Intr rocket science: How calculate mass ratio and propellant

[Dianainthesky]

Homework Statement

[/B]
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.

Homework Equations

I_sp=(i/delta_mpropellant*g)=C/g

Delta-v=Cln(M₀/M_f)

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

M₀=M_f*e^(delta-v/C)

M_total=M_structure+M_propellant+M_payloand

For a two-staged rocket:

M_total=M_{stage1structure}+M_{stage1propellant}+M_{stage2structure}+M_{stage2propellant}+M_payloand

Delta-v_total=g*I_sp*ln(M₀/M_f)

The mass ratio for stage 1 is:

MR₁=M_total/(M_total-M_propellant1)

The Attempt at a Solution

I was trying to solve this problem with a M_f=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 M_f 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.

 

[SteamKing]

Homework Statement

[/B]
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.

Homework Equations

I_sp=(i/delta_mpropellant*g)=C/g

Delta-v=Cln(M₀/M_f)

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

M₀=M_f*e^(delta-v/C)

M_total=M_structure+M_propellant+M_payloand

For a two-staged rocket:

M_total=M_{stage1structure}+M_{stage1propellant}+M_{stage2structure}+M_{stage2propellant}+M_payloand

Delta-v_total=g*I_sp*ln(M₀/M_f)

The mass ratio for stage 1 is:

MR₁=M_total/(M_total-M_propellant1)

The Attempt at a Solution

I was trying to solve this problem with a M_f=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 a
I realized that this M₀ is probablye the M_f 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.

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

 

[Dianainthesky]

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 m_f*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 m_f*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.