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Intr rocket science: How calculate mass ratio and propellant

  1. Nov 23, 2015 #1
    1. The problem statement, all variables and given/known data

    I was wondering if you'd be able to help me with this problem: Given a two-stage launch vehicle with an engine that produces an Isp =400 sec, a payload mass of 10.000 kg, stage 1 structure mass of 10.000 kg, stage 2 structure mass of 10.000 kg, determine the mass ratio and the total mass of propellant required to reach LEO. Asume the total delta-v required is 7.700 m/sec. Determine the detal-v after each stage and the propellant mass for each stage.

    2. Relevant equations


    Isp=(i/deltampropellant*g)=C/g


    Delta-v=Cln(M0/Mf)

    Delta-v=Cln(MR); MR=Mass Ratio

    M0=Mf*e(delta-v/C)

    Mtotal=Mstructure+Mpropellant+Mpayloand

    For a two-staged rocket:

    Mtotal=Mstage1structure+Mstage1propellant+Mstage2structure+Mstage2propellant+Mpayloand

    Delta-vtotal=g*Isp*ln(M0/Mf)

    The mass ratio for stage 1 is:

    MR1=Mtotal/(Mtotal-Mpropellant1)


    3. The attempt at a solution

    I was trying to solve this problem with a Mf=10.000 kg +10.000 kg=20.000 kg, C=9.8m/s2 and a delta-v=7.700m/seg, then a find M0 replacing the equation, but I realized that this M0 is probablye the Mf of the stage 1...That two-stage rocket confuses me.
    As you can see I'm lost. I don't need you to solve the problem for me, just give me guidelines to resolve and so I can leave my confusion.
    I thank you for your attention and time spent.
     
    Last edited: Nov 23, 2015
  2. jcsd
  3. Nov 23, 2015 #2

    SteamKing

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    Staff Emeritus
    Science Advisor
    Homework Helper

    Your rocket mass at lift-off must include:
    1.) the payload mass
    2.) the structure mass of the two stages
    3.) the mass of fuel in each stage

    At some point, the fuel from the first stage is exhausted, and this stage is then jettisoned, leaving the second stage (w/fuel) + the payload to reach orbit before running out of fuel.

    There is a section at the bottom of this article which discusses how to use the rocket equation to analyze multistage rockets:

    https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation
     
  4. Nov 23, 2015 #3
    Thank you for your answer...

    Could you tell me if this is correct?:

    The final mass of the rocket is the result of stage 2 structure mass + payload mass (because the fuel is totally exhausted at that point) so, the initial massof stage 2 will be mf*e(delta-v/C)...Then, the final mass of stage 1 will be the initial mass of stage 2 + stage 1 structure mass. And the initial mass of stage 1 will be mf*e(delta-v/C)...

    So, mass ratio will be initial mass of stage 1/final mass of stage 2.

    And mass of propellant will be initial mass of stage 1-final mass of stage 2.

    Hope I made my point.
     
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