1
100
100
Tonnes of Distilled
Water
100 kW VASIMR
Engines
84
0.000192
0.016128
18
10
180
5 times the “10K +
One-Fourth Rule”,
because it’s a rocket.
2.70E+06
0.0001
270
"Solar Cell
Technology and
Application". Aj Rha
3 m Aluminum
Water Tanks
6 x 3.5 m Toriodal
Water Tank
900 kW Power
Transformer
600 kW Signal
Conditioner
Lower Habitat
Section
Middle Habitat
Section
Upper Habitat
Section
Docking Module
3
10.27
30.81
3
25.675
77.025
3
11.64
34.92
3
11.64
34.92
3
22
66
3
15
45
3
22
66
1
66
66
10K + One-Fourth
Rule
2.5 times as much as
the 3 meter tank.
10K + One-Fourth
Rule
10K + One-Fourth
Rule
10K + One-Fourth
Rule
10K + One-Fourth
Rule
10K + One-Fourth
Rule
10K + One-Fourth
Rule
Coil Radio Antenna
High Gain Radio
Antenna
Thruster Pod Set
Mission Operation
Labor Years
Astronaut Pay Years
Project
Management
Utilities
1
12
5
1
5
12
18
2.5
1
37.5
18
93.75
3.5
7
0.8
5
2.8
35
2.5
12.5
31.25
1 Watt of Solar
Power
TOTAL
Total Cost ($
Millions)
540
1677.24
Table 2: Mission cost estimates, totaling $1,677,240,00
Source / Reasoning
spacex.com
nasa.gov/
spacex.com *
chemworld.com
30 Ground Crew,
120 Support Crew
2 astronauts.
10 Project
Managers.
Operations of
ground facilities.
The habitat modules also used the heuristic, but it was applied to the entire unit, which,
unencumbered, is estimated to weigh 4,562 kg. The total for all three units was calculated, and
then the cost was divided based somewhat on the complexity. The lower habitat section has the
crew quarters, and the upper section has the electrolysis unit, docking systems, and the viewing
port, but the middle section is basically just a pressurized, open-ended metal barrel, so it was
given a lower cost than the other two.
The cost estimate for the VASIMR engine was less straight forward, but basically, it was
assumed that propulsion technology would be more costly to develop than general aerospace
technology, so the heuristic based estimate was multiplied by five.
The cost of the Dragon Capsule was based on the difference between the individual
mission cost of SpaceX’s Commercial Resupply Contract with NASA ($1.6 Billion over 12
mission is $133 million per mission), and the cost of a Falcon 9 launch vehicle, plus a 25%
increase to account for the fact that the vehicle requires the addition of life support and crew
escape systems.
The cost of the solar panels was estimated based on a line out of the textbook “Solar Cell
Technology and Applications” by AJ Rha, stating that as of 2009, solar cells for use in space cost
less than $100 per Watt, so $100 / watt was used as the estimate.
As far as salary, it was assumed that each astronaut would cost $400,000 per year in
salary and benefits, including hazard pay. Ground and support crew were estimated to cost
$200,00 each per year, and managers were assumed to cost $500,000 per year and work over the
entire duration of the project.
Conclusions
A mission scenario capable of supporting a crew of two people for the duration of a Mars
flyby was presented. The mission duration is estimated to be 825 days for the manned portion.
The mission used a combination of advanced electric propulsion technology, artificial gravity,
and a simplified ECLSS system. The cost for this mission was estimated to be on the order of
$1.7 billion.
APPENDIX A: PLANET LOCATION PROGRAM
The locations of the planets were determined using the methods found at the website
http://www.stargazing.net/kepler/ellipse.html, posted by Keith Burnett. The sample QBasic program was
downloaded from the website and minor modifications were made to run the program using Scilab
software. This program includes the portions of the program relevant to Earth and Mars, as well as
modifications made by the authors of this paper to calculate the planetary velocities and plot their
locations.
//clear memory
clc
clear
//Inputs tstep = 86400 //length of time step in seconds
n_tstep = 1825
year=2017 //year
month=1 //month
day=1 //day of month
hour=12 //hour
mins=0 //minute
m_init_sc = 78000 // initial mass of spacecraft in kg
maxpower = 250000 //maximum power production capability at 1 AU
maxIsp = 4000 //maximum specific impulse in seconds
minIsp = 1000 //minimum specific impulse in seconds
eta=.72 // efficiency of electric thruster
inc_0 = 28 //initial orbital inclination in degrees
vel_0= 7800 // initial velocity of spacecraft in m/s
alt_0= 13100 // initial altitude of spacecraft
//Function relating power, efficiency, and specific impulse is needed.
hour = hour + mins / 60 //corrected hour including minutes
d =367 * year - 7 * (year + (month + 9) \ 12) \ 4 + 275 * month \ 9 + day - 730531.5 + hour / 24
d_init = d
//Geometric Constants
tpi = 2 * %pi
twopi = tpi
degs = 180 / %pi
rads = %pi / 180
//Astronomical Constants
G = 6.67e-11 //Universal gravitational constant. m^3/*kg-s^2)
m_sun = 1.989e30 //mass of sun in kg
m_venus = 4.8672e24 //mass of Venus in kg
m_earth = 5.972e24 //mass of Earth in kg
m_moon = 7.347e22 //mass of moon in kg
m_mars = 6.39e23 //mass of Mars in kg
m_jupiter = 1.898e27 //mass of Jupiter in kg
aum = 149597870700 // 1 Astronomical Unit. m
// List of the osculating elements of Earth and Mars. Other planets omitted for this paper.
