Mission to Mars. MAE 598: Design Optimization Final Project. By: Trevor Slawson, Jenna Lynch, Adrian Maranon, and Matt Catlett

Transcription

1 Mission to Mars MAE 598: Design Optimization Final Project By: Trevor Slawson, Jenna Lynch, Adrian Maranon, and Matt Catlett

2 Motivation Manned missions beyond low Earth orbit have not occurred since Apollo 17 (1972). Astronomical objects outside the Earth s sphere of influence are prime for exploration. NASA has plans for a mission to Mars, but the tentative date is somewhere in Increasingly ambitious rover missions suggest that the logistics of a human mission may be possible even sooner.

3 Basic Rocket Science Rocket propulsion is achieved by burning energetic fuel mixtures and expelling the exhaust in the opposite direction: Unfortunately for us (and NASA), things can get much more complicated from there. NASA Exploration Page (Grades 9-10):

4 Less Basic Rocket Science During atmospheric flight, several forces are active all at once: Thrust Weight Lift Drag During orbital maneuvering, the calculations are dependent only on propulsion forces (no atmosphere): Thrust For now, focus on the orbital part NASA Exploration Page (Grades 10-12):

5 Orbital Maneuvering In orbit, change in altitude is proportional to change in speed. When orbital maneuvering is performed, the motion of a rocket can be described by the Tsiolkovsky rocket equation: Δv = v e ln m 0 m 1 The exhaust velocity (v e ) and the ratio of masses returns the maximum change in speed, referred to simply as delta-v (Δv). Fortunately this model can also be applied to non-orbital maneuvers via the concept of delta-v budget. Unfortunately, the fuel required to move a certain payload mass increases exponentially (Tyranny of the Rocket Equation).

6 Approach Four-step plan: 1. Launch the payload and some fuel into LEO 2. Launch extra fuel and astronauts into LEO 3. Dock the two halves together, then fly to Mars 4. Land on the Martian surface Goal: Oppose the tyranny of the rocket equation and get as many people on Mars as possible!

7 Approach Four-step plan: 1. Launch the payload and some fuel into LEO 2. Launch extra fuel and astronauts into LEO 3. Dock the two halves together, then fly to Mars 4. Land on the Martian surface Goal: Oppose the tyranny of the rocket equation and get as many people on Mars as possible!

8 Approach Four -step plan: 1. Launch the payload and some fuel into LEO 2. Launch extra fuel and astronauts into LEO 3. Dock the two halves together, then fly to Mars 4. Land on the Martian surface Goal: Oppose the tyranny of the rocket equation and get as many people on Mars as possible!

9 Approach Four -step plan: 1. Launch the payload and some fuel into LEO 2. Launch extra fuel and astronauts into LEO 3. Dock the two halves together, then fly to Mars 4. Land on the Martian surface Goal: Oppose the tyranny of the rocket equation and get as many people on Mars as possible!

10 Subsystem Overview Orbital Launch Booster (OLB) The OLB is a three stage rocket launch system similar to the Saturn V Rocket that will be used to get the IPV halves into low earth orbit. Interplanetary Vehicle (IPV) The IPV is the vehicle that will make the trip from LEO to Mars. It is made up of two halves (one being the payload) that are launched into LEO atop the OLB. Proactive Supply Launch (PSL) The astronauts on Mars will inevitably be faced with equipment failures. This launch plan will ensure that replacement gear is delivered in an optimal way.

11 Objectives and Tradeoffs A delta-v of roughly 18 km/s is required to land softly on Mars, therefore mass is a consideration in the tradeoff for every subsystem. Orbital Launch Booster Objective: Minimize the OLB mass while still achieving LEO Interplanetary Vehicle Objective: Maximize the number of astronauts who can be sent in 1 trip Proactive Supply Launch Objective: Minimize the number of supply launches needed. Trades: Lighter rockets are cheaper Heavier rockets can lift a bigger IPV Trades: Less astronauts are easier to send More people means more sustainability Trades: Few launches means bigger payloads Launches are very expensive

12 IPV Subsystem System Objective: Maximize the number of astronauts Assumptions: 1. The trip will take 9 months 2. The IPV will carry 4000 kg of gear 3. 89% of food mass is lost during the trip 4. The IPV will stage during both burns 5. LEO to TMI delta-v is 4.6 km/s 6. TMI to Soft-Land delta-v is 5.6 km/s 7. Aerobraking and parachutes are used to assist with the soft landing Radius Variables Height of each section Fuel Remainder Ratio (Amount of fuel in each half of the IPV) Number of Astronauts Constraints Delta-v requirements Food/water per person 3 Stages Each half of the IPV has the same mass Crew Space Equipment Food/Water Fuel IPV-1 Jumpseat Fuel IPV-2 Outputs Payload Mass and Volume IPV Mass and Dimensions

13 IPV Subsystem Subsystem Verification: Feasibility was checked with the Saturn V payload limit (118 metric tons) as a constraint. Crew Jumpseat Fuel IPV-2 Results: An IPV with capacity for 3 astronauts will meet all of the requirements and has the following dimensions: Overall Radius: 2 m Overall Height: 22.6 m IPV-1 Mass: 112 metric tons IPV-2 Mass: 112 metric tons Equipment/ Consumables Crew Living Space Lander IPV-1

