Space Shuttle Ascent Mass vs. Time

Transcription

1 Space Shuttle Ascent Mass vs. Time Backgrund This prblem is part f a series that applies algebraic principles in NASA s human spaceflight. The Space Shuttle Missin Cntrl Center (MCC) and the Internatinal Space Statin (ISS) Cntrl Center use sme f the mst sphisticated technlgy and cmmunicatin equipment in the wrld. Teams f highly qualified engineers, scientists, dctrs, and technicians, knwn as flight cntrllers, mnitr the systems and activities abard the space shuttle and the ISS. They wrk tgether as a pwerful team, spending many hurs perfrming critical simulatins as they prepare t supprt each missin and crew during nrmal peratins and any unexpected events. Since its first flight in 1981, the space shuttle has been used t extend research, repair satellites, and help with building the ISS. NASA plans t retire the space shuttle but, space explratin has made majr advances due t the success f space shuttle missins. Critical t any space shuttle missin is the ascent int space. Figure 1: Main cmpnents f the space shuttle Figure 2: Space Shuttle Discvery at liftff The ascent phase begins at liftff and ends when the space shuttle reaches Earth s rbit. The space shuttle must accelerate frm zer t apprximately 7,850 meters per secnd (which is apprximately 17,500 miles per hur) in eight and a half minutes t reach the minimum altitude required t rbit Earth. It takes a very unique vehicle t accmplish this task. There are three main cmpnents f the space shuttle that enable the launch int rbit (Figure 1). The main cmpnent is the rbiter. It nt nly serves as the crew s hme in space and is equipped t dck with the ISS, but it als cntains maneuvering engines fr finalizing the rbital trajectry, r flight path. Space Shuttle Ascent: Mass vs. Time 1/6

2 The External Tank (ET), the largest cmpnent f the space shuttle, supplies the prpellant (liquid xygen and liquid hydrgen) t the Space Shuttle Main Engines (SSMEs) which are liquid prpellant rcket engines. The third cmpnent is a pair f Slid Rcket Bsters (SRBs) which are reusable. They are attached t the sides f the ET and prvide the main thrust at launch (Figure 2). One f the flight cntrllers in the Space Shuttle Missin Cntrl Center is the Bster Engineer. This psitin, r cnsle, knwn as Bster, is in charge f mnitring the SSMEs, the SRBs, and the ET during the cuntdwn and the ascent phase, until all f thse systems are safe. The cmpnents f the space shuttle experience changes in psitin, velcity, and acceleratin during the ascent int space. These changes can be seen by taking a clser lk at the entire ascent prcess (Figure 3). Figure 3: Space shuttle ascent prcess The ascent prcess begins with the liftff frm the launch pad. Prpellant burns frm the SRBs and the ET causing the space shuttle t accelerate very quickly. This high-rate f acceleratin causes a rapid increase in dynamic pressure, knwn as Q in aernautics (smetimes called velcity pressure). As the space shuttle breaks the sund barrier, its structure can nly withstand a certain level f dynamic pressure befre it suffers damage. Befre this critical level is reached, the engines f the space shuttle are thrttled dwn t abut 67% f full pwer t avid damage. Abut 50 secnds after liftff, the dynamic pressure reaches its maximum aerdynamic lad (Max Q). The air density then drps rapidly due t the thinning atmsphere, and the space shuttle can be thrttled t full pwer withut fear f structural damage. The cmmand is given, G at thrttle up! As the space shuttle climbs, the velcity is increasing and the density f the air is decreasing. Abut 2 minutes after liftff the atmsphere is s thin that the dynamic pressure drps t near zer. The SRBs, having used their prpellant, are cmmanded by the space shuttle's nbard cmputer t separate frm the ET. The jettisning f these bster rckets marks the end f the first ascent stage and the beginning f the secnd. The spent SRBs fall int the cean and are recvered, refurbished, reladed with prpellant, and reused fr several missins. The secnd stage f ascent lasts abut six and a half Space Shuttle Ascent: Mass vs. Time 2/6

3 minutes, during which time the Bster flight cntrller cntinues t mnitr the ET and the SSMEs until MECO (Main Engine Cut Off) and ET Separatin. The ET re-enters the Earth's atmsphere, breaking up befre impact in the cean, and the space shuttle maneuvers int rbit. This lessn fcuses n the first ascent stage, which ccurs during the first tw minutes after liftff. Instructinal Objectives Yu will create scatter plts frm a data table. Yu will determine the crrelatin f the data and interpret its meaning. Yu will find linear regressin equatins. Yu will find the slpe and y-intercept f a linear equatin. Yu will cmmunicate the meanings f slpe and y-intercept as they relate t a real-wrld prblem. View the vide, Space Shuttle Ascent-Clip_ STS-121, and reference the Backgrund sectin t answer questins In the launch f the Space Shuttle Discvery what des aut sequence start mean? 2. What are the 3 main cmpnents f the space shuttle? 3. Which cmpnent is the first t ignite? Which cmpnent ignites next and what is the result? 4. At abut 40 secnds after launch, due t the velcity f Discvery, what ccurs? 5. Abut hw many secnds after liftff d the main engines thrttle back t abut 67% f rated perfrmance t reduce the structural stress that ccurs as the space shuttle breaks the sund barrier? 6. Discvery Hustn, G at thrttle up! is the cmmand given when the atmsphere is s thin that there is n danger f structural damage due t dynamic pressure. Abut hw many secnds after liftff des this ccur? 7. What ccurs at apprximately 2 minutes int flight? 8. What happens t the depleted SRBs? 9. What pwers Discvery after SRB separatin? Space Shuttle Ascent: Mass vs. Time 3/6

