3.0 Propulsion/Parachute

3.0 Propulsion/Parachute Jon Edwards

3.1 Propulsion Concepts

Propulsive devices must be utilized during our mission to provide en route maneuvering to ensure that our vehicle enters the mars atmosphere at the proper entry angle and to control the attitude of the Marvin vehicle during its interplanetary flight and Mars orbit. A propulsive device is also utilized if apogee burns become necessary to raise or lower the periapsis during Aerobraking.

There is also a spin up maneuver at the start of the mission that the spring class worked on. The Project PERForM engineers calculated a v of 99.51 m/s for this maneuver (Table 4.4.2 Project PERForM Final Report). This v was therefore used in Project Marvin’s tank sizing calculations but was not further analyzed.

To decide upon a main engine and reaction control system (RCS) a few prerequisites were instituted. First an engine that ran off non-cryogenic hypergolic propellants would be utilized so that there would not be a cryogenics system on the vehicle. A cryogenic system would increase the cost of the program and add unneeded mass to the vehicle. Examples of non-cryogenic propellants are monomethyl hydrazine and nitrogen tetroxide. These propellants have boiling points that are around 300K (a little higher than room temperature). Cryogenic propellants must be kept much cooler (below 90K). Monomethyl hydrazine (fuel) and nitrogen tetroxide (oxidizer) is a common combination in space vehicles.

Of course a high Isp (specific impulse) is desired so that we can get greater thrust for a smaller propellant mass flow. An engine with a high Isp needs less propellant to deliver the same thrust as an engine with a lower specific impulse. This cuts down in the amount

3-1 of propellant that needs to be sent along with the vehicle to Mars and this in turn decreases cost.

It is also important to use an engine that has been historically proven to be reliable. Such engines decrease the risk of the mission. As well as decreasing the risk of the mission more empirical data over the known range of operation is available for such engines.

For the Marvin vehicle the main engine will be used for spin-up and apogee burns during Aerobraking. For these engine requirements a thrust-to-weight ratio lower than 0.1 can be used to find how much thrust is required (Humble p. 17). Using a thrust-to-weight ratio of 0.05 and a vehicle mass estimate of 50 tonnes, equation 1.36 in Humble gives a thrust of around 25,000 N.

All of these prerequisites led to the decision to use the Shuttle Orbiter Orbital Maneuvering System (OMS) as the main engine of Marvin and the Marquardt R-40A RCS engines for the RCS system. The OMS engine provides 26.70 kN of thrust with an Isp of 313 s. It is 118 kg in mass and the propellants it uses are nitrogen tetroxide and monomethyl hydrazine (both non-cryogenic hypergolic propellants). The OMS engine is capable of 100 missions and 500 starts in space. The R-40A RCS engines provide 3.9 kN of thrust with an Isp of 306 s. Each engine is 10 kg in mass and the propellants are also nitrogen tetroxide and monomethyl hydrazine. The OMS engine and the R-40A RCS engines have been used on the Shuttle Orbiters since 1981. These specifications were taken from Walter Hammond’s AIAA Education Series “Space Transportation: A Systems Approach to Analysis and Design”, 1999. Other specifications were available from Astronautix.com.

For the RCS system the number of RCS engines must be decided upon. The desired attitude is accomplished by firing RCS thrusters to do roll, pitch, and yaw movements. For each dimension 4 thrusters are needed at opposite points on the vehicle that create the largest moment arms. It was decided that for redundancy reasons, 2 engines must be used together in case any were to fail. Therefore the number of RCS engines for the

3-2 Marvin vehicle is 3 (dimensions) * 4 (thrusters each) * 2 (redundancy) = 24 Marquardt R-40A RCS engines.

3.2 Propulsion Design Methods

To calculate the propellant/pressurant masses and corresponding tank sizes and masses a tank sizing code was written using Matlab. The code is called tanksize.m and was originally written by Casey Kirchner for the spring 2001 Project PERForM. This semester’s propulsion engineer has modified this code extensively for the Fall 2001 Marvin vehicle and the code is attached as Appendix A.3.1.