// Below are the osculating elements for JD = 2450680.5 referred to mean ecliptic and equinox of J2000
//Earth
el(15) = .00041 * rads
el(16) = 349.2 * rads
el(17) = 102.8517 * rads
el(18) = 1.00002
el(19) = .9855796 * rads
el(20) = .0166967
el(21) = 328.40353 * rads
//Mars
el(22) = 1.84992 * rads
el(23) = 49.5664 * rads
el(24) = 336.0882 * rads
el(25) = 1.5236365
el(26) = .5240613 * rads
el(27) = .0934231
el(28) = 262.42784 * rads
//Dates
el(64) = 2450680.5 //date of elements
el(65) = 2451545 //date of mean ecliptic and equinox of elements
//
// Get the days to J2000. h is UT in decimal hours
// FNday only works between 1901 to 2099 - see Meeus chapter 7
//
for i=1:n_tstep //loops through every timestep
t(i)=tstep*i
funcprot(0)
function [xloc, yloc, zloc, radius]=location(d, p)
funcprot(0)
function [a]=FNrange(x)
b=x/tpi
a=tpi*(b-int(b))
if a<0 then a=tpi+a
end
endfunction
function [v]=FNkep(m, ecc, eps)
e=m
delta = .05
while abs(delta) >= 10 ^ -eps
delta = e - ecc * sin(e) - m
e = e - delta / (1 - ecc * cos(e))
end
v = 2 * atan(((1 + ecc) / (1 - ecc)) ^ .5 * tan(.5 * e))
if v < 0 then v = v + tpi
end
endfunction
funcprot(0)
function [degm]=FNdegmin(w)
// number - ddd.mm - the digits after the decimal point are the minutes.
adeg=int(w)
bdeg = w - adeg
edeg = int(60 * bdeg)
// deal with carry on minutes
if edeg >= 60 then
edeg = 0
adeg = adeg + 1
end
degm = adeg + edeg / 100
endfunction
//
// Save Osculating Elements
//
q = 7 * (p - 1)
ip = el(q + 1)
op = el(q + 2)
pp = el(q + 3)
ap = el(q + 4)
np = el(q + 5)
ep = el(q + 6)
lp = el(q + 7)
eldate = el(64) - 2451545
// find position of planet in its orbit
mp = FNrange(np * (d - eldate) + lp - pp)
vp = FNkep(mp, ep, 12)
rp = ap * (1 - ep * ep) / (1 + ep * cos(vp))
// heliocentric rectangular coordinates of planet
xh = rp * (cos(op) * cos(vp + pp - op) - sin(op) * sin(vp + pp - op) * cos(ip))
yh = rp * (sin(op) * cos(vp + pp - op) + cos(op) * sin(vp + pp - op) * cos(ip))
zh = rp * (sin(vp + pp - op) * sin(ip))
//Print Heliocentric coordinates of the planet
xloc = xh * aum
yloc = yh * aum
zloc = zh * aum
radius = rp * aum
endfunction
//Location of Mars
[xloc,yloc,zloc,radius]=location(d,4)
xlocm(i)=xloc
ylocm(i)=yloc
zlocm(i)=zloc
radm(i)=radius
if i == 1 then
day_0=d
end
if i<n_tstep then
day(i)=d-day_0
end
if i>=2 then
xvelm(i-1)=(xlocm(i)-xlocm(i-1))/tstep //x-velocity of Mars in m/s
yvelm(i-1)=(ylocm(i)-ylocm(i-1))/tstep //y-velocity of Mars in m/s
zvelm(i-1)=(zlocm(i)-zlocm(i-1))/tstep //z-velocity of Mars in m/s
end
//Location of Earth
[xloc,yloc,zloc,radius]=location(d,3)
xloce(i)=xloc
yloce(i)=yloc
zloce(i)=zloc
rade(i)=radius
if i>=2 then
xvele(i-1)=(xloce(i)-xloce(i-1))/tstep //x-velocity of Earth in m/s
yvele(i-1)=(yloce(i)-yloce(i-1))/tstep //y-velocity of Earth in m/s
zvele(i-1)=(zloce(i)-zloce(i-1))/tstep //z-velocity of Earth in m/s
end
d=d+tstep/86400
end
locm=[xlocm,ylocm,zlocm,radm]
loce=[xloce,yloce,zloce,rade]
plot(ylocm,zlocm)
plot(yloce,zloce)