vehicle configurations with either RSRM or RSRM V boosters. Drag profiles are ... The F-1, stage 1 engine on the Saturn V, and the upgraded version, the F-1A ...
48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit 30 July - 01 August 2012, Atlanta, Georgia
AIAA 2012-4268
Design and Selection Process for Optimized Heavy Lift Launch Vehicles
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Paul A. Ritter1 and James E. Lyne2 The University of Tennessee, Knoxville, TN 37996
Optimization of a launch vehicle can be specified in terms of many different variables. In the case of a heavy-lift vehicle, the objective is often to minimize the weight of the vehicle on the launchpad. Minimization of this particular variable is essential for designing efficient vehicle capable of bringing specified payloads to orbit. In this paper we discusses a process used to achieve a minimum gross liftoff weight for a vehicle with a flexible payload capability that utilizes pre-existing or near-term propulsion systems. Determining the optimized configuration is accomplished with a combination of brute force methods and with mathematical and visual data organization. Through the variation of five different independent variables, millions of trajectories are simulated for different vehicle configurations to provide the necessary data. Organization of this data presents the means to identify and locate the configurations that meet the performance constraints and minimize overall system mass.
Nomenclature α єs h γi mi mpi q Vi ΔV
= = = = = = = = =
angle of attack inert mass fraction for ith stage altitude inertial flight path angle inert mass for ith stage mass of propellant for ith stage dynamic pressure inertial velocity velocity budget
I. Introduction / Objectives
F
UTURE manned lunar and interplanetary missions will require a heavy lift platform far more capable than any American vehicle available today. An ideal design could be adapted to meet a wide range of potential mission and payload requirements. Our group was tasked by colleagues at NASA Marshall Space Flight Center to develop a system level design and initial proof of concept for a vehicle that could transport payloads ranging from 60 to 130 MT to low Earth orbit (LEO) using existing or near term propulsion components. Primary objectives of the process were to keep the gross liftoff weight (GLOW) as low as possible and to have a “plug and play” design that could be quickly and inexpensively adapted for various payloads. Analysis of the vehicles consists of a conceptual design of each configuration, including the number of stages, engine selection, aerodynamic considerations, and overall vehicle size. The propulsion system utilizes previously designed engines and motors to provide the thrust required in the different stages. The different configuration types to be analyzed vary in the number of stages, engines, boosters, and propellant and are illustrated in Fig. 1. The first type is called a 2 stage vehicle and has two propulsion systems stacked one on 1
Student, Department of Mechanical, Aerospace and Biomedical Engineering, 2180 Crestwood Drive, Clarksville, TN, Professional Member. 2
Clinical Associate Professor, Department of Mechanical, Aerospace and Biomedical Engineering, 414 Dougherty Building, The University of Tennessee, Knoxville, TN 37996. 1 American Institute of Aeronautics and Astronautics Copyright © 2012 by Paul A. Ritter. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
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top of the other. The first stage is usually designed to perform efficiently for lift off and low altitude propulsion where the second stage is designed to bring the vehicle to orbital velocity. There is a sub group within this category called a 2 stage booster. This type employs the use of a prefabricated booster such as the Reusable Solid Rocket Motor (RSRM) as the first stage of the vehicle. The next category is 2.5 stage vehicles. These vehicles are similar to 2 stage vehicles except that there are a number of boosters strapped on that burn parallel to the first stage of the vehicle. The boosters generally separate before 1st stage cutoff which is where the ½ label comes from. The third type is a 1.5 stage configuration. This is very similar to a 2.5 stage except that there is no 2 nd stage and the 1st stage fires for the entire launch. The Space Shuttle is an example of this type of vehicle (Ref. 12).
(a) (b) (c) (d) Figure 1. Sample Configurations. A side and bottom view for the 2 stage (a), 2 stage booster (b), 2.5 stage (c), and 1.5 stage (d) configuration types. There are seven launch configurations to be analyzed for minimization of GLOW. Each is classified as a variant of one the types illustrated in Fig. 1. The seven configurations are described in Table 1, and are selected for the range of differing boosters and stage configurations. This broad selection of vehicles for analysis provides the means to determine patterns associated with minimizing GLOW. Table 1. Cases to Analyze for Optimized Configuration. Stage 1 Engines
Stage 2 Engines
Booster Stage
Configuration
Class
Type
Number
Type
Number
Motor
Number
A
2.5 Stage
F-1
2
SSME
2
RSRM
2
B
2.5 Stage
F-1A
3
SSME
3
RSRM V
2
C
2.5 Stage
F-1A
3
J-2X
5
M550 FW3
3
D
2.5 Stage
F-1A
3
SSME
3
P80
6
E
2 Stage
F-1A
4
J-2X
3
-
-
F
2 Stage Booster
RSRM
2
SSME
3
-
-
G
1.5 Stage
SSME
5
-
-
RSRM V
2
2 American Institute of Aeronautics and Astronautics
Constraints for the analysis are defined to the vehicle and trajectory. Vehicle length is limited to 100 m with a core stage diameter limited to 10 m. Other than these two parameters, free reign is given to vary the physical dimensions and properties of the vehicle. Target altitude (h) is specified as a 400 km circular orbit above the surface of the earth. This orbital position requires an inertial velocity (Vi) of 7670 m/s and an inertial flight path angle (γ i) of 0 deg. Lastly, aerodynamic considerations are limited to a maximum dynamic pressure (q) of 800 psf and a maximum angle of attack (α) of 6 deg during defined atmospheric flight. These five constraints provide values for the target conditions and boundaries (Ref. 8).
