Conceptual Design and Analysis of a Small and Low-cost Launch Vehicle

Transcription

1 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile AE8900 MS Speial Problems Report Spae Systems Design Lab (SSDL) Shool of Aerospae Engineering Georgia Institute of Tehnology Atlanta, GA Author Kohei Taya Advisor Dr. John R. Olds Spae Systems Design Lab (SSDL) April 29, 2005

2 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile Table of Contents List of Figures... i List of Tables...ii Aronyms and Symbols...iii 1.0 Introdution Miroosm Launh Vehiles Sorpius Family Sprite Launh Vehile Approah Method Design Struture Matrix Aerodynamis Analysis APAS Inputs APAS Run Conditions and Run Setup APAS Results Propulsion Analysis Trajetory Analysis (Part I) POST Inputs POST Results for Original Design (Single Burn) POST Result for Original Design (Two-Burn) Weight and Sizing Analysis Trade Study Design of Experiments and Response Surfae Methods Optimized Values by Response Surfae Method Refined Vehile Analysis Design Comparisons Conlusions Referenes 37 Appendix A: APAS Analysis Data...38 Appendix B: POST sample input file ii

3 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile List of Figures Figure 1: Miroosm Sorpius Family....2 Figure 2: Sprite Configuration.4 Figure 3: Sprite Payload Performane to Cirular Orbit at Various Inlinations....6 Figure 4: Design Struture Matrix of Part I.9 Figure 5: Design Struture Matrix of Part II...9 Figure 6: Sprite Configuration for Aerodynamis.10 Figure 7: Sprite First Stage APAS Geometry 11 Figure 8: Sprite Seond Stage APAS Geometry 11 Figure 9: Sprite Third Stage APAS Geometry..12 Figure 10: 1st stage Cl vs Cd.13 Figure 10: 2nd stage Cl vs Cd 14 Figure 12: 3rd stage Cl vs Cd 14 Figure 13: Altitude vs. Down Range (i=28.5 [deg] Alt=108 [nm], Single burn)..18 Figure 14: POST Output Altitude vs. Time (i=28.5 [deg] Alt=108 [nm], Single burn) 19 Figure 15: POST Output Veloity vs. Time (i=28.5 [deg] Alt=108 [nm], Single burn)...19 Figure 16: POST Output Mass vs. Time (i=28.5 [deg] Alt=108 [nm], Single burn).20 Figure 17: Performane of Published and Simulated (Single burn, i = 28.5) 21 Figure 18: Performane of Published and Simulated (Single burn, i = 51.6) 22 Figure 19: Performane of Published and Simulated (Single burn, i = 98.6) 22 Figure 20: Altitude vs. Down Range (i=28.5 [deg] Alt=108 [nm], Two-burn)..23 Figure 21: POST Output Altitude vs. Time (i=28.5 [deg] Alt=108 [nm], Two-burn) 24 Figure 22: POST Output Veloity vs. Time (i=28.5 [deg] Alt=108 [nm], Two-burn)...24 Figure 23: POST Output Mass vs. Time (i=28.5 [deg] Alt=108 [nm], Two-burn).25 Figure 24: Performane of Published, Single Burn, and Two-Burn (i = 28.5) 26 Figure 25: Performane of Published, Single Burn, and Two-Burn (i = 51.6) 26 Figure 26: Performane of Published, Single Burn, and Two-Burn (i = 98.6) 27 Figure 27: Weight and Sizing Analysis Spreadsheet..28 Figure 28: Central Composite Design..29 Figure 29: Response Surfae 32 Figure 30: Performanes Comparison (i=28.5).. 34 Figure 31: Performanes Comparison (i=51.6).. 35 Figure 32: Performanes Comparison (i=98.6).. 35 Figure 33: Payload of all three data (i=28.5[deg], alt=108[nm]) iii

4 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile List of Tables Table.1: Sprite Launh Vehile Physial Charateristis...5 Table 2: Sprite Configuration Data 11 Table 3: HABP Analysis Runs.12 Table 4: Propulsion Data and REDTOP input...15 Table 5: REDTOP output...15 Table 6: Post alulation onditions..17 Table 7: Sprite Physial Charateristis for POST 17 Table 8: Single Burn Trajetory Analysis Result..21 Table 9: Two-Burn Trajetory Analysis Result.25 Table 10: Upper and Lower Boundaries of Expansion Ratio Table 11: Central Composite Design Setting 30 Table 12: Design of Experiments 31 Table 13: Refined Sprite vs. Original Sprite 32 Table 14: Refined Sprite Data 33 Table 15: Refined Vehile Trajetory Analysis Result.33 iv

5 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile Aronyms and Symbols A exit Alt APAS CCD C D C L dia DOE DSM i Isp KSC LEO LOX NASA O/F POST REDTOP RSM S fairing sl SLV Sref T/W UDP va VAFB Wallops W fairing W&S Exit Area (of Engine Nozzle) Altitude Aerodynami Preliminary Analysis System Central Composite Design Drag Coeffiient Lift Coeffiient Diameter Design of Experiments Design Struture Matrix Inlination Speifi Impulse Kennedy Spae Center Low Earth Orbit Liquid Oxygen National Aeronautis and Spae Administration Oxidizer to Fuel weight ratio Program To Optimize Simulated Trajetories Roket Engine Design Tool for Optimal Performane Response Surfae Method Fairing Surfae Area Sea Level Small Launh Vehile Referene Wing Area (= Maximum Cross Setion Area in this paper) Thrust to Weight ratio Unified Distributed Panel Vauum Vandenberg Air Fore Base Virginia Spaeport Authority, Wallops Flight Faility Fairing Weight Weight and Sizing Angle of Attak Coeffiients of Response Surfae Equation Expansion ratio v

