As shown in AppendixVIII, the optimum arrangement for multistaging is that the payload and...

As shown in AppendixVIII, the optimum arrangement for multistaging is that the payload and structural ratio λi, and ϵi, be the same for all stages. Consider the effect of a departure from this optimum arrangement for a three-stage rocket with the same engine specific impulse (Isp = 400) for all three stages. The mass distribution for the stages is as follows:

a.For each stage determine λi, and estimate the total velocity increment for the three stages with drag and gravity effects neglected.

b.Now consider an optimized stage with the same payload, total propellant mass, and total structural mass (tankage plus engine plus all other structural mass). What velocity increment ∆u could be obtained in this case?