II. Optimization Tools
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To perform the optimization of these heavy lift configuration, a series of tools were developed. These tools are capable of a range of functions and assist in the analysis by performing necessary simulations and organizing generated data into manageable sets. A. Trajectories for Heavy Lift Evaluation and Optimization THEO The trajectory simulation program used for this analysis is titled Trajectories for Heavy-lift Evaluation and Optimization (THEO). This program was developed for this project with the intention to model vehicles from launch to the necessary orbit. It has been validated in comparison with NASA’s Program to Optimize Simulated Trajectories (POST) (Ref. 7). THEO is a 3 DOF simulation program with the capability to model a wide range of differing launch vehicle configurations. Configurations are built in THEO using input files that describe the vehicle dimensions, stage sizes and propulsion, booster properties, aerodynamic coefficients, and pitch events. Using equations of motion (Ref. 11) and an iterative time step process, THEO simulates the trajectory based on the user input. THEO also has an advanced capability that allows it to simulate numerous trajectories. This is accomplished through the variation of five independent variables. The user inputs a minimum, maximum, and interval for each variable, and utilizing DO loops, THEO generates the results based on each step within the specified range. The data from all the cases is stored in a matrix format that can be utilized in a graphical analysis. This ability is very useful as it can show the affect of changing certain vehicle properties on the burnout velocity, altitude, and flight path angle. The independent variables are stage one propellant mass, stage two propellant mass, and the primary pitch parameters of start time, length, and pitchrate (Ref. 8). B. Burnout Constraint Surface Plots With five independent variables, it is impossible to graphically visualize the effects of all variables at once. A graphical representation is instead completed by breaking the data into effective groups for analysis. A three dimensional (3D) plot allows the user to view data as a function of two variables. By holding three of the variables constant, the effects of changing two independent variables can be represented graphically. Consider the example of varying primary pitch event length and pitchrate for a 2.5 stage vehicle while propellant masses and pitch start time are held constant. The simulations generated for this case are shown in Fig. 2 for the burnout condition of altitude.
Figure 2. Vehicle Burnout Altitude. Function of pitch length and pitchrate. 3 American Institute of Aeronautics and Astronautics
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This 3D surface illustrates the effects of varying the pitch length and the pitchrate on altitude. Notice that the plot also contains a horizontal plane. This plane indicates the desired burnout condition for that particular configuration, and an intersection between the 3D surface and this plane implies a potential solution (Ref. 8). These plots can also be generated for the additional burnout conditions of inertial velocity and flight path angle. C. Intersection Curve Plot To be present in the desired target orbit, a vehicle must satisfy the three orbital constraints of altitude, inertial velocity, and inertial flight path angle. An intersection on one of the surfaces does not imply that the vehicle has satisfied all three conditions. There must be an intersection on all three burnout surfaces at the same value of pitchrate and length of pitch. A 2D plot can be generated to illustrate the intersection curves from the 3D plots for altitude, inertial velocity, and flight path angle. Possible solutions are shown at an intersection of all three conditions, and example solutions are identified in Fig. 3. The plot displayed in Fig. 3 is very functional as it illustrates to the user how a change in the two independent variables can bring the vehicle to the correct orbit (Ref. 8). It should also be noted that this intersection curve group is specifically for a start time 7.7 s. The visual representation can be increased to three independent variables by plotting intersection curve groups for multiple start times. This is demonstrated in a later section.
Figure 3. Sample Intersection Curves. For a start time of 7.7 s.