The code works by first setting the v’s for each of the following maneuvers:  Spin-up maneuver  En-route course corrections  Entry angle change  Apogee burns

Once these v’s have been entered and the OMS and R-40A RCS engine specifications are set, the code uses the rocket equation (Humble Eq. 1.16) to solve for the vehicle mass fractions.

v FinalMass  e gIsp InitialMass

It starts by using the desired landing mass and the v needed for the apogee burns to find the mass of the vehicle before the apogee burns are done. Then the code takes this mass along with the v needed for the entry angle change to find the mass before the entry angle change maneuver is done. It does the same thing for the en-route corrections and the spin-up maneuver to finally come to the launched mass.

3-3 Once all the mass fractions are found the total propellant mass is calculated and used along with the oxidizer-to-fuel ratio to find oxidizer and fuel masses and volumes. The code also finds all the pressure drops through the feed system and adds this to the needed chamber pressure to calculate the tank pressures. Using the known tank pressure and propellant volumes along with Eq. 5.83 in Humble the pressurant mass is found.

(Oxidizervolume Fuelvolume)TankpressureMolecularweightofhelium Massofpressurant  RuFinaltemperature

Using the calculated pressurant mass and the ideal gas law, the pressurant volume is found. Now that the oxidizer, fuel, and pressurant volumes are known the tank sizes can be calculated.

The propellant tanks are cylindrical with hemispherical ends. The pressurant tank is spherical. The tank thicknesses are calculated by finding the design burst pressure according to Humble Eq. 5.73:

Burstpressure  safetyfactor Tankpressure

This burst pressure is then used in Humble’s Eq. 5.76 and Eq. 5.80 to find the thicknesses.

BurstpressureRadius thickness  2MaterialStrength (for spherical shapes)

BurstpressureRadius thickness  MaterialStrength (for cylindrical shapes)

The propellant tanks are made of graphite with a 0.5mm aluminum tank liner. This material was chosen because we typically wish to choose a material that gives us the most strength for a given mass and also must be chemically compatible with the propellant. Both monomethyl hydrazine and nitrogen tetroxide are compatible with

3-4 aluminum. The pressurant tank has no aluminum liner since helium and graphite are compatible.

Now that the code calculated the thicknesses and surface areas of the tanks, the tank masses can be calculated. The tank masses are added to the other inert masses (engine masses and structural support masses) to get the total inert mass. This is added to the propellant/pressurant masses and therefore the total propulsive mass has been found.

3.3 Parachutes Concept

Once the vehicle has aero-braked effectively and has reached mach 3 somewhere in the Martian atmosphere, the rest of the trajectory is controlled using parachutes. The parachutes bring the vehicle through supersonic speeds to subsonic speeds and eventually land the vehicle safely on the Martian surface.

To decide upon what sort of parachute scheme to use, historical systems were analyzed such as the Apollo Landing System, the X-38 Parafoil Landing System, and the Mars Pathfinder Atmospheric Entry System. T.W. Knacke’s book Parachute Recovery Systems Design Manual was also used extensively in this analysis.

According to Knacke (p 5-99), hemisflo ribbon parachutes are the most practical for velocities up to Mach 3. These parachutes are generally used only for speeds in the range of 1.0 < mach number < 3.0. These parachutes have also shown to be reliable by the Northrop Corporation who summarized all available information on supersonic ribbon parachutes in the 1970s. According to Knacke Fig. 5-94, hemisflo ribbon parachutes have shown fair to excellent stability for mach numbers between 1 and 3 in both free fall and wind tunnel tests done by the Northrop Corporation.

Once the supersonic parachute effectively brings the vehicle to a subsonic velocity, the next stage of the descent is implemented. For this stage subsonic parachutes must be used that have shown historical reliability and have a large drag coefficient. Ringsail

3-5 parachutes have shown to be successful as the main descent parachutes used for the Mercury, Gemini, and Apollo spacecraft. However, according to Knacke, these parachutes are generally used for applications where the Mach number is less than 0.5. In our case we need something like the ringsail parachute but that can be used effectively for greater velocities. The ringslot parachute can be used for velocities between 0.1 and 0.9 and has shown to produce a drag coefficient of 0.60 (Knacke p. 5-29), therefore this is the parachute which the Marvin vehicle uses in the second stage of its descent.

