Spaceflight Mechanics Questions and Answers – Rocket Propulsion – Parallel Staging

This set of Spaceflight Mechanics Multiple Choice Questions & Answers (MCQs) focuses on “Rocket Propulsion – Parallel Staging”.

1. What is the advantage of parallel staging over serial staging?
a) Increasing total efficiency
b) Less time consuming
d) Aesthetics

Explanation: In case of parralel staging, unlike serial staging all the stages are simultaneously burnt thus getting rid of propellant mass much more quickly and producing more thrust. Due to this it has a better efficiency.

2. In case of parallel staging, the stages of rocelts are burnt sequentially.
a) True
b) False

Explanation: A parralel stage rocket makes use of two or more stages attached alongside another stage. They are all burnt at the same time unlike serial rockets in which the stages are burnt one after the other in a sequence.

3. What is the term used to describe the stages of rocket attached to the space vehicle in parallel rocket?
a) Strap on booster rocket
b) Space shuttle
c) Engine
d) Subsidiary stages

Explanation: The term used to describe the stages of rocket attached to the space vehice is strap on rocket boosters which are burned simultaneously. For enhancing the performance, these boosters can be added or removed.

4. The zeroth stage for parallel staging rockets incorporates only the parral boosters which are attached to the space shuttle.
a) True
b) False

Explanation: The zeroth stage of the parralel staging rockets incorporates not just the strap- on boosters but also the core first stage. These burn simultaneously. When the zeroth stage’s propellants are all burned out, what’s left is first stage of the core followed by second stage, third stage etc.

5. What is the equation of thrust for zeroth stage of a parallel rocket?
a) fT = -veb $$\frac{d_{mb}}{dt}$$ – ve1 $$\frac{d_{m1}}{dt}$$
b) fT = veb $$\frac{d_{mb}}{dt}$$ + ve1 $$\frac{d_{m1}}{dt}$$
c) fT = veb $$\frac{d_{mb}}{dt}$$ – ve1 $$\frac{d_{m1}}{dt}$$
d) fT = -veb mb – ve1 m1

Explanation: When the boosters and core first stage is burnt, it is known as zeroth stage. After burning the propellants, what’s left is the first stage of the rocket. The equation to compute the thrust of the zeroth stage is given by:
fT = -veb $$\frac{d_{mb}}{dt}$$ – ve1 $$\frac{d_{m1}}{dt}$$ = -ve0 $$\frac{d_{m0}}{dt}$$
Where, veb is the exhaust speed of the boosters
ve1 is exhaust speed of core first stage
mb is the mass of the boosters
m1 is the mass of the core first stage
ve0 is the ehaust speed of th overall zeroth stage
m0 is the mass of the overall zeroth stage.

6. What is the special case of parallel staging called in which the burn time of the boosters is same as the burn time of the core stages?
a) Serial staging
b) Compund staging
c) Cluster staging
d) Aggregate staging

Explanation: In case of parrael staging, the burn time of the boosters is usually less than the first stage. So when they expend all the propellants, boosters are separated from the vehicle and the first stage continues to burn. But a special type of parralel staging rockets is cluster staging in which the burn time of both the boosters and core stage is same.

7. What is the average exhaust velocity of the zeroth stage?
a) ve0 = $$\frac{v_{eb} \frac{d_{mb}}{dt} + v_{e1} \frac{d_{m1}}{dt}}{\frac{d_{m0}}{dt} + \frac{d_{m1}}{dt}}$$
b) ve0 = $$\frac{v_{eb} \frac{d_{mb}}{dt} v_{e1} \frac{d_{m1}}{dt}}{\frac{d_{m0}}{dt}}$$
c) ve0 = $$\frac{\frac{d_{m0}}{dt} + \frac{d_{m1}}{dt}}{v_{eb} \frac{d_{mb}}{dt} + v_{e1} \frac{d_{m1}}{dt}}$$
d) ve0 = veb $$\frac{d_{mb}}{dt}$$ + ve1 $$\frac{d_{m1}}{dt}$$

Explanation: The average exhaust velocity of the zeroth stage is calculated from the formula given below:
fT = -veb $$\frac{d_{mb}}{dt}$$ – ve1 $$\frac{d_{m1}}{dt}$$ = -ve0 $$\frac{d_{m0}}{dt}$$
Where, veb is the exhaust speed of the boosters
ve1 is exhaust speed of core first stage
mb is the mass of the boosters
m1 is the mass of the core first stage
ve0 is the ehaust speed of th overall zeroth stage
m0 is the mass of the overall zeroth stage.

8. What is the rocket equation for parallel stage rocket?
a) Δv = –$$\Sigma_{k=0}^N \frac{v_{ek}}{ln⁡[\sigma_k + (1 – \sigma_k)\lambda_k]}$$
b) Δv = –$$\Sigma_{k=0}^N$$ [σk + (1 – σkk]
c) Δv = –$$\Sigma_{k=0}^N$$ vek ln⁡(σk λk)
d) Δv = –$$\Sigma_{k=0}^N$$ vek ln⁡[σk + (1 – σk) λk]

Explanation: The rocket equation for a parallel staged rocket is given by:
Δv = –$$\Sigma_{k=0}^N$$ vek ln⁡[σk + (1 – σk) λk]
Where, σk is the structural ratio
vek is the average exhaust velocity.

9. Which of these is not comprised in total mass of the rocket?
a) Propellant mass
b) Structural mass
d) Material mass

Explanation: While computing the total mass of the rocket, propellant mass, structural mass and payload mass are all incorporated. Material mass comes under Structural mass itself.

10. What is the process of getting rid of burnt out modules of the rocket once its propellant has been consumed called?
a) Staging
b) Space tugging
c) Ejection
d) Expulsion

Explanation: In case of multi-stage rockets, once the propellant of a stage has been consumed it is removed. This helps in reducing the structural mass resulting in a larger exhaust velocity.

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