How Does Rocket Propulsion Affect Burnout Metrics and Altitude Achievement?

[tonymiller]

Question I) For a single stage rocket: T = 955.23 kN, n = 16, Isp = 400 s and m0 = 70, 000 kg. The rocket is launched into a vertical trajectory. Neglecting drag and assuming g is constant at its sea level value, Find (a) the time until burnout, (b) burnout altitude, (c) burnout velocity, (d) max altitude reached

Question II) For a given rocket: mpl = 10,000 kg, payload structural fraction = 0.05, structural ratio = 0.15, Isp = 350 s, and take normal value for g. Find (a) payload velocity at burnout, the empty mass of the vehicle, and propellant mass for a single stage, (b) repeat part (a) for restricted 2 stage rocket, (c) repeat part (a) for a restricted 3 stage rocket

 

[Valkarie]

.Answer I:a) Time until burnout: Tb = m0*Isp/nT = 70,000 kg * 400 s / (955.23 kN * 16) = 21.85 sb) Burnout Altitude: hb = gtb^2/8 = 9.8066 m/s^2 * 21.85 s^2 / 8 = 728.6 mc) Burnout Velocity: vb = gtb = 9.8066 m/s^2 * 21.85 s = 214.3 m/sd) Max Altitude Reached: hmax = gtb^2/4 = 9.8066 m/s^2 * 21.85 s^2 / 4 = 1457.2 mAnswer II:a) Single Stage Rocket: Payload Velocity at Burnout: vplb = Isp*g = 350 s * 9.8066 m/s^2 = 3426.1 m/s; Empty Mass of Vehicle: me = mpl/(1-structural fraction) = 10,000 kg / (1 - 0.05) = 10,526.3 kg; Propellant Mass: mp = me*(1-structural ratio) = 10,526.3 kg * (1 - 0.15) = 8971.9 kgb) Two Stage Rocket: Payload Velocity at Burnout: vplb = Isp1*g = 350 s * 9.8066 m/s^2 = 3426.1 m/s; Empty Mass of Vehicle: me = mpl/(1-structural fraction) = 10,000 kg / (1 - 0.05) = 10,526.3 kg; Propellant Mass: mp = me*(1-structural ratio) = 10,526.3 kg * (1 - 0.15) = 8971.9 kgc) Three Stage Rocket: Payload Velocity at Burnout: vplb = Isp1*g = 350 s * 9.8066 m/s^2 = 3426.1 m/s; Empty Mass of Vehicle: me = mpl/(1-structural fraction) = 10,000 kg / (1 - 0.05) = 10,526.3 kg; Propellant Mass