6 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile 1.0 Introdution Small, mini, and miro-satellite tehnologies are leading to many innovative spae appliations. A primary obstale to suessful operational transition of these systems is the lak of affordable small launh apability. In addition, the broader spae launh market in general demands lower launh osts. One of solution is Miroosm s Sprite launh system. This vehile is planned to meet the need for low-ost, small-payload apability while verifying the tehnology for larger vehiles with muh lower ost per pound 1. In this projet, we treat Sprite launh vehile as an example of small and low-ost launh vehile. The goal of projet is to analyze its design onept, onfirm performane, and refine its design. The projet onsists of two parts. The first part is onfirming part (Part I). Using disiplinary analysis tools, the performane of Sprite vehile is simulated. In this part, mainly two disiplinary analyses are used, suh as aerodynamis and trajetory. Aerodynamis is simulated by APAS (Aerodynami Preliminary Analysis System), and trajetory is simulated by POST (Program to Optimize Simulated Trajetories). In addition, propulsion analysis using REDTOP (Roket Engine Design Tool for Optimal Performane) is done by Chris Tanner, a student member of the Georgia Teh Spae System Design Laboratory. Analyzing disiplinary details show the pratiability of Sprite launh vehile. Using data from these analyses, the performanes of original design Sprite are estimated The seond part is design refining part (Part II). Based on Part I simulation, we find the room for improvement of Sprite vehile. Adding weight and sizing disiplinary analysis, the vehile is re-designed with optimal design tehniques. Same analysis as Part I is done for new vehile, and the performanes of re-designed Sprite are estimated. In the end of this projet, we ompare the performane of published data, simulated data of original design, and simulated data of refined design. This will be the result and the onlusion of this projet. 1

7 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile 2.0 Miroosm Launh Vehiles In order to meet the inreasing needs for responsive launh for various defense and other related programs, Miroosm has been developing the onept of operations for the Sorpius family of launh vehiles for over eleven years. The Sorpius family of pressure-fed launh vehiles shown in Figure 1 inludes two suborbital vehiles that have been flown suessfully and other orbital vehiles in development with apabilities ranging from 700 lb to 50,000 lb to Low Earth Orbit (LEO) 2. The Sorpius program goal is to redue the ost of launh by a fator of 5-10 below existing launh systems. Sorpius launhers are also designed for responsive launh operations. Figure 1: Miroosm Sorpius Family On the left, are the SR-S and SR-XM suborbitals and the Sprite Small Launh Vehile. The intermediate-sized vehiles in the enter are Antares and Exodus. The Heavy Lift Spae Freighter is on the right. (Soure: James R. Wertz, Robert Conger, Jak Kulpa, Responsive Launh with Sorpius of Low-Cost Expandable Launh Vehile, Miroosm In, AIAA LA Setion/SSTC ) 2

8 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile 2.1 Sorpius Family Two key features of the Sorpius family that have been a part of the design are dramatially lower ost than traditional vehiles and launh within 8 hours of demand. Miroosm has been working toward reating a responsive launh system for nearly a deade and has had to fae many of the hurdles involved in their proess. The small payload lass member of the family workhorse, the Sprite SLV is expeted to have the apability of 700 lb payload into LEO (100 nm irular orbit due east from the launh site) for $2.5 million. The other workhorse is a medium type lift vehile. Exodus is expeted to have the apability of 15,000 lb payload into LEO for $12.5 million. The Sprite and suborbital vehiles are expeted to be the most used for truly responsive missions beause of their low ost. Also the Sorpius family of launh vehiles is designed to provide very low-ost aess to spae by using simple, modular design. All of the Sorpius vehiles share a number of features that signifiantly assist the responsive harater and its low ost 3 : (i) Assembled at or near the primary launh site (ii) Assembled vertially on a reusable launh radle on whih they are also moved about the faility as needed (iii) Short, fat design for rapid movement and handling (iv) Transported vertially at the launh site on their radles on rails or on a flatbed trailers (v) No gantry or servie tower needed for transportation or launh (vi) Ground level serviing (vehiles are short enough that the avionis bay and payload ompartment an be reahed by a herry piker if required) (vii) All stages use environmentally friendly LOX/kerosene propellants The kerosene that is used is Jet-A, available at essentially any airport worldwide. In the next setion, more detail about Sprite launh vehile, whih is the objet of this paper, is explained. 3

9 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile 2.2 Sprite Launh Vehile Figure 2: Sprite Configuration (Soure: James R. Wertz, Robert Conger, Jak Kulpa, Responsive Launh with Sorpius of Low-Cost Expandable Launh Vehile, Miroosm In, AIAA LA Setion/SSTC ) The three-stage Sprite SLV is the first orbital vehile in the Sorpius family. The baseline onfiguration shown in Figure 2 is apable of arrying 700 lb to LEO (100 nm due east) or 330 lb to Sun synhronous orbit at 400 nm. Sprite uses seven ommon pods and a small upper stage. Sprite is a three-stage, pressure-fed roket onsisting of six external booster pods omprising the first stage, a enter or sustainer seond stage pod, and a third stage affixed to the top of the seond stage. The first and seond stages share the same omponents with the exeption of a modified high-altitude nozzle in the seond stage. This ommonality redues the number of unique parts on the vehile whih ultimately redues ost and manufaturing time. The third stage is designed to meet mission requirements as either a small satellite launh system or long-range, tatial, sub-orbital roket and inludes provisions for a deorbit maneuver to avoid beoming orbital debris. 4 4

