Question

lets estimate a multiple stage rocket. In this case, we find the delta-v by finding the delta-v's of each stage separately then adding them. The key difference, is the dry mass of the first stage is discarded before the second stage begins.

Suppose we have a total mass of our two-stage rocket that is 3,042 metric tons (where 1,000 kg = 1 metric ton). If the first stage has a wet mass that is 0.83 times that of the total wet mass, and a dry mass of 372 metric tons with an exhaust velocity of 3.61 km/s, then what is the total delta v of this rocket?

Answer 1

given
velocity of fuel, vo = 3.61 km/s = 3.61*10^3 m/s
initial mass of the rocket, Mo = 3042 metric ton

= 3042*10^3 kg

mass of dry fuel = 372 metric ton

= 372*10^3 kg

mass of wet fuel = 0.83*372 = 308.76 metric ton

= 308.76*10^3 kg

mass of the rmaining rocket when dry fuel is over, M = Mo - 372*10^3

= 3042*10^3 - 372*10^3

= 2670*10^3 kg

change in velocity of the rocket, during dry fuel exhastst,

delta_V1 = vo*log(Mo/M)

= 3.61*10^3*log(3042/2670)

= 204.5 m/s

mass of the rocket when wet fuel also over,
M' = M - 308.76*10^3

= 2670*10^3 - 308.76*10^3

= 2361.24*10^3 kg

change in velocity of rocket during wet fuel exhasts,

delta_v2 = vo*log(M/M')

= 3.61*10^3*log(2670/2361.24)

= 192.7 m/s

total change in velocity of th rocket, delta_v = delta_v1 + delta_v2

= 204.5 + 192.7

= 397.2 m/s <<<<<<<<<<------------------------Answer