Propulsion
Jon Edwards
Parachutes
For the supersonic portion of the descent after Mach 3 is reached,
hemisflo ribbon parachutes will be deployed to slow the vehicle down to Mach 1.
Hemisflo ribbon parachutes are used since according to Knacke they prove to be
the most practical for velocities up to Mach 3 (Knacke, 5-99).
After the vehicle reaches Mach 1, the hemisflo ribbon parachutes are cut
and reefed ringsail parachutes are deployed. After a certain amount of time the
reefing lines are cut and the parachutes are allowed to expand to their full area.
Ringsail parachutes are being used due to their historically proven success rate.
Ringsail parachutes were used successfully for the Mercury, Gemini, and Apollo
spacecraft as the main descent parachutes.
The Spring 2001 AAE450 class decided upon a retro rocket final descent
stage in order to slow the vehicle down to an appropriate landing speed and to
steer to the desired landing spot. However this induced a very large V. Instead
of using a retro rocket we have decided that a maneuverable parachute such as
a parafoil could be used to create some lift so that the vehicle could be slowed
down and steered to the desired landing spot. However the code to simulate this
is as of yet unwritten.
Parachute Code
The code which calculates the descent stage of the vehicle after Mach 3 is
reached in the Martian atmosphere was written by Jeremy Davis for the Spring
2001 AAE 450 class and modified by Jon Edwards for the Fall 2001 AAE 450
class. The code consists of six Matlab files. Their filenames and purposes are
as follows:
subreefeom.m / supereom.m
The subreefeom.m function solves the ordinary differential equations of
the vehicle during the subsonic stages of the descent. The supereom.m function
is identical to the subsonic solver except it uses a different drag coefficient and
parachute surface area. The equations of motion that these functions utilize
come directly from Newton’s second law of motion (F = m*a). In the y direction
the equation of motion is as follows:
Drag of parachutes = dragsub
Mass of spacecraft = msc
Acceleration = xdot(4)
Velocity = v
Velocity in y direction = x(4)
Flight Path Angle = theta
-cos(theta) * dragsub – msc * 3.7 = msc * xdot(4)
cos(theta) = x(4) / v
-x(4) *dragsub / v – msc * 3.7 = msc * xdot(4)
xdot(4) = -(dragsub*x(4))/(v*msc) – 3.7
The eom’s in the x direction are identical to the ones in the y direction
except there is no gravity term.
superdiam.m / subreefdiam.m
These functions calculate and return all the variables that the
supersubhm.m function needs to calculate the trajectory during the supersonic
and subsonic parts of the descent. Most of the variables are self-explanatory
and most of the functions are taken from the Knacke parachute book. The
source of each equation is explained in the codes.
supersubhm.m
This is the main body of the code where the descent is simulated. The
descent is broken up into 3 stages. The first part is the supersonic portion of the
descent in which the hemisflo ribbon parachutes are deployed. After mach 1 is
reached the hemisflo chutes are cut and the ringsail chutes are deployed with a
reefing line keeping the area of the chute well below the full expansion area. In
the last part of the code, the reefing line is cut and the ringsail chutes are allowed
to expand to their entire area. The velocity, acceleration, and position histories of
each section are stuck together to complete the descent simulation.
acceldiff.m
This code is used by the main code to numerically differentiate the velocity
vectors in order to obtain the acceleration history of the vehicle.
Sample Case
Since the trajectory code is not yet complete the sample case had to be
ran with estimates for most of the variables. In this sample case the altitude
where Mach 3 is reached is estimated to be around 17.5 km. This is where the
Spring 2001 class got their vehicle to reach Mach 3. The flight path angle is
estimated to be 45 deg and the vehicle mass is 57520 kg.
For the supersonic stage of the descent, 7 hemisflo ribbon parachutes are
used each with a diameter of 25 m. The total mass of the supersonic parachutes
is 278 kg and the deployment time till Mach 1 is reached is 42 s.
Once Mach 1 is reached the reefed ringsail parachutes are deployed and
reefed for 10 seconds with a reefing factor of 0.3. Then the reefing lines are cut
and the 3 ringsail parachutes are allowed to open to their full diameter of 38.5 m.
The total deployment time of the unreefed ringsail parachutes is 39 seconds at
which time the vehicle lands on the ground with a velocity of 55.7 m/s (much to
fast but this is just a sample case). Figure 1 shows the altitude history as a
function of time. Figure 2 shows the velocity history and Figure 3 shows the g
loading as a function of time.
Figure 1: Altitude History - Sample Case
18000
16000
14000
Altitude [meters]
12000
10000
8000
6000
4000
2000
0
-2000
0
10
20
30
40
50
60
Time [sec]
70
80
90
100
Figure 2: Velocity History - Sample Case
700
600
Velocity [m/s]
500
400
300
200
100
0
0
10
20
30
40
50
60
Time [sec]
70
80
90
100
80
90
100
Figure 3: G Loading - Sample Case
2.5
2
Gload
1.5
1
0.5
0
0
10
20
30
40
50
60
Time [sec]
70
One can easily see that the in this sample case the vehicle is landing
much to fast. This will be corrected when the maneuverable parafoil stage is
coded.