10 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile Table.1: Sprite Launh Vehile Physial Charateristis (Soure: Yellow: Steven J. Isakowitz, Joshua B. Hopkins, Joseph P. Hopkins Jr., International Referene Guide to Spae Launh System, AIAA, 2004, Green: James R. Wertz, Robert Conger, Jak Kulpa, Responsive Launh with the Sorpius Family of Low-Cost Expendable Launh Vehiles, AIAA-LA Setion/SSTC , Beige: REDTOP simulation result by Chris Tanner) Payload volume Gross payload to 28.5deg 108nmi Launh sites Stage 1/2/3 main propellant Gross WT Liftoff Configuration Dry WT Dimensions 38"dia X 63" long 700 lbm KSC, Wallops or VAFB Jet fuel and LOX 83,643 lbm 12,683 lbm 53.3 ft X 11.2 ft dia. Stage 1 Stage 2 Stage 3 Gross Weight lbm lbm 3090 lbm Empty Weight lbm 1851 lbm 578 lbm Height 38.1 ft 33.2 ft 15.2 ft Diameter 11.2 ft 3.5 ft 3.5 ft Thrust X6 lbf (sl) lbf (va) 2530 lbf (va) O/F Ratio Chamber Press. 385 psi 385 psi 154 psi Isp 285 se (va) 317 se (va) 330 se (va) Expansion Ratio Table 1 shows the physial harateristis of Sprite vehile. The Sprite vehile is approximately 53 feet in length and 11 feet wide at its base. Six 20-Klbf first stage engines provide 120,000 lbs of thrust while the seond and third stages provide 20,000 lbs and 2,500 lbs of thrust respetively. The Sorpius launhers are pressure-fed liquid rokets with mostly arbon omposite strutures. Liquid oxygen and kerosene (Jet-A) were hosen as propellants beause of their low toxiity, good performane, and low ost. Jet-A is readily available and LOX an be brought in or produed on site. Beause the vehile is pressure-fed, the tanks are robust enough to support themselves and an endure asual handling expeted during the transportation and launh ampaign without problems. The shorter, wider nature of the vehile makes it stable while vertial, enabling easier movement of an integrated vehile to the launh pad. The dry weight of the Sprite vehile is omparable to a small bulldozer (about 10,000 lb) and an be easily towed by a standard truk trator. All normal serviing of the vehile on the pad is done at ground level thus eliminating the need for a gantry or tower. 5 Aording to James V. Berry, the Sprite SLV addresses the need for small- and mini- 5

11 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile payload apability with a prie to orbit objetive of less than $2.5 million (FY02$) for 700 lb to LEO 6. The minimum available payload volume is omparable to the Sout and Pegasus large fairing, i.e., 38-inh diameter by inhes long. The payload area, with provisions to deploy single or multiple payloads, an be aessed as needed with standard ommerial equipment. The payload performane for different orbit inlinations is shown in Figure 3. Launh sites are depended on inlination (KSC for 28.5, Wallops for 51.6, and VAFB for 98.6) Payload [lb] Cirular Orbit Altitude [nm] 28.5 [deg] 51.6 [deg] 98.6 [deg] Figure 3: Sprite Payload Performane to Cirular Orbit at Various Inlinations (Original data soure: Robert E. Conger, James R. Wertz, Jak Kulpa, The Sorpius Expendable Launh Vehile Family and Status of the Sprite Mini-Lift, AIAA ) 6

12 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile 3.0 Approah The fous of this projet is the Sprite SLV as the example of small and low-ost vehile. Here is one question about Sprite SLV. As shown in pervious setion, Sprite vehile has 120-Klbf (vauum) total thrust in first stage. Compare to other small and low-ost vehile, for example, Falon I launh vehile has only 85-Klbf (vauum) thrust. However, Falon I has the apability of 1472 lb payload into 108 nm LEO while Sprite has only about 700 lb apabilities into same orbit. Even though there are many differenes suh as shapes or mass ratio between Sprite and Falon I, almost 700 lb payload differene seems too muh. Thus, independently onfirming the performane of Sprite is desired. Basially, the performane an be estimated by aerodynamis, propulsion and trajetory analysis. This is going to be the first part of the projet (Part I). Also one more question might our after onfirming the performane. Based on the onfirming analysis, we might notie there is the room for improvement in the original design of Sprite SLV. If there is, refining design proess is desired. Sine Sprite SLV projet is already started in Miroosm, minor hange in engine parameters is going to be key of this part, but not major hange in shapes, weight, or engine. Using same engine, but some hanging in nozzle (thus Isp) an make the better performane of Sprite SLV. This is going to be the seond part of the projet (Part II) 7

