Welcome to Aeospace Engineeing DESIGN-CENTERED INTRODUCTION TO AEROSPACE ENGINEERING Notes 9 Topics 1. Couse Oganization. Today's Deams in Vaious Speed Ranges 3. Designing a Flight Vehicle: Route Map of Disciplines 4. Mission Specification & Take Off Weight 5. Foce Balance duing flight 6. Eath's Atmosphee 7. Aeodynamics 8. Populsion 9.Pefomance, Stability & Contol 1. Stuctues and Mateials 11. High Speed Flight 1. Space Flight
SPACE FLIGHT Luna Excusion Module. Fom the Boeing Web Page, Galley, Histoy Section. See www.boeing.com
Conside a ocket with effective exhaust velocity c e. The effective exhaust velocity is a way of expessing the thust t in a simple manne by adding up the momentum thust t and the pessue thust and dividing it by the mass flow ate. As popellant is blasted out the exhaust nozzle, the mass of the vehicle deceases. This is substantial in the case of the ocket as compaed to ai- beathing engines, because all the popellant comes fom inside the vehicle. Fom Newton's Second Law, dm dv ce M M v c 1 eloge M M V c e M1 dm M whee M 1 is the initial mass, which includes the popellant, and M is the mass afte the popellant has been used up to achieve the velocity incement V. V
Define the Specific Impulse of the popellant Specific Impulse and Mass Ratio c I e sp g whee g is the standad value of acceleation due to gavity at sea-level (9.8m/s ). Note that the unit of Specific Impulse is seconds. Using this definition, v gi sp Log e M 1 M 1 Mass Ratio of a ocket is M M 1 e V gisp Note: Some Space Agency websites expess Specific Impulse without the g. Thus thei Isp is simply C e.
Example: Fo missions fom Eath's suface to escape fom eath's gavitational field, Mass Ratio is lage. Fo Isp of 39 s, g = 9.8 m/s, and V = 11,186 m/s (367 fps), the mass atio is 18.67. This means that the ocket at launch time must be at least 18.67 times as big as the spacecaft which is left afte all the fuel is buned. To get a high specific impulse like 39 s, we have to use a costly system like liquid hydogen - liquid oxygen. Fo eath obit, the velocity incement V needed is 5, fps, while 36,7fps will enable escape fom Eath's gavitational field.
Newton's Law of Gavitation To find the velocity incement equied fo vaious missions, we must calculate tajectoies and obits. This is done using Newton's Law of Gavitation: F GMm Hee the lhs is the "adial foce" of attaction ti due to gavitation, ti between two bodies; the big one of mass M, and the little one of mass m. The univesal gavitational constant G is 6.6767 * 1-11 Nm /kg.
Keple's Laws (applied to satellite of mass m, obiting a much bigge object of mass M. ie i.e, m << M): 1. The satellite tavels in an elliptical path aound its cente of attaction, which is located at one of focii of the ellipse. The obit must lie in a plane containing the cente of attaction.. The adius vecto fom the cente of attaction sweeps equal aeas of the obit pe unit time. As the satellite moves away, its speed deceases. As it neas the cente of attaction, its speed inceases. 3. The atio of the squaes of the obital peiods of any two satellites about the same body equals the atio of the cubes of the semi-majo axes of the espective e obits.
1 Speed at any point in an elliptical obit: 1 a g V 1 whee g is accln due to gavity at adius min 1 1 V a g V apogee whee eccenticity is given by 1 min max 1 1 V a g V peigee a Time fo one obit is: Cicula Obit and Escape Velocity at Radius : g V cic V escape Vcic g V escape escape
Example: Speed fo Cicula Obit and Speed fo Escape Eath's Volumetic Radius ~ 6,37.9986853 km ( 3,958.755 mi; 3,44.64 nmi) (Souce: Wikipedia). Howeve, note that in calculating the standad value of g, A slightly diffeent adius is used (also fom Wikipedia): http://en.wikipedia.og/wiki/acceleation_due_to_gavity Conside a cicula obit at = 7km V cic g Escape speed at adius V escape Vcic
USA 196s Moon Rocket Launch
Space Shuttle Liftoff and Landing Configuations Coutesy: Deneba Canvas clip at
Pesent NASA Luna Pogam (all images coutesy NASA) Cew Exploation Vehicle + Lande Aes 1 Cew Vehicle Aes V Cago Launch Vehicle
Pesent NASA Luna Pogam
http://antwp.gsfc.nasa.gov/apod/image/7/m51_noao_big.jpg M51, o NGC 5194, Whilpool Galaxy ; 3 million light yeas away, 65,light yeas acoss JAXA spacecaft at Hayabusa Asteoid. Bottom pictue shows shadow cast by caft on asteoid. Images coutesy JAXA