III. Vehicle Properties A. Aerodynamics The aerodynamic data for each case is approximated using drag and lift coefficient profiles. The drag coefficient profiles originates from two sources. For this analysis, NASA provided lift tabulated drag data for the 2.5 stage vehicle configurations with either RSRM or RSRM V boosters. Drag profiles are generated for additional configurations using the Air Force aerodynamic tool Missile Datcom (Ref. 2,Ref. 6). A comparison of the Datcom generated data with known aerodynamic profiles confirms the reliability of this tool for estimating drag (Ref. 8). NASA also provided lift coefficient data for the 2.5 stage configurations with RSRM or RSRM V boosters. For additional configurations, an attempt was made to model lift using Datcom, but the results were over an order of magnitude off from the expected values. Lift has a relatively small effect on heavy-lift launch vehicles. This is generally due to the low of angle of attack (α) during atmospheric flight, and trajectory path that is dominated by a gravity turn and not a forced pitch event. The question is, how much does lift affect the burnout conditions of the vehicle? By running one of the 2.5 stage configurations with lift turned on and off, the data showed that there was a 4 American Institute of Aeronautics and Astronautics
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negligible difference between the final conditions for the different scenarios. This implies that lift can be assumed to be zero with no major effect on the final results. The details of this check are discussed further in Ref. 8. Also, a biconic nose cone is chosen as the nose cone shape based on the objectives of minimizing mass, maximizing payload volume, and low average acoustical levels. The assumed fairing mass was assumed to 19,674 kg based on a POST input deck supplied by NASA (Ref. 3). B. Propulsion Systems Selection of the propulsion systems used on the cases in Table 1 are limited to engines and motors that are currently in use, have been used, or are in a near-term stage of development. All selections are based on either a solid grain or stored liquid propulsion system. These propulsion types are very conventional in terms of a technology that has been used and verified through years of historical use (Ref. 9). This decision supports high engine reliability as well as a faster design and construction time for the final optimized vehicle. Stage one engines are high thrust in order to overcome the large mass of a heavy-lift launch vehicle. For launch it is imperative that the thrust to weight ratio be greater than one. The F-1, stage 1 engine on the Saturn V, and the upgraded version, the F-1A are some of the few American engines that show promising capability of bringing such a heavy payload to orbit (Ref. 10). It should be noted that per request of NASA, there is one configuration that uses the Space Shuttle Main Engine (SSME) as its stage one engine. After stage one separation, second stage engines fulfill the purpose of accelerating the payload to the necessary orbital velocity. The necessary acceleration is supported by an efficient exchange of momentum between the exhaust particles and the vehicle. This desired high performance is available in engines with a high specific impulse. As such, the SSME and J-2X were chosen to fulfill this position in hopes to minimize GLOW (Ref. 9). The SSME was chosen for an additional reason. NASA currently has a number of them that are not in use, and if a purpose could be found or them, there would be potential cost savings for future vehicles and/or missions. The final propulsion system included in some of the cases is a booster. Boosters are a standalone system that simply strap onto the core of the vehicle to provide extra thrust. They are typically designed with a solid propellant, but there are some, such as the Delta IV boosters that utilize liquid propellant. The independence of the booster provides a lot of variability as it is relatively simple to attach them to a configuration to provide extra thrust when needed. There are four different boosters that are used on the different cases. The first is the Reusable Solid Rocket Motor (RSRM) which is a four segment solid propellant motor with high thrust and high mass (Ref. 1). The RSRM V is the upgraded version, designed with a higher performance thrust profile. The next type is titled the Monolithic 550 FW3. It is a single segment motor with a lower thrust profile than the RSRM boosters and a much lower mass. The last booster is also a single segment propellant and is called the P80. It has very low thrust and mass when compared to the RSRM booster (Ref. 5). C. Inert Mass Inert mass (mi) of the vehicle is estimated in THEO using Eq. (1). This term accounts for hardware and structural masses that separate from the vehicle after each stage burnout. It is a function of the inert mass fraction (єi) for the ith stage and the mass of the ith stage propellant. The inert mass fractions used for these estimations are 0.06 for the first stage and 0.08 for the second stage. These values are based on trending data shown in Ref. 4. (1)
IV. Methodology Determination of the overall optimized configuration can be somewhat of an overwhelming task. To simplify the process, it is helpful to approach each case in Table 1 individually. By determining the minimum GLOW for each case, it is then possible, through the comparison of the results to determine the final optimized case. The first step in the optimization process is to perform a general analysis of the first configuration. A general analysis is defined as a simulation in THEO that varies the five independent variables described earlier over a wide range. A simulation such as this serves the purpose of locating regions of potential solutions. A potential solution is characterized as a particular configuration that comes close to bringing the vehicle to the necessary orbital constraints of altitude, inertial velocity, and inertial flight path angle. This technique zones in these regions by eliminating stage propellant and vehicle pitch properties values that steer the configuration away from the desired solution. If there are no solutions, modifications are made to the configuration such as adding or removing engines or boosters and adjusting secondary pitch events. The general analysis is reevaluated. 5 American Institute of Aeronautics and Astronautics
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After completing the general analysis and locating the lightest region for potential solutions, a check must be completed to ensure that all three burnout conditions meet at an intersection point. This step is similar to the curves in Fig. 3. If all three meet, then the configuration has shown the potential to be the minimized configuration for that case. If not, minor adjustments can often be made to the vehicle that will correct the curves so that there is an intersection point. When that correction is insufficient, it is important to return to the general analysis and search for new solution regions. If all three burnout constraints converge on the intersection curve plot, there is one last step to ensure that the configuration is minimized. It is possible that with a slight reduction in propellant mass, the vehicle could still be capable of reaching orbit. Using a refined analysis in THEO, which is a simulation that varies the independent variables local to the current solution, will establish if propellant can be removed. If there are successful cases with less propellant, the lightest case is chosen that is still capable of reaching the desired orbital constraints. Once this is completed, a check is performed to ensure that the propellant fits inside the vehicle, and that the dimensions match with the aerodynamic data. The additional payload requirements of 100 mt and 60 mt are evaluated with the objective of maintaining as much of the original 130 mt configuration as possible. The best configuration would be the one that would provide adaptable payloads simply by removing boosters. The final optimized choice will not only have a minimized GLOW but will also support the required payload requirements without much change to the core of the vehicle. The process describe in this section is repeated for each of the cases in Table 1, revealing the minimum GLOW configuration and potential adaptable payloads. The final optimized configuration will be the lightest case with high capability for adaptable payload situations (Ref. 8).