13 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile 4.0 Design Method To analyze and onfirm the original design or refined design, integrated design proess is required. Several disiplinary design works are required for this type of system design, thus it is needed to integrate the results from eah disiplinary. In this setion, integration design tehnique is disussed first. Then we fous on three disiplinary odes, APAS, POST and REDTOP, whih are used both Part I and Part II in this projet. Then trade study about engine refining is disussed after onfirming the performane of original design. Also additional weight and sizing alulation tool developed by Mirosoft Exel spreadsheet is disussed in seond half part of this setion. In the end of this setion, results of Part I and Part II are shown. 4.1 Design Struture Matrix DSM (Design Struture Matrix) is the hart, whih shows the relationship of eah disiplinary analysis in whole oneptual design. We an easily identify the design proess, espeially feed-forward and feedbak among several disiplinary analyses. Figure 4 shows DSM of Sprite SLV in part I. There is no feedbak beause all onfigurations of Sprite SLV are original one, and no hange is allowed sine this is onfirming part. The first step is the aerodynamis analysis by APAS. The shape of Sprite vehile is input. Output of aerodynamis disiplinary is lift oeffiient, drag oeffiient and pithing momentum oeffiient, and these data beome the input of trajetory analysis. With propulsion analysis data by REDTOP, POST simulates optimized trajetory for Sprite SLV. Then the performane data, whih is maximum payload to speifi orbit, will be given. In this projet, we stop the simulation we get the performane data, but usually it will be ontinue to weight and sizing, ost or other disiplinary analysis. 8

14 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile Aerodynamis APAS Propulsion REDTOP CL, CD Thrust VAC A exit Isp VAC Trajetory POST W Payload W&S COST Figure 4: Design Struture Matrix of Part I Gray disiplinary and dotted lines are not simulated in this projet Figure 5 shows DSM for Part II. This part is refining part, thus there is a feed bak between trajetory and propulsion. As mentioned before, hanging in nozzle (expansion ratio) or Isp is ourred for better performane. The simulation looped among Propulsion, Trajetory, and Weight and Sizing alulation. Aerodynamis APAS Propulsion REDTOP CL, CD Thrust VAC A exit Isp VAC Trajetory POST W Payload W Gross W gross W fuel S ref W&S Exel COST Figure 5: Design Struture Matrix of Part II Gray disiplinary and dotted lines are not simulated in this projet 9

15 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile 4.2 Aerodynamis Analysis As shown in DSM, the first thing of design is aerodynamis analysis. In this projet, APAS (Aerodynami Preliminary Analysis System) program is used for aerodynamis analysis. The Aerodynamis Preliminary Analysis System was developed by the NASA Langley Researh Center and the Rokwell International Corporation. APAS analysis an be done relatively quikly allowing multiple design iterations, and results are usually within twenty perent of atual values. Suh results are good enough for oneptual design, and the speed with whih they an be ahieved allows designer to inlude aerodynami alulations in Multi-Disiplinary Design Optimization loops. Based on the shapes or onfiguration of objet, the program provides an effiient analysis for systematially performing various aerodynami onfiguration tradeoff and evaluation studies APAS Inputs 2 nd Stage 48.4 [ft] 2 nd & 3 rd stages 3.5 [ft dia] 3 rd stage 15.2 [ft] 1 st stage 53.3 [ft] 1 st stage 11.2 [ft dia] Figure 6: Sprite Configuration for Aerodynamis (Original Piture Soure: James R. Wertz, Robert Conger, Jak Kulpa, Responsive Launh with Sorpius of Low-Cost Expandable Launh Vehile, Miroosm In, AIAA LA Setion/SSTC ) Table 2: Sprite Configuration Data (Data Soure: James R. Wertz, Robert Conger, Jak Kulpa, Responsive Launh with the Sorpius Family of Low-Cost Expendable Launh Vehiles, AIAA-LA Setion/SSTC ) 10

16 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile Stage 1 Stage 2 Stage 3 Total Height 53.3 ft 48.4 ft 15.2 ft Overall Diameter 11.2 ft 3.5 ft 3.5 ft The Input of APAS is the shape or onfiguration of vehile. Figure 6 and Table 2 shows the atual Sprite vehile onfiguration. Based on these data, three-dimensional model geometry is built in APAS. Figure 7-9 shows atual input model in APAS for fist stage to third stage. Unfortunately, detail data of one half-angles for the vehile are not available, and these are estimations [ft] 11.2 [ft] Figure 7: Sprite First Stage APAS Geometry As illustrated in Figure 7 above, or other figures, the overall Sprite design is relatively short and squat, as are the other Sorpius launh vehiles. Thus the vehile is expeted to be stable while vertial, enabling easier movement of an integrated vehile to the launh pad. Relatively smaller numbers of C L (Lift Coeffiient) and C D (Drag Coeffiient) are expeted by APAS simulation ompared to general penil looks launh vehiles [ft] 3.5 [ft] Figure 8: Sprite Seond Stage APAS Geometry Figure 8 shows the APAS input geometry of seond stage. Different from the first stage, it looks like normal launh system long and sharp. Sine the length of seond stage is 11

17 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile not different from the first stage, higher numbers of C L and C D are expeted by APAS simulation [ft] 3.5 [ft] Figure 9: Sprite Third Stage APAS Geometry Figure 9 are APAS input geometries of third stages. This is also looks like normal higher stage of launh system. Sprite is designed to have a similar payload fairing to the retired Sout G-1 launh vehile APAS Run Conditions and Run Setup The flight onditions of the ten HABP runs analyzed for eah trial stage are shown in Table 3. Tangent one and Prandtl-Meyer analyses methods are used for the body and shadowed regions. The base pressure is set to C p =0. The Mah number range of is onsidered to be the launh vehile flight regime. This shedule is used for all 3 trials. Angles of Attak ( ) from -15 to 30 degrees are analyzed. Table 3: UDP Analysis Runs Trials for 1-3 stages RUN Mah Altitude (ft)

