Question

Single Stage 0.0/3.0 points (graded) Consider a rocket carrying 100,000 kg of propellant, 10,000 kg of structure, and 5000 kg of payload. What is the propellant fraction of this rocket? Round your answer to at least 2 decimal places (i.e., enter 0.25 to represent 25%) incorrect 1.100 What is the payload fraction of this rocket? Round your answer to at least 2 decimal places. incorrect 0.05 Recall that the relationship between specific impulse and exhaust velocity is: Vex=g0Isp . Assuming that Isp=450s and g0=9.81m/s2 , what is the value of ΔV in m/s that this rocket will produce if all the propellant is consumed in one stage? incorrect 4414

Answer 1

Answer: The Propellant fraction is 0.87.

The payload fraction is 0.04.

Δv = 8991.81 m/s

Explanation: To determine the fractions, first, calculate the total mass of the rocket:

$m_{t} = m_{prop} + m_{str} + m_{pay}$

$m_{t} = 100,000 + 10,000 + 5,000$

$m_{t} = 115,000$

The Propellant Fraction will be

$m_{prop} = \frac{m_{prop}}{m_{t}}$

$m_{prop} = \frac{100,000}{115,000}$

$m_{prop} =$ 0.87

The Payload Fraction is:

$m_{pay} = \frac{m_{pay}}{m_{t}}$

$m_{pay} = \frac{5,000}{115,000}$

$m_{pay} =$ 0.04

The value of Δv is calculated by the formula:

Δv = $-V_{e}. ln(\frac{m_{final}}{m_{initial}} )$

The exhaust velocity ($V_{e}$) is:

$V_{e} = g_{0}.Isp$

$V_{e} =$ 9.81*450

$V_{e} =$ 4414.5

$m_{final}$ is the total mass after the rocket consume all the propellant and $m_{initial}$ is the total mass before the action.

Δv = $-V_{e}. ln(\frac{m_{final}}{m_{initial}} )$

Δv = $-4414.5.ln(\frac{15,000}{115,000} )$

Δv = - 4414.5.ln(0.13)

Δv = 8991.81

Δv will be 8991.81 m/s.