14 MARS OR BUST OLB Subsystem System Objective: Minimize the mass of the booster stages. Assumptions: 1. The IPV is the maximum mass lift requirement. 2. Delta-v budget simplifications are valid in the atmosphere 3. Earth to LEO delta-v is 9.0 km/s 4. All performance characteristics are identical to those of the Saturn V 5. Structural mass is based on the surface area of each stage Variables Radius of each stage Height of each stage Number of engines per stage (Predetermined types) Constraints Delta-v requirements Burn time less than 800 sec Can lift the IPV halves to LEO Thrust-to-weight ratio at stage start is greater than 1 Acceleration at stage end is less than 6 g Radius of stage n must be less than or equal to that of n-1 Outputs (Determines Feasibility) OLB, Stage n

15 OLB Subsystem Subsystem Verification: Feasibility was checked with the Saturn V payload limit (118 metric tons) as a constraint. The number of engines was fixed at [5,5,1]. Results: An OLB with roughly the same parameters as the Saturn V was the optimal solution!

16 PSL Subsystem System Objective: Minimize the number of launches required to sustain the astronauts. Assumptions: 1. The PSL subsystem consists of analyzing supply launches. The launches will be unmanned. 2. The subsystem uses the mass and volume values generated in IPV subsystem. 3. Lifetime = MTBF for each assembly subassembly components simplified to 7 major assemblies. 5. Launches will be scheduled yearly. 6. It is assumed that it takes 1 year to get to Mars. 7. Assemblies come from Mars One mission plan. Results: See optimal system results. Variables Oxygen Generation Assembly Carbon Dioxide Removal Assembly Common Cabin Air Assembly Urine Processor Assembly Water Processor Assembly CO2 Reduction Assembly In-Situ Resource Utilization (ISRU) Constraints Mass (9770 kg) Volume (79.87 m^3) Mean Time Between Failures (MTBF) Outputs Number & time of launches

17 System Design Flowchart System Objective: Maximize the number of astronauts that can be sent to the surface of Mars and then sustained thereafter for a period of 22 years. Interactions: The systems will solve iteratively as shown, starting with the IPV and ending with a feasible PSL. Volumetric Constraint IPV Mass Constraint OLB Mass Constraint PSL Feasibility Revision (As Needed)

18 Optimization Challenges Subsystem Interdependence Challenge: It was not possible to optimize the IPV, OLB, and PLS simultaneously due to their interdependence. Solution: Solve the IPV subsystem first (most critical), then optimize the OLB, and finally the PSL. Integer Variables Challenge: Many variables had to be integer values for the results to make sense. OLB: Number of engines per stage PSL: Number of replacement systems per launch OLB Solution: Treat the integer variables as parameters and solve each of the cases independently with loops (432 cases in < 5 min). PSL Solution: Too many variables to check all cases with loops. Instead, use genetic algorithm.

19 System Results - IPV Amount of astronauts was varied from 1 to 4 and each case was solved independently. No failure is observed at this level because this subsystem is constrained by the OLB. Greater than 4 astronauts required excessive amount of weight and did not initially seem feasible. IPV complete, proceed to the OLB optimization. Parameter Astronauts (#) Radius (m) Height (m) Volume (m³) Payload (metric ton) Half-Mass (metric ton) IPV Case Larger than Saturn V Less Feasible

20 System Results - OLB Optimal solution was found for each number of astronauts. Geometry in comparison with the Saturn V is shown for each case. First signs of failure are observed; a crew of four astronauts cannot be sent in a single trip. Eliminates the less feasible result from IPV optimization. New optimal solution of 3 astronauts (as per the objective function) n=1 n=2 n=3 Saturn V (in blue) compared with the OLB s for n=[1,2,3] astronauts Parameter Optimal OLB Saturn V Height (m) GVW (metric tons) Engines/Stage [6,6,3] [5,5,1]

21 System Results - PSL Optimal launch plan for 3 astronauts was found using the IPV and OLB combination results.

22 System Results PSL An optimized resupply plan of only 15 launches will meet the needs of the crew over a period of 22 years without any equipment downtime. Maximum Mass: 1021 kg Maximum Volume: 2.4 m³ IPV, OLB, and PLS are all optimized at this point. Since the maximum mass and volume are so low, the scope of the project could be expanded. More astronauts over time Larger bases (population growth) Smaller teams (more exploration)

23 Overall Results Interplanetary Vehicle Orbital Launch Booster Proactive Supply Launch A two-part vehicle with 95% fuel by mass will ferry three astronauts from LEO to Mars in a trip that will last nearly 9 months. They land next to an automated supply ship and set up a small colony when they arrive. Each half of the IPV will be lifted into orbit by the largest rocket ever built. With a mass 25% larger than that of the Saturn V, the OLB could put a third of the mass of the ISS into low earth orbit with a single launch. Each year replacement equipment is sent on automated IPV s. Vital systems are replaced before they fail, allowing the colony to survive for the estimated 22 years required for them to achieve self-sufficiency.

24 Questions?

25 Appendix 1 OLB Model Variables: s = [1,2,3] stage number h s height of stage s r s radius of stage s n s number of stage s thrusters

26 Appendix 2 IPV Model

27 Appendix 3 PSL Model Mass (kg) Vol (m^3) MTBF (years) Oxygen Generation Assembly Carbon Dioxide Removal Common Cabin Air Assembly Urine Processor Assemlby Water Processor Assembly CO2 Reduction Assembly ISRU Table 1: Assemblies and their respective mass, volume, and MTBF. Table 2: Number of assemblies per launch. Highlighted launches are empty launches.