V. Configuration Analysis for 2.5 Stage RSRM Vehicle A. General Analysis Consider configuration A from Table 1 with a 130 mt payload. It uses the RSRM for the booster stage, the F-1 for the stage one engines, and the SSME for the stage two engines. The first step is to perform a general analysis to reveal preliminary information as to where potential solutions might exist. It answers the initial question: is it even possible for this configuration to come close to the target burnout conditions? This initial analysis is done by varying the independent variables as specified in Table 2. Table 2. Independent Variable Specifications. Primary Pitch Event
Minimum Maximum Interval
Propellant Mass
Start Time
Length
Pitchrate
Stage 1
Stage 2
s 7.2 14.2 1
s 1 21 2
deg/s -0.1 -0.65 -0.05
kg 1100000 1600000 50000
kg 500000 900000 50000
As mentioned earlier, burnout conditions for a launch vehicle are described with the three conditions of altitude, inertial velocity, and inertial flight path angle. It is necessary to satisfy all three conditions for a successful orbit. The target orbit for this launch is a 400 km circular orbit which requires an orbital velocity of approximately 7670 m/s and an inertial flight path angle of 0º. Any variation from this velocity and flight path angle represents a different orbit. A successful configuration must have the velocity satisfied within ± 40 m/s, the flight path angle within ± 0.5 deg, and altitude within ± 2000 m of the desired burnout altitude (Ref. 8). The first general analysis for this vehicle reveals this configuration is incapable of reaching the desired burnout conditions. After launch the vehicle falls back to the surface, which is indicative of an acceleration that is insufficient. In this case, this is the result of a low thrust to weight ratio. A series of upgrades are made to the vehicle to give it the capability of reaching orbit by increasing the thrust at launch. The adjustments consist of modifying the 2 F-1 engines to 3 F-1A engines, and the 2 SSME engines to 3 SSME engines. A revised analysis with the engine upgrades reveals configurations that prove to be quite capable. Table 3 shows the top configurations that best satisfy the burnout conditions. In these tables GLOW is the sum of the propellant, inert, payload, shroud, and booster masses.
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Table 3. 2.5 Stage RSRM General Analysis Top Configurations Independent Variables Propellant Mass Primary Pitch Event Stage 1 Stage 2 Start Time Length Pitchrate Case kg kg s s deg/s 1a 900000 700000 7.2 19 -0.7 2a 1000000 650000 7.2 21 -0.7 3a 1050000 650000 7.2 15 -0.7 4a 1100000 650000 8.2 19 -0.65 5a 1150000 650000 9.7 21 -0.65 6a 1150000 700000 7.2 15 -0.45 7a 1200000 700000 7.7 21 -0.4 8a 1250000 700000 9.2 7 -0.65
GLOW kg 3039748 3091784 3144975 3198167 3251358 3305706 3358897 3412089
Burnout Conditions Inertial Property FPA Velocity Altitude Max Q deg m/s m psf -0.02 7443.9 398737 951 0.73 7600.9 400044 930 0.64 7607.9 403941 892 0.22 7669 401797 857 -0.08 7719.5 402361 823 -1.51 7625.6 396906 778 -1.66 7651.4 401009 747 -1.98 7693.7 399302 719
In terms of burnout conditions, it is obvious that configuration 4a is the top choice. It fulfills all burnout conditions within the allowed bounds. This choice is not necessarily the optimized case as it has not yet been shown to minimize GLOW. The purpose of these eight cases is to provide a starting point in searching for the optimized case. They indicate a region where it is possible a group of solutions might exist. Cases 1a – 3a are the three lightest of the cases, but notice the burnout conditions are not at the required specifications. Inertial velocity is outside of the specified bounds for all three cases. An insufficiency in this area can be the result of two things. The first possibility is that the pitch properties do not correspond well with the mass of the vehicle, and a slight adjustment of the three independent pitch parameters or the secondary pitch events can potentially bring the vehicle to the necessary orbital constraints. The other possibility is that there is simply not enough energy within the propulsion system to bring the vehicle to orbital requirements. This is adjusted by increasing the propellant mass as this increases the total energy available within the vehicle. As mentioned before case 4a reaches burnout conditions, but it is also important to consider the indicator of dynamic pressure. Cases 1a – 5a all exceed the specified constraint of 800 psf. A high dynamic pressure in this case indicates that the thrust to velocity of the vehicle weight ratio in the atmospheric region of flight is too high. This is the result of a thrust to weight ratio that is excessive. One solution to this would be to remove a first stage engine, but as discussed earlier, two first stage engines and two boosters provide insufficient thrust to bring the payload to burnout conditions. The only other option is to consider cases with slightly more