# Spaceflight Mechanics Questions and Answers – Rocket Propulsion – Single Stage Rocket Engine

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

1. What is the final to initial mass ratio for a single stage rocket if the structural ratio is 0.1 and payload ratio is 0.05?
a) 0.500
b) 0.145
c) 0.125
d) 0.250

Explanation: Given, σ = 0.1, λ = 0.05
The final to initial mass ratio is given by:
$$\frac{m_f}{m_0}$$ = σ + (1 – σ)λ
Where σ is the structural ratio given by:
σ = $$\frac{m_s}{m_s + m_p}$$
And λ is the payload ratio given by:
λ = $$\frac{m_L}{m_0}$$

Thus substituting the values we get:
$$\frac{m_f}{m_0}$$ = σ + (1 – σ)λ = 0.1 + (1 – 0.1) × 0.05 = 0.145.

2. Payload mass is included in the structural ratio of the sinle rocket.
a) True
b) False

Explanation: Rockets never include the payload mass in the structural ratio. Because for rockets with the same structure, they are capable of carrying different payloads of different masses.

3. If a spacecraft’s engine ejects a mass of a rate 25 kg/s having exhaust velocity of 2,800 m/s. The rocket has an initial mass of 50,000 kg then what is the change in velocity if spacecraft burns for 5 minutes?
a) 400 ms
b) 455 m/s
c) 500 m/s
d) 600 m/s

Explanation: Given, $$\dot{m}$$ = 25$$\frac{kg}{s}$$, Mi = 50,000 kg, Vj = 2,800$$\frac{m}{s}$$, t = 5 min = 300 sec
The change in velocity is computed using the formula:
ΔV = Vj ln$$\Big(\frac{M_i}{M_i-m ̇t}\Big)$$
Substituting the values we get,
ΔV = 2,800 ln$$\Big(\frac{50,000}{50,000-25×300}\Big)$$ = 455 m/s.

4. What is the minimum value of the structural ratio?
a) 1
b) 2
c) 0.05
d) 0.5

Explanation: In order to have an efficient rocket, it is essential to have a higher payload ratio which is possible when the structural ratio is less. The rocket’s strcuture comprises of the mass of nozzle, guidance, accessories etc. The structural ratio cannot go below 0.05 which is its lower limit else it won’t be able to withstand the external loads.

5. When the payload ratio increases to 1, the performace of the single rocket diminishes to zero.
a) True
b) False

Explanation: When the rocket carries zero payload, it has its highest performance. But when the payload ratio is increased such that it becomes 1, the performance reduces. They are both conflicting and a balance has to be provided.

6. What is the minimum specific impulse required for a single stage rocket?
a) 300 s
b) 415 s
c) 500 s
d) 525 s

Explanation: Usually the specific impulse of rockets is about 300 s which gives us a delta-v of 5.7 km/s. But the minimum specific impulse required by the rocket to escape the earth’s atmosphere is 416 s which is only attained by Space Shuttles. Today, liquid hydrogen/liquid oxygen engines provide that kind of specific impulse.

7. What is the total velocity impulse for a single stage rocket if its final to initial mass ratio is 0.04 and the exhaust velocity is 3,500 m/s?
a) 5,127 m/s
b) 9,200 m/s
c) 11,266 m/s
d) 15,500 m/s

Explanation: Given, $$\frac{m_f}{m_0}$$ = 0.04, ve = 3,500 m/s
The total velocity impulse of a single stage rocket is given by the formula:
Δv = vf – v0 = -ve ln⁡[σ + (1 – σ)λ] Where, ve is the exhaust velocity
σ is the structural ratio
And λ is the payload ratio
Subsituting the values we get:
Δv = -3,500ln$$⁡\Big[\frac{m_f}{m_0}\Big]$$
(Since $$\frac{m_f}{m_0}$$ = σ + (1 – σ)λ)
Δv = -3,500ln⁡ [0.04] = 11,266 m/s.

8. What is the ideal propellant used for single-stage rockets?
a) Cryogenic solid
b) Liquid propellant
c) Solid propellant
d) Hybrid propellant

Explanation: Usually a single stage rocket is not used because of low payload carrying capacity. But it can be used for LEO when the mass of the structure is less ad propellant efficiency is high. This can be done by using liquid propellants such as liquid hydrogen ad liquid oxygen as the propellant performace is high.

9. Why is single stage rocket not used often?
a) Low exhaust velocity
b) Lesser fuel
c) High mass
d) Low delta-v

Explanation: The maximum delta-v of the rocket for a given fuel to dry mass ratio is too less for the single stage rockets. The delta-v which is required to reach low earth orbit requires a large wet to dry mass ratio which is not present in single stage rockets. This is overcome by making use of multi-stage rockets by jettisoning the stages when they run out of propellant. This staging allows the thrust of the remaining stages to accelerate easily and reach the final speed.

10. How is the payload ratio of the single rocket computed? (Given, ML-Payload mass, M0-Initial mass, MS-Structural mass)
a) λ = $$\frac{M_L}{M_0}$$
b) λ = $$\frac{M_L}{M_0+M_S}$$
c) λ = $$\frac{M_S}{M_L+M_S}$$
d) λ = $$\frac{M_L}{M_S}$$

Explanation:Payload ratio λ of a single stage rocket is the ratio of payload mass to the initial mass. It is not included in the structural mass.
λ = $$\frac{M_L}{M_0}$$
Where, ML is the payload mass
M0 is the initial mass.

11. How is the structural ratio of the single rocket computed? (Given, ML-Payload mass, M0-Initial mass, MS-Structural mass, MP-Propellant mass)
a) σ = $$\frac{M_L}{M_P}$$
b) σ = $$\frac{M_L}{M_0+M_S}$$
c) σ = $$\frac{M_S}{M_S+M_P}$$
d) σ = $$\frac{M_L+M_P}{M_S}$$

Explanation: Structural ratio σ of a single stage rocket is the ratio of structual mass to the sum of the both structural and propellant mass. It is given by:
σ = $$\frac{M_S}{M_S+M_P}$$
Where, ML is the payload mass
MS is the structural mass
MP is the propellant mass.

Sanfoundry Global Education & Learning Series – Spaceflight Mechanics.

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