After the subsonic ringslot parachutes decelerate the vehicle to low mach numbers, we are concerned with how we are going to maneuver the vehicle to the desired landing location. The spring 2001 Project PERForM team used a retro rocket engine to steer the vehicle to its desired location. However this greatly increases the total mass of the vehicle. According to Table 4.4.2 in the spring 2001 final report, the landing portion of the descent added a v of 75.22 m/s and 3413 kg of propellant. This retro maneuver also increases the mass and volumes of the tanks and pressurants. In order to cut down the mass and cost of the vehicle a parafoil is used instead of a retro engine. The X-38 Parafoil Landing System has proven the parafoil to be a lightweight and effective way to maneuver and land a space vehicle. In our analysis much of the data was taken from that of the X-38 Parafoil Landing System and applied to our vehicle in order to do our analysis.

3.4 Parachutes Design Methods

To model the trajectory of the vehicle during the parachute controlled parts of the descent a code was written using Matlab which models the vehicle as a point mass in a 2- dimensional plane. This code named supersubhm.m (A.3.2) was written by Jeremy Davis for the spring 2001 class and was modified by this semester’s propulsion engineer to apply to Project Marvin.

Part of the code is split into 3 files that contain parameters for the hemisflo ribbon supersonic parachute (superdiam.m, A.3.3), the ringslot subsonic chutes (subreefdiam.m,

3-6 A.3.4), and the parafoil (parafoildiam.m, A.3.5). Each of these files also calculate the mass of each chute and pass important parameters such as drag coefficient and total surface area to the corresponding ‘ode’ file which uses the equations of motion to find position and velocities over time. Each leg of the descent has its own ordinary differential equation file (ODE45) as follows: supereom.m (supersonic, A.3.6), subreefeom.m (subsonic ringslot chutes, A.3.7), and parafoileom.m (parafoil, A.3.8).

The equations of motion for the supersonic and subsonic portions of the descent are identical. The free-body diagram is shown below as well as an example derivation for the equation of motion in the y-direction: Figure 3.1: Free body diagram of Supersonic and Subsonic Stages of Descent

y _ Force  mass  y _ acceleration Drag  sin( )  mass  gravity  mass  acceleration

sin( )  y _ velocity velocity

Drag y _ velocity y _ acceleration  massvelocity  gravity

In these equations mass is the mass of the vehicle, gravity is the Martian gravitational acceleration,  is the flight path angle measured down from a plane tangent to the Martian surface, and velocity is the total velocity of the vehicle. The equation of motion in the x- direction is similar and appears as follows:

Dragx _ velocity x _ accleration  massvelocity

3-7 For the parafoil part of the descent, there is a lift vector added to the free-body diagram and a lift term appears in the equations of motion. The free-body diagram of the parafoil and an example derivation for the equation of motion in the y-direction is as follows: Figure 3.2: Free Body Diagram of Parafoil Stage of Descent

y _ Force  mass  y _ acceleration Drag  sin( )  Lift  cos( )  mass  gravity  mass  acceleration

sin( )  y _ velocity cos( )  x _ velocity velocity velocity

Drag y _ velocity Liftx _ velocity y _ acceleration  massvelocity  massvelocity  gravity

The drag of the supersonic parachute is calculated by taking the mach number of the vehicle and entering it into an equation found by curve fitting from Knacke Fig. 5-96 shown below.

3-8 Figure 3.3: Drag Coefficient vs. Mach Number for Hemisflo Ribbon Parachute

The drag is calculated by taking the drag coefficient, the total surface area of the hemisflo ribbon parachute canopy, and the dynamic pressure and entering it into the drag equation (Knacke p. 4-9).

Drag  Dynamicpressure  Surfacearea  Dragcoefficient

For the ringslot parachutes, the drag coefficient is held constant at 0.60, which comes from Knacke p.5-29, and the drag is calculated as shown by the equation above.

To calculate the mass of the hemisflo ribbon supersonic parachute, the surface area of the parachute is multiplied by the specific canopy weight of nylon (units of kg/m^2). The same goes for the ringslot parachutes. However for the parafoil, the surface area can’t be

3-9 multiplied by the specific weight of nylon to get a reasonably accurate mass calculation since we do not know what the total surface area is because of the parafoil’s complex geometry. In Project Marvin’s analysis, the X-38 Parafoil Landing System served as the basis of the parafoil mass calculation. The X-38 vehicle has a mass of 11,340 kg and the X-38 parafoil mass is 390 kg. These values can serve as a ratio for the parafoil design mass. When this ratio (390/11340) is multiplied by Marvin’s vehicle mass, the parafoil mass can be reasonably estimated.