propellant because as mass increases, the thrust to weight ratio and maximum dynamic pressure will decrease. This trend is shown in Table 3 as the maximum dynamic pressure decreases while GLOW increases for cases 1a – 8a. Finding the best case is dependent on locating a balance for a vehicle with the lowest possible GLOW and a dynamic pressure that does not surpass specified limits during launch. Case 5a is just above the dynamic pressure limit, and case 6a is just below the limit. This suggests that a minimized case might exist somewhere in between. The first step to searching for the minimized case is to perform a pitch analysis on 5a to determine if the pitch properties match well with the vehicle. This is completed by varying the pitch properties for the case at a constant propellant mass with pitch bounds as shown in Table 4. This particular step indicates whether or not case 5a is capable of reaching burnout conditions. Using the intersection curve tool from described earlier, it is possible to locate a configuration that fulfills burnout conditions. For a case to be successful, all three burnout conditions must intersect at a single point. Figure 4 illustrates the curve groups for a pitch start time of 6.7, 8.7, 10.7, and 12.7 s. For a start time of 6.7 s there is a region where the curves intersect and indicate that there is a solution for this configuration. These plots also show that the burnout variable curves diverge from each other as the start time increases. Table 4. Pitch Analysis Bounds Start Time Length s s Minimum Maximum Interval
6.7 12.7 0.5
1 40 1
Pitchrate deg/s -0.01 -0.81 -0.05
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Case 6a is shown in Fig. 5 and illustrates the results of increasing propellant by 50 mt. The groups have diverged substantially as the propellant has increased, which as stated earlier, can be the result of either insufficient energy in the vehicle or secondary pitch events that do not fit this particular vehicle. Notice that the altitude and inertial velocity curves stay relatively close together in each group. It is the inertial flight path angle curve that diverges away. This serves to indicate that the pitch properties are not the best fit for this particular vehicle. A revision of the fourth secondary pitch rate to -0.149918 deg/s is shown in Fig. 6. This revision shows that correction of the secondary pitch profile brings the vehicle to curve groups that intersect.
Figure 4. Case 5a Intersection Curves. Curve groups for start time of 6.7-12.7 s.
Figure 5. Case 6a Intersection Curves. Curve groups for start time of 6.7-12.7 s. 8 American Institute of Aeronautics and Astronautics
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Figure 6. Case 6a Revised Intersection Curves. Adjusted secondary pitchrate. B. Refined Analysis The next step in the analysis is to determine if a configuration exists in between case 5a and 6a that minimizes GLOW. This is done with THEO by performing a refined analysis of different configurations with propellant masses in between those of case 5a and 6a. The top configurations in terms of burnout conditions for this analysis are shown in Table 5. Notice that the majority of the cases have a maximum dynamic pressure that is beyond the specified limit, which effectively eliminates them as possible candidates. The highlighted cases are the ones that correspond to an acceptable max dynamic pressure. None of the cases that are below the minimum for dynamic pressure fulfill the necessary 0.5% for all three target burnout conditions. This implies that a pitch analysis is necessary to determine if the secondary pitch events should be revised. The top three lightest cases are a4, a14, and a11. Case a11 has a burnout inertial velocity that is closest to the desired conditions, indicating that the energy available in the propellant has the best match in this case. This is an important consideration as it implies that a simple pitch adjustment could bring the vehicle within the desired burnout flight path angle. Case a11 is also a good case to start with, because unlike a4 and a14, there is some room for the maximum dynamic pressure to increase if the pitch analysis reveals that it is necessary. The pitch analysis is shown in Fig. 7, and just like the previous pitch analysis, the inertial flight path angle curve is offset. To remedy this, the fourth secondary pitch event is adjusted to -0.154121 deg/s. Modification of this term shifts the intersection groups to the results shown in Fig. 8. The curve groups illustrates that this case is capable of reaching the desired burnout conditions at multiple pitch specifications. The new secondary pitch rate is also applied to case 4a and a11, and the results in Table 6 illustrate that this correction brings all three cases to desirable burnout conditions. Notice also in this table that the maximum dynamic pressure increases slightly for all three cases, affirming the earlier assumption of using case a11 instead of a4 and a14.