18 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile APAS Results Aerodynamis data (C L vs. C D plots) by APAS results are shown in Figure for eah stage. In these plots, Mah number 1.5, 7, 15 and upper are not shown here due to visibility. All detail data are available in Appendix A. As expeted, the result of first stage has lower L/D ompare to the result of seond stage. 4 3 Cl Mah3 Mah4 Mah5 Mah10-2 Cd Figure 10: 1st stage C L vs C D (S ref 64.7 [ft 2 ] Length 53.3[ft]) (Figure 11 and 12 on next page) 13

19 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile Cl Mah3 Mah4 Mah5 Mah10-6 Cd Figure 11: 2nd stage C L vs C D (S ref 9.6 [ft 2 ] Length 48.4[ft]) Cl Mah3 Mah4 Mah5 Mah Cd Figure 12: 3rd stage C L vs C D (S ref 9.6 [ft 2 ] Length 15.2[ft]) 14

20 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile 4.3. Propulsion Analysis This part is done by Chris Tanner, a student in the Georgia Teh Spae System Design Laboratory, using REDTOP (Roket Engine Design Tool for Optimal Performane) program. Only the input (Table 4) and output (Table 5) are shown in here. Table 4: Propulsion Data and REDTOP input (Data Soure: Chris Tanner) Referene INPUT Spe Unit AIAA Isakowitz REDTOP Stage - 1st 2nd 3rd 1st 2nd 3rd 1st 2nd 3rd Thrust lbf (va) * O/F Ratio Chamber Press. psi * Isp se (va) 281*3 297*3 319* Expansion Ratio - N/A N/A N/A Oxidizer - LOX LOX LOX Fuel - kerosene (Jet-A) kerosene (Jet-A) kerosene (Jet-A) *1 All 1st stage thrusts are single pod, sea level *2 Unit is not avaiable for Chamber Pressure in AIAA *3 Values obtained in AIAA Table 5: REDTOP output These values are going to be feed-forward to trajetory analysis by POST (Data Soure: Chris Tanner) REDTOP Output (feed-forward to POST) Spe Unit 1st * 2nd 3rd Exit area ft Thrust lbf (va) Isp se (va) *single pod Table 4 shows propulsion data from two different referenes and atual input values used in propulsion analysis by REDTOP. Table 5 shows output values by REDTOP, and only the values, whih are going to be feed-forward to trajetory analysis by POST, are shown here. 15

21 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile 4.4 Trajetory Analysis (Part I) The next disiplinary design analysis is trajetory analysis. In this projet, POST (Program to Optimize Simulated Trajetories) program is used. POST is a generalized point mass, disrete parameter targeting and optimization program. POST provides the apability to target and optimize point mass trajetories for a powered or unpowered vehile near an arbitrary rotating, oblate planet. POST has been used suessfully to solve a wide variety of atmospheri asent and reentry problems, as well as ex-atmospheri orbital transfer problems. The generality of the program is evidened by its multiple phase simulation apability whih features generalized planet and vehile models. This flexible simulation apability is augmented by an effiient disrete parameter optimization apability that inludes equality and inequality onstraints. Data generated by APAS and REDTOP is the input of POST. Also other data, suh as weight (usually this is a feed-bak from weight and sizing analysis), launh site, or target orbit are used. Then POST estimates possible maximum payload for Sprite launh system. 16

22 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile POST inputs The POST inputs, trajetory analysis inputs, are the feed-forward or bak from disiplinary analyses shown as DSM and other harateristi data of vehile. By using POST, the maximum payload of Sprite SLV is estimated. Table 6 shows the alulation onditions. Inlination takes three patterns, 28.5, 51.6, and 98.6 degrees. Cirular orbit altitude from 108 to 500 nm is analyzed. Launh sites are deided by target inlinations as shown as in Table 6. Also start up loss of 0.5% and fuel residual of 1% after burns out are set for alulation. Table 6: Post alulation onditions Target Orbit Conditions Unit Inlination deg Altitude 108, 220, 300, 432, 500 nm Launh Site KSC Wallops VAFB - In addition to the alulation onditions, Sprite SLV physial harateristis data shown in Table 7 are used in analysis. Fairing weight is not available in any pulished paper, so it is estimated as W fairing = S fairing [ft 2 ] 2 [lb/ ft 2 ] = 165 [lb]. These data are basially same values shown in Table 1 and Table 5. The atual POST input file is attahed in the end of this paper (Appendix B). Table 7: Sprite Physial Charateristis for POST (Original data soure:yellow: Steven J. Isakowitz, Joshua B. Hopkins, Joseph P. Hopkins Jr., International Referene Guide to Spae Launh System, AIAA, 2004, Green: James R. Wertz, Robert Conger, Jak Kulpa, Responsive Launh with the Sorpius Family of Low-Cost Expendable Launh Vehiles, AIAA-LA Setion/SSTC , Beige: REDTOP simulation result by Chris Tanner) Spe Unit 1st *1 2nd 3rd Total Height ft Referene Area ft Gross Weight *2 lbm Empty Weight lbm Exit area ft Thrust lbf (va) Isp se (va) *1 Total of 6 pods values *2 Eah Stage values (without Payload) 17