Finally the main piece of code is the supersubhm.m (A.3.2) file. This code sets up the global parameters and initial conditions such as the vehicle mass, altitude where mach 3 is reached, flight path angle at this altitude, and the diameter of the vehicle. It also pieces together all the trajectories that the 3 ordinary differential equation (ODE45) files calculate in order of supersonic to subsonic to parafoil stages of the descent.

The main code pieces the trajectory together by finding the point after the supersonic ribbon parachutes are deployed where mach 0.9 is reached. Mach 0.9 is used as the cutting point because at this velocity, ringslot parachutes are applicable (Knacke Table 5- 2).

At this point it starts the subsonic reefed stage. Parachute reefing permits the incremental opening of a parachute canopy, or restrains the parachute canopy from full inflation or overinflation. This is an important procedure because it will limit the opening forces and thus keep the g-loading down. The reefing stage simply uses the same ‘ode’ file as the subsonic un-reefed stage but instead multiplies the total canopy surface area by a reefing factor, which is set by the user for an amount of time also set by the user. After this reefing time the subsonic ringslot parachutes are expanded to their entire canopy surface area until terminal velocity is reached. Terminal velocity is set to occur when the acceleration of the vehicle drops below 0.05 m/s^2. At this point the parafoil stage is begun and the parachute ‘ode’ file is ran until the vehicle reaches zero altitude at which point the code is stopped.

3-10 The supersubhm.m file also calls the acceldiff.m (A.3.9) file, which calculates the accelerations (g-loading) by differentiating the velocity vectors over time. Finally the main file plots the data and outputs important values such as the maximum g-loading, the total parachute mass, and the vertical velocity at landing.

3.5 Trade Studies

The trade studies began by picking two different vehicle diameters, one with a 13 m diameter and one with a 9 m diameter. Each of the team members then ran their codes to see how the two cases compare to each other in terms of total mass and capturing/landing ability.

The Marvin vehicle will land like an airplane since the parafoil induces a large horizontal velocity while keeping the vertical velocity small. According to the Development of the NASA X-38 Parafoil Landing System (AIAA-99-1730, p. 211) the X-38 prototypes were dropped at Edwards Air Force Base in California and were shown to achieve vertical velocities of less than 5.5 m/s at touchdown. Therefore in this analysis the parachute design must achieve a vertical velocity equal to or less than this criterion of 5.5 m/s.

Mass is also an important consideration. As the mass that needs to be sent out to Mars increases, the amount of propellant it will take to push it there will increase and hence the cost of the program will increase. However, the calculated mass of the parafoil is not effected by changing its span since it is calculated using a ratio taken from theX-38 Parafoil Landing System and Marvin’s vehicle mass. Therefore, to drive the mass of the parachute system down, the hemisflo ribbon supersonic chute and the ringslot subsonic chutes should be minimized in size while still providing an effective deceleration of the vehicle, keeping the g-loading below 5 g’s.

The 9 m diameter case was found to reach mach 3 at an altitude of 12072 m, a flight path angle of –9.417, and a vehicle mass of 47219.7 kg. The 13 m diameter case was found to reach mach 3 at an altitude of 16481 m, a flight path angle of –9.14405, and a vehicle

3-11 mass of 54020 kg. These first vehicle mass estimates included an estimated parachute mass of 2407.8 kg and neither needed any apogee burns. Since neither case needed any apogee burns nor entry angle changes the only v’s that were needed were for en-route maneuvering and the spin-up phase which stayed constant throughout the trade studies. Therefore the propulsion system and propellant/pressurant masses for each case are as follows: Table 3.1: Propulsion Data for 13m and 9m Diameter Cases Delta V Budget, m/s 13 m Case 9 m Case

Mars Orbit DV: 0.00 0.00 Entry Angle Change DV: 0.00 0.00 Spin-up DV: 99.51 99.51 Enroute RCS/Maneuvering DV: 102.00 102.00 Total DV: 201.51 201.51

Masses

OMS Engine mass (kg): 118.00 118.00 RCS Engine mass (total) (kg): 240.00 240.00 Oxidizer tank masses (kg): 29.40 26.26 Fuel tank masses (kg): 30.11 26.88 Pressurant tank masses (kg): 36.84 32.28 Struct. support mass (kg): 45.44 44.34