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Table 5. 2.5 Stage RSRM GLOW Minimization Cases. Minimized configurations based on Case 4a. Independent Variables Propellant Mass Primary Pitch Event Stage 1 Stage 2 Start Time Length Pitchrate Case kg kg s s deg/s a1 1130000 660000 9.2 26 -0.6 a2 1130000 670000 10.7 23 -0.7 a3 1130000 680000 6.2 28 -0.4 a4 1130000 690000 8.7 15 -0.6 a5 1140000 660000 6.2 17 -0.5 a6 1140000 670000 6.7 13 -0.5 a7 1140000 680000 7.2 13 -0.5 a8 1140000 690000 7.7 12 -0.6 a9 1150000 660000 6.7 20 -0.5 a10 1150000 670000 6.7 26 -0.5 a11 1150000 680000 6.7 20 -0.5 a12 1150000 690000 6.7 12 -0.47 a13 1160000 660000 10.2 24 -0.61 a14 1160000 670000 7.7 17 -0.52 a15 1160000 680000 6.7 20 -0.44 a16 1160000 690000 8.2 27 -0.46
GLOW kg 3240951 3251821 3262690 3273560 3251589 3262459 3273328 3284198 3262228 3273097 3283967 3294836 3272866 3283735 3294605 3305475
Burnout Conditions Inertial Property FPA Velocity Altitude Max Q deg m/s m psf -0.33 7688.7 399226 826 -0.68 7678 396518 817 -0.79 7642 400697 808 -1.05 7621.9 400046 799 -0.46 7705.6 397196 821 -0.57 7673.1 401738 811 -0.97 7663.9 396934 803 -1.12 7632.9 399687 793 -0.3 7694.6 403850 814 -0.6 7679.4 402523 804 -0.97 7666.6 398834 796 -1.2 7642.7 399260 787 -0.38 7707.7 403368 806 -0.68 7690.2 401903 798 -0.98 7673.1 400564 789 -1.26 7650.9 399270 780
Figure 7. Case a11 Intersection Curves. Curve groups for start time of 6.7-12.7 s.
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Figure 8. Case a11 Revised Intersection Curve. Adjusted secondary pitchrates. Table 6. Revised 2.5 Stage RSRM GLOW Minimization. With secondary pitchrate revision. Independent Variables Burnout Conditions Propellant Mass Primary Pitch Event Inertial Property Stage 1 Stage 2 Start Time Length Pitchrate GLOW FPA Velocity Altitude Max Q Case kg kg s s deg/s kg deg m/s m psf a4 1130000 690000 8.7 15 -0.593 3273560 -0.05 7649.6 400645 801 a11 1150000 680000 6.7 20 -0.459 3283967 0.05 7690.6 400472 798 a14 1160000 670000 7.7 17 -0.532 3283735 0.20 7724.5 399964 801 The final selection for this configuration with minimized GLOW is case a11. It has been shown to be optimized in terms of GLOW by performing a series of procedures that ensure the amount of propellant is minimized and that the pitch properties are well suited to the configuration. It has also been shown to fit within the required aerodynamic constraint of 800 psf. Table 7 provides a description of the optimized vehicles properties for the 130 mt payload case. The dimensions have been sized based on the volume propellant requirements as well as the room required for the engines and payload. The room necessary for the engines is based on dimensions specific to each engine, and it is also assumed that the payload bay fills the nose cone as well as 10 m into the body of the vehicle. Table 7. 2.5 Stage RSRM Configuration for 130 mt Payload. Length Diameter Propellant Inert Engine # Engines Burnout Alt 400000 m m m kg kg (Shape) Burnout Vel 7691.3 m/s Booster 35.05 3.75 1003399 168354 RSRM 2 Burnout FPA -0.011 deg Stage 1 25.88 8.50 1150000 73407 F-1A 3 Max Q 798.1 psf Stage 2 51.89 8.50 680000 59133 SSME 3 GLOW 3283966 kg Shroud 12.19 8.50 19674 Biconic Start Pitch 6.7 s Total 89.96 2.5 Stage Pitch Length 20 s Secondary Pitch Revision 4th -0.154582 deg/s Pitchrate -0.459 deg/s 11 American Institute of Aeronautics and Astronautics
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C. GLOW Stability To be a valid candidate, the vehicle must be shown to be stable in terms of a GLOW versus ΔV analysis. The velocity budget (ΔV) is representative of the amount of energy that is available within the different stages of the vehicle. The ΔV fraction is a percentage of that total velocity budget that corresponds to the particular stages. GLOW is function of this variable, and this necessary check provides the means to illustrate if a slight change in the ΔV fraction for each stage will require a significant change in GLOW for the vehicle (Ref. 4). This is done by plotting GLOW as a function of the ΔV contribution for two different stages of flight in a 2.5 stage vehicle. If the vehicle is on a relatively shallow portion of the surface, it can be considered stable and a valid configuration. A ΔV analysis of case a11 is shown in Fig. 9.