23 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile POST Results for Original Design (Single Burn) 900 Altitude (k-ft) Downrange (nmi) Figure 13: Altitude vs. Down Range (i=28.5 [deg] Alt=108 [nm], Single burn) Figure 13 shows one of POST outputs, the trajetory of Sprite vehile (Inlination = 28.5 [deg], Altitude = 108 [nm] Single burn ase). X-axis represents downrange of vehile in nautial miles, and Y-axis represents altitude of vehile in kilo-feet. At point 1 on Figure 13, first stage burns out and jettison. Then fairing separate at point 2. Seond stage burns out and jettison at point 3 on Figure 13. The vehile reahed to higher altitude than target altitude (108 nm = 657 k-ft), and then it desends into target altitude. Also Figure are same ase detail results from POST. (Figure on next page) 18

24 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile Altitude (k-ft) Time (se) Figure 14: POST Output Altitude vs. Time (i=28.5 [deg] Alt=108 [nm], Single burn) Veloity (k-ft/s) Time (se) Figure 15: POST Output Veloity vs. Time (i=28.5 [deg] Alt=108 [nm], Single burn) 19

25 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile Weight (k-lb) Time (se) Figure 16: POST Output Weight vs. Time (i=28.5 [deg] Alt=108 [nm], Single burn) Figure 14 shows vehile altitude hange by time. Figure 15 shows vehile veloity hange by time. From these two graphs, it is found that vehile reahes target altitude before its veloity reahes required veloity for irularize. Thus, vehile passes the target altitude one, and gets more veloity by thrusting. This phenomenon is only happen in 108 nm ases, whih required high veloity for irularize but low altitude. Also Figure 15 shows separation points of eah stage very well. Just before the jettison, vehile uses almost all fuel and gets lighter, so the aeleration gets muh better than start. But after the jettison points, aeleration gets worse beause of hanging to smaller engine (and starts again). Figure 16 shows vehile weight hange by time. Same as Figure 15, this plot also shows jettison points very well. Of ourse, the vehile weight dramatially falls by separating burned out stages. Fuel onsumption rate is known by Figure 16, too. 20

26 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile Table 8 shows POST trajetory analysis results. Maximum payloads for speifi altitudes and inlinations are shown. Table 8: Single Burn Trajetory Analysis Result Inlination [deg] Altitude [nm] *Values in [lb] Figure show performane of published data and simulated data. The simulated data marks better performane in lower altitude, but it drops in higher altitude. In ontrast, the published data draws gentle deline urve. The differene is probably burn times. The simulation uses single burn for the upper stage trajetory. The published data does not mention about burn times, but usually two-burn shows slower deline like the published performane data of Sprite vehile. Thus, using same ondition showed in setion 4.4.1, the two-burn simulation is analyzed in next setion. Original POST Single Burn Payload [lb] Altitude [nm] Figure 17: Performane of Published and Simulated (Single burn, i = 28.5) 21

27 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile Original POST Single Burn Payload [lb] Altitude [nm] Figure 18: Performane of Published and Simulated (Single burn, i = 51.6) Original POST Single Burn Payload [lb] Altitude [ft] Figure 19: Performane of Published and Simulated (Single burn, i = 98.6) 22

28 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile POST Result for Original Design (Two-Burn) As disussed in former setion, two-burn simulation was assessed. Two burns tehniques usually inrease maximum payload, and show better performane in higher altitude than single burn. In Atlas launh system ase, for example, in a single burn mission, payload is injeted diretly into a transfer or irular orbit. In a two-burn mission, the first burn injets the payload into a parking orbit followed by a oast period. The seond engine burn plaes the vehile in the desired orbit, followed by separation of the payload. The POST input file has minor hange about two-burn. The same simulation onditions shown in Table 6 and same harateristis shown in Table 7 are used. Figure show example trajetory analysis results of two burns upper stage ase. These figures are orrespondene to Figure of single burns. Compare to single stage ase, vehile reahed to the target orbit very smoothly. Figure 22 and 23 shows it is atually two-burn upper stage. In third stage, the aeleration is stopped when vehile stop the first burning. It started the engine again to irularize when it reahed to the target altitude Altitude (k-ft) Down Range (nmi) Figure 20: Altitude vs. Down Range (i=28.5 [deg] Alt=108 [nm], Two-burn) 23

29 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile Altitude (k-ft) Time (se) Figure 21: POST Output Altitude vs. Time (i=28.5 [deg] Alt=108 [nm], Two-burn) Veloity (k-ft/s) Time (se) Figure 22: POST Output Weight vs. Time (i=28.5 [deg] Alt=108 [nm], Two-burn) 24

30 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile Weight (k-lb) Time (se) Figure 23: POST Output Weight vs. Time (i=28.5 [deg] Alt=108 [nm], Two-burn) Table 9 shows POST trajetory analysis results. Two burn ase maximum payloads for speifi altitudes and inlinations are shown. Table 9: Two-Burn Trajetory Analysis Results Inlination [deg] Altitude [nm] *Values in [lb] 25

31 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile Original POST Single Burn POST Two-Burn Payload [lb] Altitude [nm] Figure 24: Performane of Published, Single Burn, and Two-Burn (i = 28.5) Original POST Single Burn POST Two Burns Payload [lb] Altitude [nm] Figure 25: Performane of Published, Single Burn, and Two-Burn (i = 51.6) 26

32 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile 800 Original POST Single Burn POST Two-Burn 600 Payload [lb] Altitude [ft] Figure 26: Performane of Published, Single Burn, and Two-Burn (i = 98.6) Figure shows performane omparison of published data, single burn simulated data, and two-burn simulated data. For all points, two-burn simulated data superior to others. Also the urvature of two-burn is similar to published urve. It an onlude that Sprite SLV s published data is two-burn on the upper stage. 27