4 Prblem On July 4, 2006, Space Shuttle Discvery was launched frm Kennedy Space Center n missin STS- 121 t begin a rendezvus with the Internatinal Space Statin, r ISS. Befre each missin, the prjected data is cmpiled t assist in the launch f the space shuttle and t ensure safety and success during the ascent. T cmplete this data flight design specialists take int cnsideratin a multitude f factrs, such as space shuttle mass, prpellant used, mass f paylad being carried t space and mass f paylad returning. They must als factr in atmspheric density, which is changing thrughut the year. After running multiple tests, infrmatin is cmpiled in a table shwing exactly what shuld happen each secnd f the ascent. Table 1: STS-121 Discvery Ascent data (ttal mass) Time (s) Space Shuttle Ttal Mass (kg) 0 2,051, ,935, ,799, ,681, ,567, ,475, ,376, ,277, ,177, ,075, , , ,377 Table 1 shws the ttal mass f Discvery fr missin STS-121 every 10 secnds frm liftff t SRB separatin. Ttal mass includes the rbiter, SRBs, ET, prpellant, and paylad. It is during the first stage f the ascent, that the space shuttle is burning the greatest amunt f prpellant. Yu can see in the table that the space shuttle has a ttal mass f 2,051,113 kg at t = 0. After 2 minutes its ttal mass is nly 880,377 kg, r 43 % f the riginal mass. The burning f this vast amunt f prpellant is needed t get the space shuttle thrugh Earth s atmsphere and int rbit. 10. What happens t the mass as time prgresses? 11. If this data were t be graphed with time n the x-axis and mass n the y-axis, which f the fllwing wuld be characteristic f the graph? The graph slpes dwn and the y-intercept is negative The graph slpes dwn and the y-intercept is psitive The graph slpes up and the y-intercept is negative The graph slpes up and the y-intercept is psitive Space Shuttle Ascent: Mass vs. Time 4/6

5 On yur TI-Nspire Handheld pen the file titled, NASA_Shuttle_Ascent-Mass_Time. Read the directins and review the data n pages embedded in the Nspire dcument. Create a scatter plt f the mass f the space shuttle vs. time n Nspire page 1.5 and mdel the data using linear regressin. Answer questins (fund n Nspire pages ) in yur grup. Discuss answers t be sure everyne understands and agrees n the slutins. 12. Des the line fit the data? Explain 13. What is the crrelatin f the data? 14. Hw much prpellant des Discvery burn per secnd? Explain what this represents with regard t the equatin. 15. What is the y-intercept f the equatin f the line that mdels the mass versus time data? Explain what this represents in relatin t the space shuttle. 16. T gain perspective regarding the magnitude f the prpellant cnsumptin f the space shuttle, find the apprximate number f each type f bject that it wuld take t equal the mass f the entire space shuttle system at launch. Rund t the nearest whle number. Table 2: Mass f varius Objects (als lcated n Nspire page 2.2) Object Apprximate mass (kg) Apprximate number f bjects t equal the mass f the space shuttle at launch Statue f Liberty 204,117 Being 747 airplane 158,757 Fuel tank truck 27,216 Schl bus 11, A Being 767 airplane burns abut 24,500 kg f fuel n a 6 hur flight frm New Yrk t Ls Angeles. Apprximately hw much time wuld it take the space shuttle t burn an equivalent amunt f prpellant? Space Shuttle Ascent: Mass vs. Time 5/6

6 Table 3 is n page 3.2 in the TI-Nspire dcument. Cmplete the scatterplt n page 3.4 using yur TI-Nspire handheld and answer questins (fund n Nspire pages ). On May 12, 2009, Space Shuttle Atlantis launched frm Kennedy Space Center n missin STS-125 t repair the Hubble Space Telescpe. Astrnauts installed tw new instruments, repaired tw inactive nes, and perfrmed the cmpnent replacements t keep the telescpe functining int at least Table 3 shws the ttal mass f Atlantis fr missin STS-125 every 10 secnds frm liftff t SRB separatin. Table 3: STS-125 Atlantis Ascent data (ttal mass) Time (s) Space Shuttle Ttal Mass (kg) 18. Des the data appear t be linear? Explain. 0 2,049, ,932, ,795, ,676, ,562, ,468, ,374, ,264, ,163, ,061, , , , What is the crrelatin f the data? (psitive, negative, cnstant, r n crrelatin)? 20. What is the slpe f yur equatin? Explain what this represents in relatin t the space shuttle. 21. What is the y-intercept f the equatin f yur line that mdels the mass versus time data? Explain what this means in relatin t the space shuttle. 22. Cmpare the rate f burn f prpellant (slpe) fr missins STS-121 (Discvery) and STS-125 (Atlantis). Which space shuttle has the fastest burn rate and what might be the reasn. Space Shuttle Ascent: Mass vs. Time 6/6