Rocket Equation( Cont) M-Mielsp g-1=M △/spg Mn=mass of propellant M =initial mass M =final mass Av vehicle velocity change vehicle mass
Rocket Equation (Cont.) Mp Mf e ' V Isp g § © ¨¨¨¨¨¨¨¨¨ ·¹¸¸¸¸¸¸¸¸¸ 1 ª ¬ « « « « « « « º ¼ » » » » » » » Mo 1 e ' V/Isp g § © ¨¨¨¨¨¨ ·¹¸¸¸¸¸¸ ª ¬ « « « « « º ¼ » » » » » M p = mass of propellant M o = initial mass M f = final mass 'V = vehicle velocity change Mveh = vehicle mass
Staging Near burnout. rocket acceleration is diminished because payload mass includes entire launch systems structure Staging removes lower stage structural weight △V;=g1pnx2 Mi =initial mass of rocket including all upper stages and payload Mi=final mass after stage has burned before separation i= stage number △V=∑AV
Staging • Near burnout, rocket acceleration is diminished because payload mass includes entire launch systems structure. • Staging removes lower stage structural weight Moi = initial mass of rocket including all upper stages and payload. Mfi = final mass after stage has burned before separation. i = stage number 'V = 'Vi 'Vi g Isp "n Moi Mf i § © ¨ ¨ ¨¨ · ¹ ¸ ¸ ¸¸
Staging(Cont) n=payload fraction= payload or 2=Payload Ol Mpavload i mass of payload plus all upper stages Structure fraction a. 4 MM+mtm Ol payload l Msi= mass structure for stage i Mri mass propellant for stage i
Staging (Cont.) O = payload fraction = or Mpayload i = mass of payload plus all upper stages Structure fraction Msi = mass structure for stage i Mpi = mass propellant for stage i Mpayload Mo O i Mpayload moi i O 3 i 1 n O i H si Msi Moi Msi Mpi Msi Mpayload i
Launch vehicle forces V Angle of attack flight path angle cp W ax =g sino+a Do cos a+sina W W W az=g -( +a+Dsin a+ l cos a
Launch Vehicle Forces W L D V x z cp T I D Flight path angle Angle of attack ax g T W sin I D § © ¨¨ ·¹¸¸ D W cos §©¨D·¹¸ L W sin §©¨D·¹¸ ª ¬ «««« º ¼ »»»» az g cos I D § © ¨¨ ·¹¸¸ D W sin D L W cos D ª ¬ «««« º¼»»»»
Launch system Selection process Mission needs and objective Mission requirements Altitude Inclination Right ascension of ascending node (raand Payload dimensions Launch system performance, availability, cost, reliabili Fairings Upperstage
Launch System Selection Process • Mission needs and objective • Mission requirements – Altitude – Inclination – Right ascension of ascending node (RAAN) – Payload dimensions • Launch system performance, availability, cost, reliability • Fairings • Upperstage