Figure 9. 2.5 Stage RSRM Stability Surface for 130 mt Configuration. Describes GLOW as a function of the velocity contribution from the different stages of the launch. This surface shows that the vehicle is somewhat stable in terms of this ΔV property. The location of the vehicle described in Table 7 is indicated by the yellow dot in the figure. The axis labeled Stage A dV signifies the portion of the launch where the core engines and boosters burn together, and Stage B dV represents the contribution of the core after the boosters have separated. The position of the dot indicates that a modification of these stage contribution fractions will have a slight but not significant effect on GLOW. D. Additional Payload Requirements An analysis with smaller payload requirements shows that Configuration A is not suited for adaptable payload capability. The RSRM boosters are extremely powerful which has somewhat of an adverse effect when adjusting the vehicle to smaller payloads. If the boosters are left on, the maximum dynamic pressure of the vehicle surpasses the limit by 100 psf – 400 psf. If the boosters are taken off, the vehicle is not capable of reaching orbit. Ref. 8 provides more specifics pertaining to this analysis and suggests that this configuration does not perform well except for its original optimized design configuration.
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VI. Optimization Results
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The evaluation of the 2.5 stage vehicle with two RSRM boosters has served as an example as to the method for determining the minimum GLOW for a specific type of vehicle. A similar process is used for the additional cases in Table 1. Results are shown in Table 8. For details on this process for each case refer to Ref. 8. This next section discusses the results from each of the cases, and outlines the selection process for the final optimized configuration. A. Case Comparisons The RSRM family configurations have the highest GLOW out of any of the analyzed cases. This is directly a result of the booster size. The RSRM family boosters have high thrust output and heavy initial masses and as a result, no more than two can be used on a launch vehicle. More than this will result in a vehicle that surpasses maximum dynamic pressure values. Even with two boosters, the thrust to weight ratio and acceleration are high, which can then only be decreased by increasing the weight of the vehicle. Also, notice the difference between the 2.5 Stage vehicle with RSRMs and RSRM Vs. The RSRM V is a more powerful engine than the RSRM and drives GLOW to be 117 mt heavier than the vehicle with 2 RSRMs. The high thrust from these boosters drives up the final optimized weight for these configurations. It was also determined that the 100 mt and 60 mt payload variants could not be derived from the original configuration. Considering this and the high GLOW, these configurations are removed from candidacy as the final optimized solution. Table 8. Overall Configuration Comparison. Propellant Configuration Payload GLOW Historical Vehicles mt kg 2.5 Stage RSRM 130 3283966 2.5 Stage RSRM V 130 3401459 130 2994521 2.5 Stage M550 100 2354541 60 1524120 130 2806800 2.5 Stage P80
Engine
Stage 1 kg 1150000 960000 1180000 1180000 682976 1170000
Stage 2 Booster kg Type 680000 RSRM 710000 RSRM V 400000 M550 FW3 370000 M550 FW3 129263 M550 FW3 600000 P80
# 2 2 4 2 2 8
Stage 1 Engine # F-1A 3 F-1A 3 F-1A 2 F-1A 2 F-1A 1 F-1A 3
Stage 2 Engine SSME SSME J-2X SSME J-2X SSME
# 3 3 4 2 2 3
100
2396667
1170000
600000
P80
3
F-1A
3
SSME
2
60 130
1438411 2899915
818599 1870000
273993 700000
P80 -
2 -
F-1A F-1A
2 5
SSME J-2X
1 5
1.5 Stage RSRM V Space Shuttle Delta IV Heavy
100 130 29 22.7
2459514 3189645 2030000 775643
1882708 984295 729007 658320
2 2 2
Saturn V
120
3039000
2286217
309997 *RSRM V* RSRM 26014 RS-68 Stage 1 490778 F-1
F-1A 4 SSME 5 SSME 3 RS-68 1 Stage 2 J-2 5
2 Stage
5
J-2X(84%) 2 RL-10B-2 1 Stage 3 J-2 1
*(*RSRM V*) represents modified RSRM V booster. The 2.5 stage M550 FW3 case shows major improvement over the RSRM configurations. The M550 booster has a lower thrust and propellant mass per booster. This implies that to reach orbit, the vehicle will require more boosters. A concept such as this is very useful as it allows thrust to be added in smaller increments as compared to the RSRM family boosters. Smaller thrust and propellant mass increments imply that the vehicle can be tailored to a specific payload without greatly increasing the thrust to weight ratio, acceleration, and maximum dynamic pressure. Use of the M550 booster allows the vehicle to have a GLOW 300 – 400 mt less than the RSRM configurations for a payload of 130 mt. Notice as well that the 100 mt payload can be brought to orbit by simply removing two M550 boosters and performing a slight modification to the stage two propellant mass. The 60 mt payload requires more significant adjustments to the core as Table 8 illustrates, but is still able to use the M550 for reaching orbital conditions. The P80 is an even smaller booster, and as such, further increases the capability of a vehicle to be designed for a heavy lift configuration and still be adaptable for different payloads. The 130 mt payload case requires eight P80 13 American Institute of Aeronautics and Astronautics