Total inert mass (kg): 499.80 487.76

Oxidizer masses (kg): 2308.16 2022.05 Fuel masses (kg): 1442.60 1263.78 Pressurant masses (kg): 11.38 9.97 Total prop/press masses (kg): 3762.14 3295.81

Total mass (kg): 4261.93 3783.56

Tank and Engine Geometry Length (m) Diameter (m) Length (m) Diameter (m) OMS Engine: 1.96 1.17 1.96 1.17 OMS Engine Throat: N/A 0.02 N/A 0.02 RCS Engines on Hab : 1.00 0.50 1.00 0.50 Oxidizer tank on Hab: 2.43 1.00 2.17 1.00 Fuel tank on Hab: 2.49 1.00 2.22 1.00 Pressurant tank on Hab: Spherical 2.12 Spherical 2.03

The parachute code was ran numerous times, each time the parachute constructed diameters and the parafoil’s span were changed to keep the g-loading below 5 g’s and to get smaller vertical velocities at touchdown until the vertical velocity was less than 5.5

3-12 m/s. Once these criteria were met, the two cases could be compared. The following table gives the parachute information for both the optimized 9 m diameter case and the 13 m diameter case. For each case the parafoil is deployed at an altitude of 1000 m and the subsonic chutes are reefed for 10 seconds with a reefing factor of 0.3. This deployment altitude was chosen because it is near the altitude where the vehicle reaches its terminal velocity. It also provides enough altitude for the parafoil to cover nearly 3 km of horizontal distance to maneuver to its desired landing point. The reefing time and factor were chosen to effectively keep the g-loads low when the subsonic ringslot parachutes are deployed. Table 3.2: Parachute Data for 13m and 9m Diameter Case

Diameter of Vehicle (m) 13 9 Altitude where Mach 3 is reached (m) 16481 12138 Flight path angle at this alt. (deg) -9.11405 -9.41 Vehicle mass estimate (kg) 54020 47042.7

Time to land (s) 121 115 Velocity at landing (m/s) 69.6753 59.5276 Horizontal velocity at landing (m/s) 69.6169 59.4109 Vertical velocity at landing (m/s) -2.8511 -3.726

Max g-load (g's) 3.7817 3.4123

Supersonic constructed diameter (m) 20 20 Subsonic constructed diameter (m) 70 70 Parafoil span (m) 196 184

Supersonic chute mass (kg) 49.05 43.34 Subsonic chute mass (kg) 622.13 563.21 Parafoil mass (kg) 1857.83 1617.87 Total mass (kg) 2529 2224.4

Comparing the 9m-diameter case with the 13 m-diameter case proves that while both cases will land, the 9 m-diameter case needs 10% less propulsion/parachute mass to accomplish the mission. From a propulsion/parachute standpoint, the 9 m-diameter case is the better configuration.

3.6 Final Design Trade Studies

3-13 After the 9 m-diameter case was chosen as the final vehicle design, trade studies were done to come to an optimized system configuration. The way it worked from a propulsion standpoint was that the estimated vehicle mass, altitude where mach 3 is reached, and the flight path angle at this altitude were taken from the trajectories engineer, and then these values were fed into the parachute and tank sizing code. The tank sizing code produces different results only when the vehicle mass is changed. The parachute code produces different results depending on what the initial conditions are, what constructed diameters the user wishes to use for the supersonic and subsonic parachutes, and what span to use for the parafoil. Thus the propulsion and parachute masses were calculated and these masses were fed back to the systems engineer who re- calculates the vehicle mass and center of gravity. These values are then sent to the trajectories engineer and a new trajectory is determined. The new altitude where mach 3 is reached, the new flight path angle, and the new vehicle mass are then given back to the propulsion engineer and a new set of propulsion/parachute masses are calculated. This goes on till everyone’s data converges.

It is also important that while this iterative process is being done, values such as the altitude where the parafoil is deployed, the reefing factor and reefing time, the number of subsonic ringslot parachutes, and the constructed diameters and span of the parachutes are changed to see how the changes effect the system. In this way the system can be optimized.