33 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile 4.5 Weight and Sizing Analysis Before design refining analysis, new disiplinary tool is required. As DSM shown in Figure 5, weight and sizing (W&S) analysis is used in Part II of this projet. This new tool is made by Mirosoft Exel, and based on same type tool made by Janssen Pimentel, a former student in the Georgia Teh Spae System Design Laboratory. Inputs are Sprite s dimensions, payload weight, and engine data. Figure 27 displays weight alulation of first stage in this Exel spreadsheet tool. Figure 27: Weight and Sizing Analysis Spreadsheet (First stage breakdown) Sine engine parameter hanging is our in Part II, engine weight equation is key of this spread sheet. The equation used in this tool is W engine ( h! h ) mdot e = (1) k where W engine : Engine weight, mdot: Mass flow rate, h,h e : Combustor/Exhaust plane flow enthalpy, and k: Weight relation oeffiient. This equation and value of k is determined by D. W. Way (AIAA ) 8. In Sprite SLV ase, k=520 [BTU/s/lbf] is used. 28

34 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile 4.6 Trade Study From this setion, seond part of the projet begins. For refining design, minor hange of engine is deided. First of all, visualization of trade study is required. Table 10 shows available design spae of expansion ratio. Based on these upper and lower boundaries, Design of Experiments (DOE) between expansion ratio and maximum payload is generated. Third stage engine is eliminated from trade study. Third stage almost always burns in vauum environment, thus no hange is expeted on third stage. Using Response Surfae Methods, model is generated so that it an used to determine optimum values and for sensitivity studies and design spae visualization. Expansion Ratio : _ baseline Lower Bound Upper Bound 1st stage nd stage Table 10: Upper and Lower Boundaries of Expansion Ratio Design of Experiments and Response Surfae Methods Design of experiments (DOE) is a systemati, rigorous approah to engineering problem-solving that applies priniples and tehniques at the data olletion stage so as to ensure the generation of valid, defensible, and supportable engineering onlusions 9. In this projet Central Composite Design (CCD) Type of DOE is used (Figure 28). Error an be lager than full fatorial design, but it redues the number of test points. Test points are set as Table 11. Figure 28: Central Composite Design (Three Parameter Case) 29

35 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile Table 11: Central Composite Design Setting k = 2 No x1 x _ 0 6 _ _ 8 0 _ * _ = f o r 2 p a r a m e t e r s Response Surfae Method (RSM) is a tehnique for building and optimizing empirial models of ontinuous funtions. RSM approximates the underlying dependene of output responses to input parameters with an empirial polynomial relationship based on a given set of data (DOE). Advantage of using RSM is that simplified equation representing a omplex system. Initially, the dependent parameter is assumed to be a seond-order equation, base on a Taylor series approximation, of the form: k k 2! # i xi +! # ii xi +!! i= 1 i= 1 k " 1 Re sponse = # + # x x + error (2) 0 k i= 1 j= i+ 1 where Response is the dependent parameter (response) of interest i are regression oeffiients for the first order terms ii are oeffiients for the pure quadrati terms ij the oeffiients for the ross-produt terms x i, x j are the independent variables error is the error assoiated with negleting higher order effets ij i j Payload = " + (3) " 1! 1 + " 2! 2 + " 3! 1 + " 4! 2 " 5! 1! 2 Equation (3) shows the response surfae (payload) of this part (Part II). To determine these oeffiients in equation, DOE of Part II are generated. Responded payload is alulated by APAS, REDTOP, POST and W&S spreadsheets for eah expansion ratio in CCD. Simulation inludes the loop alulation as shown in DSM (Figure 5). At least five 30

36 _ 2 P a y l o a d _ _ _ _ Coneptual Design and Analysis of a Small and Low-ost Launh Vehile time iterations are simulated for eah. In addition, T/W ratio and O/F ratio are fixed. These simulation results are shown in DOE (Table 12). Table 12: Design of Experiments No CCD Sets Parameters Response x1 x2 _1 From the DOE, the oeffiients in equation (3) are solved. To get the equation, JMP, the statistial data handling program, is used in this projet. Equation (4) shows the result of JMP alulation. The alulation error is one digit in seond order error. This is not small, but aeptable in this ase. Payload = ! "!! (4) ! 2 " ! 1 " ! Optimized Values by Response Surfae Method In last setion, RSM is defined for Sprite Refining. Figure 29 shows visualized response surfae from equation (4). Top of hill, where is the maximum payload point, is in our ranges (6< 1 <18, 25< 2 <45). This means optimal values of expansion ratios are in range. By alulation, maximum value of equation (4) is [lb] when 1= , 2= Table 13 shows omparison of payload. Refined Sprite SLV has better performane than original. Also it shows both payload from RSM equation, and simulated payload with 1= and 2= (Figure 29 and Table 13 are shown in next page) 31

37 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile Payload [lb] ε 2 ε Figure 29: Response Surfae Table 13: Refined Sprite vs. Original Sprite Case i=28.5 alt=108[nm] Original Part II Part I (Published) RSM Cal. Simulate _ _ Payload [lb] Maximum Payloads between RSM alulation and Atual simulation are slightly different. This is happened beause of error in RSM. RSM is very useful Tehnique for system designing, but it assumes response surfae has quadrati form in this ase. This makes some error in alulation, thus the expansion ratios we have might not be the best answer. Hopefully, the values are not so far from entral point (middle values point) so that error might be small as ignorable. Also the payload of simulated value in Part II is larger than Part I. This means the expansion ratios are may not the best but these values atually makes improvement. From this reason, we take these expansion ratios for refined design vehile. From next setion, refined vehile analysis is started with these new values. 32

