Need help finding required Propellant Fraction for equation

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Discussion Overview

The discussion revolves around calculating the required propellant fraction for a cryogenic chemical propulsion system using the rocket equation. Participants explore the relationship between specific impulse, delta velocity, and propellant mass in the context of a homework problem.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant questions whether they can reverse the standard rocket equation to find the propellant fraction, suggesting a formula involving delta velocity and specific impulse.
  • Another participant points out the need for mass information and provides the formula for propellant fraction as mprop/mi = 1 - exp(-ΔV/Vex).
  • It is noted that specific impulse is part of the exhaust velocity equation, Vex = g0 Isp.
  • There is a query about how to input the exponential function exp(-ΔV/Vex) on a calculator, with suggestions varying based on the type of calculator used.

Areas of Agreement / Disagreement

Participants express uncertainty about the correct approach to calculating the propellant fraction and whether additional equations or information are needed. There is no consensus on the best method to solve the problem.

Contextual Notes

The discussion lacks specific mass information and relies on assumptions regarding the application of the rocket equation. The input method for calculators varies, which may affect the calculation process.

BilboBombadillo
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Homework Statement


Consider a cryogenic chemical propulsion system with Isp (specific impulse) = 450 s
Enter the required propellant fraction as a proportion with at least two decimal places.

The ΔVelocity is provided. ΔV = 9.6 km/s

Homework Equations


Rocket equation:
ΔV = Vex x Ln (initial mass/final mass)

The Attempt at a Solution


I'm atrocious at math, yet this question has come may way nonetheless. Do I just reverse the standard rocket equation one uses to find the Delta Velocity?
Propellant/final mass = ΔV x Isp?
I need smart folk.
 
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BilboBombadillo said:

Homework Statement


Consider a cryogenic chemical propulsion system with Isp (specific impulse) = 450 s
Enter the required propellant fraction as a proportion with at least two decimal places.

The ΔVelocity is provided. ΔV = 9.6 km/s

Homework Equations


Rocket equation:
ΔV = Vex x Ln (initial mass/final mass)

The Attempt at a Solution


I'm atrocious at math, yet this question has come may way nonetheless. Do I just reverse the standard rocket equation one uses to find the Delta Velocity?
Propellant/final mass = ΔV x Isp?
I need smart folk.
In the rocket equation you listed, where does Isp fit in? Is there another relevant equation, or perhaps one that is more relevant to your problem?
 
Apologies I forgot the actual equation. The rocket equation I figured was necessary anyway, as no mass information is provided.
Here:
Propellant Fraction:
mprop/mi = 1 - exp(-ΔV/Vex)
 
Isp is part of the Exhaust velocity equation
Vex = g0 Isp
In fact, I think a better question would be - How does one input exp(-ΔV/Vex) on a calculator?
 
BilboBombadillo said:
Isp is part of the Exhaust velocity equation
Vex = g0 Isp
In fact, I think a better question would be - How does one input exp(-ΔV/Vex) on a calculator?
It depends on the kind of calculator you have. If it's a standard scientific calculator, enter ΔV, divide by V, change the sign (usually marked +/-), and then hit the ex button. Some of the fancier calculators these days allow you to enter the formula in the display.
 

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