When the altitude where the parafoil is deployed is changed, the horizontal range of the vehicle in this final stage of the descent is increased however the velocity of the vehicle is greater when the parafoil is deployed earlier. Since the velocity of the vehicle is greater, the opening force will be greater and this is an important consideration. Figure 3.4 shows that when this altitude is changed by 200 m the max horizontal range is increased by 2.4 km. However the velocity when the parafoil is deployed is increased from mach 0.33 to mach 0.4. The extra 2.4 km is well worth the increase in velocity at the time the parafoil is deployed since this increase in velocity does not critically affect the system. However, if it was decided to deploy the parafoil at even a higher altitude, the mach number would

3-14 approach mach 0.5 which is the limit for parafoil use (Knacke Table 5-2). For this reason the altitude where the parafoil is deployed was chosen to be 1200m for the initial trade studies. When the final case is being optimized the parafoil deployment will be dependent on the terminal velocity, not some predetermined altitude. Studying how the deployment altitude affects the trajectory is important for knowing whether we want to deploy at a high altitude or closer to the Martian surface.

Figure 3.4: Parachute Trajectory for Various Altitudes of Parafoil Deployment

P a r a c h u t e T r a j e c t o r y

2 0 0 0 E n d o f R e e f e d S t a g e

1 5 0 0

) P a r a f o i l d e p l o y e d a t 1 2 0 0 m ( r e d ) m (

e P a r a f o i l d e p l o y e d a t 1 0 0 0 m ( b l u e ) d u t i

t 1 0 0 0 l a

0 2 . 8 5 2 . 9 2 . 9 5 3 3 . 0 5 3 . 1 3 . 1 5 3 . 2 3 . 2 5 3 . 3 3 . 3 5 3 . 4 h o r i z o n t a l p o s i t i o n ( m ) 4 x 1 0

To examine how the reefing factor affects the system trade studies were done by varying the reefing factor for constant values of ringslot diameters. Figure 3.5 plots the g-loading vs. time for 3 different reefing factors applying to 3 ringslot parachutes with a constructed diameter of 70 m. The spikes in the plot occur at the time when the stage is changed, i.e. when the supersonic chutes are cut and the subsonic reefed chutes are deployed. Spikes also occur when the reefed stage is expanded to its un-reefed diameter

3-15 and when the parafoil is deployed. These points are also marked with black x’s. This figure shows that reefing factors greater than 0.3 produce g-loads that approach and surpass the 5 g limit. It can also be seen that as the reefing factor decreases, the g-loads for the un-reefed stage of the descent goes up and approaches the 5 g limit. For these reasons 0.3 was chosen as the appropriate reefing factor.

Figure 3.5: Maximum G-Loads for Various Reefing Factors

G - l o a d v s . T i m e 8 R e e f i n g f a c t o r = 0 . 7 , g = 7 . 5 7 3 5 7 R e e f i n g f a c t o r = 0 . 5 , g = 5 . 3 5 5 5 6

4 d R e e f i n g f a c t o r = 0 . 3 , g = 3 . 1 3 5 5 a o l

- 1 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 T i m e [ s e c ]

One of the most important things to decide upon is what diameter of supersonic chute to use. This is the chute that slows the vehicle down to subsonic speeds so that landing on a hard surface is possible. Some things to consider are the g-loading and the mass of the chute. However the supersonic chute is the least massive of the three, and only comprises around 6% of the total parachute mass. Therefore the mass is not a critical issue. The main design criterion behind the supersonic chute is to use the largest diameter possible to slow the vehicle down as fast as possible without going over the 5 g limit. This makes it possible to deploy the subsonic chutes and eventually the parafoil at a higher altitude, thus increasing the maximum horizontal range of the vehicle. This is

3-16 important so that the vehicle can effectively be maneuvered to its desired landing spot. Figures 3.6 and 3.7 show that using a diameter of 40 m for the supersonic chute will slow the vehicle down to subsonic speeds at a high altitude while still staying under the 5 g limit. Using a 30 m diameter would produce less g-loading but would not slow the vehicle down as fast, while using a diameter of 50 m would produce more than 5 g’s. Figure 3.6: Altitudes of Subsonic Deployment for Various Diameters of Supersonic Chutes

A l t i t u d e v s . T i m e

1 2 0 0 0

1 0 0 0 0 ] s r 8 0 0 0 A l t = 6 7 4 5 . 9 m , D i a m = 5 0 m e t e A l t = 5 9 7 3 . 6 m , D i a m = 4 0 m m [

d 6 0 0 0

u A l t = 4 8 7 2 . 9 m , D i a m = 3 0 m t i t l A 4 0 0 0

2 0 0 0

0 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 T i m e [ s e c ]