38 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile 4.7 Refined Vehile Analysis In this setion, performane of refined Sprite SLV is simulated with new expansion ratios. Due to hanging of expansion ratios and other values, Table 14 shows new inputs values for simulation. New Sprite SLV has smaller first and seond stages. Simulation methods are basially same as Part I, so analysis details are omission. Same onditions are used for all alulations. Table 14: Refined Sprite Data Spe Unit 1st *1 2nd 3rd Total Height ft Referene Area ft Gross Weight *2 lbm Empty Weight *2 lbm Exit area ft Thrust lbf (va) Isp se (va) *1 Total of 6 pods values *2 Eah Stage values (without Payload) Table 15 shows simulation results of New Sprite SLV. In this setion, only this table shows the simulation results. Basially, table shows the better performane of refined design vehile. The performane omparison graphs are shown in next setion with omments. Trajetory detail graphs are omission here. Sine there is not so muh big differene in Input data, trajetory is almost same as Figure Table 15: Refined Vehile Analysis Results Inlination [deg] Altitude [nm] *Values in [lb] 33

39 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile 5.0 Performane Comparison All simulations and alulations are ompleted. Performane of Published Data, Simulated Data of Original Design (two burns ase), and Simulated Data of Refined Design are gathered. Then performane omparison of all three models with omments is here. Let s start from i=28.5 ase in Figure Original Part I Part II Payload [lb] Altitude [nm] Figure 30: Performane Comparison (i=28.5) Figure 30 shows the maximum payload of these three designs. It shows the refined design vehile has the slightly better performane than Part I design (Original, simulated). It means the improvement of Sprite SLV is sueeded. Basially all urves shows almost same grade of delines. Figure 31 and 32 shows same performane omparison graphs, but inlinations are 51.6 [deg] and 98.9 [deg]. These also show better performane of Part II analyses. In Figure 31, Part I analysis shows minute better performane than Part II analysis at around 200 [nm]. It should be lower, but it is possible there is an error beause of some noise. At the other altitude, it shows better performane, thus it an be negleted. 34

40 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile Original Part I Part II Payload [lb] Altitude [nm] Figure 31: Performane Comparison (i=51.6) Original Part I Part II Payload [lb] Altitude [ft] Figure 32: Performane Comparison (i=98.6) 35

41 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile 6.0 Conlusions All simulations and alulations are done. Figure 33 shows the maximum payload of all three data. From these results, we an onlude that the projet is suess Payload [lb] Published Simulated (Original) Simulated (Refined) Type of Data/Design Figure 33: Payload of all three data (i=28.5[deg], alt=108[nm]) The simulated data of original design is better than published data. As expeted in the approah of the projet (see 3.0 Approah), the Sprite SLV has better performane, whih orresponds to the engine sizes. Upper stage burns time (single burn or two burns) is unknown when the projet starts. These data are not published so far. However, it is able to onlude that Sprite SLV uses two burns upper stage from the simulation results in this projet*. The refining part is also suess. As mentioned before, the expansion ratios are alulated by RSM equation with some error. Thus, it might not be the optimal values for Sprite vehile. However, the simulation results show better performane enough. That is the reason we an say this is suess. *Aording to Miroosm engineer, it is atually two burns upper stage. 36

42 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile 7.0 Referene 1 Shyama Chakroborty, Thomas P. Bauer, Using Pressure-Fed Propulsion Tehnology to Lower Spae Transportation Costs, AIAA , Shyama Chakroborty, Robert E. Conger, James R. Wertz, Responsive Aess to Spae The Sorpius Low-Cost Launh System, IAC-04-IAF-04, Miroosm In, Robert Conger, James R. Wertz, Responsive Launh with the Sorpius Family of Low- Cost Expandable Launh Vehile, AIAA LA Setion/SSTC , James V. Barry, Robert E. Conger, Sprite Mini-Lift, an Affordable Small Expendable Launher, AIAA , Rober E. Conger, Shyama Chakroborty, James R. Wertz, The Sorpius Expendable Launh Vehile Family and Status of the Sprite Mini-Lift, AIAA , James V. Berry, Robert E. Conger, James R. Wertz, The Sprite Mini-Lift Vehile: Performane, Cost, and Shedule Projetions for the First of the Sorpius Low-Cost Launh Vehiles, SSC99-X-7, Miroosm In, Mark D. Guynn, Aerodynamis Preliminary Analysis System Beginner s Guide, NASA Langley Researh Center, Way, D. W., Olds, J. R., "SCORES: Web-Based Roket Propulsion Analysis Tool for Spae Transportation System Design," AIAA , Mihelle R. Kirby, The How To Guide for Response Surfae Methodology, Georgia Institute of Tehnology Aerospae Systems Design Laboratory,

43 Coneptual Design and Analysis of a Small and Low-ost Launh Vehile Appendix A: APAS Analysis Data Frist Stage Data (Sref = [ft 2 ], Length=53.3 [ft]) Run 1 Run 5 mah alpha beta l d m mah alpha beta l d m Run 2 Run 6 mah alpha beta l d m mah alpha beta l d m Run 3 Run 7 mah alpha beta l d m mah alpha beta l d m Run 4 Run 8 mah alpha beta l d m mah alpha beta l d m