Question

A total Δν of 15 km/s is required to achieve an interplanetary mission. The proposed rocket has two stages. The first stage alone has a mass of 1000 tonnes and consists of 10 solid rocket boosters and a liquid rocket motor. The liquid rocket has a specific impulse of 300 s and a fuel mass flow rate of 1500 kg/s. The solid rocket boosters have a specific impulse of 250 s and a fuel mass flow rate of 200 kg/s. The first stage burn time is 1 minute. The first stage is jettisoned immediately after burn-out. The second stage has an initial mass of 150 tonnes. The second stage motor provides an effective exhaust velocity of 4 km/s and has a structural coefficient of 0.05. The rocket carries a 2 tonne payload. a. What is the jettisoned mass of the first stage?

Answer 1

Answer:

102000 kg

Explanation:

Given:

A total Δν = 15 km/s

first stage mass = 1000 tonnes

specific impulse of liquid rocket =  300 s

Mass flow rate of liquid fuel = 1500 kg/s

specific impulse of solid fuel = 250 s

Mass flow of solid fuel = 200 kg/s

First stage burn time = 1 minute = 1 × 60 seconds = 60 seconds

Now,

Mass flow of liquid fuel in 1 minute = Mass flow rate × Burn time

or

Mass flow of liquid fuel in 1 minute = 1500 × 60 = 90000 kg

Also,

Mass flow of solid fuel in 1 minute = Mass flow rate × Burn time

or

Mass flow of solid fuel in 1 minute = 200 × 60 = 12000 kg

Therefore,

The total jettisoned mass flow of the fuel in first stage

= 90000 kg +  12000 kg

= 102000 kg