3-17 Figure 3.7: Max G-Loads for Various Supersonic Chute Diameters

G - l o a d v s . T i m e 7

6 M a x g = 6 . 0 6 8 2 , D i a m = 5 0 m

4 M a x g = 3 . 8 6 8 6 , D i a m = 4 0 m d a

G M a x g = 2 . 2 9 6 4 , D i a m = 3 0 m

- 1 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 1 6 0 T i m e [ s e c ]

Now that the constructed diameter of the supersonic chute is frozen, the diameter and number of subsonic ringslot chutes needs to be decided upon. In this case the subsonic chutes constitute 30% of the total parachute system mass and about 1.5% of the total vehicle mass. Therefore the important design issues here are to get the vehicle to reach its terminal velocity at a high altitude while keeping the g-loading below 5 g’s, and to minimize the mass. The following table gives the trade study data:

3-18 Table 3.3: Trade Studies of Subsonic Ringslot Chutes Number of Chutes Diameter (m) Max g's Altitude at terminal vel. (m) Total canopy mass (kg) 1 200 3.2148 3114.5 1297.92 1 225 4.1305 3338.8 1625.25 1 250 5.1534 3510.5 1988.38 2 150 3.6458 3230.7 1507.87 2 170 4.7486 3448.9 1908.55 2 180 5.3514 3536.4 2124.86 3 100 2.3646 2808.2 1069.26 3 125 3.8074 3265 1609.4 3 140 4.8347 3459.6 1987.66 3 70 2.1468 1751.4 563.21

By inspecting the previous data, it can be seen that the study with the smallest mass is the 3 ringslot chutes at a diameter of 70 m. This situation also has the least amount of g- loading and deploys the parafoil at an altitude of 1751.4 m which leaves reasonable altitude for maneuvering to the landing site.

To design the parafoil span length, many parameters are held constant. Such parameters as the aspect ratio, the lift and drag coefficient, and the max thickness are held constant so that the parafoil is proportional to the parafoil used for the X-38 Parafoil Landing System. Then the span is increased (which increases the surface area and thus the lift and drag) until the parafoil reaches a vertical velocity below 5.5 m/s at touchdown. Figure 3.8 shows trajectories for different parafoil wing spans. Each plot in the figure starts at the point where the parafoil is deployed and ends when zero altitude is reached. One can see that the trajectory of the 176 m span parafoil system has a very small slope as it reaches zero altitude. Figure 3.9 shows the vertical velocities of the same parafoil wing spans as in the previous figure. Each plot in this figure begins when the parafoil is deployed and ends when it reaches zero altitude. The 176 m span parafoil has the

3-19 smallest vertical velocity (2.6 m/s) when it lands. Therefore this is the span that the parafoil should be.

Figure 3.8: Parachute Trajectories for Various Parafoil Wing Spans

P a r a c h u t e T r a j e c t o r y

1 6 0 0

1 4 0 0

1 2 0 0 )

m 1 0 0 0 (

e S p a n = 1 6 0 m d u t

i 8 0 0 t l a 6 0 0 S p a n = 1 7 0 m S p a n = 1 7 6 m S p a n = 1 9 0 m 4 0 0

0 2 . 3 2 . 3 5 2 . 4 2 . 4 5 2 . 5 2 . 5 5 2 . 6 2 . 6 5 h o r i z o n t a l p o s i t i o n ( m ) 4 x 1 0

3-20 Figure 3.9: Vertical Velocities vs. Time for Different Parafoil Wing Spans

V e r t i c a l V e l o c i t y v s . T i m e 8 0

6 0 ) s /

m S p a n = 1 6 0 m , V y ( l a n d ) = 4 4 . 0 m / s

c S p a n = 1 7 0 m , V y ( l a n d ) = 2 2 . 9 m / s o l

e 4 0 v

l S p a n = 1 7 6 m , V y ( l a n d ) = 2 . 6 m / s a c i t

r 3 0 e v S p a n = 1 9 0 m , V y ( l a n d ) = 2 0 . 6 m / s 2 0

0 9 0 1 0 0 1 1 0 1 2 0 1 3 0 1 4 0 1 5 0 t i m e ( s )