Propulsion System
Besides the nuclear thermal rocket which will put the vehicle into its
interplanetary trajectory, the vehicle must have some sort of retro/boost engine to
make an entry angle change and to do apogee burns in order to raise/lower the
periapsis so that the vehicle will aerobrake effectively.
There were a few prerequisites to this design:
(1)
We wanted something that was historically proven to be reliable
(2)
It must work off of hypergolic non-cryogenic propellants
(3)
It must provide > 5000 lbf of thrust
Once these conditions were realized the Shuttle OMS Engine was decided
upon. The OMS engine will provide 6000 lbf of thrust with an Isp of 313 s. The
propellants are nitrogen tetroxide (NTO, oxidizer) and monomethyl-hydrazine
(MMH, fuel). Both of which are non-cryogenic. The OMS engine is also reusable
and reliable, with success on over 100 missions, 1000 starts and 15 hours of
burning time.
For the RCS system the same prerequisites were effective, except that we
wanted the thrust to be greater than 500 lbf. The Marquardt R-40A RCS engine
was developed for the shuttle orbiter reaction control system and has proven to
be a reliable engine. 24 R-40A’s will be used with 8 in each plane to make up
the RCS system.
Engine Tank Sizing
The engine tank sizing code (tanksize.m) was originally written by Casey
Kirchner for the Spring 2001 class. The main differences between the original
code, and the code as it appears now is that there is no retro burn during the
descent to the Martian surface, there is no hovering maneuver near the surface,
and there is no heat shield to worry about.
In order to use the code without making drastic changes only a few things
needed to be changed. The ΔVs for the descent and hovering burns were set to
zero. This makes the mass fraction for these burns zero and therefore no
propellant mass is taken into effect for these maneuvers. The mass of the heat
shield was also set to zero to eliminate any effect that it might have had on the
sizing calculations. A few other things needed to be changed including the RCS
and OMS Isp’s, the OMS expansion ratio, the landing mass, and the vehicle
dimensions.
Sample Case
For the sample case a landing mass of 57520 kg was used along with a
V of 20 m/s for perigee raising/lowering. The HAB length and diameter was
programmed to be 16.5 m and 13 m respectively. With this information the
following output was given:
Delta V Budget, m/s
Landing DV:
Hovering DV:
Mars Orbit DV:
Spin-up DV, tether deployed:
Spin-up DV, tether not deployed:
Enroute RCS/Maneuvering DV:
Total DV:
0.00
0.00
20.00
62.00
121.34
102.00
305.34
Masses
Descent Engine mass (kg):
RCS Engine mass (x10) (kg):
Oxidizer tank masses (kg):
Fuel tank masses (kg):
Pressurant tank masses (kg):
Struct. support mass (kg):
Stage inert mass (kg):
Oxidizer masses (kg):
Fuel masses (kg):
Pressurant masses (kg):
Total prop masses (kg):
Total stage masses (kg):
Tank and Engine Geometry
Retro Engine:
Retro Engine Throat:
RCS Engines on Hab (each):
RCS Engines on NTR (each):
Oxidizer tank on Hab:
Fuel tank on Hab:
Oxidizer tank on NTR:
Fuel tank on NTR:
Pressurant tank on Hab:
Pressurant tank on NTR:
Hab Subsystem
0.00
15.44
10.78
11.00
4.70
4.19
46.11
NTR Subsystem
0.00
13.11
12.35
12.62
5.33
4.34
47.74
1725.03
1078.14
6.07
2809.24
2855.35
2059.03
1286.89
6.88
3352.80
3400.54
Length (m)
3.28
N/A
1.76
0.33
0.90
0.94
1.20
1.26
Spherical
Spherical
Total
0.00
28.55
23.12
23.62
10.03
8.53
93.85
3784.05
2365.03
12.95
6162.04
6255.89
Diameter (m)
1.81
0.03
1.10
0.15
1.00
1.00
1.00
1.00
1.36
1.44
We are not necessarily concerned with the NTR Subsystem information,
only the Hab subsystem. The main reason why this code was used mostly
unmodified from the original version is that the engine tanks must be big enough
to allot space for the propellants needed to spin up the vehicle at the beginning of
the interplanetary trajectory and the enroute RCS maneuvering V, which this
code takes into account. We (the Fall 2001 class) are not responsible per the
RFP to do these calculations or worry about the nuclear thermal rocket and
tether systems therefore most of the data needed to calculate the tank sizes are
assumed to be correct while only a small portion of the it was modified.
Figure 4: Delta V Mass Breakdown of Mars Trip - Sample Case
64
63
Mass (Tonnes)
62
61
60
59
58
57
1
Earth Departure
2
3
S p i n - u p
4
RCS
5
6
Mars Orbit
7
Hover
Land
References
1Henry,
Gary N., Humble, Ronald W., and Larson, Wiley J., “Space
Propulsion Analysis and Design,” McGraw-Hill, Inc., 1995, pp.1-30, 179-294.
2Sutton,
George P., “Rocket Propulsion Elements,” John Wiley & Sons,
Inc., New York, NY, 1949, pp.22-36, 188.
3Knacke,
T.W., “Parachute Recovery Systems: Design Manual”, Para
Publishing, Santa Barbara, CA, 1992.