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boosters, and is able to decrease the required GLOW from the 2.5 stage M550 configuration by approximately 200 mt. A lower GLOW is supported with a higher number of smaller boosters that can be matched better with the necessary propellant and engine properties. The 100 mt payload is capable of being brought to orbit by simply adjusting the number of boosters from eight to three. The 60 mt payload can also be brought to orbit, but does require modifications to the core vehicle. The 2 stage vehicle is quite capable in terms of optimization as it has been shown to have the second lowest GLOW of 2899.9 mt. Compared to 2.5 stage vehicles; it is simple and able to bring the 100 mt payload to orbit. The disadvantage associated with this vehicle is that the core must be modified to bring different size payloads to orbit. This configuration has almost no variability in being able to minimize changes to the core of the vehicle. It should be noted, when comparing to the Saturn V, there is approximately a 100 mt decrease in GLOW that is simply a result of upgrading the engines. Configuration F is a two stage vehicle as well, but is not included in the final results because it proved incapable of reaching the necessary orbit. The last case is a 1.5 stage configuration using modified boosters. This case was tasked by NASA to determine how a RSRM V booster should be modified to bring a constant core configuration to orbit. Thrust, propellant mass, and burn time are adjusted in the modified booster to minimize GLOW of the vehicle and bring the payload to orbit. The minimized GLOW is high and as result can be eliminated for potential candidate. It is interesting to note that in comparison with the Space Shuttle, which is another 1.5 stage vehicle, a 60% increase in GLOW has increased the payload to four times that which the Shuttle was capable of (Ref. 8). B. Final Optimized Configuration In consideration of all this, the configuration that minimizes GLOW and also provides a large amount of adaptability to different payload requirements is the 2.5 Stage vehicle using the P80 booster. It has been proven using THEO and velocity budget optimization techniques to be a very capable vehicle. This is the final optimized configuration for this analysis, and is illustrated in Fig. 10.
Figure 10. Optimized Configuration. 2.5 Stage Vehicle with 8 P80 Booster. Illustrates side, bottom, and exploded view. 14 American Institute of Aeronautics and Astronautics
VII. Conclusion Optimization of a heavy lift launch vehicle for multiple payloads is driven by two consideration. The first requirement is to minimize GLOW of the vehicle. The second consideration is to design the vehicle so that it is adaptable for multiple payloads without requiring significant changes and modifications to the core vehicle. After a thorough analysis of multiple configurations, the data implies that high number of smaller sized boosters supports a the lowest possible GLOW vehicle for adaptable payloads.
Acknowledgments
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P. A. Ritter thanks NASA for the research opportunity and financial support necessary to complete this project. P. A. Ritter also thanks Dr. Jonathan Jones, Jason Campbell, Dale Jackson, and Tim Kibbey for their patience and support. Lastly, P. A. Ritter thanks Dr. James Evans Lyne and The University of Tennessee for their inspiration and neverending support.
References 1
Alliant Techsystems. (n.d.). The Space Shuttle Reusable Solid Rocket Motor. 2 Auman, L., Doyle, J., Rosema, C., Underwood, M., & Blake, W. (2008). Missile DATCOM User's Manual - 2008 Revision. Air Force Research Laboratory. 3 Campbell, J. (2010). POST Input Case. NASA. Huntsville. 4 Humble, R. W., Henry, G. N., & Larson, W. J. (1995). Space Propulsion Analysis and Design. (R. W. Humble, Ed.) New York: The McGraw-Hill Companies, Inc. 5 Kibbey, T. P., & Campbell, J. J. (2010). Catalog of Solid Rocket Motor Designs Available for Heavy-Lift Propulsion. Huntsville. 6 McDonnell Douglas Corporation; Air Force Reasearch Laboratory. (2008). Missile Datcom. Ohio. 7 NASA. (1970). Program to Optimize Simulated Trajectories. 8 Ritter, P. A., Optimization and Design for Heavy Lift Launch Vehicles. Masters Thesis, Mechanical, Aerospace, and Biomedical Department, The University of Tennessee, Knoxville, TN, 2012. 9 Sutton, G. P., & Biblarz, O. (2010). Rocket Propulsion Elements (8th Edition ed.). Hoboken, NJ: John Wiley & Sons, Inc. 10 Turner, M. J. (2000). Rocket and Spacecraft Propulsion (1st Edition ed.). (R. A. Marriot, Ed.) Chichester, UK: Praxis Publishing Ltd. 11 Weiland, C. (2010). Computational Space Flight Mechanics. Berlin, Germany: Springer-Verlag. 12 Weisel, W. E. (1997). Spaceflight Dynamics (2nd Edition ed.). Boston, MA: Irwin/McGraw-Hill.
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