3.7 Final Case

Now that the parachute design is frozen the trajectory and masses can be calculated. The following table summarizes the parachute system:

3-21 Table 3.4: Parafoil Data for Final Case

Diameter of Vehicle (m) 9 Altitude where Mach 3 is reached (m) 12138 Flight path angle at this alt. (deg) -9.41 Vehicle mass estimate (kg) 47042.7

Reefing factor 0.3 Reefing time (s) 10

Time to land (s) 130 Velocity at landing (m/s) 72.0252 Horizontal velocity at landing (m/s) 71.9778 Vertical velocity at landing (m/s) -2.613

Max g-load (g's) 2.1468

Supersonic constructed diameter (m) 20 Subsonic constructed diameter (m) 70 Number of subsonic ringslot chutes 3 Parafoil span (m) 176

Supersonic chute mass (kg) 87.87 Subsonic chute mass (kg) 563.21 Parafoil mass (kg) 1617.87 Total mass (kg) 2268.9

Figure 3.10 shows the altitude vs. time. The black x’s separate the stages. The first black x represents where the supersonic parachutes are cut and the reefed subsonic chutes are deployed. The second black x represents where the subsonic chutes are un-reefed to their full area. The last black x represents where the subsonic ringslot chutes are cut and the parafoil is deployed.

Figure 3.11 plots the velocity vs. time. Remember this is the total velocity not the vertical velocity. That is why it has a high value at the end (72 m/s).

3-22 Figure 3.12 plots the g-loading vs. time. In this plot the peaks occur right when the chutes are opened. The g-loading is negative right when the parafoil is deployed since the vertical force of the parafoil does not overcome the weight of the vehicle as soon as the parafoil is deployed. The vehicle accelerates towards the ground for a few seconds before the vertical force of the parafoil grows and finally does overcome the weight.

Finally Figure 3.13 shows the trajectory of the vehicle during its entire descent. It starts at the point where mach 3 is reached and ends as the vehicle lands safely on the Martian surface. Figure 3.10: Altitude vs. Time for Final Case

A l t i t u d e v s . T i m e

1 2 0 0 0

1 0 0 0 0 ] s r 8 0 0 0 e t e m [

d 6 0 0 0 u t i t l A 4 0 0 0

2 0 0 0

0 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 T i m e [ s e c ]

3-23 Figure 3.11: Velocity vs. Time for Final Case

V e l o c i t y v s . T i m e 7 0 0

5 0 0 ] s / 4 0 0 m [ y t i c o l 3 0 0 e V

0 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 T i m e [ s e c ]

Figure 3.12: G-Loading vs. Time for Final Case

3-24 G - l o a d v s . T i m e 2 . 5

1 . 5 d a

o 1 l G

- 0 . 5 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0 T i m e [ s e c ]

Figure 3.13: Descent Trajectory for Final Case

P a r a c h u t e T r a j e c t o r y 1 8 0 0 0

1 6 0 0 0

1 4 0 0 0

1 2 0 0 0 ) m

( 1 0 0 0 0 e d u t i

t 8 0 0 0 l a

6 0 0 0

4 0 0 0

2 0 0 0

0 0 0 . 5 1 1 . 5 2 2 . 5 h o r i z o n t a l p o s i t i o n ( m ) 4 x 1 0

3-25 3-26 References

(1) Braun, Robert D., “Propulsive Options for a Manned Mars Transportation System”, pp. 85-92, 1991.

(2) Braun, R.D., “Mars Pathfinder Atmospheric Entry Navigation Operations”, AIAA Paper 97-3663, 1997.

(3) Hammond, Walter, “Space Transportation: A Systems Approach to Analysis and Design”, AIAA Education Series, 1999.

(4) Humble, Ronald W., “Space Propulsion Analysis and Design”, McGraw-Hill, Inc., 1995.

(5) Knacke, T. W., “Parachute Recovery Systems Design Manual”, 1992.

(6) Seiff, A., “Post-Viking Models for the Structure of the Summer Atmosphere of Mars”, Chapter 1, 1982.

(7) Smith, John, “Development of the NASA X-38 Parafoil Landing System”, AIAA-99- 1730, pp. 205-239, 1999.

(8) Wade, Mark, Astronautix.com, http://www.astronautix.com/engines/r40a.htm, http://www.astronautix.com/engines/ome.htm